Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management

Global climate likely trends and the consequent global sea level rise, combined with potentially increased rates of extreme storms, necessitate the reconsideration of current planning, engineering and management practices of infrastructure. Recent storms, such as the 2012 Hurricane Sandy, resulted in inundation of coastal areas, flooding of tunnels and subway stations, power loss, shutdown of nuclear power plants, etc. Risks from such storms entail significant uncertainties. This paper examines trends of hazards with climate change considerations. Three hazard types are examined: wind speed, waves and sea level rise. The sea level rise is examined in detail for illustration purposes. The paper offers a preliminary, conceptual framework for quantifying SLR and extreme storm risks. The paper focuses on the Washington DC area as a case study; however, the methodology can be used to examine other regions. The DC inventory used in this paper was based on open sources and is incomplete and/or inaccurate along the coastal lines. The increase in storm activity, with wave run-up intensity escalation due to the rising sea level, requires further investigation. The impacts of such increased activities at coastal lines would lead to interdependence with land-use and human-activity changes, creating a need to examine SRL in socioeconomic system modeling.

Epistemic uncertainties create difficulties for the quantitative estimation of uncertainties associated with environmental models. The nature of the issues involved is discussed, particularly in how to assign likelihood values to models when the forcing data and evaluation data might both be subject to epistemic uncertainties. A case study of a rainfall-runoff model of the River Brue catchment is developed with the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. Model evaluation is carried out using limits of acceptability set from considerations of the available data prior to running a model, while the errors associated with a model are treated non-parametrically for different parts of the hydrograph.

The basic concepts related to the complexity of modern critical infrastructures are presented, and the issues related to the analysis of their vulnerability and the assessment of the related risk are discussed. To substantiate the discussion, exemplifications are made in relation to the electric power grids. The integration of different types of analyses, and methods thereof, is propounded for capturing the inherent structural and dynamic complexities of critical infrastructures, and confidently evaluate their vulnerability and risk.

This paper first outlines how and why the authors have, in the past, defined "robust simulation" to be the employment of alternative credible quantitative evaluations of risks to systemic issues. Next, this paper outlines how structural engineering evaluations for severe winds and earthquakes may be considered as requiring this sense of "robust simulation" with respect to building codes and others issues. Diverse models of seismicity, strong ground motion attenuation, and performance of soils - including possible liquefaction displacement analysis - show how hazards may have very competitive alternative quantitative procedures. Different levels of evaluations of building responses to earthquakes and severe winds likewise show how there may be diverse, but competitive, alternative quantitative procedures and how these may, on occasion, illustrate catastrophic trajectories. After these discussions, there will be a brief discussion of how the ensemble of outcomes from diverse competitive models can assist, rather than hinder, the decision-making process.

This paper presents an example of the application of S-PSA using FEM to an existing structure and a study on the seismic retrofit approach based on the risk estimated by the failure probability obtained from the S-PSA. In this paper, an example considers the possible effect of a new, gigantic Nankai-trough earthquake published by the Japanese government after the Tohoku earthquake (2011), and the previous example without considering the earthquake are introduced and compared.

Realistic mathematical modeling of phenomena is an important issue in engineering. Models are commonly based on strong theoretical foundations, but validated by comparison with experimental data. On some occasions, these parameters can be measured directly from experiment; but, in other cases, methodologies are needed to infer the parameters from experimental observations. This inference should reflect the inherent uncertainty in measurements associated with the phenomena. In this work, a methodology is proposed to probabilistically characterize model parameters predicting the response of a magneto-rheological (MR) damper. The methodology is illustrated by an examination of the hyperbolic tangent (HT) damper model. This mathematical model predicts the force produced by an MR damper due to the relative displacement and velocity between the two ends of the device. Traditionally, the parameters in the HT damper model are treated as deterministic parameters and are fit to experimental data by minimizing an objective function, which measures the error between model and experiment. Here, the model parameters are treated as random variables. Bayes' inference is used to estimate the probability density function (PDF) of the parameters given a set of experimental data. Gibbs sampling, using the Metropolis Hasting algorithm, is used to determine samples of this PDF. The results of this approach are illustrated by: (1) using the probabilistic parameters to simulate the damper response and (2) comparing the simulated responses to both experimental data and the damper response predicted using a deterministic set of parameters. The strength of this modeling approach is that it has the potential to be used to explore correlations between parameters, to estimate the relative contributions of individual parameters and to help compare multiple models for the same device. While the techniques presented here are well established in the literature, their application as a tool for modeling structural control devices is novel.

This paper first introduces innovative Composites Structural Insulated Panels (CSIPs) for structural wall and floor applications against multiple hazards. It then presents an innovative risk-consistent design approach for designing such a system. The proposed composite panel is made of low-cost thermoplastic orthotropic glass/polypropylene (glass-PP) laminate as a facesheet and Expanded Polystyrene Foam (EPS) as a core with a very high facesheet/core moduli ratio. The proposed CSIPs are intended to overcome problems of traditional wood panels against multiple natural hazards (including earthquake, flood and windstorm to poor penetration resistance against wind borne debris, termite attack and mold build-up. On the other hand, despite most of recent structures having been designed according to the desired code requirements, failure of those structures due to recent natural hazards (such as hurricanes and earthquakes) have shown the weakness of the current design methods. It has also raised the need for a new methodology for structural design that accounts for the risks due to natural hazards. Therefore, a comprehensive design approach for developing hazard-resistant structures was developed. The approach considers the life cycle cost (LCC) of the structure and safety indices for strength and drift. It also accounts also for the uncertainty in both loading and strength. The variability in the strength, drift and load is expressed by mean values with their coefficient of variance (C.O.V) which is referred to as aleatory uncertainty. The LCC was calculated based on the concept of quantitative risk assessment (QRA) that incorporates the damage cost due to certain hazards and the probability of occurrence of those hazards. Based on the importance and the type of the structure, the structural engineer and the decision-maker can determine or optimize the most appropriate building model. The method was demonstrated with case studies on two structures: one for traditional wood and another for CSIP. Seismic and wind hazards were considered in the analysis. Two locations were considered — Los Angeles, CA and Charleston, SC. These locations are critical for seismic and wind load, respectively. The results showed that CSIP building is cost effective and provides higher safety indices than traditional wood structure.

This work explores the effect of using updated reliability measures in the context of reliability-based optimization problems of stochastic dynamical systems. A Bayesian probabilistic methodology for model updating is first implemented for the purpose of updating the structural model using dynamic data. The updated distribution of the system model parameters is then used for updating the system reliability. The effect of updated information on the design of dynamical systems under stochastic excitation and modeling uncertainty is illustrated by an application problem.

As the bridge inventory ages and traffic volumes increase, the bridge owners are spending more on maintaining their current structures. AASHTO considers virtually all two-girder bridge systems as non-redundant, and each girder is considered as the fracture-critical member (FCM). Redundancy analysis of the two-girder bridges considering the uncertainty (damage scenarios) is investigated through a case study on a three-span, continuous twin I-girder bridge. The FE analysis is employed to evaluate the load-carrying capacity after fracture of one main girder of the twin girder bridge. The damage locations are chosen at the mid-span section of the middle span, the side span, and the section near the continuous pier support. Damage to shear connectors near the moment contra-flexure regions and missing one bearing at the middle and end support locations are also considered as potential damage scenarios in this study. On the basis of the direct redundancy analysis results, the present continuous two-girder composite bridge can be classified as redundant.

As structural optimization is a demanding task, most applications encountered in the literature approximate structural systems subjected to stochastic excitations as linear. In this regard, this paper addresses optimal design of nonlinear/hysteretic structural systems subjected to stochastic excitations. Specifically, relying on a statistical linearization technique and employing time-variant reliability analysis concepts, a numerical optimization problem is formulated and solved to obtain structural systems optimal designs. Comparisons between the linear and the nonlinear cases demonstrate the effects of nonlinearity. Further, the above optimal design formulation also utilizes the concept of performance-based design by integrating various levels of loading and of continuous damage caused by extreme responses in the analysis. As a numerical example, a reinforced concrete building modeled as a MDOF nonlinear/hysteretic system subjected to wind excitation is studied. The hysteretic behavior is modeled by the versatile Bouc-Wen model. Optimal stiffness of the building is obtained for the linear and nonlinear cases and for various design life values, as well.

Design under uncertainty problems which employ the probabilistic performance as objective function and estimate it through stochastic simulation are discussed. A gradient-based algorithm is adopted for the numerical optimization and the focus is on the adaptive implementation of importance sampling (IS) across the iterations of the algorithm. The IS densities are selected based on samples distributed proportional to the integrand quantifying the probabilistic performance, and kernel density estimation is considered for constructing them. The characteristics of the selected density - including the specific model parameters for which IS is considered - are optimally selected by minimizing the anticipated coefficient of variation (for the objective function estimate) if this density were used as IS distribution. A global sensitivity analysis is integrated within the approach to guide the selection of the parameters for which IS is formulated. The framework is developed with marginal additional computational effort, utilizing information readily available from the objective function estimation, and contributing ultimately to great computational savings.

Facades, mounted as non-structural elements on the exterior of buildings, contribute to their aesthetics and technical performance, including protection of the building interior from any exterior aggressive environment. Unfortunately, design and detailing of facades have received much less attention than the building structure itself. Serious incidents of façade failures, including several fatal ones, have occurred all over the world. This paper reports the results of a research program aimed at: (1) examining the performance and reliability of building facades; (2) considering the various safety-related issues associated with risks involved in design, construction, maintenance, repair; and (3) overall performance of these facades over their entire service life, along with the various failure modes. Appropriate strategies are recommended to minimize these risks through improved life-cycle design and construction, and regular inspection and maintenance programs.

Levee risk control is crucial. Regrettably, these long linear structures are badly maintained most of the time, showing signs of weaknesses on numerous occasions. Only imperfect information is usually available. In this particular context, a probability-based model is suggested for evaluating the levee performance, taking into account expert engineer's uncertain assessments in a probabilistic format. After a brief presentation of the development of a levee deterministic performance evaluation model, we describe in greater details an original approach based on subjective probability implemented to take into account uncertain levee performance assessments and the use of sensitive coefficient for decision aid.

This contribution presents an approach for performing fuzzy structural analysis of linear structures subject to static loading where uncertainties are present in both material properties and loadings. The responses of interest are displacements of the structure. The proposed approach is based on a non-linear approximation of these responses. This non-linear approximation is constructed by taking into account the linearity of the displacements with respect to loading and by introducing intervening variables. In this manner, high quality approximations of the structural responses are obtained allowing to determine membership functions performing a single structural analysis.

Spatial optimization is used to identify the best trade-off spatial development plans which mitigate conflicts between risk and sustainability objectives. A spatial optimization framework was developed to optimize the following risk and sustainability objectives:(1) minimizing risk from heat waves; (2) minimizing risk from flooding; (3) minimizing the distance of new development to the current CBD to minimize travel costs; (4) minimizing urban sprawl to prevent increased travel costs; and (5) preventing the development of green space. The framework is applied to a real case study in the North East of England, where the implications of forecast development on these objectives are assessed against the objectives outlined. The resulting Pareto-optimal solutions provide planners with a range of robust spatial development patterns known to be best trade-offs. Finally, the implications and utility for risk planners are considered.

Optimization under uncertainties is a computationally demanding problem due to the nested structural analysis, reliability analysis and optimization loops. While many shortcuts have been proposed and developed for reliability-based design optimization, no such shortcuts for risk-based optimization were available until today. In reliability-based design optimization, failure probabilities are constraints which can sometimes be replaced by deterministic constraints. In risk-based optimization, failure probabilities are part of the objective function. Due to this fundamental difference, shortcuts for solving reliability-based design optimization problems do not apply to risk optimization. In this paper, a novel approach to solving structural risk optimization is presented. This approach leads to a several-fold reduction in the computational effort for solving risk optimization problems. For each directional (line) search, a couple of Monte Carlo samples are used to obtain critical values of the design variables, leading to a complete description of the expected cost of failure function. Optimization algorithms can then be used for solving for the global optimum. The total cost of the optimization solution is equivalent to a single solution of the reliability problem by means of Monte Carlo simulation. The technique presented in this paper opens new possibilities for the solution of real-world, large, numerical, structural optimization problems.

The uncertain nature of risk estimates can lead to a loss of confidence in the dependability of risk-based decisions. Risk-based decision-making is robust and dependable only if it produces acceptable decisions that would also be considered acceptable if the true risks were perfectly understood and known. The term `fiducial confidence' is used to refer to the level of confidence that a risk estimate will provide a dependable basis for decision-making. In this paper, the concept of fiducial confidence is used to assess the robustness of risk-based optimisation, considering not only the uncertainty in probability estimates, but also the uncertainty in estimated costs and benefits. In this context, a robust optimisation must limit the expected costs of a decision that would be considered inappropriate if the true probabilities and true expected costs and benefits were known to the decision-maker.

Most engineers might have been in a situation where they need to make a decision for an engineering problem. This decision engineers make should be consistent and correct based on information related to the problem. With sufficient information to solve a problem, a decision might be made easily with this information. However, if information is conflicting within a problem, it is difficult to make a consistent decision. In this study, possibility theory is introduced in order to make consistent decisions for a decision-making problem with conflicting information. Information is modelled as weighted intervals based on its importance. A methodology to generate a possibility distribution from the weighted intervals is presented to fuse information with respect to its importance. A case study for decision-making from Structural Health Monitoring (SHM) data is presented.

The target reliability levels recommended in national and international documents vary within a broad range, while the reference to relevant costs and failure consequences is mentioned only very vaguely. In some documents the target reliability index β is indicated for one or two reference periods (1 year and 50 years) without providing any link to the design working life. This contribution attempts to clarify the relationship between the target reliability levels, construction costs, failure consequences, reference period, the design working life and the discount rate. The theoretical study based on probabilistic optimization is supplemented by recommendations useful for code developers and practicing engineers. It appears that the optimal reliability level depends primarily on the construction costs, failure costs, and relative cost for improving structural safety, and less significantly on the discount rate and the time to failure. In design based on the partial factor method, it is recommended that the characteristic values of the basic variables be defined independently of the design working life and specified target reliability.

Structural fire safety is a topic of general concern, but the utility of investments in structural fire safety is often questioned based on the fact that the probability of fire exposure during the lifetime of a structure is generally small. Considering the current trend towards performance-based design, optimum design solutions have to be determined in which upfront investments are balanced with gains in fire safety during the lifetime of the structure. In this paper, a basic framework is presented, taking into account the probability of fire ignition and successful fire suppression, the probability of structural failure during fire and the costs of rehabilitation after fire exposure. The presented methodology is applied to determine the optimum concrete cover for a concrete slab as a function of the fire load density in case of natural fires.

Reliability assessment of a structure is crucial in the evaluation of the structure's feasibility, integrity and safety. Moreover, conventional structural reliability assessment methods mostly employ traditional probability theories. The First Order Reliability Method (FORM) is one of the probabilistic-based methods that is widely accepted and used. However, because of its inherent approximation, the FORM may not always accurately consider the presence of uncertainties in the structure. This is especially true when the system consists of interconnected modes of failure. One of the methods to quantify the presence of uncertainty is interval or (unknown-but-bounded) analysis. In this paper, a new method for reliability assessment of structures is developed that enhances FORM for consideration of uncertainties using interval analysis. This method will hereafter be referred to as the Interval First Order Reliability Method (IFORM). IFORM benefits from the simplicity of both FORM and interval analysis by avoiding the requirement for the prior knowledge of joint probability density function for the input parameters. Using IFORM, first, uncertain input parameters are quantified by independent interval variables. Then, the first order reliability analysis is performed using input interval parameters leading to the determination of the bounds on the probability of failure (damage) for the entire structure. Several numerical examples that illustrate the capability and feasibility of this method are presented. The results are then compared with those using the FORM and Monte Carlos Simulations, in which the advantage of IFORM over the traditional FORM is demonstrated.

An efficient robust design optimization (RBO) framework is developed for linear multi-degree-of-freedom (MDOF) structural systems subject to evolutionary stochastic earthquake excitations. A significant feature of the developed RBO framework relates to the consideration of both inter-storey drift and floor acceleration second-order statistics as performance measures. Further, an efficient frequency domain approach is utilized for determining the system response Evolutionary Power Spectrum (EPS) matrix circumventing computationally intensive Monte Carlo simulations. Furthermore, the optimization problem is solved by employing a Genetic Algorithm based approach. An illustrative numerical example is included to demonstrate the efficiency and robustness of the proposed framework.

Sivakasi town of Virudhunagar District, Tamilnadu in India is famous for the manufacture and supply of fire crackers and safety matches, meeting the International demand. The process of manufacturing fire crackers is being carried out inside the traditional clay brick masonry structures of 230-mm wall thickness without incorporating any explosion resisting features. Very often, accidental explosions during the manufacturing process caused collapse of brick masonry structures, leading to loss of human lives and infrastructure. Existing construction guidelines are inadequate to resist against failure/collapse of brick masonry structures in the event of such accidental explosions. Hence, an attempt is made to identify the optimum structure/configuration which can perform satisfactorily against such accidental explosions. Clay brick masonry model structures with flat, sloped and curved roofing with wall thicknesses of 115 mm, 150 mm and 230 mm, along with rectangular, square and hexagonal configurations were considered in this study. The input data are arrived at from the static and dynamic analysis conducted using ANSYS software on brick masonry models of various wall thicknesses and roofing configurations. The Taguchi-based optimization technique using Minitab software is used to arrive at the ideal model structure for fireworks industrial building showing satisfactory performance against the accidental explosive loading and the results presented.

Buckling of load-carrying beam-columns is a severe failure scenario in light-weight structures. The authors present an approach to actively stabilize a slender beam-column under static axial load to prevent it from buckling in its first buckling mode. For that, controlled active counteracting forces are applied by two piezoelectric stack actuators near the column's fixed base, achieving a 40% higher axial critical load and leaving most of the column's surface free from actuation devices. However, uncertain actuator properties due to tolerances in characteristic maximum free stroke and blocking force capability have an influence on the active stabilization. This uncertainty and its effect on active buckling control is investigated by numerical simulation, based on experimental tests to determine the actual maximum free stroke and blocking force for several piezoelectric stack actuators. The simulation shows that the success of active buckling control depends on the actuator's variation in its maximum free stroke and blocking force capability.

The current methods for designing reinforced concrete (RC) columns are mainly based on the reliability calibration under fixed eccentricity criterion. However, for an RC column under combined vertical gravity load and horizontal earthquake action, its eccentricity would be random due to probability properties of these loads. According to the capacity models in Chinese code, the failure function with random eccentricity is obtained and found to be a complex one, which is largely different from the one obtained by the fixed eccentricity criterion. Based on the prescribed statistical models of relevant variables, the differences of failure probability are analyzed for RC columns with different load effect ratios and different strong column factors by the Monte Carlo method. Compared with the fixed eccentricity case, such differences under random eccentricity would be much larger among different cases. Thus, with the current design method of RC columns, it is hard to achieve a robust design.

Hydrological forecasting is one of the most essential tasks in operational hydrology; however, predictions are usually subject to several sources of uncertainty (both epistemic and aleatory). These uncertainties can be due to, for example, inadequacies in the model structure and/or parameters, forcing data, initial conditions and updating procedures. Here, we analyse medium-scale (10 days) hydrological forecasts across 71 selected indicator stations in Sweden and aim to identify typical uncertainties in the forecasting production chain and ways to reduce them, and analyse different performance characteristics. In particular, the analysis is based on two operational systems using the HBV and S-HYPE hydrological models. We investigate the effect of autoregressive updating of the forecasted discharge, and of using ensemble instead of deterministic forecasts. The recently proposed Kling-Gupta Efficiency and its decomposed terms are used to identify the remaining uncertainty in different characteristics of the flow signal. Results show that uncertainty in operational hydrological forecasting can be significantly reduced by updating using an autoregressive method for discharge. This is particularly significant in the short lead time, due to the emphasis towards improving the volume error in the system. However, in this study, the use of the median ensemble forecast could not reduce the remaining epistemic uncertainty in terms of an improved model performance.

There remains a great deal of uncertainty about uncertainty estimation in hydrological modelling. Given that hydrology is still a subject limited by the available measurement techniques, it does not appear that the issue of epistemic error in hydrological data will go away for the foreseeable future. It may be necessary to find a way of allowing for robust model conditioning and more subjective treatments of potential epistemic errors in model applications. In this study, we have made an attempt to analyse how this is the result of the epistemic uncertainties inherent in the hydrological modelling process and its impact on model conditioning and hypothesis testing. We propose some ideas about how to deal with assessing the information in hydrological data and how it might influence model conditioning based on hydrological reasoning, with an application to rainfall-runoff modelling of a catchment in Northern England where inconsistent data for some events can potentially introduce disinformation into the model conditioning process. A methodology is presented to make an assessment of the relative information content of calibration data before running a model that can then inform the evaluation of model runs and resulting simulation uncertainties.

Scientific models are quantitative approximations that depict selected aspects of reality and ignore others. Scientific models create simplified images of reality that facilitate the understanding, prediction and control of complex relationships. The use of a mathematical model for these purposes depends intimately on the human-language interpretation of the model. Scientific models, together with their linguistic meanings, are mathematical metaphors of real relationships. We discuss the various types of mathematical metaphors that are exploited by scientific models. We examine the implications for risk management, in particular, by stressing the importance of both historical and epistemological understanding. The risk manager need not be a professional historian or philosopher, but the risk manager must be able to engage in a competent professional dialog with these disciplines.

Recent international flood events have demonstrated the large damage and potential loss of life that flooding can cause. In order to accurately quantify flood risk and how it may change in the future, we need to improve our understanding of the uncertainties associated with making such predictions. Improvements in remote sensing have facilitated the use of high resolution models; however, without consideration of the uncertainties, these models can produce spuriously precise predictions. This paper has explored this by assessing how changing the scale of flood inundation models impacts on probabilistic flood inundation and flood hazard maps for the Imera basin, Sicily. We have demonstrated that, although coarse scale models can perform just as well as fine scale models, the results are dependent on both grid scale and likelihood measure. Furthermore, these results have highlighted the uncertainty associated with flood inundation predictions and the need to consider these uncertainties when performing flood risk analysis.

Predictions of environmental models are affected by potentially large uncertainty due to a range of factors ranging from observation errors in the model forcing to uncertainty in model parameters and structure. Depending on the model application, such uncertainties can undermine the robustness and credibility of the modelling results up to the point that the usefulness of environmental models for supporting decision-making is called into question. Sensitivity Analysis (SA) is a valuable tool for both model developers and users to quantify the uncertainty in model outputs, estimate the relative contribution of the different input factors to such uncertainty, and thus prioritize efforts for its reduction. In the last few years, the development, application and comparison of SA techniques have been the subject of an increasing number of contributions in the literature. In this paper, we provide an overview of this literature and develop practical guidelines to help support researchers and practitioners in the application of SA in environmental modeling. By discussing the most critical and controversial steps in the application of SA methods, we also identify priorities for further research in the field.

Fuel cell systems are promising devices for an efficient decentralized supply with electricity and process heat. However, such power supply systems are typically characterized by a dominant, non-stationary behavior because of small grid sizes with variable power demands. In addition, storage and load shaping devices - such as battery systems - have to be kept as small as possible to guarantee cost-effectiveness. Due to non-stationary operating conditions, it is necessary to develop nonlinear control strategies to ensure high efficiency and to guarantee robustness against a-priori unknown load variations. In previous work, fundamental control procedures have been developed which comprise ideas of sliding mode and model-predictive control. The sliding mode strategies are extended in this paper towards higher-dimensional system models, resulting from a finite volume representation of the thermodynamics of solid oxide fuel cell stacks (SOFC stacks). Simulations and preliminary experimental results are presented to highlight the corresponding design procedures and their practical applicability.

Bounded and stochastic disturbances form a very important impact on system models in general. The consideration of these in control and observer strategies is a challenge for researchers. The problem is that common control procedures may depend on special properties of the system. Often, procedures for linear system models cannot be used for nonlinear ones. In this contribution, sliding mode techniques are further developed for control and estimation tasks such that the principle procedure is not limited to linear systems. To consider uncertain but bounded parameters and stochastic disturbances simultaneously, intervals are introduced in the resulting stochastic differential equations. Additionally, stability of the presented procedures can be guaranteed by involving the Itô differential operator and linear matrix inequalities to obtain sliding mode strategies for robust control and estimation tasks in combination with interval arithmetic.

Whether a structure is stable depends on the values of the parameters θ = (θ₁, . . . , θ_n) which describe the structure and its environment. Usually, we know the limit function g(θ) describing stability: a structure is stable if and only if g(θ) > 0. If we also know the probability distribution on the set of all possible combinations θ, then we can estimate the failure probability P. In practice, we often know that the probability distribution belongs to the known family of distributions (e.g., normal), but we only know the approximate values p˜_i of the parameters p_i characterizing the actual distribution. Similarly, we know the family of possible limit functions, but we have only approximate estimates of the parameters corresponding to the actual limit function. In many such situations, we know the accuracy of the corresponding approximations; i.e., we know an upper bound Δ_i for which |p˜_i - p_i| ≤ Δ_i. In this case, the only information that we have about the actual (unknown) values of the corresponding parameters p_i is that p_i is in the interval [p˜_i - Δ_i, p˜_i + Δ_i]. Different values p_i from the corresponding intervals lead, in general, to different values of the failure probability P. So, under such interval uncertainty, it is desirable to find the range [P_, P^– ]. In this paper, we describe efficient algorithms for computing this range. We also show how to take into account the model inaccuracy, i.e., the fact that the finite-parametric models of the distribution and of the limit function provide only an approximate descriptions of the actual ones.

If it is desired to obtain answers with correct topological form, then the problem of computing regularized Boolean operations in solid modelling is ill-conditioned. To say that the answer has correct topological form here means that not only is the computed model topologically well-formed, but also that it has the same topological form as the true (exact) result (i.e., the exact and computed objects are linked by a homeomorphism). That the problem is ill-conditioned means that small changes in the problem data (smaller than the uncertainty in this data) can cause the true result of the operation to change topological form, so that the true result corresponding to the new data is not just erroneous, but different in kind. The ill condition implies that the resulting computational difficulty cannot be resolved by designing better numerical algorithms. It is shown in this paper, however, that in at least one situation, there is enough information available to resolve the problem of correct topological form even though the available information does not eliminate the uncertainty involved. The situation referred to is that of feature-based design, where information concerning attachment of features is available. It is shown here how to produce a posteriori guarantees on topological form in the case when the faces of the solids and features are defined by logically-locally-planar Bézier patches. This case is general enough to cover, by means of representation conversion, many practical representation methods. Our approach is based on existing methods for the production of consistent trimmed surfaces, and existing methods permitting a posteriori verification that the patches forming the faces do not have self-intersections or extraneous intersections. The main contribution of the paper is to observe that uncertainty can affect the results of computing Boolean intersections at different levels of severity and that, in certain important practical situations, although the uncertainty cannot be removed, its effects can be rendered almost completely harmless.

How to compare different range estimators for multivariate functions under uncertainty? To answer this question, we analyze which utility functions can be used for this task. Specifically, we: (1) introduce various invariance assumptions, (2) describe the class of all utility functions which satisfy these assumptions, and (3) show how the resulting utility functions can be used to compare different range estimators.

The technology of solid oxide fuel cells is one of the important topics in modern engineering. One research direction is to design robust and accurate control strategies for this kind of fuel cells based on models spatially discretized into ordinary differential equations. To allow users to employ new models and techniques easily in combination with different verified and traditional tools, we implement the environment VeriCell. It features an intuitive graphic interface for construction of fuel cell models from pre-defined building blocks. In this paper, we describe modeling and verification possibilities available in VeriCell for the analysis of solid oxide fuel cells.

Interval arithmetic underwent a standardization effort starting in 2008 by the IEEE P1788 working group. The structure of the proposed standard is presented: the mathematical level is distinguished from both the implementation and representation levels. The main definitions are introduced: what is an interval? How are mathematical functions, such as arithmetic operations or trigonometric functions, extended over intervals? What are the comparison relations? How are set operations, such as the union or the intersection, extended over intervals? While developing this standard, some topics led to hot debates: these topics correspond to points most delicate and difficult to define. Such a hot topic is the handling of exceptions. Eventually, the system of decorations was adopted. A decoration is a piece of information that is attached to each interval. Rules for the propagation of decorations have also been defined by the standardization group. Another hot topic is the mathematical model used for interval arithmetic. Historically, the model introduced by R. Moore in the 60s covered only non-empty and bounded intervals. The set-based model includes the empty set and unbounded intervals as well. Tenants of Kaucher arithmetic also insisted on offering "reverse" intervals. It was eventually decided that an implementation must provide at least one of these flavors of interval arithmetic. The standard provides hooks for these different flavors. Finally, a tentative list of missing items is given. As the preparation of the draft should end at the beginning of 2014, no chapter is missing. However, a reference implementation would be welcome to validate the choices made during the development of the standard for interval arithmetic.

An analytical expression for the probability density function (PDF) of a random process power spectrum value at a given frequency is derived. The significance of the derived PDF relates to cases where incomplete process realizations are available for power spectrum estimation applications. Specifically, standard power spectrum estimation techniques subject to missing data - such as zero-padding and least squares regression - normally provide a deterministic estimate for the power spectrum value at a given frequency. In this regard, no information is provided concerning the uncertainty in the estimates. In this paper, relying on the assumptions of stationarity and ergodicity, and on minimum assumptions about the missing data, an explicit closed-form analytical expression for the PDF of the power spectrum value at each and every frequency is derived. In this manner, the uncertainty propagation - from the measured incomplete process realization in the time/space domain to its power spectrum estimate in the frequency domain - is efficiently quantified. Further, the derived results can, potentially, be used for assessing the performance of alternative power spectrum estimation techniques subject to missing data which provide a deterministic estimate for the power spectrum value at a specific frequency.

Most port infrastructure projects are large in scale and have a long lifetime during which they are confronted with multiple uncertainties. Many of these can be dealt with reasonably using standard management practices. However, some uncertainties - such as future demand, shipping traffic and future technology - are difficult to forecast. If these uncertainties are not taken into account during planning, the resulting infrastructures may not be functional in a new or different future. This paper suggests that standard `project' or `risk' management practices are not adequate to deal with exogenous uncertainties which can form vulnerabilities for a project. It proposes Adaptive Port Planning (APP), an approach that offers a unified approach for strategic planning and risk management, and guides planners to systematically deal with uncertainties that appear over the lifetime of an infrastructure project. APP is a dynamic and effective management tool that can provide structure during realization and exploitation phases of a civil engineering project.

In this paper an innovative, scientifically developed, and in practice tested approach for implementing risk management in infrastructure projects is introduced. There are two main objectives of this paper: (1) raising awareness about the inherent and often undervalued complexity of implementing risk management and (2) providing a route to implementing risk management in infrastructure projects. The innovative approach focuses on developing organizational conditions for effectively, cost-efficiently, and routinely applying risk management by balancing three dimensions: (1) the risk management method, (2) the project organization, and (3) the individual human factor. For facilitating, designing, and executing a well-planned risk management implementation process, a toolbox has been developed. Using this risk management implementation toolbox in over 15 organisations proved to facilitate embedding risk management in projects. Because the presented organization-focused and managerial way of risk management implementation is still rather new, a lot of additional researcs on this topic is highly recommended.

In the special background of social transformation and fast urbanization in China, as a new work, social stability risks assessment of major construction projects has been carried out in recent years. Currently, the research about social risks and social impact assessment has been more mature, but the monographic study of social stability risk assessment in major construction projects has been weak. First, combing the research methods of sociology and the characteristics of engineering objective impact, this article explored some investigation methods of social stability risks for collecting the data needed in risks analysis. Then, the project's social stability risk can be identified in general by summarizing and analyzing. Second, this article adopted the "single factor risk degree method" and "overall risk index method" to calculate the overall risk index of the major construction projects and to work out the major construction projects' social stability risk level by contrasting "project's integrated risk judging reference standard". Third, on the basis of the major projects' participants' and project phases' characteristics, this paper designed an organization model of risk assessment and management and defined responsibilities of all participating units, which can provide guidance to effectively prevent and manage the social stability risks in major construction projects.

This study proposes a method to separate data into several groups and perform regression analysis for each group at the same time statistically by using EM (Expectation and Maximization) algorithm or its extended formulation to nonlinear regression problem. Using the proposed method, a group of deterioration curves is estimated based on a health index database of 341 bridges by visual inspection in Gifu prefecture, Japan. The ordinary EM algorithm can only treat linear regression, so the algorithm is extended to nonlinear regression problems. In our proposed method, the hidden parameter and standard deviation of error are estimated following the ordinary EM algorithm, whereas nonlinear coefficients are estimated by using Particle Swarm Optimization - one of the global optimization methods. Deterioration curves of the four bridge groups are estimated with the inspection database by the proposed algorithm.

Engineering risk management in China is being paid increasing attention. More than ten years ago, risk assessment was only used for very large-scale infrastructure projects and focused on the project's economic risk. After 2002, engineering risk management was recommended for China's large-scale infrastructure construction. Project accidents were happening continuously, which lead to a lot of economic loss and severe injuries. All of the accidents on big projects provoked an urgency to take measures for dealing with risks. The government recognized that project risk management (RM) could manage the engineering construction risks and published some new guidelines/standards for large scale projects. The project RM guidelines/standards are focused chiefly on large infrastructure projects (tunnels, roads, railways, bridges, and harbor works) to manage the technical risks during project feasibility study, design and construction phases. The present article addresses the state-of-the-art risk management on tunnels and underground works in China. The features and functionality of the Project PM application (as illustrated from national data on accidents and casualties from 2003 -2011) can reduce the hazards and control the economic loss significantly.

In order to evaluate the risk factor of population safety in the transport corridor of Georgian military roads, field expeditions and monitoring research were implemented in 2000-2012. On the basis of the conducted research, vulnerability was established in sectors of mountain landscape and the transport corridor, impacting on populated sectors. Population safety and the risk of car accidents on sectors of military roads during the formation of natural disaster phenomena have been estimated by the use of the reliability and risk theory.

In the past two decades, publi- private partnership (PPP) has been one of the prevailing ways for the development of infrastructure in Malaysia. However, it involves many risks and uncertainties due to a large amount of investment and long concession period. It is very important to recognize and find out the ways to cope with the critical risks that are related to the investments made in PPP projects for the foreign investors. The aim of this article is risk ranking associated with the PPP projects using risk matrix. First, the paper reviews the current literature, consultation and a written survey distributed to the panel of experts to identify common risks in PPP projects. The risks identified from the literature were classified according to the type of risk. From the results, it was found that the critical risks associated with the PPP projects include the third party tort liability, interest rate volatility, construction cost overrun and the change in law. This research study is supposed to provide awareness and highlight the management of the risks associated with the PPP risks in Malaysia.

Brake systems generate different sorts of noises and vibration due to various frictional mechanisms. Of these noises, brake squeal is an irritating high-frequency noise causing many problems for car manufactures. Several frictional mechanisms have been put forward on the root cause of squeal instability among which mode-coupling has attracted the most attention in the literature. This frictional mechanism leads to asymmetry of the stiffness matrix and positive real parts of one or more pairs of eigenvalues of the system. The latter is considered to indicate squeal instability as the amplitude of vibration in the linearised system grows without bound due to this term. The typical approach to the brake squeal problem is running the complex eigenvalue analysis to find eigenvalues with positive real parts. However, the major drawback of this deterministic approach is that variability and uncertainty are not taken into consideration. Variability stems from manufacturing processes, material properties and component geometries. Uncertainty is mostly caused by contact and friction. All these factors, therefore, necessitate implementing a stochastic approach to the brake squeal problem. The main difficulty associated with the uncertainty analysis of brake squeal is the computational cost and time. Running the complex eigenvalue analysis of the actual brake system under this study takes one or two days. Hence, running some uncertainty algorithms demanding thousands of runs to produce results is not feasible in this case. This study, in turn, is proposing an efficient stochastic way of predicting brake squeal instability. A surrogate model of the finite element model for the real brake is constructed which can produce results comparable with the finite element model and, thus, saves a massive amount of computing time and data storage.

A new random vibration-based assessment method for coupled vehicle-track system with uncertain parameters subjected to random track irregularity is proposed in this paper. The dynamic equations of the coupled vehicle-track system under the mixed physical coordinates and symplectic dual coordinates are established based on the wheel-rail coupling relations. The control equation, with respect to the uncertain parameters, is derived by using the Hermitian orthogonal polynomials for dynamic analysis of the coupled systems. By using the periodic features of the track, the "curse of dimensionality" of the control equation is effectively reduced.

The paper considers robustness of dynamic response analysis of pile groups in foundations for vibratory machinery in case of stochastically and spatially varying soil elastic properties. In the dynamic case, the pile group response is highly and irregularly frequency-dependent. A new methodology of group stiffness definition is described, involving Monte Carlo simulation of the pile group response with different soil parameters from the given range; enveloping the resulting response curves; and fitting them with a theoretical amplitude-frequency curve, which yields the real and imaginary part of pile group stiffness parameter. Through theoretical and numerical studies, it has been proven that the group stiffness thus defined eliminates anomalies occurring in conventional dynamic group stiffness analysis and is robust against soil properties variation, random non-uniformity of soil properties over the pile depth, and boundary effects at the periphery of the pile.

The problem of stochastic model updating is addressed by means of the application of two methods (covariance and interval model updating) to the DLR AIRMOD structure which is repeatedly disassembled and reassembled to provide a database of modal variability due to uncertainty in joint and support stiffnesses and masses of cables and screws. It is shown that the measured data is fully enclosed by the results of both methods. The interval method is the more conservative, but does not assume any form of probabilistic model. The covariance method involves an assumption of normality.

The free wave propagation and forced vibrations of rectangular thin plate assemblies are investigated by using the symplectic method. Initially, the governing equations of motion of the plates are introduced into the symplectic dual system, and the wave propagation parameters, as well as wave shapes, can be founded by solving the symplectic eigenvalue problem. The responses of the plates described in physical domain can be then transformed into the wave coordinates. The amplitudes associated with the mode shapes can be obtained by solving the equations involving excitation, scattering and propagation. Superimposing the wave amplitudes gives the physical responses. The method is applied to the forced vibration of a built-up structure consisting of three directly connected plates and the results are compared with those yielded by the ABAQUS finite element software. A significant improvement of accuracy and computational efficiency is achieved. The time-averaged energy and power flow for the example structure are also obtained and analyzed.

Rockets experience severe loading environments during launching, especially in transonic buffeting state. In order to determine these loads, this paper presents a force estimation method which considers both white noise in measured vibration data and modeling errors in structural systems. A regularization technique based on the Tikhonov-like method of total least square is utilized to alleviate the ill-posedness of the force estimation problem. Finally, the proposed method is utilized to estimate the transonic buffet loads during ascent phase of a launch vehicle, using telemetry acceleration data. The force estimation results indicate that this force estimation technique is valid.

The exposure of seated people to whole body vibration has been extensively researched and modelled during the past two decades. The trend is to use the average biodynamic responses. This paper investigates the relation of apparent mass to the natural frequencies of the seated human body with the help of the ISO 5982 and a 2-dof model. The experimental biodynamic transfer functions and natural frequencies of 43 males were investigated. The results show that for each of the 3 modes that were identified between 0 and 30 Hz, a great amount of variance exists. A heuristic method utilizing differential evolution has been used to estimate the individual masses, stiffness values and damping factors of the subjects. The results show a wide scatter among the group with the corresponding statistics computed and presented.

Currently, the classical spectral representation method for nonstationary simulation suffers from lower efficiency due to unavailability of fast Fourier transform. In this paper, an efficient hybrid simulation method is proposed for the vector-valued nonstationary process, which contains the spectra decomposition via wavelets and spectral representation method. This method can take advantage of fast Fourier transform and is also easy to use. Numerical examples are employed to evaluate the proposed method. Results show that the method performs fairly well for the scalar process and vector-valued process with real coherence function. Its limitation is that the process with complex coherence function cannot be simulated.

This study presents the development of a set of fragility functions for six reinforced concrete building typologies, categorized based on the date of construction (which has a direct relation with the design code level) and number of storeys (height of the building). The structural fragility of the Portuguese building stock has been the target of only limited investigation in recent years and, moreover, the existing studies relied mainly on simplified methodologies which might not be sufficient to represent the structural characteristics of the RC building typologies in Portugal. An analytical methodology was adopted in which thousands of nonlinear dynamic analyses were performed on 2D moment resisting frames with masonry infills, using one hundred ground motion records as much as possible compatible with the Portuguese tectonic environment. The generation of the structural models was carried out using the probabilistic distribution of a set of geometric and material properties, compiled based on information gathered from a large sample of drawings and technical specifications of typical Portuguese reinforced concrete buildings, located in various regions in the country. Various key aspects in the development of the fragility model are investigated herein, such as the selection of the ground motion records, the definition of the damage criterion and the evaluation of dynamic (i.e. period of vibration) parameters of the frames. The resulting fragility model can be applied directly in earthquake loss assessment, which is a fundamental tool for the development of risk mitigation actions.

There is no distinctive boundary in RC members when the short-term deflection ends and long term begins. Simplified procedures for predicting deflections in design codes are not compatible with actual deflection under service loads, especially in sensitive elements such as floor slabs. Design codes generally predict the time-dependent deflection by multiplying an empirical amplification factor by an instantaneous deflection. Despite the negligible difference in instantaneous and short-term deflection, the calculated value for long-term deflection that is due to decrease in stiffness overtime due to the inelastic deformation of concrete shrinkage and creep, is sometimes significantly less than the actual deflection. In this paper, simplified calculations for the ratio of long-term to short-term deflection in codes and some empirical works have been compared. Based on the comparison between simplified methods and data obtained from experimental investigations of Gilbert and Guo (2005), it is evident that the long-term/ short-term ratio is sometime significantly beyond the range of codes of practice.

Several design concepts for considering fuzzy or stochastic quantities are known. However, the consideration of polymorphic uncertain a priori and design parameters with these concepts is not possible. This contribution presents related numerical models to take polymorphic uncertainty in a parameterized design task into account. The design tasks can be performed by optimization or solving of the inverse problem. Additionally, an approach for an early design stage is presented. Examples show the applicability.

Computational reliability analyses of engineering structures are often time-consuming, in particular, if time-dependent structural behavior is considered. If (almost) real time prognoses are required, surrogate models may be used to approximate the structural behavior described by advanced numerical models. In this paper, a hybrid surrogate modeling strategy based on a combination of Proper Orthogonal Decomposition (POD) and Artificial Neural Networks (ANN) is introduced. The hybrid approach is developed for the approximation of time variant surface settlements in mechanized tunneling due to uncertain geological and process parameters. The approximation capabilities are demonstrated by means of an example. The new hybrid surrogate model can be applied for numerical, efficient, real-time reliability analyses in mechanized tunneling.

This paper describes the socio-technical restoration process and impact associated with Hurricane Isaac (August 2012) in Louisiana. Hurricane Isaac had few other impacts besides the power outage—there was extremely limited wind and flood damage. This isolation provides a relatively rare opportunity of seeing the linkages between electrical network disruption dependent infrastructure, and impacts and responses that might be obscured or overlooked in a larger disaster. Thirty-three participants were asked five open-ended questions about:(1) the significant impacts from the outage; (2) what, if any, lasting effects would result from the outage; (3) the relative performance of Entergy's restoration; (4) the effectiveness of Entergy's communication: and, (5) factors influencing the public and political dissatisfaction with the restoration performance. Other collected data included content from the news and social media, government documents, press releases, situation reports, and publicly available data. In sum, these data were synthesized to develop a broad understanding of the case study and identify significant themes with respect to impacts, as well as public and political reactions.

Critical infrastructures provide essential services for the functioning of the society, and vulnerability analysis is an important basis for decisions concerning increasing their robustness against hazards and threats. Since critical infrastructures can be regarded as complex systems, such analyses can prove challenging. To analyze the system response to strains, several different functional models have been suggested in the scientific literature, ranging from simple topological to more advanced engineering models. The simple models are computationally less burdensome which enables more comprehensive vulnerability analyses. The downside, however, is that they may not describe system performance accurately enough. The advanced engineering models, on the other hand, capture the system performance more accurately, but are computationally burdensome which leads to less comprehensive analyses. In the present paper, ten different functional models are used to assess the vulnerability of the IEEE RTS96 transmission power test system. The results from these analyses are then used in two decision contexts - (1) identification of critical components; and (2) ranking of structural improvements - to study to what extent the models provide a good decision support. The results suggest that the use of functional model significantly impacts the decision and, hence, care should be taken when choosing which functional model to use as a basis for decisions of critical infrastructure improvements.

An objective of infrastructure asset management of drinking water network is to minimize risks (service outage or disruption of vehicular traffic). However, there are several methods to assess their frequency. This paper first discusses the different models used in predicting structural deterioration because it is a compulsory preliminary step to calculate risk. Risk models for service outage are then discussed.

The potentiality of natural hazards to trigger simultaneous failures, leading to technological disasters (i.e. also referred as Natech events), requires tools and methods able to realistically simulate events and interactions between natural phenomena and simultaneous technological failures. The task of the present paper is to highlight the advantages and potentialities of Bayesian Networks (BNs) as a risk assessment tool for simultaneous failures triggered by extreme natural events. For this purpose, a simplified BN model for the risk assessment of a spent nuclear fuel pond of facilities subject to extreme weather conditions is provided. The network is then applied to a real-case study integrating different data-set and models available in literature to show the extreme flexibility of this approach and its ability to integrate climate change projections to evaluate future risks.

Extreme winter storms in northern regions bring heavy snowfall, strong winds and cold weather. Winter storms accumulate snow on power lines, causing damage, power outages and communication breakdowns. They may disrupt society's normal interactions, especially in sparsely populated areas, due to snow-blocked roads, isolating people and preventing rescue operations in cases of emergency. In the worst cases, when the electricity is cut off for a long time, many houses are at risk of rapid cooling. Hence, people are in danger of hypothermia if they cannot move or be evacuated to warm and safe places. Foreign visitors may be even more vulnerable because of language problems and different safety cultures, including, e.g., not knowing how to dress properly for cold weather This paper presents part of the results of activities performed within the EU project CRISMA, "Modelling crisis management for improved action and preparedness". It shows how vulnerability analyses are produced in the case of an extreme winter storm in northern Finland. The analysis is based both on risk-hazard and socio-constructive approaches, combined to achieve the most effective results for the use of rescue services and regional planning authorities.

During the construction stage of the bridge, the elevation control could be influenced by many random factors, the allowable deviation of elevation control could be obviously influenced by human factors, and the threshold of controlled elevation depends on both the requirement of structural design and the subjective factors of controller, which is characterized by strong fuzziness. A composite beam cable-stayed bridge is composed of complex structure members which have the characteristic of complexity in structure analysis, strong randomness in parameters, and difficulty in construction control. Therefore, it couldn't be better to set the composite beam cable-stayed bridge as the target for fuzzy random structure analysis. The Direct Differentiation Method was used to obtain structural response gradients of composite beam, and it was combined with the method of transforming fuzzy membership function equivalently to the random density function. Finally, based on a real bridge construction process, the fuzzy random reliability analysis of the bridge elevation control was finished availably.

Goal-oriented, rational threat agents attack a complex ICT infrastructure by composing elementary attacks against distinct components into an attack chain or attack plan. To compute statistics on the success probabilities of these plans, we have designed and implemented Haruspex, a tool that implements a Monte Carlo method by simulating the agent plans. A proper set of Haruspex experiments returns a set of data to compute statistics on the agent plans and their success probabilities even before deploying a system. In this way, we can assess with high confidence the robustness of a system and the risk it poses by considering scenarios where it is attacked by a set of agents. To fully automate the assessment, we have also developed GVScan, a tool that maps the output of a vulnerability scanning into the inputs of Haruspex. This paper describes both Haruspex and GVScan and their adoption to automate the assessment of the control plant of a power generation system.

The introduction of new links to network topology could potentially contribute to greater capability to withstand system breakdowns. This paper analyzes the value of adding new cross-radial links for public transport network robustness. The value is evaluated in terms of passenger welfare under disruptions. Using a model that considers passengers' dynamic travel choices, stochastic traffic conditions, timetables and capacity constraints, a new light rail transit line in Stockholm, Sweden is evaluated. The results show that: (1) the cross-radial link reduces the impacts of disruptions of critical links; and (2) the total value of robustness is positive and significantly offsets the loss in welfare caused by disruption of the cross-radial link itself.

This paper presents A methodology for the characterization of vulnerability within current and future configurations of large-scale electricity network systems. We provide a demonstration for Great Britain using a spatial hierarchical network representation of the transmission and distribution infrastructure consisting of more than 180,000 nodes. Alongside the current configuration, we develop nuclear and renewable future configurations by assigning known and forecast capacity and demand values to individual generator and load-point network assets. A capacity constrained shortest-path resource allocation model has been used to map flow pathways between generators and load centers, providing a path-set that bridges multiple scales. Vulnerability is characterized by exploring the distribution of path lengths and the number of intermediate components of the path set. Results highlight that a renewable future configuration has a reduced number of very long paths, resulting in a reduced vulnerability of exposure to hazards when compared to a nuclear future.

This paper looks into the vulnerabilities of the electric power grid in the face of intermittent power generation from renewable energy sources and uncertain load demand profile within a complex network framework of analysis. We extend the purely-topological complex network modeling framework by inclusion of relevant physical aspects of the system. We focus on the self-limitations that the electric power grid imposes on its operations due to its structural configuration and to the limits on flow-carrying capacities of lines. To this aim, we assess how the transmission system copes with requests to increase power generation due to enhanced power consumption at a load bus. In the application to the 380 kV Italian power transmission network, we introduce vulnerability measures that allow ranking the elements of the electric power network. Moreover, we find that topological centrality measures are not adequate in predicting the criticalities of the electric power network.

Several approaches have been used for assessing the importance of network components during an outage. For example, indicators based on network topology, such as node/links betweeness, allow ranking components from the most to the least important. Such models, however, do not consider specific aspects associated with network components outages that may trigger additional events. For example, the outage of a transmission line in an electric power system could produce a redistribution of the power flow and cause overload in nearby lines. To cope with such effects, several cascade models have been presented in the literature. These models, based on different assumptions, could produce different importance rankings. In this paper, ranks of components derived from three simple cascade models are combined through a non-parametric technique and are able to produce a unique ranking without considering decision-maker preferences. A version of the Italian high voltage power grid illustrates the proposed approach.

National infrastructures form critical components of present day societies because they provide services leading to economic prosperity and social well being. Disruptions due to extreme hazard events have shown the growing vulnerability and frequent breakdowns of national infrastructures. Due focus on critical infrastructure vulnerability and risk analysis is important in planning for risk reduction. This research focuses on the risk of failures of national infrastructure networks due to extreme spatial hazard events that have the potential of causing widespread infrastructure disruptions. Our aim here is to develop a spatial risk assessment framework that calculates infrastructure risk from multiple infrastructure network failure configurations resulting from exposure of extreme hazard loading. We have formulated and implemented a methodology for estimating reliability, disruption and overall risk for spatial infrastructures. The implementation of the methodology is discussed here through an example case study analysis on national scale extreme hazards and infrastructure networks.

Integrating Bayesian methods with kernel methods has recently garnered attention, as Bayesian methods make use of previous data in order to estimate posterior probability distributions of the parameter of interest given that it follows a specific prior distribution. As the quantification of resilience has become a vital component of infrastructure risk analysis, we use the Beta Bayesian kernel model to estimate resilience metrics used to analyze the recovery process of disrupted critical infrastructure systems. More specifically, stochastic resilience-based component importance measures are assessed using the component's characteristics and disruption data. Such estimates would help risk managers determine the overall best recovery strategy of an infrastructure system in case of a disruption impacting multiple components. The model is deployed in an application to an inland waterway transportation network, the Mississippi River Navigation system, for which the recovery of disrupted locks and dams on sections of the river is analyzed by estimating the resilience using the Bayesian kernel model.

The input-output approach proposed by Wassily Leontief is regarded as a key tool for the quantitative analysis of the interdependencies between different interconnected sectors within an economy, especially in today's highly interactive networks of producers/ service providers. In recent years, Leontief's model was also extended in order to assess their resilience to critical events, such as a disruption affecting some sectors and propagating through others according to their vulnerability, reaction times and centrality to the overall economy. In this context, a key factor towards the mitigation of monetary losses is represented by preparedness which, to a large extent, is associated with: (1) the availability of inventories; and (2) the ability to ensure extended continuity of product/service delivery in spite of the temporary, partial, or complete inoperability of some sectors. In this paper - building on an approach based on the dynamic inoperability input-output model with inventory (originally proposed in Barker and Santos 2010) - we formulate an optimization problem and propose an algorithm to determine how a proper sizing of each sector's cumulative inventory level can enhance the overall resilience to selected critical events.

Analysis of vulnerability to climate-related hazards, such as flooding, typically starts with the distribution of people and economic assets in flood-prone locations. However, this approach provides limited information about the severity of disruption that may be caused in extreme and disastrous events, as it does not fully account for the economic and social dependence on vulnerable assets. Infrastructure assets are particularly significant in this regard because of the very high social and economic dependence on these systems, which can extend far outside the hazard zone. In this paper, we demonstrate a methodology that is capable of understanding this spatial aspect of the vulnerability for the Chinese infrastructure system to flooding impacts on both a broad and local scale. We apply the methodology to the rail and electricity sectors. The results show the locations of critical infrastructure that are exposed to risk of flooding on a broad scale. We are also able to calculate the potential number of customers affected - should infrastructure assets fail owing to one or a series of flooding event(s) - on a local scale. Interestingly, our results show that the critical infrastructure in these sectors is not exposed to high flooding risks; however, climate change may increase the frequency of flooding events in these locations and planners should at least investigate the flood defence structures in these areas.

In this paper, we look at the robustness of connected critical infrastructures under a systems-of-systems framework, taking into account:(1) the dependencies and interdependencies among the components of a critical infrastructure and between different critical infrastructures, respectively; (2) the variability of the performance of each component by means of a multistate model; and, (3) the epistemic uncertainty in the transition probability between different component states by means of probability intervals. We adopt the Goal Tree Success Tree - Dynamic Master Logic Diagram for system modelling and we perform a quantitative assessment of the systems-of-systems performance by Monte Carlo simulation. We illustrate the approach by way of a simplified case study consisting of two interdependent infrastructures (electric power system and a gas network) and a supervisory control and data acquisition system connected to the gas network.

Large-scale outages on critical infrastructures (CIs) resulting from small initial failures, although infrequent, are increasingly disastrous to society. Thus, it is imperative to optimally design these systems in order to maximize their resilience against cascading failure. The optimization task requires the understanding and modelling of the dynamics of these systems. In this paper, we consider two approaches to infrastructure modelling: (1) a simplified (computationally cheap) graph-theoretical (topological) approach based on network theory; and (2) a realistic (computationally intensive) physical approach based on power flow models. The objective of the work is to investigate whether the optimal network obtained using a simplified topological model is also physically optimal when a more realistic power flow model is embraced. This is performed through simulations on the 400kV French power transmission network. A discussion of the usefulness of topological models to study the dynamics of cascading failures in electrical infrastructures is also contributed.

Ensuring the continued flow of resources - such as materials, energy, and water - is crucial to securing resilience. Interdependencies between the infrastructures that enable the flow of these resources have the potential to increase the vulnerability of these systems to disruption via cascading mechanisms. To analyse the disruption of resource flows within interdependent systems, this paper introduces a resource model that pulls together two established modelling methodologies: input-output modelling and network analysis. Data on supply, demand and flows are typically only provided at coarse spatial scales, so an important development was the disaggregation of regional economic input-output data into smaller spatial units suitable for flood impacts analysis. The results highlight a large degree of interdependency between different industries that enables a flood that inundates 11,000 m² to disrupt 22% of the region's resource flows. Further analysis reveals that the magnitude of resource disruption responds non-linearly to the return period of the flood event. These interdependencies appear to amplify the disruption from flooding in the case study site, although different locations will exhibit different types of response.

Critical Infrastructures (CIs) are recognized to be of high societal and economic importance globally. Due to population impact, attacks against their components can cause serious damage and performance degradation, putting wide geographical regions at risk. Therefore, it is imperative, to protect them against any type of cyber or physical risks by protecting CIs against threat consequences, blocking the threats from taking place, and predicting threat occurrence and eliminating its roots. In this paper, we present a decision tool (RTRM) that imprints a methodology capable of alerting the infrastructure security operators of the existence of new threats, of threat actions, and even of the possible existence of threats. Monitored data is captured and fed into a Data Stream Management System. This data set is applied on a behavior analyzer that translates the raw data events into possible CI asset behaviors, which are added into semantics ontology through an incremental model generator. The updated models are then injected into threat classification and estimation modules and the new security map of the system is displayed on the RTRM that alerts the security CI team of any new threat situation. All these are real time processes and actions.

This paper tests the applicability of two existing international methodologies - HAZUS (USA) and SYNER-G (Europe) - for predicting electrical substation damage. It compares observed damage from the September 2010 and February 2011 Canterbury earthquakes in New Zealand with damage/failure probabilities generated by the two methodologies based on observed ground accelerations. Only two substations were damaged in the September earthquake, and only one in the February earthquake. For both methodologies, failure probabilities were calculated for each substation and a short Monte Carlo simulation exercise was run in which the probabilities were used to generate 1,000 potential city-wide damage scenarios. Both simulations yielded results which over-predicted the collective level of damage, with probabilities of less than 1 in 1000 that the observed scenarios could occur. This indicates that neither method is appropriate and that new fragility functions should be developed for New Zealand for future seismic risk assessments.

The objective of this paper is to present a methodology that integrates Mixed Integer Programming (MIP) optimization methods into the calculation of metrics related to the reliability and resilience of a system of interdependent infrastructure networks, improving over mitigation strategies and vulnerability assessment that do not consider interdependence relations within an optimization framework. This methodology aims to provide tools to simulate diverse failure scenarios, assess their impact on the system's performance and recoverability, and quantify its sensitivity to adverse events. For the system's performance and recoverability measurement, this methodology builds upon the Interdependent Network Design Problem (INDP), which focuses on finding optimal recovery strategies given a disaster scenario. A computational experiment is carried out on simplified versions of the water, power, and gas networks in Shelby County, TN, which are geographically and physically interdependent. Results show that the approach permits comprehensive analysis about the fragility and vulnerability of a system of multiple correlated networks; hence, providing useful information for decision-makers to determine efficient mitigation actions directed to resilience enhancement.

Population evacuation in an area with high population density is a very serious problem which should be paid more attention. Knowing the road vulnerability for population evacuation and having efficient reconstruction plans of roads, buildings and emergency shelters play a very important role in emergency response. In this paper, a complex network was used to analyze the road vulnerability for population evacuation in an objective way instead of the traditional subjective methods like the expert evaluation approach. Through the data analysis, road-load vulnerability, accessibility and safe distance to emergency shelter of each road and intersection in population evacuation are studied in detail. Furthermore, the improvement plans of each road, intersection and emergency shelter are put forward. The process and the results that were obtained are essential for improving the efficiency of evacuations and reducing the potential risk in population evacuation, which should considerably reduce the possible injury, deaths and other losses in disasters.

First-passage reliability of structures has been playing a central role in engineering performance evaluation and design for decades. It is well recognized that nonlinear stochastic dynamics of high-dimensional systems is the embedded essential tool for reliability evaluation, but great challenges still exist in this field. In the past decade, a family of probability density evolution method (PDEM) was developed. In this method, the coupling between the nonlinearity and the randomness was broken and, thereby, a family of generalized density evolution equations was derived. Most recently, it is also applied in the dimension reduction of FPK equation for additively excited systems. In the present paper, this method is employed to capture the first-passage reliability of additively excited systems by imposing an absorbing boundary condition on the governing probability density evolution equation. Numerical examples are illustrated. Problems to be further studied are discussed.

This work presents a case study comparing the results of two reliability analyses developed with the objective of determining optimum schedule maintenance intervals to guarantee adequate levels of components reliability. Using field failure data, the first analysis took into account every reported failure (no clear information if the failures were really related with the failure mode in question), and the second analysis did not take into consideration one of the failure reports on the reliability analysis. On the contrary, one may think the second analysis (considering one less failure) identified a smaller schedule maintenance interval to obtain the same level of component reliability. This real case indicates that taking into account failure reports where it is not clear if the failure should be part of the analysis may lead to non-conservative results.

Based on a probability density evolution method (PDEM), a nonlinear stochastic seismic analysis program for buried pipeline systems is carried out. Firstly, a finite element model of buried pipeline systems subjected to seismic wave propagation is established. Secondly, a physical-mechanism-based method is employed to establish the random ground motion field for the area where the pipeline systems are located. Then, when the ground motion field acts on buried pipeline systems, the seismic response of the systems can be given. Thirdly, taking into account the basic random variables of ground motion and pipelines, the PDEM is employed to yield the probability density function of the seismic responses of pipeline systems. Finally, to validate the proposed program, a numerical example is investigated.

Using the idea of random function, the standard orthogonal random variables in the spectral representation method are expressed as the orthogonal function form of basic random variables. Through the construction of two different forms of stochastic orthogonal trigonometric functions, non-Gaussian orthogonal random variables and Gaussian independent random variables can be represented by the orthogonal trigonometric functions of the basic random variables. Combining the power spectral density function of ground motion acceleration process, a numerical example is given to illustrate the effectiveness of the hybrid random function and spectral representation approach. It is natural to combine the recently developed probability density evolution method (PDEM) and the random function model of ground motion to study the non-linear random earthquake response. Moreover, the seismic reliability of structures is assessed using the idea of equivalent extreme-value, which can be used accurately to evaluate structural systems under compound failure criterion. Finally, an example which deals with a non-linear frame structure subjected to ground motions is illustrated to validate the above approach.

The damper control has demonstrated its value for risk mitigation of civil engineering structures subjected to seismic excitations, while logical treatment on the randomness inherent in the seismic excitation and its effect upon the design of damper control have still not received sufficient appeal. In this paper, stochastic seismic response analysis and reliability assessment of six-storey steel-framed structures with viscous dampers are carried out using the probability density evolution method and the theory of extreme value distribution. The base excitation is represented by a physical stochastic ground motion model. Numerical results reveal a significant reduction upon the inter-storey drift of structure. The reliability of storey components and the structural system are enhanced significantly after the control devices act in effect. It is indicated that the minimum design requirement needs to be satisfied allowing for an effective control gain ensuring structural safety, and an additive control gain would be improvident if the sufficient safe design is provided.

Present earthquake design methodology is based on response spectra representing a certain percentile of maximum responses of an oscillator to a ground motion excitation. The production of response spectra relies on the suite of accelerograms selected, lognormal assumption of the maximum responses, and approximation in the use of pseudo-velocity and pseudo-acceleration. In this study, we define a probabilistic resonance concept, and then propose an alternative variance spectra approach that has the advantage to be theoretically more consistent with the probabilistic framework than the current methodology based on the maximum responses.

Several national steel design standards allow, in principle, the use of inelastic system analysis to check the integrity of a steel structural system. However, system reliability considerations have yet to be implemented in any rational way in such design-by-inelastic analysis methods. This paper considers a representative steel moment frame subjected to combined gravity and wind loads. The frame is designed using second-order inelastic analysis with a set of postulated system resistance factors. The probabilities of occurrence of strength and serviceability limit states are evaluated. The effects on these limit state probabilities of system resistance factor and wind-to-gravity load ratio are examined.

To evaluate the failure probability of structures considering post-instability behavior, a two-step absorbing method based on PDEM is proposed in the present paper. First, a physical stability criterion is introduced into PDEM to decouple the global stochastic response to be stable one and unstable one. For an unstable stochastic response, an inverse absorbing strategy is put forward to investigate the post-instability stochastic response independently. Further, a complementary process is constructed to impose the pre-instability stochastic response evolved in the safe domain of post-instability and let the stochastic system probability be preserved. The failure probability after dynamic instability eventually can be assessed by imposing a safe boundary on the constructed complementary process together with the real post-instability behavior, which is identical to imposing a safe boundary on the post-instability stochastic response straightforwardly. The numerical example demonstrates the effectiveness and accuracy of the proposed methodology to evaluate the failure probability when dynamic structural instability is unavoidable and structural failure results from losing strength after instability.

Engineering structures are usually modelled as input-output maps. The response is a function of input parameters and driving forces, both being nondeterministic and uncertain. The paper addresses recent methods combining stochastic processes and imprecise probability - namely, random fields for the description of loads and random sets for the description of uncertain input parameters. This approach covers interval analysis, fuzzy sets, Dempster-Shafer structures and random variables and their hybrid combination with stochastic processes. The focus is on a firm mathematical analysis of the methods. Applications are demonstrated using a simple example from geotechnics.

Recently, generalized interval probability was proposed as a new mathematical formalism of imprecise probability. It provides a simplified probabilistic calculus based on its definitions of conditional probability and independence. The Markov property can be described in a form similar to classical probability. In this paper, an expectation-maximization approach is developed to train generalized hidden Markov models with generalized interval probabilities. With the consideration of systematic error in measurement, the training process provides a robust learning mechanism where data quality requirement is not as restrictive as the traditional hidden Markov model.

In this work, we are interested in estimating the uncertainty that a system will work, given the probabilities that its components will be either failing or working. Usually, this estimation is done by propagating the component uncertainties through a structure function. This problem is well-studied when component probabilities are known and when the componenst are assumed to be independent. In this paper, we first recall some results obtained when considering that probabilities are unknown and when one either assumes component independence or no knowledge about the component's dependence. We also explore some structures not studied up to now, such as consecutive k-out-of-n structures.

Confidence structures (c-boxes) are imprecise generalizations of confidence distributions. They encode frequentist confidence intervals at every confidence level for parameters of interest and, thereby, characterize the inferential uncertainty about distribution parameters estimated from sparse or imprecise sample data. They have a purely frequentist interpretation that makes them useful in engineering because they offer a guarantee of statistical performance through repeated use. Unlike traditional confidence intervals, which cannot usually be propagated through mathematical calculations, c-boxes can be used in calculations using the standard methods of probability bounds analysis and yield results that also admit the same confidence interpretation. This means that analysts using them can now literally compute with confidence. We provide formulas for c-boxes in several important problems, including parametric and nonparametric statistical estimation from random sample data. The results are imprecise characterizations analogous to posterior distributions and posterior predictive distributions. We contrast this c-box approach to statistical estimation using traditional maximum likelihood and Bayesian methods.

The focus of the present paper is the determination of the lower and upper bounds of the probability of failure under uncertain inputs by means of random set theory. Under this general framework, it is possible to model uncertainty in the form of probability boxes, fuzzy sets, cumulative distribution functions, Dempster-Shafer structures or intervals. In addition, the dependence between the input variables can be expressed using copulas. In order to speed up the calculation, a very efficient probability-based reliability method - known as "subset simulation" - will be used. This method is specially suited for finding small probabilities of failure in both low- and high-dimensional spaces, disjoint failure regions and nonlinear limit state functions. The proposed method represents a drastic reduction of the computational labor implied by plain Monte Carlo simulation for problems defined with a mixture of representations for the input variables, while delivering similar results. A numerical example shows the usefulness of the proposed approach.

In this paper, a novel implementation of the Line Sampling method for computing imprecise probabilities is presented. The model of uncertainty is generalised to include both aleatory and epistemic uncertainties which comprise gaps of knowledge and scarcity of data. The proposed generalised uncertainty model allows for sets of probability distribution functions - also known as credal sets - and sets of bounded variables. The proposed implementation, based on the Adaptive Line Sampling algorithm, not only makes the computation of single probabilities a lot faster but, most importantly, eases the search for lower and upper bounds of the failure probability.

The United Nations Office for Disaster Risk Reduction reported that the 2011 natural disasters, including the earthquake and tsunami that struck Japan, resulted in $366 billion in direct damages and 29,782 fatalities worldwide. The rational management of such reduction and recovery is facilitated by an appropriate definition of resilience and associated metrics. In this paper, a resilience definition is provided that meets a set of requirements with clear relationships to the metrics of the relevant abstract notions of reliability and risk. Those metrics also meet logically consistent requirements drawn from measure theory and provide a sound basis for the development of effective decision-making tools for multi-hazard environments. A proposed resilience definition consistent with a 2013 presidential directive that lends itself for quantification is " the persistence under uncertainty of a system's performance in the face of disturbances." Current definitions do not always lend themselves naturally and intuitively to the development of consistent resilience metrics with clear relationships to the most relevant metrics of the abstract notions of reliability and risk. For example, defining resilience by the operative word of ability does not set the measurement process on the appropriate tracks by focusing on the abilities rather than the outcomes of these abilities. The primary outcome of these abilities is the continuance of performance, including bouncing-back, a characteristic that could be appropriately termed as performance persistence. Performance persistence would naturally set measurement in terms of availability of the performance or continuance of system's states of normalcy. Subsequent sections of this paper provide metrics based on this definition that meet logically consistent requirements drawn partly from measure theory, and provide a sound basis for the development of effective decision-making tools for multi-hazard environments.

Due to the aerodynamic effects on rotating blades and wave action on the tower, the offshore wind turbine tower system is actually a high-dimensional, time-variant, nonlinear system. With the increase of their size, the safety and serviceability of offshore wind turbines become increasingly important. Generally, evaluation of the global reliability of such systems - which involves high-dimensional, nonlinear. stochastic dynamics - is still a great challenge. In the present paper, a simplified integrated multi-degree-of-freedom model which characterizes the rotation of blades and the aerodynamics of blades is adopted. The probability density evolution method (PDEM) is then employed to evaluate the global reliability when the randomness of wind is involved. The example shows that it is feasible to design a complex structure exhibiting nonlinearity subjected to concurrent external dynamic excitations based on the global reliability.

In 2011, earthquakes and flooding caused historic insured losses of over USD $126 billion, the highest ever recorded. To save lives, reduce economic losses and improve societal wellbeing, regions should develop resilience engineering frameworks to adapt to possible extreme events. Gap analyses of infrastructure services are required to estimate the restoration time caused by a selected extreme event. Implementation of a resilience engineering framework should adopt performance-based critical infrastructure targets in order to restore services to the "Triple 3 Resilience Target": 3 days for emergency services, 3 weeks to restore basic utility services and 3 years to achieve improved critical infrastructure systems. Resilience offices are needed to help lead, coordinate, implement, and track progress focusing on the reliability of critical infrastructure components and interdependencies.

Lateral spreads have been extensively found near waterfronts after major earthquakes as a consequence of liquefied saturated sandy soils, and they pose significant detrimental effects on widely-spreading urban lifelines. This paper proposes a displacement-based procedure for liquefaction hazard zonation by using a newly-developed probabilistic model of liquefaction-induced lateral displacements exceeding a pre-defined threshold. The probabilistic function was formulated from a regression analysis on case histories of liquefaction by employing probit modeling. The procedure for generating the liquefaction hazard map with this proposed model was demonstrated through a selected case study. The comparison between the predicted probability and the field measurements indicates that the model can provide reasonable prediction particularly in cases of large deformations. The displacement-based procedure is promising, providing a probability map that highlights the regions where relatively large deformations have been observed.

Flood insurance is an important non-engineering measure for flood control and disaster reduction. China is a country with frequent floods every year, and the direct economic losses caused by flood continue to rise, which exerts a great threat on economic development and social stability in China. Therefore, the establishment ofan effective flood insurance is imminent. In this paper, based on the analysis of an international flood insurance model and the fundamental realities of China, a government-led flood insurance mode is proposed which should be operated by commercial insurance companies. Then, the position and function of the government in the implementation of flood insurance, risk diversification mechanism, organization and management of flood insurance, reinsurance, and flood insurance policies and regulations have been studied systematically in order to promote the establishment of a flood insurance system and lay a foundation for further research in China.

This paper explores the practical role of the interaction between critical lifeline systems that can impact their mutual performance as well as their ability to serve the community, especially in the aftermath of seismic events. In particular, the emergency and recovery planning of individual lifeline systems is discussed in relation to power and telecommunication system resilience as seen from different post-earthquake reconnaissance investigations and future evolution of these increasingly coupled systems. Seismic hardening of lifeline systems is improving either by means of enforcing standards, material advances, installation practice and quality control; but, these efforts are concentrated on individual components of individual systems. Hence, a new focus is needed that includes interconnections between components and coupling across systems, while distinguishing functional and management layers for enhanced tractability. Advances in telecommunication technologies make lifeline systems rely more on automated system control and monitoring during normal and abnormal operation regimens. Therefore, communication systems are critical for uninterrupted service and coordinated restoration across modern lifeline systems after a major disaster — all essential to community resilience. An example of the new methods to assess the observability and potential management of coupled networks is thus presented, while also highlighting research and implementation tasks for resilience based on practical operational and post-disaster observations on interdependencies in the last decade.

In the reliability calculation of the current structural codes, the variable load distribution is Gumbel set for one-year loads. This calculation includes two deficiencies: (1) the variable load distribution must be set for the working life, normally for 50 years; and (2) the standard Gumbel distribution is questionable as it has a robust upper tail which unrealistically affects the calculation. The first error is unsafe while the second is safe. The overall effect is unsafe. A feasible option is that the upper tail of Gumbel distribution is cut at about 1.5-times the mean 50-year load, corresponding to about 1000-year return loads. This modified distribution has virtually the same lower tail as standard Gumbel distribution. The normal distribution as another option, however, is probably somewhat unsafe. The variable load safety factors of the Eurocodes are given here based on Gumbel distribution, modified Gumbel distribution and normal distribution set for 1-year and 50-year locations.

Shanghai, located along the sides of the Huangpu River, is the economic center of China. However, as rainstorms, typhoons and upstream floods strike the city frequently, Shanghai is faced with a high risk of flooding disaster. Therefore, the aim to ensure economic sustainable development and residents' safety, flood control and disaster mitigation are becoming the hot issues in Shanghai. In the present investigation, the causes and character of flood disasters are analyzed first. Hence, the flood control system in Shanghai - including an engineering system and a non-engineering system - is demonstrated. Meanwhile, prevention, warning and the main defense schemes supported by city government are shown. Last, the flood management plan in Shanghai is summarized and suggestions and prospects are given for future development and application in the whole country.

This paper aims to study the method of satellite spectral reflectance indexes harnessed for crop productivity control and forecasting. The general method is proposed and discussed in the framework of a general stochastic model of socio-economic regional development. The set of spectral indexes have been selected for control of bio-productivity and its variability analysis. The method for analysis of uncertainties of the method of productivity assessment by remote sensing data has been proposed. The separate components of uncertainties and corresponding errors have been estimated. The way to control the threshold productivity toward the harmful impact (for example, droughts) as the approach to risk assessment is proposed. Spectral reflectance indexes NDVI, VCI, VHI, TCI, PDI, SAVI have been proposed for assessment of crop productivity and control of critical values of productivity. Other functions of used indexes -for example, FPAR, LAI -are effective tools for control of modeling variables.

Some aspects of the theoretical and methodological basis for the use of remote sensing data of snow cover for hazards assessment related to meteorological, climatic, hydrological and hydrogeological risks over urban areas are discussed in this paper. A method for determining the snow cover parameters on remote sensing data base - in particular, MOD10A1 and SWE products, normalized index of snow depth (NDSI) and local meteorological observations - have been proposed. A method for data integrating from various sources on the basis of the modified Ensemble Transform Kalman Filter (ETKF) and Kernel Principal Component Analysis (KPCA) of data distributions have been proposed. It is shown that the proposed approach has quite high relative accuracy in comparison with existing methods, algorithms and products (if MOD10A1 and SWE products have been used separately) with application for urban agglomeration. As an example, the approach has been used to analyze extreme snowfall in Kiev (21-23 March 2013). Quantitative assessments of risk indicators and vulnerability parameters of municipal infrastructure under emergency effects have been proposed.

In this study, a seismic vulnerability assessment at urban scale is carried out in a high-seismic city in Southern Italy using building stock data from different sources:(1) data from an airborne Remote Sensing mission carried out over the municipality, providing a detailed estimate of 3D geometric parameters of buildings, and (2) data from a field survey, providing detailed information on geometrical and structural characteristics of each single building. Such data are used within a multilevel approach in order to evaluate the influence of the detail level of input data on seismic vulnerability assessment at urban scale. Data from the detailed field survey are assumed as a reference, and when using Remote Sensing data, due to the lack of information affecting such source, some of the input parameters to the seismic vulnerability assessment procedure are assumed as random variables, using aggregate information on buildings provided by census data. Hence, the error introduced by the use of less detailed (but easier, faster and less expensive to collect) data is analyzed and discussed in order to evaluate the reliability of alternative data sources within a cost/benefit approach to large scale seismic risk assessment.

We provide a new approach towards the analysis of the response of higher order systems whose coefficients are subject to norm bounded perturbations. Based on the magnitudes of the perturbations, we obtain bounds of the response of the system. The first order case - that is, state space or, more generally, descriptor systems - has been extensively studied in the past using a variety of approaches and many results have been produced. On the other hand, a very popular strategy to overcome the difficulty of high order systems is to reduce them to first order equivalents. Our approach utilizes the aforementioned techniques to study the response of polynomial systems under perturbations.

This paper deals with the problems of robust stabilization and robust H∞ control of uncertain linear stochastic systems with multiplicative Brownian noise and Markovian switching. The system coefficients have norm-bounded uncertainties with Markovian switching. In addition, the mode transition rate matrix is assumed to have an interval uncertainty. We give sufficient conditions for the solvability of these two problems in terms of linear matrix inequalities (LMIs).

The premium pricing process and the stability of the reserves are two very challenging issues in the insurance industry. In practice, a premium which is sufficient enough to cover the expected claims and to stabilize the derived reserves is always required. This paper proposes a premium pricing model for general insurance products which implements a negative feedback mechanism for the known reserves with time-varying, bounded delays and is based on the recent claim experience into a stochastic framework with norm-bounded parameter uncertainties. The robust stability for the reserve process is investigated using Linear Matrix Inequality (LMI) criteria in a discrete-time stochastic framework. A numerical example illustrates the main result of the paper.

In this paper, we consider an infinite horizon version of the generalised risk-sensitive control problem. Two different infinite horizon criteria are considered. In each case, the solutions are found in an explicit closed-form. The change of measure and the completion of squares methods are used for this purpose.

In this paper, we consider the risk-sensitive control problem for a class of nonlinear systems. The nonlinearity consists of quadratic and square-root terms in the state. By using the completion of squares method, the solution to such an optimal control problem is obtained in an explicit closed-form.

In this paper, a novel mathematical model for the Tuned Liquid Column Damper (TLCD) is presented. Taking advantages of fractional derivatives and related concepts, a new equation of motion of the liquid inside the TLCD is obtained. Experimental laboratory tests have been performed in order to validate the proposed linear fractional formulation. Comparison among experimental results, numerical obtained using the classical formulation and numerical with the new linear fractional formulation are reported. Results in frequency domain show how the new linear fractional formulation can predict the real behavior of such a passive vibration control system, more correctly than the classical mathematical model, widely used in literature.

In order to understand the possible loss of building structure to debris flow, the establishment of vulnerability is necessary. With vulnerability, the loss can be calculated. This study followed HAZUS damage state probabilities concept to establish the fragility curves of building structure under debris flow impact. It indicates the relationship of damage state probability and spectral displacement related to velocity and inundation height. In this study, the assuming inundation height and velocity were taken to establish the fragility curves, and fragility curves were integrated into a unitary curve as a proxy of vulnerability of building structure with inundation height as X-axis and loss ratio as Y-axis. In this study, the brick structure type building in Taiwan was chosen to demonstrate the concept. The vulnerabilities and possible (predicted) loss ratio of brick structure could be established under various combinations of inundation height and velocity (ranging from 2 to 20 m/s).

Natural hazard analysis involves various kinds of assumptions and approximations. Observations and data used in calibration processes are subject to errors. Consequently, probabilistic hazard assessments are uncertain. The methodologies for natural hazard analyses have evolved rapidly by improving the quantification and visualization of uncertainties associated with probabilistic hazard estimates. However, approaches across different natural hazards are not uniform. Aiming at developing a cross-hazard framework for natural disaster assessment, the current methods for seismic and tsunami hazard analyses are reviewed. In light of current needs for a dynamic and integrated framework for cascading hazards, a multi-hazard approach for earthquake and tsunami is presented.

The prevalence of flooding in the world in recent times has arguably been unprecedented. It is particularly challenging for developing countries such as Nigeria, where the hazard is often poorly understood and understudied. With predictions of worse future scenarios, it is important to develop integrated approaches - which include flood modelling and vulnerability assessment - aimed at assisting human populations to cope with the hazard. This paper presents an ongoing research into flood risk mitigation in the Lagos metropolis of Nigeria. Maps of social vulnerability index, and land cover of the area have been produced. The results tend to show that two-thirds of the study area may be classed as highly vulnerable to the hazard, with Ajeromi-Ifeledun local government area, most vulnerable. Rapid urbanization tends to expose a wider population to flood risk as new developments are increasingly being put up in flood-prone areas. While this research is at a relatively early stage, the interim results will inform flood risk mitigation efforts in the study area.

Two key outputs from a catastrophe model are the aggregate and occurrence losses by return period. Robust catastrophe models for European extra-tropical cyclones allow for aggregate losses to be larger than occurrence losses, particularly because multiple extra-tropical cyclone events tend to occur in a given winter season and, hence, there is a notable difference between the largest loss and the total loss. This work describes the relationship between aggregate and occurrence losses, both historically and as obtained from a catastrophe model. Analyses show that the aggregate/occurrence ratio tends to be higher for larger countries and lower as the return period increases. Also, the aggregate/occurrence ratio tends to decrease when moving from Atlantic coast countries to those in central Europe. Critically, the paper quantifies the impact of the renewal date of a reinsurance contract on modelled losses and provides insights to reinsurance companies on what the optimal inception dates are for reinsurance contracts.

Recent natural disasters - like the 2010 Haiti Earthquake, the 2011 Tohoku Earthquake and Tsunami, and the 2011 Joplin Tornados - have shown how destructive dynamic loads can be on the built environment. These events left an overwhelming amount of construction and demolition debris behind, requiring the need to find ways of effectively disposing or recycling/reusing. It is proposed that a sustainable approach would be to recycle and reuse the disaster debris for the construction of temporary shelters. Therefore, this study will assess the structural performance of structural wall panels composed of recycled materials. The work will include the evaluation of different concrete mix designs with varying aggregate replacement including: recycled concrete, steel shavings and crumb rubber. The research begins with the performance assessment of recycled concrete. Lateral load tests were performed on shear wall panels to measure the shear capacity of the experimental mix. In addition, the compressive strength and toughness was evaluated and compared. The preliminary results showed that, although the experimental mix showed a significantly lower shear capacity, 123.2 kN (27.7 kips), compared to the shear capacity, 180.2 kN (40.5 kips), of the control mix, it was greater than shear demand, 93.9 kN (21.1kips). The experimental mix also displayed reduced compressive strength.

Repairing and rebuilding structures following an extreme event requires a substantial outlay of resources to achieve full disaster recovery. Demographic shifts toward high-risk communities are increasingly placing both populations and the built environment at substantial loss exposure to such extreme events. Instead of retaining extreme event risks associated with these communities, property owners expect to transfer the risk to government regardless of the exploding municipal debt. The shrinking municipal assets restrict availability of resources for post-disaster recovery operations. The associated construction increases in disaster-prone areas dictate disaster planning to safeguard at-risk populations during the recovery phase of the disaster life cycle, and this planning necessitates a temporal recovery metric. This paper presents a shift moment approach to estimating post-disaster built environment recovery. Specifically, the research considers a Fisher-type, price-adjusted spatial residential construction time series for new residential units. The research compares changes in residential construction with accompanying declared disasters to ascertain any relationships. The approach examines spatiotemporal residential construction variability to determine built environment rapidity by measuring the duration between sequential time series shifts. The resultant temporal metric allows estimation of post-disaster residential built environment recovery for operative disaster planning and municipal resource allocation.

Although vital to any preparedness plan, a comprehensive database of facilities essential in aiding the state of New Mexico, USA, to recover from an earthquake does not currently exist. Therefore, as a first step in assisting the New Mexico Department of Homeland Security and Emergency Management (NM-DHSEM) to improve the state's preparedness to earthquakes, the seismic performance of essential facilities in eight counties was assessed using the Rapid Visual Screening (RVS) method developed by the Federal Emergency Management Agency (FEMA 2002). The counties studied were: Valencia, Bernalillo, Sandoval, Santa Fe, San Miguel, Los Alamos, Rio Arriba, and Taos. These counties were selected by the NM-DHSEM due to the vulnerability of the region to seismic events, the population density, and the high number of unreinforced masonry and adobe buildings present in the area. This paper summarizes the findings of this project and, more importantly, highlights the challenges encountered in the obtention of data, and the implications of using incomplete or inaccurate data for RVS of facilities. Finally, it emphasizes the importance of inter-agency collaboration in the development of a database of essential facilities and their seismic assessment.

The development of the world economy increases trade, thereby inducing a large amount of goods transportation. In many developing countries, such as Brazil, the transportation system is predominated by the highway mode. Municipal highways, most of time, are part of the main road cargo transportation system, and this makes the traffic of hazardous materials a risk to society and the environment. The goal of the paper is the use of a multi-criteria analysis methodology, for modeling of the environmental risk of Road Transport of Hazardous Materials (RTHM) in Sao Paulo State - Brazil. Therefore, a methodological discussion is presented to explore the issues inherent to the composition of the panel of experts to assign weights to each criterion and to quantify the relative importance of each for risk analysis of environmental damage.

This paper investigates disappointment aversion (DA) in financial markets within a typical asset allocation framework. Drawing upon the seminal study of Ang et. al. (2005), we incorporate disappointment aversion (that is, aversion to outcomes that are worse than prior expectations) within a simple theoretical portfolio-choice model. Based on the results of this model, we then empirically address the portfolio allocation problem of an investor who chooses between a risky and a risk-free asset using international data from 19 countries [see Xie et al. (2013)]. Our findings strongly support the view that disappointment aversion leads investors to reduce their exposure to the stock market (i.e., disappointment aversion significantly depresses the weights to equities in all cases considered). Overall, it appears that disappointment aversion plays an important role in explaining the equity premium puzzle around the world.

In recent years, the issue of life expectancy has become of upmost importance to pension providers, insurance companies and the government bodies in the developed world. Significant and consistent improvements in mortality rates and, hence, life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data in order to anticipate future life expectancy and, hence, quantify the costs of providing for future aging populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age and cohort, and forecast these trends into the future using standard statistical methods. The modeling approaches used failed to capture the effects of any structural change in the trend and, thus, potentially produced incorrect forecasts of future mortality rates. In this paper, we look at a range of leading stochastic models of mortality and test for structural breaks in the trend time series.

A novel technique for determining the Wiener path integral approximately through a variational formulation is outlined and applied to the Geometric Brownian motion and Vasicek asset pricing processes. The potential for finding approximate analytical solutions to the path integral is exploited and the results found to agree exactly with the known analytical solutions for geometric Brownian motion and the Vasicek process. The method can potentially be applied to option pricing theory, and the possible next steps in this direction are briefly stated.

The aim of this paper is to design an automatic balancing mechanism based on minimizing changes in the main variables that play a part in a Pay-As-You-Go (PAYGO) pension system (contribution rate, normal retirement age and indexation of pensions) using nonlinear programming. This mechanism identifies and applies an optimal path of these variables to a PAYGO system and absorbs fluctuations in longevity, fertility rates, life expectancy, salary growth or any other random events in a pension plan.

In this paper, we propose an interval-based model to capture the dynamics of the range process of asset prices. Particularly, this model is an alternative in forecasting the range-based volatility. By modelling the evolution of interval-valued price process over time, the proposed model utilizes more information than modelling the range process only. In the empirical study, the in-sample and out-of-sample forecasting performances based on the U.S. stock market daily data show that the interval-based model produces more accurate range forecasts than the linear range model.

One of the pricing strategies for Bonus-Malus (BM) systems relies on the decomposition of the claims' randomness, namely, one part accounting for claims' frequency and the other part for claims' severity. For a Negative Binomial number of claims, we focused on the modelling of claim severities using a hybrid structure. While Weibull distribution is suggested for constructing smaller-sized claims, Pareto severities employed by (1) were applied to model large ones. A generalised function for the BM premium rates is then derived. Results are illustrated by a numerical example.

In this paper, we propose a new way to keep an insurance company solvent by managing the reserve capital as well as the financial market competent that the insurance company has invested. We propose a hedging method which finds the capital requirement for keeping the company solvent by constructing a viable portfolio in the market. We will discuss an example of hedging the solvency with mean variance risk measure.

In this paper, analysis of risk of the new glass-reinforced plastic (GRP) panel failure during installation in sewers with the use of short relining technology, was investigated. Although past experience indicates that the assembly phase poses a significant risk of panel failure, structural analysis for this phase is usually not carried out at the design stage. The paper presents results of numerical analysis based on the author's computational model for egg-shaped panels which was carried out for the assembly phase. States of stress and deformation were analyzed during grout distribution for different methods of protecting panels. The results of analysis allow for a more accurate selection of method for protecting GRP panels against failure during the assembly phase, which can reduce the risk of its occurrence and reduce the time and cost of renovation which will make this non-disruptive technology more competitive than traditional methods.

The structural effects of chloride-induced corrosion include loss of reinforcement area, reduction of strength and ductility of the corroded bars, loss of bond between reinforcement and concrete, and cracking and spalling of the concrete cover. As a consequence, corrosion affects both strength and serviceability of reinforced concrete structures. A probability-based approach is generally used for the assessment of deteriorated structures in order to take into account the uncertainties related to the actual condition and its evolution in time. Although several models about the initiation and propagation phases of corrosion have been formulated, a probabilistic characterization of the uncertainty related to the structural modeling is still lacking. The paper presents a probabilistic investigation of the uncertainty of the structural response predicted by a non-linear finite element model. The attention is focused to the prediction of the failure load of beams subjected to chloride-induced corrosion of the reinforcement. Concrete and reinforcement are modeled by two-node beam and truss elements, respectively. The bond between concrete and reinforcement, as well as the structural effects of corrosion, are taken into account in the finite element equilibrium equations. Statistics of the modeling uncertainty are obtained from comparisons of loading tests and model predictions.

The strengthening or upgrading of reinforced concrete girders with carbon fiber reinforced polymer (CFRP) composites has become a common procedure in the last years. However, the lack of standards or codes proposed within the same design philosophy of the Eurocode, and which are capable of assuring an adequate confidence level for the CFRP as for steel or concrete, often implies that the safety of prestressed girders strengthened with CFRP has to be evaluated using probabilistic tools. This manuscript presents a reliability study of a Portuguese prestressed high strength concrete (HSC) girder strengthened with CFRP. The selected bridge is representative of what has been constructed in Portuguese highways during the last two decades. First, the reliability level and the importance of design and load variables are computed using the following two codes: Portuguese RSA (1983) and European EC1 (2002). Next, partial safety factors are determined for the CFRP.

A numerical approach to safety estimation of the plate-girder bending structures from the shakedown theory point of view is considered. In the analysis, the uncertainties of the physical and geometrical structure's parameters, and also the load parameters, have been taken into account. It has been assumed that the structure is subjected to the dead load and variable live loads. The structure's parameters uncertainties, as well as the load magnitude, are treated as fuzzy variables or mutually independent random variables. On the basis of the theory of the yield lines and the kinematic formulation of the shakedown problem, the limit state function is being built. From this, it follows that some structural and material parameters - such as the plate thickness, plate reinforcement, girder cross-sections and yield point - are hidden in the limit moments. In case of describing the load parameters by random variables as the safety measure, the Hasofer-Lind reliability index is chosen. If all uncertain parameters which appear in the limit state functions are treated as fuzzy variables, the dominant failure mechanism and the minimum load factor for the non-shakedown which correspond to them can be obtained by applying α-level optimization. The shakedown analysis of a two-span plate-girder has been done and the results have been presented. The main advantage of the presented method is that it can be applied without a need for developing special software. It seems to be an effective approach to safety analysis of industrial roof and highway bridges.

Offshore wind turbines are relatively new structures that are expected to become important contributors to sustainable energy production in the future. In order to make offshore wind energy a reliable source of clean energy as well as a profitable investment, it is essential that the wind turbines operate with very high availability, usually for more than 20 years. The long design lifetime and the intensive environmental loading from wind and waves makes fatigue a key design driver. The support structures must be designed carefully and close to the natural frequency. The increased fatigue damage, due to dynamic amplification, has to be considered. A posteriori changes are extremely expensive in an offshore environment in such tall structures. Therefore, support structures need to be robust to changing parameters, such as the soil parameters and the stiffness of the foundation. In this paper, a methodology for rapid frequency domain fatigue damage estimation is presented. The accuracy of frequency domain fatigue damage estimation methods is evaluated by comparison to rainflow counting using site measurement data from an offshore wind turbine.

A multi-grid composite wall was recently proposed for seismic resistance. A seismic design method for the multi-grid composite wall, based on dynamic reliability calculations and using the subset simulation method is proposed in this paper. A hysteretic model of multi-grid composite walls for nonlinear analysis is proposed according to the hysteretic curves obtained from cyclic lateral loading tests. Parameters of the tri-linear envelope curve are obtained by empirical models and regression analysis. Parameters of the hysteretic rules are identified by the least-squares method. Procedures of the seismic design method are presented. Initial design of the composite walls is made according to Chinese code for seismic design of buildings. A random earthquake ground motion model is obtained by multiplying the time envelop function with Gaussian stationary processes. Parameters of the model are determined by Chinese code for seismic design of buildings. A subset simulation method is employed for failure probability calculations. Dynamic Reliability-based seismic design of a 6-story multi-grid composite wall with the aforementioned procedures is taken as an example to demonstrate the proposed method.

The pushover analysis is a nonlinear static procedure wherein monotonically increasing loads are applied to the structure. It is a popular tool for seismic performance evaluation of existing, as well as new, structures. In the literature a lot of research work has been carried out on conventional pushover analysis and, after knowing deficiencies, efforts have been made to improve it. However, actual experimental test results to verify the analytically obtained pushover results are rarely available. Also, the procedure involves certain approximations that some amount of variation is always expected to exist in seismic demand prediction of pushover analysis. In this paper, an ttempt is being made to assess the uncertainty of pushover analysis results to modeling methods and results compared with experimentally obtained results based on tests carried out on a G+2 storied RCC framed structure. Stochastic analysis is carried out by considering uncertain parameters as the strength of concrete, strength of steel, cover to the reinforcement, hinge location and hinge length which are randomly generated and incorporated into the analysis. The hinge lengths are found using various hinge length formulations available in literature. The results are then compared with experimental observations.

Fragility analysis is one of the most popular tools for the computation of the probability of reaching each investigated limit state for a given value of the external load intensity. Because of its versatility and computational efficiency, fragility analysis is particularly appropriate for regional loss estimations and risk analyses. Several different techniques have been proposed in the literature to compute the fragility of buildings and bridges. However, most of these techniques rely on simplifications and assumptions which, in some cases, are made more for analytical convenience than for adherence to reality. This paper investigates the effect of three of these common assumptions made on the engineering demand parameters for the case of seismic fragility analyses of bridges: (1) the marginal distribution is lognormal, (2) the median of such distribution follows a power law of the seismic intensity measure of choice, and (3) the dispersion of such distribution is constant for any value of the intensity measure. Numerical analyses have been performed running extensive Monte Carlo simulations on computational clusters, focusing on structural models of different complexity. The results suggest that assumption (1) is not realistic in general, but it does not induce a significant error on the final results, whereas assumptions (2) and (3) significantly corrupt the quality of the results, introducing substantial errors. A comprehensive methodology for the assessment of fragility curves for structural components and systems is then proposed, which does not rely on the above-mentioned assumptions.

The paper analyses the main reasons why NDT assessment of concrete properties is a complex problem. Based on real data and synthetic simulations, it shows how material variability, measurement uncertainties, variation of uncontrolled influencing factors and model uncertainties can be tackled. It points at the issue of model error resulting from the measurement and calibration process and draws some conclusions in order to improve the efficiency of on site NDT assessment.

This paper examines the development of real-time hurricane/storm surge risk assessment tools utilizing existing databases of high-fidelity simulations. The foundation of the approach is the formulation of a surrogate model that can provide an approximation to storm responses utilizing the information in any such database. Kriging metamodeling is adopted here for this purpose, as it facilitates a matrix-based, computationally efficient evaluation of the response over an extensive coastal region, including a large number of points (nodes) for which this response is evaluated. To alleviate problems related to the high-dimensionality of this output, principal component analysis is considered as a dimensional reduction technique, contributing significantly to computational efficiency (lower memory requirements and faster evaluations). Additionally, a correction stage is introduced to address problems for nodes that have remained dry for certain storms in the initial database. The developed surrogate model can be ultimately utilized for real-time predictions. The approach is illustrated for estimation of the surge risk in the New Orleans region.

We have applied a Bayesian framework for the analysis and testing of possible non-stationarities in extreme meteorological events in an area around Ouagadougou, Burkina Faso. Considering the results obtained for the historical period (1950-2005), it can be seen that, for a given exceedance probability, the intensities of extreme temperature and extreme consecutive dry days ECDD data are positively correlated. The higher values of extreme temperature and ECDD are identified at the Eastern part of the domain. This result suggests that those areas can be more likely exposed to desertification processes. Some of these areas are also coincident with areas in which extreme rainfall events may occur, and this combination can be a factor amplifying the possibility of flood events. Looking at the effects of the two climate change scenarios considered (RCP4.5 and RCP8.5), different patterns were found for the three variables analyzed; whereas, the ECDD data indicate that the stationary model is the one that dominates most of the solutions. The extreme temperature and extreme precipitation show remarkable trends in both scenarios. In this paper, analyses of the spatial distribution of the extreme events and the temporal trends observed when considering scenarios of climate change are performed.

Current projections suggest the frequency and intensity of some environmental extremes will be affected due to a changing climate, thereby raising questions regarding the treatment of future extreme environmental loading for the design of buildings and other structures. The estimation of future environmental loading is benefitted from the knowledge of the various uncertainties at each step of the estimation process. Possible changes due to climate add yet another uncertainty into environmental load estimation for which research has been limited. Characterization of extreme environmental loading, therefore, poses serious challenges to the engineering community. For this work, two environmental variables -wind speed and wave height - will be considered in a case study approach. Uncertainties in observations and climate projections will be identified for both variables. These uncertainties will be characterized using best available knowledge and, subsequently, will be attributed and quantified with respect to a "typical" extreme environmental load estimation process in engineering.

Mapping is a necessary phase for the establishment of plans for prevention of flood risk. It is absolutely mandatory for defining the constructability rules in areas subject to flooding. The mapping of risk is based on the flood evaluation with specified return period. The proposed methodological approach is structured in three steps, characterized by the adoption of hydrological, hydraulic and mapping techniques, respectively. In the hydrological step, the input conditions are defined by the flow-duration-frequency modelling, the synthetic hydrographs and the objective of safety to attribute to an area through variables related to the vulnerability factor. The hydraulic calculation provides information on the hazard factor and allows the evaluation of the local rating curve. The mapping technique allows the translation of the results obtained following the two previous steps in the form of geographic maps, which respond to the hydrological model and operate as both pre- and post-processors of the hydraulic model. An application of the methodology proposed for the flood risk mapping is shown with reference to the Mekerra watershed in Western Algeria, aiming at an implementation of a prevention plan against the risk associated with flooding.

Extremes of sub-daily precipitation may be associated with flash flooding, particularly in urban areas, but have been studied relatively little in the UK. This paper describes initial work on the construction of a dataset of hourly precipitation for the UK, based on three different sources of rain gauge data. Significant problems in the use of tipping bucket rain gauges for the analysis of long-term climate and climate variability are recognised and quality control procedures are described. Initial analysis reflects the different mechanisms that generate sub-daily precipitation, but in most parts of the UK, the largest totals generally occur in summer. Some significant long-term trends in mean hourly precipitation intensity are observed over the last 30 years, but few significant trends in annual maxima are detected. Significant break points in the time series are also detected and may, in some cases, suggest a shift in the precipitation regime.

In operational flood forecasting, the decision to issue a warning to the community at risk has to be made in real time based on evolving probabilistic forecasts of the hazard. However, not only is the hazard forecast changing in time, but so too are the exposure and vulnerability. This may be the result of changes in the location of assets and people, or - more qualitatively - in a loss or gain for the reputation of the forecasting authority. In this work, we take the first steps towards quantifying these to form a risk-based framework for making the decision to issue a warning using an example catchment in the UK.

Landslides are widespread andevery yearcausecasualties and extensive damage. Predicting the spatial and temporal occurrence of landslides is a problem of scientific and societal interest. Empirical threshold model approaches proposed in the literature have limitations related to the heuristic identification of rainfall conditions triggering landslide, to the subjective choice of threshold model, to the biased probability estimation related to the classical empirical threshold model, and to limited use of rainfall events not associated to landslides. A new probabilistic empirical prediction schema is proposed to overcome these limitations. The model was applied successfully in the Umbria region considering rain gauge measures and satellite rainfall estimates.

The development of detailed flood inundation maps is typically done through the use of hydraulic models. However, the development of a hydraulic model for a large hydrological basin requires the availability of a significant amount of data, time and computational resources. This becomes challenging in countries that lack detailed and high-resolution topography data, and information on stream and floodplain characteristics. Regression-based approaches can be used as an acceptable alternative for the development of depth versus river discharge relationships in catchments with sparse data, provided that a suitable data set exists in another data-rich basin for the generation of the necessary regression relationships. In this study, we describe a methodology to build hybrid statistical-physical regression equations to estimate the flood depths in flood-prone, yet data-scarce basins. These regression relationships use physically-based flood data from other data-rich basins with similar characteristics. Furthermore, the methodology uses the geomorphological properties of individual watersheds and the characteristics of the site as explanatory variables to derive these statistical relationships. An illustrative example of the developed methodology is presented for some selected catchments in Southeast Europe. The regression relationships are developed by using the output from a numerical inland flood model developed for Germany.

This study presents an innovative approach to obtain flood hazard maps where hydrological input (synthetic flood design event) to a 2D hydraulic model has been defined by generating flood peak discharges and volumes from a bivariate statistical analysis through the use of copulas. Synthetic hydrographs were generated by means of two different approaches: an indirect one, where rainfall was generated by a stochastic bivariate rainfall generator to be entered, a distributed conceptual rainfall-runoff model that consisted of a soil moisture routine and a flow routing routine; and a direct one, where stochastic generation of flood peaks and flow volumes have been obtained via copulas which describe and model the correlation between these two variables independently of the marginal laws involved fitted on flood recorded data. Finally, to highlight the advantages of the presented approach, flood hazard maps derived by bivariate analysis are compared to maps from conventional univariate analysis. The procedure is applied to a real case study located in the southern part of Sicily, Italy, where flood hazard maps have been obtained and compared.

The present study introduces a probabilistic approach able to estimate the mudflow peak discharge through the use of a Monte Carlo simulation method. In a classical deterministic approach, for a specific catchment, the parameters involved in estimation of the peak flow (topographical, hydrological parameters) are assumed to be known. As a result, in such approaches, the only source of uncertainty in evaluation of the peak discharge is due to rainfall intensity and frequency estimation. In this work, the standard Monte Carlo simulation is also used in order to propagate the unceratinties in various parameters related to hydrographic basin modelling and to obtain a probability distribution for the peak-discharge flow for a given return period. As a test case, the peak discharge of a mudflow in the basin of the Mandrizzo River, located in the town of Cava dei Tirreni in Southern Italy, is evaluated.

Identification of the flood-prone areas can be considered as a fundamental step in a flood risk management procedure. This work focuses on a fast procedure for hazard zoning within the flood-prone areas at a meso-scale. To this end, a semi-probabilistic GIS-based methodology for hazard zoning of the potentially flood-prone areas is presented. The main output consists of GIS-compatible maps for the hazard zoning (by flood height) of the potentially flood-prone areas. A flood height-dependent extension of the topographic wetness index (TWI) threshold is proposed as the lower-limit TWI for zones with flood height larger than a prescribed value. This procedure relies on calibrating the flood height-dependent topographic wetness index (TWI) threshold through maximum likelihood estimation and based on the inundation profiles calculated at micro-scale level for a given spatial window. This calibration is performed for different values of flood depth in order to investigate the correlation between the TWI threshold and the flood depth conditioned on return period, through simple linear regression. The resulting regression model is used in order to up-scale the results from the micro-scale spatial window to the meso-scale level. As a demonstration, the procedure has been applied for the city of Addis Ababa, Ethiopia.

Flooding can result in billions of dollars of loss to property and businesses and disruption to the normal function of a region or a state. Catastrophe models are used to evaluate the flood risk, and these models incorporate uncertainty of components of hazard and vulnerability in the loss computation. A framework to derive the aleatory vulnerability uncertainty of a catastrophe model is presented. The framework demonstrated the development of sub-grid hazard variability using elevation variability of a DEM and private defense use. The development of building specific vulnerability uncertainty was discussed using data and judgment. Finally, convolution using Monte Carlo simulation or weighted sum of probability distributions was considered as a method to combine flood depth variability and building specific vulnerability uncertainty to obtain aleatory vulnerability uncertainty.

Making decisions for flood control investment is challenging. This difficulty is because of some of the variables involved in the problem have uncertainty in them. Real Options theory is an approach to handle future uncertainties in risk management by providing flexibility in investment decisions. This work presents a real options-based framework to evaluate the financial value of having flexibility for deciding the time of investment in flood control. The framework considers the uncertainty associated with future water discharge events. Extreme water discharges are responsible for flooding events. The water discharges are considered as the random variable. The historical information of these variables is used to estimate the probability of future events. A lattice of options based in the probability of future events of the random variable is built. The option of delaying the investment is analyzed by calculating the payoffs of cost and benefits of each option. A hypothetical application is presented to validate the effectiveness of the proposed model. The result shows an option with an optimum investment time for flood control.

The paper presents a component-based methodology for probabilistic assessment of cyclonic damage and evaluating vulnerability to cyclonic wind for rural houses in the coastal region of India in which the failures of different components of the houses are described in terms of probability distributions of wind velocity. The method obtains different damage states by combining different possible damage scenarios and, accordingly, a damage probability matrix is determined. The effects of important parameters like distributions of failure velocity of damage states, coefficients of variation of failure velocity of components, and ratio of non-engineered to semi-engineered houses on the annual mean damage or the probability of failure are investigated.

The durability and long-term behaviour of many construction materials (RC, bituminous mixes, timber) are highly dependent on environmental parameters like temperature and humidity. Since the average values - but also their time-dynamics and cross-correlation - may govern the material response, it is important to analyze these patterns in order to be able to reproduce them through synthetic signals. The detailed statistical analysis of long-range series of climatic records of typical French climates is carried on rain, temperature and humidity leading to the identification of their main patterns. How synthetic signals can be generated and used for understanding the building material response is finally described.

This paper presents the application of state estimators in nonlinear structural systems. The objective is to provide a comparison of the effectiveness to reconstruct the state time history in nonlinear building-type structures of four existing algorithms - namely, extended Kalman filter, unscented Kalman filter, ensemble Kalman filter and the particle filter. We compare their accuracy under ideal conditions and their robustness to different types of modeling errors. The uncertainty in the estimate of the quantities of interest is described by their covariance matrix. The systems of interest are nonlinear frames, where the material nonlinearity is given by piecewise linear hysteretic force deformation functions.

Bayesian multi-level modeling establishes a convenient framework to account for aleatory variability and epistemic uncertainty in inverse problems. In view of engineering applications, we will place this framework into the context of classical and probabilistic inversion and demonstrate its additional potential to infer material properties as intermediate variables within a hierarchically defined Bayesian multi-level model. The objective of probabilistic inversion is to infer such probability distributions that describe the variability of model inputs across a number of experiments. Inference, therefore, focuses on so-called hyperparameters that parametrize population distributions. To that end, intermediate or latent variables are considered nuisance and commonly marginalized out from the problem. However, instead of integrating out intermediate quantities, one can just as well fade the hyperparameters from the inferential spotlight and marginalize them out. This allows for an "optimal" inference of the intermediate quantities with respect to the available prior information, structural assumptions and the acquired data. We will devise a simple academic example within the domain of mechanical engineering that will be used to study this optimal kind of inference. The system under consideration is an ensemble of simply supported beams with uncertain material properties. Over the sample of beams, Young's moduli are subject to aleatory variability, while the knowledge about the true hyperparameter values suffers from epistemic uncertainty. We will show how individual Young's moduli can be optimally estimated in a series of three-point bending experiments. It will be shown that, in hierarchically defined models, one can learn more about a specific specimen than what is encoded in dedicated data directly associated with that single specimen. One can indirectly utilize information from different specimen, within the same sample in order to improve the assessment of a specific one. In this contribution, we will demonstrate the potential and challenge of this learning mechanism and we will investigate the underlying flow of information.

Markov models are often used to describe the behaviors of power systems and components - like generating units, transformers and others - which show stochastic behaviors due to failure occurrences, environmental and operational conditions. In this paper, Global Sensitivity Analysis techniques are applied to consider the simultaneous effect of transition rates (TR) variations on the state probabilities (PS). Importance measures are determined for steady-state and transient probabilities for a multi-state generating unit.

The model updating based on measured data is a challenging problem that has received attention and resulted in different approaches. Depending on the intended level of accuracy and availability of data, the adoption of the right approach may bring important information to the updated parameters and ultimately may reduce the systematic (Epistemic) uncertainty and quantify the irreducible statistical uncertainty (Aleatory). This paper explains, applies and compares three model updating techniques (i.e. Sensitivity model updating, Interval model updating and Bayesian model updating) to simple numerical examples. Remarks related to the performance, accuracy and information provided by the different approaches are drawn along the examples.

An important consideration for experimental setups throughout various fields of science and engineering is whether the quantities measured suffice in determining the desired states of the underlying dynamic system (i.e., whether the measurements render these states observable). More often than not, there is uncertainty with regard to the real parameters of the dynamic system. The purpose of system identification methods is to obtain the most likely values for the parameters and the states given a set of measurements. This uncertainty with regard to the parameters of the system results in them being treated as new states in an augmented dynamic system. Consequently, even in the simplest case of a linear underlying dynamic system, the corresponding augmented system becomes nonlinear. Thus, the question of whether a system identification method could succeed for given measurements in defining the parameters and states of a system (i.e., the augmented states) becomes a problem of nonlinear observability. If only the parameters of the system are of interest, identifiability methods may, in certain cases, be used. Thus, observability and identifiability methods enable the design of experimental setups that would at least work if the measurements were free of noise and the rejection of those that would not work even in this ideal scenario. In this work, three methods for the observability and identifiability of nonlinear dynamic systems are studied and compared against each other. For a system whose state and measurement equations are analytic, geometric observability methods based on Lie Derivatives may be used. Moreover, if the equations are rational, algebraic methods are also available. For this last category of systems, identifiability methods may be used to investigate not only the finiteness of the possible parameter values, but their uniqueness as well.

In this paper, several statistical methods are evaluated with respect to their applicability for the probabilistic analysis of a coupled flow-thermo-mechanical model of a low pressure turbine rotor. The probabilistic analysis is comprised of a sensitivity analysis followed by an uncertainty analysis. The sensitivity analysis is performed to gain a better understanding of the coupled flow-thermo-mechanical system. The uncertainty analysis, using probability distributions derived from the manufacturing process, allows the effect of the input uncertainties on the life duration of the rotor to be predicted.

This work is part of the research aimed towards the multidisciplinary robust shape optimization of low pressure turbine (LPT) vane clusters. Here, we focus on the global sensitivity analysis needed to identify the most important design variables and reduce the design parameter space for further optimization. Identifying shared important variables for different disciplines will help to find a suitable multidisciplinary optimization architecture. To deal with high computational costs associated to the multidisciplinary analysis chain, a surrogate-based approach for sensitivity analysis is proposed here. Two well-known high-dimensional test functions are used to validate the accuracy of the surrogate-based sensitivity analysis. Finally, the process is successfully applied to the multidisciplinary analysis of the vane cluster. The results obtained show clearly the importance of performing advanced non-linear sensitivity analysis in addition to the computation of linear correlations.

Composite materials are being implemented in numerous engineering applications including, though not limited to, the aerospace, auto-mobile and wind turbine industries. Advancements in manufacturing processes enable the production of composites whose macroscopically observed properties are elaborately determined at the microscale. Composites are, therefore, inherently multiscale materials. Consequently, the reliability of structural systems being comprised of composites heavily depends on the micro-mechanical properties of the latter. In this work, a methodology is presented for the evaluation of failure probabilities of composite structures. The hysteretic multiscale finite element method (HMsFEM) is implemented for the modelling of composites while the subset simulation method is used to evaluate the corresponding probabilities of failure. In the HMsFE method, the nonlinear behaviour of the constituents is accurately modelled in the fine scale, while global solution of the structure is performed in a macro-scale -thus, significantly reducing the computational cost of the reliability analysis procedure.

In this paper, we are interested in using the incomplete modal data identified from the system to update the robust failure probability that any particular response of a nonlinear structural dynamic system exceeds a specified threshold during the time when it is subjected to future stochastic dynamic excitation. Uncertainties from structural modeling - the modeling of the stochastic excitation that the structure will experience during its lifetime - and any other uncertainties can all be taken into account. A new efficient approach based on stochastic simulation methods, which is very robust to the number of random variables and uncertain model parameters, is proposed to update the robust reliability of the structure. The efficiency and effectiveness of the proposed approach are illustrated by a numerical example involving a nonlinear structural dynamic model of a building.

The distinction between epistemic and aleatory uncertainty can sometimes be useful for practical purposes. In principle, epistemic uncertainty is reducible by obtaining more or better information. However, the boundaries between both types of uncertainties are often blurred. Fortunately, it is often the case that not all sources of uncertainty have the same impact on the predictive performance of numerical models, so that there is considerable computational benefit from investigating potential simplification in the number of parameters that should be modelled as being stochastic. In order to determine which parameters are the most important in terms of their contribution to the output's uncertainty, probabilistic sensitivity analysis can be performed. We apply this idea to a numerical model of corrugated skins. Corrugated skins are particularly suitable for morphing applications in aerospace structures, largely due to the very high compliance they offer along the corrugation direction.

Analysis of awater distribution system requires input data from many sources. The value of these data are uncertain due to their spatial-temporal variability, measurement error and limited sampling. This uncertainty in estimating model input parameters generates through the governing equations an uncertainty in the predicted model output. Such uncertainty affects notions of risk, reliability and confidence associated with engineering decisions for planning, design and management of water distribution systems. This paper examines the impact of model output uncertainty as affected by uncertain input parameters. The effects of the uncertainties of pipe roughness, junction demand, and water tank's level on the pressure heads and chlorine residual at the junctions are investigated. The methodology, which is applied on real water distribution network, consists of using Monte Carlo Simulation (MCS) to generated input parameters for the hydraulic simulation model considering extended period simulation (EPS). Results indicate that nodal pressure is more sensitive to parameter uncertainty compared to chlorine residual and tank water level has higher influence on pressure compared to the uncertainties of nodal demand and pipe roughness.

Pre-posterior analysis can be used to assess the potential of an experiment to enhance decision-making by providing information on parameters characterized by uncertainty. The present paper describes a framework for pre-posterior analysis for support of decisions related to maintenance of structural systems. In this context, experiments may refer to inspections or techniques of structural health monitoring. The Value of Information concept provides a powerful tool for determining whether the experimental cost is justified by the expected benefit and for identifying the optimal among different possible experimental schemes. This concept is elaborated through principal examples for structural components and system models. Sensitivity analyses are performed to investigate how the decision problem is influenced by the level of uncertainty that characterizes the structural properties, the amount and quality of information and the probabilistic dependencies between components of a system.

The Bayesian framework for hierarchical modeling is applied to quantify uncertainties, arising mainly due to manufacturing variability, for a group of identical structural components. Parameterized Gaussian models of uncertainties in structural model parameters are introduced that depend on a set of hyperparameters. Laplace methods of asymptotic approximation and, more accurate, stochastic simulation algorithms are used for estimating posterior joint and marginal distributions of structural model parameters and hyper-parameters. The posterior distribution of the hyperparameters is formulated as the product of as many multi-dimensional integrals as the number of structural components tested, with the dimension in each integral equal to the number of physical uncertain model parameters. Novel analytical approximations of these integrals are proposed that are shown to be computationally efficient, accurate and highly parallelized. A parallelized blocked Gibbs sampler is also proposed to efficiently generate samples simultaneously along the different uncertain parameter subspaces associated with the different number of structural component tested. Theoretical and computational developments are illustrated using simulated data for modal frequencies obtained from a number of identical bar structures.

A response evolutionary power spectrum (EPS) determination technique based on harmonic wavelets is developed for nonlinear multi-degree-of-freedom (MDOF) structural systems. Specifically, first a linear relationship between the evolutionary power spectrum matrices of the excitation and of the system response is obtained by utilizing a recently proposed locally stationary wavelet-based representation of non-stationary stochastic processes. The relationship can be construed as an extension to the wavelet domain of the celebrated spectral excitation-response relationship of the linear stationary random vibration theory. Further, a harmonic wavelet-based statistical linearization technique is proposed for the MDOF nonlinear systems. The developed technique can be viewed as a generalization of a recently proposed technique by some of the authors to account for MDOF chain-like nonlinear systems. Numerical examples demonstrate the reliability of the proposed approach.

A simulation-based procedure was adopted to generate fragility curves for five Chinese code-conforming reinforced concrete (RC) frame structures with increasing design-based earthquake (DBE) intensities. Two important elements, namely probabilistic seismic demand analysis (PSDA) and probabilistic seismic capacity analysis (PSCA), were involved in the procedure. In PSDA, 100 real ground motion records were selected to perform nonlinear time history analyses for representing the influence of earthquake uncertainties on structural demands. In PSCA, a group of ten structural parameters were considered as random, and then the conventional (deterministic) pushover analysis was extended by introducing 100 building samples according to the principle of the Latin hypercube sampling technique. From the derived pushover curves, the thresholds corresponding to the limit states - namely, "slight damage", "moderate damage", "extensive damage" and "complete damage" - were obtained for statistics. Finally, fragility curves were generated through combining the results of PSDA and PSCA, and the exceeding probabilities of the example frames conditioned on the three mostly concerned earthquake levels, i.e. frequent earthquake (FE), DBE and maximum considered earthquake (MCE), were consequently calculated. The results show that the increase of fortification earthquake intensity cannot correspondingly promote the probabilistic safety level.

Seismic protection measures for bridges can be used both for obtaining acceptable performances from new structures and for retrofitting existing ones. With the modern design philosophy based ontheprobabilistic Performance-Based Earthquake Engineering (PBEE) approach, the engineers are allowed to investigate different design solutions in terms of vulnerability assessment. However, if probabilistic PBEE approaches are nowadays well established and widely studied also for bridges, the topic of using the PBEE frameworks for the evaluation of the effectiveness of seismic protection devices for bridges is not extensively treated in literature. The first objective of this work is to deal with the problem of assessing the earthquake performance of a highway bridge equipped with different bearing devices - the elastomeric bearings (ERB) and the friction pendulum systems (FPS). The second purpose is to evaluate the efficiency of a structure-dependent IM in case of an isolated system. The examined structure is a highway bridge with concrete piers and steel truss deck. A FE model of the bridge is developed by using nonlinear beam-column elements with fiber section and the devices are modeled by specific elements implementing their nonlinear behavior. The effectiveness of the different retrofitting strategies has been carried out in terms of damage probability. Choosing the example of slight damage, and referring to the curvature ductility as EDP, the probability of damage during a period of 50 years is: 23% for the structure without isolation, 7% for the structure equipped with ERB, and 3% for the structure equipped with FPS isolation.

This paper focuses on a simulation-based framework for quantification/assessment of seismic risk (expressed through life-cycle cost), relying on stochastic ground motion models for description of the earthquake hazard. It discusses the opportunities provided by recent advances in high-performance computing (parallel/distributed simulations), focusing on methodologies that allow an efficient, concurrent estimation of the risk for different scenarios (related, for example, to regional seismicity). It also reviews a novel methodology for global sensitivity analysis which is integrated within the risk assessment and aims to identify what factors contribute more towards the overall risk. As an illustrative example, a benchmark case study of a three-storey concrete structure is presented. In this example, repair costs are estimated using an assembly-based vulnerability approach that uses the nonlinear time history of the structural response to provide a detailed estimate of earthquake losses at a component-level.

Several capacity spectrum assessment methods exist for determination of structural performance of building models subjected to earthquake loading. The repetition of such analysis for earthquakes of increasing intensity will result in the derivation of analytical fragility functions. A comparison of three capacity spectrum assessment approaches (N2, SPO2IDA and FRACAS) has been carried out, highlighting the advantages and limitations of the approaches. Two experimental case studies have been chosen to evaluate the IM-EDP (S_a-S_d, ISD_max%) estimates obtained from the three different capacity spectrum procedures, as well as from non-linear time-history analyses (NLTHA). It is found that all three approaches perform well in estimating the response of a simple steel frame, but that FRACAS provides the best estimate of the response of an irregular reinforced concrete frame. It is concluded that further comparisons of the capacity spectrum approaches with large-scale experiments on structures are required to draw more general conclusions.

In performance-based earthquake engineering, fragility curves constitute an essential component, providing a probabilistic link between the earthquake intensity measure and the structural response, expressed as an engineering demand parameter. In this study, we apply a capacity spectrum method that uses inelastic response spectra derived from earthquake accelerograms to construct fragility curves for an example reinforced concrete structure. This approach has the advantage of simplicity and rapidity over methods using the accelerograms directly. Various sets of scaled and unscaled accelerograms are used to investigate the impact of record-to-record variability on the derived curves. It is found that the variability in the input spectra at periods longer than the natural period of the undamaged structure has a direct impact on the standard deviation associated with the curves. When the spectra closely match a target, the curves are almost vertical (small standard deviations); but, as the variation around the target increases ,the curves become flatter (high standard deviations). A variant of the peak-to-trough measure introduced by Stafford and Bommer (2010) provides a useful way of measuring the variability in the input spectra.

Natural hazards, conflicts and faults can result in an extreme loading condition causing loss in lives and infrastructures. The reinforced concrete frame structures are considered in this work. The area of collapse control received significant attention; however, numerical models of reinforced concrete (RC) demand advancement to capture failure patterns and response beyond normal design limits. To benchmark safety level, robustness indicators are required; however, calculation of indicators demands efficient modeling. Although models are being proposed, not many focus on quantifying the risk as an essential element of safety assessment of structures In this paper, rational framework for the level of safety assessment and probability of disproportionate collapse of reinforced concrete frame buildings are proposed. On the subject, the US Department of Defense (DoD) accepted an alternative path (AP) method as a means for the structural analysis. The proposed framework addresses the variance in risk level results from the change of position of the damaged bearing element and the possible models of collapse progression. It also names the key affecting parameters and proposes means for quantifying risk/safety level for the defined failure mechanism. The proposed framework can be used in codified standard through appropriate factors of safety. It can be used in comparing various mitigations.

In the Tohoku region, the effects of the seismic shocks and the tsunami waves due to the 2011 Great East Japan earthquake were felt with very high intensity. Many structures and infrastructures were severely damaged or washed away. Because tsunami effects have not been taken into consideration in the seismic design and retrofit specifications in Japan, code provisions regarding tsunamis need to be established based on the failure mechanisms observed in the tsunami-induced damage to bridges. In this paper, using both analytical fragility curves and tsunami hazard curves, the basic procedure to estimate the failure probability associated with tsunami hazard is presented. The tsunami fragility of a concrete girder bridge is estimated based on Monte Carlo Simulation (MCS). Seismic reliability of a bridge is compared with tsunami reliability of the same bridge. The need to consider the tsunami effect in the design of concrete girder bridge is discussed in an illustrative example.

A novel scaling algorithm for ground motion accelerograms (GMs) is proposed in support of incremental dynamic analysis used to establish dependable statistical relationships between scalable intensity measures (IMs) and engineering demand parameters (EDPs) within a performance-based earthquake engineering framework. Specifically, an iterative harmonic wavelet-based scheme is employed to accomplish "surgical" changes to the spectral shape of suites of GMs to span various pre-defined levels of the spectral acceleration at the structural fundamental natural period, the most widely adopted IM. Since the target IM values may not be accomplished precisely by the local spectral modifications, a second step involving global uniform GM scaling is further considered. The proposed algorithm requires significantly smaller global (amplitude) scaling factors compared to the currently used scaling approach in which no initial local GM modification is undertaken. A numerical application of the proposed algorithm to elastoplastic structural systems shows the extent to which spectral shape may influence the displacement response of yielding structures and explains the conservative bias introduced by uniform global scaling.

This article presents a proposal for an innovative approach for including multiple intensity measure types (IMTs) in the representation of building fragility. Thousands of nonlinear dynamic analyses are performed in a 2D environment in which reinforced concrete frames are simulated using a Monte Carlo approach, according to geometrical and material variability of typical pre-code reinforced concrete buildings in Portugal. Seismic action variability is foreseen through the selection and scaling of appropriate Spectrum-compatible record sets, following the most recent proposals for linking nonlinear dynamic analysis back to probabilistic seismic hazard. A literature review of seismic Intensity Measures is performed in order to select a number of IMTs capable of representing a comprehensive set of earthquake shaking characteristics. A proposal for multiple IMT-based fragility is outlined, whereby variability in structural damage effects along the considered seismic intensity range is accounted for by including the explicative power of an additional set of IMTs.

The computation of fragility models can be carried out using post-earthquake damage data or through the development of numerical models capable of reliably representing the structural behaviour of a given building typology when subjected to a set of ground motion records. In Portugal, due to the lack of data regarding ground-shaking damage, analytical methodologies are often followed to evaluate the structural vulnerability of the existing building stock. However, these methodologies require advanced knowledge about the geometric and material characteristics of the building typologies, which is often not available or is poorly characterized. In this study, the material and geometric properties of the RC buildings, which represent approximately 50% of the Portuguese building stock, were thoroughly analysed. In order to do so, 400 drawings and design specifications from real buildings were gathered throughout the country, in cooperation with private practitioners, design offices and public institutions. For each building drawing, the main frames in the structure that would resist eventual lateral loads were chosen in order to measure the following set of geometric parameters: ground story and upper storys heights, column widths and depths, beam lengths, widths and depths, and slab thicknesses. The distribution of each geometric property was modelled considering several probabilistic distributions (normal, lognormal, exponential, gamma, beta), and their statistical parameters were derived using the maximum likelihood approach. These results can be used for numerical analysis, thus allowing a better understanding of the physical vulnerability of the RC building stock in Portugal.

During the last two decades, Performance-Based Seismic Design (PBSD) was introduced as the preferred approach for seismic assessment and design of the structures. In recent years further developments have focused on using probabilistic approaches to arrive at an informed decision with regard to achieving the desired objective. This will also provide for a better control on the extent of economic losses during the earthquakes, which appears to be an important concern based on recent earthquake experiences. To this end, the next generation of PBSD has recently been proposed by Federal Emergency Management Agency (FEMA P-58). This paper reviews the pro and cons for probabilistic PBSD considering existing practical constraints and limitations. The randomness and uncertainties in demand and capacity parameters are discussed in some detail with regards to RC frames. FEMA P-58 performance assessment methodology is discussed and a review of recent research studies on RC frame structures is presented. It is concluded that, despite the powerful conceptual base and the provided guidelines, probabilistic approaches are still faced with considerable practical limitations and require additional efforts. However, for important structures, extra efforts may well be warranted.

Seismic risk management is a multidisciplinary process in which a broad range of variables, as well as a great deal of uncertainty, is involved with both parameters and the modeling process.A disaster system can be seen as a combination of not only physical and structural consequence of a natural hazard, but also socio-economical and environmental impacts also influence the assessment process. Decision-making in such a complex system that often relies on subjective and objective knowledge should be handled though a knowledge-based approach. The study was launched to review and discuss the multifaceted character of seismic risk and examining the feasibility ofaknowledge base system to model such problems effectively and efficiently. Such a knowledge base system should be capable of: (1) integrating various perspectives of seismic risk; (2) conducting seismic risk assessment; and (3) handling uncertainty within risk assessment and to support mitigation strategies.

In recent years Performance-based Earthquake Engineering (PBEE) techniques have been gaining significance as an alternative to existing deterministic assessment procedures. Briefly, on the basis of an extensive probabilistic framework, PBEE intends to provide information to various stakeholders in terms of monetary losses, downtime and/or casualties associated to a return period. These expected losses are the end result of three fundamental components: the hazard, the exposure and the vulnerability. The aim of the present study is to evaluate the influence of the record selection procedures on the quantification of the physical vulnerability, and consequently on the seismic loss estimations, arguably recognized within the scientific community to produce a higher level of variability in structural demands when comparing to material properties and different numerical modelling solutions.

Viscous dampers are energy dissipation devices widely employed to control the structural response of mechanical and civil systems subjected to dynamic loadings. In particular, such dampers have been extensively applied in earthquake engineering to enhance the seismic performance of new and existing building frames. Although simplified methodologies for the preliminary design of the optimal damper properties are well established, they are often based on deterministic or semiprobabilistic approaches neglecting the response dispersion due to the uncertainties inherent to the seismic input and the system model. This paper proposes a reliability-based methodology for the optimal design of viscous dampers in structural systems subjected to the uncertain seismic input. The methodology is capable of controlling the probability of exceeding limit states related to the structural failure, while limiting the damper forces. Thus, it provides a useful means to identify the optimal damper properties based on performance-based criteria.

Reinforced concrete walls are well-known lateral resisting systems in seismic-prone regions. Their design procedure, according to the new performance-based design framework, requires thorough structural and damage analysis. Such analysis may easily become costly when it comes to complex structures. In the case of damage analysis, where the output is the fragility function, the possibility to replace the extensive computations with ready-made fragility curves sounds promising. In this study, we have developed the fragility functions for several cantilever RC walls. The walls had ten different variable parameters, including geometrical, material, reinforcement layout and loading properties. Nonlinear static analysis was performed on each wall and the performance limits according to FEMA356 were found on the pushover curves. Finally, the fragility functions were created and the influence of the axial load ratio on them was studied. The corresponding results are presented and discussed here.

In civil and offshore engineering, the safety and serviceability of complex structures are of great concern due to the randomness involved in both external excitations and structural properties. Therefore, nonlinear stochastic dynamics of multi-dimensional complex systems plays a central role in the performance assessment of such structures. In the past decade, a new family of probability density evolution method (PDEM) was developed for this purpose. In this method, based on the principle of preservation of probability, a generalized density evolution equation was derived. In contrast to the celebrated FPK and Liouville equations, the dimension of this family of equations depends only on the number of quantities of interest instead of the dimension of the original dimension. In this paper, a newly proposed generalized F-discrepancy (GF-discrepancy) is outlined and adopted as the objective function in point selection of PDEM. By doing so, the efficiency and accuracy of PDEM could be improved and guaranteed for random variables of general distributions. Numerical examples are illustrated. Problems to be further studied are discussed.

For the complexity of the coal prices, this paper uses nonlinear methods to investigate the three coal prices in Chinese and International markets. From the analyses of the basic statistics of the above coal prices, the results found that the two coal prices of China and Australia coal have the character of fat tails, which means that the time series of the coal prices do not meet the requirements of efficient market hypothesis. Then, this paper applies Surrogate Data method based on BDS statistic to analyze further if the time series are nonlinear. The results show that China's and international coal prices are nonlinear. Meanwhile, the nonlinearity of China's and international coal markets also indicates the invalidation of the Efficient Markets Hypothesis. The evidence of nonlinearity of the coal prices perhaps improves on conditional forecasts in China 's and the international coal markets.

The very large floating structure (VLFS) designed for a floating airport and giant operating platform on sea consists of multiple floating modules with flexible connectors, which is a typical nonlinear dynamic network involving complex collective dynamics. The study focuses on the typical behaviors of amplitude death (AD) that is significantly important to the global dynamic stability of the VLFS system. A nonlinear dynamic model for a chain-formed VLFS with piecewise-nonlinear-coupling is developed. We investigate the onset of amplitude death in design parametric domain, and discuss the mechanism of the phenomenon corresponding to the coupling strengths. The numerical results show that by varying coupling strengths, a weak periodic oscillation can be rapidly bifurcated into high-order periodic or chaotic motions with large oscillations. The amplitude death is illustrated in the parametric domain of coupling strengths, which provide a new insight and theoretical guidelines for the VLFS safety design.

Complexity of a time series is inherently related to the entropy, randomness and deterministic of the complex system which it is generated from. Analysis of time series data can reflect the hidden nature of systems. This paper applies the approximate entropy measurement, sample entropy measurement and fuzzy entropy measurement of the nonlinear analysis to analyze the complexity of the 7.2 seismic data for the Baja California Earthquake(2010). Based on these characteristic parameters, it is illustrated qualitatively that the exhibit the irregular and complex properties. By comparison, the fuzzy entropy can characterize better the earthquake time series than the approximate entropy and sample entropy. The entropy fluctuations are found to increase upon approaching bursting. The results illustrate that the fuzzy entropy measurement method is more applicable than the approximate entropy and sample entropy.

Researches about the Cournot model have appeared in previous works, yet all the established models considered only in the certain case, which indicates the players in the game will not change their strategy. Thus, a Cournot duopoly model based on uncertain strategy is designed with a payoff matrix. Results show that complex dynamical properties, like bifurcation and chaos, in the certain model don't exist in the uncertain model any more. An index, aggregate profit or A.P., is introduced to demonstrate the performance of the firms in the game process. The indices of the firms are steady in the uncertain model, while they are going in the opposite directions in the certain one. Practically, it means simple strategy brings fierce competition while complex strategy leads to mutual benefit. This explains that uncertainty of the market can be reduced by rational choices of the firms, a method implemented by firms in the real world unconsciously.

The stochastic dynamic responses of viscoelastic systems with real-power exponents of stiffness term under randomly disordered periodic excitations are studied. The assumed viscoelastic forces depend on the past history of motion via convolution integrals over an exponentially decaying kernel functions. The method of multiple scales is used to derive the equations of modulation of amplitude and phase. The changes of the shape of resonance curve are obtained with real-power exponents of stiffness term and viscoelastic parameters which are confirmed numerically. Theoretical analysis and numerical simulations show that, as the intensity of the random excitation increases, the steady state solution changes from a limit cycle to a diffused limited cycle. Under some conditions, the system may have two steady state solutions and the phenomenon of jumps will happen between them under the random excitations.

The purpose of this work is to use the stochastic averaging method to study the response of a vibro-impact system excited by additive and multiplicative colored noises. The non-smooth transformation of state variables is used to transform the vibro-impact system to a new system without impact term. The Fourier series is applied to obtain the stationary probability density function. The validity of the analytical results is verified by the numerical simulations. Moreover, stochastic P-bifurcations are also explored.

The problem of zero-crossings is of great historical prevalence and promises extensive application. The challenge is to identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process. In this paper, we address the zero-crossing problem for a Gaussian process and investigate the effect of introducing oscillations into the prescribed auto-correlation function. Statistics for the number of zero-crossings occurring within a set time period are calculated and verified by simulations of the process. We find that highly oscillatory auto-correlation functions cause realizations of the stochastic process to become increasingly `regular' or `deterministic'. Zeros occur at more regular intervals, implying that the inter-event PDF has an exponential tail with large persistence exponent. The persistence exponent exhibits a complex phenomenology that is strongly influenced by the oscillatory nature of the auto-correlation function. Comparison is made between the theoretical predictions and numerical simulation results.

The rich dynamic response of a parametric pendulum to a harmonic excitation acting on its pivot point has been shown to include, among others, rotational trajectories. On this foundation, the potential of developing a wave energy converter (WEC) has been suggested exploiting the bobbing motion of waves as the necessary excitation for the pendulum to establish rotary motion. Quite often in the study of dynamical systems, the random nature of environmental inputs cannot be ignored, rendering deterministic analyses inadequate. Thereafter, stochastic analysis of these systems has to be employed. Considering a pendulum structure floating on ocean waves, the need for a stochastic frame is raised due to the strong randomness dictating the motion of waves. In this paper, the probability density function of the energy transferred to the pendulum is calculated using a path integration (PI) algorithm. Subsequently, this information is utilized to evaluate the probability of the pendulum to lay in a rotational regime.

Structural systems (e.g., building systems, bridge systems) are large and complex systems including many uncertain factors. Therefore, for structural reliability analysis, the effects of uncertain factors on the structural systems must be taken into account in order to make proper reliability analysis. The uncertainty in structural reliability analysis has caused more attention by the planners and designers; however, how to make reasonable uncertainty model is rarely studied in the analysis of structural reliability. This paper firstly describes the copula theory - especially the Gaussian copula theory - then, based on the time-dependent parameters of the Gaussian copula, the dynamic measure of time-variant correlation coefficients, with respect to Gaussian copula, is treated as a time series, and then a Bayesian dynamic linear model was introduced. Based on the time-variant monitored data of the structures, the correlation coefficients of the two monitored variables are solved and predicted. What is more, a framework for analyzing the time-dependent uncertainty parameters from Gaussian copula involved in the processes of structural reliability analysis is proposed. Finally, based on the predicted time-dependent uncertainty parameters, the first order reliability method (FORM) is adopted to solve the time-variant reliability indices, which are compared with the reliability indices solved with first-order, second-moment method (FOSM) without considering the correlation coefficients of two monitored variables. Finally, a numerical example is provided to illustrate the feasibility and accuracy of the solved reliability indices.

Nonlinear vibrations due to time delay effects in metal cutting systems - such as turning, milling, and drilling operations - are undesirable as it might lead to a poor finish and low precision on the workpiece. In this paper, the authors study a very simplified model for turning processes. In the model, the exact geometry of the workpiece surface are taking into consideration, while other nonlinear factors - such as distributed time delay, exponential cutting force, and state-dependent delay - are neglected. Thus, the time delay system at hand simply suffers nonlinearities from the loss of contact effects. To deal with this system, a novel concept is proposed, based on which the system can be described by a combination of a partial differential equation (PDE) and an ordinary differential equation (ODE). Compared with literature, the PDE-ODE model can be concise to include the time-delay, loss of contact, and multiple-regenerative effects. A high-dimensional map system from the PDE-ODE model is obtained via semidiscretization method. By iteration of the map, the high-dimensional behavior of the cutting system is studied in the time domain. The simulations show the route from stable cutting to bifurcation, chaos, and hyperchaos. The Poincare maps and the bifurcation diagrams from the high-dimensional attractors also illustrate the rich nonlinear dynamical behavior of this very simplified system.

A bounded damping feedback method to stabilize the stationary state in a class of autonomous and non-autonomous chaotic systems is presented in this paper. The controller needs the measurement of damping signals constantly. In applications, this is difficult to achieve for the high sensitivity of noise in damping feedback. Actually, the filters of signals which mean energy loss lead the system more stabilization. In this way, the proposed method has advantage of being easy to implement without precise knowledge of the target trajectory. In applications, examples of autonomous Chen system and non-autonomous Gyro system are employed to illustrate the control effect. Accordingly, a rigorous stability proof of controlled version is provided based on Routh-Hurwitz criteria and LaSalle Invariance theorem. Numerical simulations verify the effectiveness of the feedback control method by increasing the maximum amplitude of the control law.

The problem of equivalent replacement plays a basic role in many fields of science and technology. In the classical approach the original object A is to be replaced by an equivalent object kB by using the mean square minimum criterion. When the difference between A and B is significant, the replacement leads to unaccepted errors. To reduce the errors, one may apply the dual approach. The advantage of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. The main idea of this paper is to propose a special form of weighted dual mean square criterion. Numerical results are carried out for a Euler buckling problem and Lutes-Sarkani oscillator to show an improved accuracy of the proposed criterion.

In this paper a novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators with fractional derivative elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes. In this manner, the analytical Wiener path integral-based technique developed by some of the authors is extended and generalized herein to account for systems with fractional derivative terms. Results are compared with pertinent Monte Carlo simulations demonstrating the reliability of the technique.

The aim of this paper is to investigate the phenomena of stochastic resonance in an underdamped linear system with multiplicative trichotomous noise and an external periodic force. First, the exact expression of output amplitude gain of the system is obtained by using the Shapiro-Loginov procedure. The two kinds of stochastic resonance can be obtained for the output amplitude gain. One is called bona fide stochastic resonance, which is induced by input signal frequency; the other is called general stochastic resonance which induced by noise flatness parameter or noise switching rate. Then, it is demonstrated that the output amplitude gain exhibits nonmonotonic dependence on the noise parameters (noise flatness parameter, noise switching rate etc). Finally, the influence of trichotomous noise and system parameters on output amplitude gain is analyzed by the numerical method. The results show that the system damping rate restrained stochastic resonance, while noise switching rate enhanced noise flatness-induced stochastic resonance.

For the purpose of evaluating multiple variables in finite populations, we use multivariable power function approximation to construct a new index variable which is dependent on estimator from the erase variables, which helps reduce the number of indices in a survey. By discussing its properties, we draw a conclusion that the estimated sampling errors and the reciprocal of sample size are in the same order.

In this paper, the Galerkin method is presented to estimate the approximate stationary and non-stationary responses of nonlinear random dynamical systems with fractional derivative damping. Based on equivalent linearization method, the equation of motion is reverted to a linear equation in terms of envelope and phase process at first. After that, stochastic averaging method is used to get an averaged Ito differential equation with fractional derivative approximated by a periodic function. Finally, the approximate non-stationary probability density function solution of the associated Fokker-Planck equation is obtained by applying the Galerkin method. The application on a Rayleigh oscillator shows that the methods we utilized in this paper are efficient and reliable by comparing the stationary solution between the exact and approximated one.

We consider the planned replacement of equipment in a system of sub-units such as a water collection, processing and supply network. The planner must specify what equipment will be replaced, subject to a budget constraint. The main challenge arises from severe uncertainty in the estimates of the likelihood of equipment failure and of the cost of failure should it occur. The replacement plan must reliably prevent the average cost from exceeding the allocated budget. We employ info-gap decision theory to model and manage the uncertainties and to support the replacement-planning decision.

In contrast to many other engineering fields, the uncertainties in subsurface processes (e.g., fluid flow and contaminant transport in aquifers) and their parameters are notoriously difficult to observe, measure, and characterize. This causes severe uncertainties that need to be addressed in any decision analysis related to optimal management and remediation of groundwater contamination sites. Furthermore, decision analyses typically rely heavily on complex data analyses and/or model predictions, which are often poorly constrained, as well. Recently, we have developed a model-driven decision support framework (called MADS; http://mads.lanl.gov) for the management and remediation of subsurface contamination sites in which severe uncertainties and complex physics-based models are coupled to perform scientifically defensible decision analyses. The decision analyses are based on Information Gap Decision Theory (IGDT). We demonstrate the MADS capabilities by solving a decision problem related to optimal monitoring network design.

The typical high number of constraints and decision variables, the nonlinearity, and the non-smoothness of the head-flow-water quality governing equations are inherent to water distribution systems, which make their problem solutions a complex task. Recent methodologies are employing heuristic optimization techniques such as genetic algorithms or ant colony as stand alone or hybrid data driven-heuristic frameworks. Almost all models treat the data and variables as deterministic. Uncertainty inclusion in water distribution systems simulation and management is in its infancy. This paper briefly reviews the current state of the art on the inclusion of uncertainty and risk in water distribution systems management models, and suggests future challenges on this topic.

This paper presents a risk-based methodology for water planning under climate change. A risk-based methodology considers the probability and consequences of undesired outcomes in the future. In the context of water resources, we think of undesired outcomes as water shortages of different levels of severity. The probability of exceeding a target frequency of water shortages of different severity is proposed as a risk metric for water planning under climate change. A simulation framework for estimating this risk metric is presented and applied to a water system in southern England to estimate the probability of water shortages of different levels of severity. Future climate conditions are represented using a stochastic weather generator conditioned on the United Kingdom Climate Projections (UKCP09). The flexibility of the framework allows for other non-climatic uncertainties to be considered simultaneously and their impacts on the risk metric to be evaluated.

Irregular occurrence of dry spells in cropping rainy seasons leads to the vulnerability of subsistence rainfed agriculture. A fundamental concept is presented in this paper to comprehend alternation of dry and wet spells in the rainy seasons of theWest African savanna. A stochastic process model consisting of the Langevin equation - which is a stochastic differential equation governing a zero-reverting stochastic process - is developed to model the phenomena. Soil moisture was monitored for five years at a study site, which is located in the Guinea savanna agro ecological zone of Ghana with monomodal rainfall pattern. Values of model parameters are identified so that the observed data series are consistent with the transition probability of the zero-reverting stochastic process. A numerical scheme using the finite element method is proposed as well, to compute the transition probability in the infinite state space. The model, with appropriately identified parameter values, is applicable to a variety of problems in subsistent rainfed agriculture.

The identification of flood-prone areas is a critical issue becoming everyday more pressing for our society. A preliminary delineation can be carried out by DEM-based procedures that relay on basin geomorphologic features. In the present paper, we investigated the dominant topographic controls for the flood exposure using techniques of pattern classification through linear binary classifiers based on DEM-derived morphologic features. With this aim, local features - which are generally used to describe the hydrological characteristics of a basin - and composite morphological indices are taken into account in order to identify the most significant one. The analyses highlight the potential of each morphological descriptor for the identification of the extend of flood-prone areas. Our findings may help the definition of new strategies for the delineation of flood-prone areas with DEM-based procedures.

The present work summarizes the theoretical development process and the preliminary results of a research activity oriented to the definition of a Decision Support System (DSS) to be used for managing drinking water systems exposed to different hazard classes. The core of such DSS is a probabilistic vulnerability assessment tool based on Bayesian Belief Networks, mainly developed integrating expert knowledge and literature information. This vulnerability assessment tool proved able to define a reliable map of vulnerability levels for complex and interconnected infrastructures, thus helping decision-makers in the selection of the optimal strategies to respond to emergencies. The DSS is based also on the implementation of hydraulic models, both for gravity and pressurized water mains, which should provide information regarding the changes in the hydraulic behavior of the network due to a specific event or an action. A case study is described, confirming the potentialities of the proposed tool.

In Bayesian inference, many problems can be expressed as the evaluation of the expectation of an uncertain quantity of interest with respect to the posterior distribution based on relevant data. Standard Monte Carlo method is often not applicable because the encountered posterior distributions cannot be sampled directly. In this case, the most popular strategies are the importance sampling method, Markov chain Monte Carlo, and annealing. In this paper, we introduce a new scheme for Bayesian inference, called Asymptotically Independent Markov Sampling (AIMS), which is based on the above methods. The efficiency of AIMS is demonstrated with an example that involves a multi-modal target distribution.

This paper integrates a Monte Carlo Simulation (MCS)-based reliability based design (RBD) approach (namely the expanded RBD approach) for foundations with an efficient MCS method called Subset Simulation to improve efficiency and resolution at small probability levels. Equations are derived and implemented in a commonly-available spreadsheet environment to effectively remove the hurdle of reliability computational algorithm and make the proposed approach available to geotechnical practitioners. The proposed approach is illustrated through a drilled shaft design example. It is shown that the proposed approach provides results that are consistent with those from previous studies and significantly improves the efficiency and resolution at small probability levels. Subset Simulation enhances the expanded RBD approach in the design situations with a small target failure probability.

An adaptive response surface method based efficient Monte Carlo Simulation (MCS) algorithm, intended for reliability assessment of large complex structures, is proposed. The initial response surface (RS) is constructed based on saturated design considering the mean values of the random variables as the centre point. Now, this centre point is updated successively to obtain a converged centre point to construct the final RS. For this, the RS polynomial coefficients are obtained by the moving least squares method to achieve desired level of accuracy instead of conventionally adopted least squares method. The use of simplified design of experiment instead of usually adopted computationally involved one is the basis to achieve desired efficiency. Once converged RS is obtained, the direct MCS is performed to estimate the reliability. The improved performance of the proposed approach with regard to accuracy and efficiency is elucidated with the help of numerical examples.

In the structural reliability-based design, the `failure probability function (FPF)' is referred to the failure probability as a function of the distribution parameters of random variables. This problem generally requires repeated reliability analyses to estimate the failure probability for different distribution parameter values, which is a computationally expensive task. A "weighted approach" is proposed based on the adaptive kernel density (AKD) sampling to locally evaluate the FPF efficiently by means of a single simulation. The basic idea is to rewrite the failure probability estimate for a given set of random samples in simulation as a function of the distribution parameters. In this work the AKD is taken as the instrumental sampling density which is used to carry out the reliability analysis for the weighted approach. It owns high efficiency and is independent of design point. Numerical example is given to illustrate the performances of the method.

This paper presents a novel approach, referred to as Limit State Sampling, for estimating failure probabilities of engineering structures. The majority of methods used to evaluate failure probabilities involve a large number of simulations of the structural model. In situations with low failure probability and numerically complex structural models, this can become a computationally unpractical task. The Limit State Sampling approach is developed here with the intention of reducing the number of simulations of the structural model in the process of evaluation of the failure probability. This is performed by introducing a pseudo probabilistic density function with the purpose of sampling around the failure limit state. Samples from the pseudo probability density function are then used to construct a surrogate model of the structural behavior at the failure limit state. Finally, the failure probability is estimated by utilizing the efficiency of the surrogate model, with reduced computational expense. The novelty of the approach comes from the formulation of the pseudo probability density function and the application to the probabilistic analysis of structures.

Subset Simulation provides an efficient and robust method to estimate the failure probabilities at small probability levels for a single failure mode defined by the system response concerned. However, estimating failure probabilities of multiple stochastic responses using a single run of Subset Simulation remains quite a challenging task in structural reliability analysis. To address this problem, this study develops a generalized Subset Simulation (GSS) approach, in which a unified intermediate event is defined to drive the simulation procedure progressively approaching multiple failure regions, and estimate the corresponding failure probabilities simultaneously. The sorting difficulty arising in the multiple stochastic responses is bypassed by the definition of the unified intermediate event. Finally, two representative examples are used to demonstrate the performance of the proposed GSS approach.

Spectral representation method based on the direct decomposition of the power spectral density (PSD) or evolutionary power spectral density (EPSD) matrix through Cholesky decomposition usually results in large computational time and storage memory. In this study, a new formulation of the Cholesky decomposition for the EPSD matrix and corresponding simulation scheme are presented. The central idea of this approach is to separate the phase from the complex EPSD matrix. The derived real modulus matrix evidently expedites decomposition compared to the direct Cholesky decomposition of the complex EPSD matrix. In the proposed simulation scheme, the separated phase can be easily assembled. The modulus of EPSD matrix could be further decomposed into the lagged coherence matrix, which is independence of time and thus remarkably improves the Cholesky decomposition efficiency. The application of the proposed schemes to the spatially varying ground motion simulation is presented. Also the proposed approach facilitates the application of interpolation technique in stochastic simulation.

The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-temporal evolution of seismicity in the short-term. In such a context, the forecasted seismicity usually makes reference to a 24-hour forecasting interval. Focusing the attention on clustering of events in time only, a robust seismicity forecast based on (a simplified version of) the ETAS model takes into account the joint probability distribution for the model parameters conditioned on the events already registered with the ongoing sequence. The advanced simulation procedures such as Markov Chain Monte Carlo simulation provide very efficient means of estimating the robust seismicity forecasts. In addition to the uncertainty in model parameters, the robust simulation-based forecasting of seismicity can also take into account the uncertainty in the sequence of events that are going to happen during the sampling interval. With regard to a specific application to the L'Aquila 2009 seismic sequence, the daily robust ETAS forecasts in the first ten days elapsed after the main event can predict the seismicity within plus/minus one standard deviation interval.

This work presents an improvement to a Monte Carlo-based algorithm of literature for the estimation of small failure probabilities. The original algorithm of literature is based on the implementation of the optimal importance density by a surrogate, kriging-based metamodel approximating the response function which determines the failure by reference with a given threshold. The significant improvement of the algorithm is obtained by a more effective training of the metamodel, and allows for a further decrease of the computational efforts required in the failure probability estimation. The performance of the new algorithm is demonstrated on a few analytic examples of literature.

The contribution of uncertain parameters to the variability of a model may be estimated by means of global sensitivity analysis. The use of the first order Sobol' indices is relevant in this context. However, accurate estimation of these coefficients may be a challenging problem, since as many Monte Carlo simulations as the dimension of the input parameters of the problem have to be performed in order to compute all the first order Sobol' indices. Such numerical efforts are not practicable for many large scale applications. This paper presents a novel procedure which requires to perform a single Monte Carlo simulation to determine all the Sobol' indices associated with the input parameters. The benefits of the method are illustrated with an application example.

This paper investigates the integration of MCMC in the Failure Sampling (FS) technique. FS is a simulation-based reliability analysis method intended to solve complex reliability analysis problems with minimum computational effort. An important step in FS is to simulate the resistance portion of the limit state function, which is typically conducted using crude MCS. However, introducing MCMC can further improve the efficiency of the FS technique. The results show that a reduction in computational effort can be obtained if incorporating MCMC. Further, MCMC-FS was observed to produce accurate and consistent results for all of the probabilistic problems considered.

This paper reports a practical case study of structural model updating utilizing measured vibration data from an ambient vibration field test. The target structure consists of two inter-connected floor steel trusses, and each truss is supporting a reinforced concrete slab. This paper first briefly describes the target structure, the experimental setup and the measurement arrangements of a field test for obtaining the ambient vibration data. The natural frequencies and mode shapes of the first three vertical vibration modes were identified from the measured time-domain accelerations from the ambient field test. The identified modal parameters together with the associated uncertainties were then employed for the structural model updating of the structure following the Bayesian statistical system identification approach. Very encouraging results were obtained showing that the idea of structural model updating using measured modal parameters is possible.

We present a new approach to buckling analysis of columns under parametric uncertainty. The approach is based on possibility theory, where the uncertain parameters are modeled by possibility distributions and an analytical approach is used to propagate the uncertainties through the computations. In order to quantify the risk of a column to buckle, the concept of possibility of buckling is introduced and discussed.

The aim of this paper is to illustrate that the existing ideology of aseismic design cannot provide the reliable prognosis of the levels of damages to buildings in future. If the mankind does not realize the necessity to reduce the level of risk contained in the current ideology of aseismic design, the number of seismically instable buildings will increase even more in the XXI century. The only way of reducing the risk associated with the ideology of aseismic design appears to be the requirement for the undamaged structural behavior of building. The requirement for the undamaged structural behavior of building is something like a threshold (a level), the raising of which increases the reliability of constructions planned to be built in seismically active regions and, on the contrary, its lowering increases the uncertainties and makes the behavior unpredictable. The modern global tendencies of aseismic design are to lower this level as much as possible and to make the constructions cheaper. According to the opinion of the present writer though the level, on the contrary, should be raised, in order to keep off the chaos.

This paper extends the scope of classical limit analysis to incorporate the influence of uncertain, but still non-probabilistic, applied forces that can vary independently within specified ranges. We focus on the use of interval analysis or so-called "convex" model in determining the two extreme (maximum and minimum) bounds to the collapse load limit of ductile rigid perfectly plastic structures. The formulation for the interval limit analysis uses the well-known piecewise linear yield concept, and can be formulated as a challenging form of optimization programs, known as a linear program with interval coefficients (LPIC). We propose a novel reformulation of the original LPIC into a standard nonlinear programming (NLP) problem with bounded constraints that can be solved using any NLP code. The proposed NLP approach can efficiently and robustly capture, within a single step, the maximum collapse load limit in one case and the minimum collapse load limit in the other, and thus eliminates the need for any combinatorial search schemes.

The influence measures defined within the Transformation Method of fuzzy arithmetic have proven useful for the analysis of systems with epistemic uncertainties. This contribution presents a generalized formulation of these influence measures so that they are applicable for uncertainty analysis in a universal sense where the uncertainties are described by fuzzy numbers or intervals. Formulas are derived exemplarily for the Transformation Method although the measures are likewise independent of the solution method applied.

The paper is focused on the uncertainty analysis of reinforced concrete beams in aggressive environments. In particular, the case of reinforcement corrosion due to chlorides is considered. The probabilistic investigation is performed by means of the perturbation method. The time of corrosion initiation and the failure load are expressed as Taylor series expansions in terms of the input random variables. The material resistances of concrete and reinforcement steel, the concrete cover, the diffusion properties of the concrete and the environmental conditions are modeled by random variables. The Taylor series expansion of the structural response is derived from the non-linear FE model, which is used to simulate the behavior of corroded structures.

A hybrid probabilistic and interval method is presented in this paper to address static response and reliability analysis of structures with random and interval parameters. Equations for calculating the mean value and standard deviation of random interval structural responses are formulated based on first-order perturbation method. Then, structural reliability is investigated by using a first-order reliability method. Reliability index, failure probability and reliability of elements, series and parallel systems are expressed in terms of interval variables. Two numerical examples are given in the end to demonstrate feasibility of the presented method.

For both tropical cyclones and earthquakes, there is variability in the values used in the intensity calculations critical for estimating losses from catastrophe models. Currently, the distribution around intensity is not fully incorporated in the uncertainty estimate around the final loss exceedance probability (EP) curves. For earthquakes, ground motion prediction equations produce not just a point estimate, but variation around this point estimate. For tropical cyclones, when downscaling gradient windspeeds to the surface (known as the Gradient Wind Reduction Factor), there can be large variability in the downscaling factor used. When estimating the damage to a property from an earthquake or tropical cyclone, for a given fixed hazard intensity there is a variation in damage modeled. In both cases, two properties vary - the intensity associated with the peril and the vulnerability of the structure. This paper investigates how the uncertainty distributions in intensity and vulnerability can be combined to give a single probability distribution of damage and how this can be computationally expedited through approximations.

An original procedure for the static analysis of Timoshenko beams with uncertain Young's modulus is presented. Within a non-probabilistic framework, the uncertain material property is modeled as an interval field according to the definition recently introduced by the first two authors. The key idea is to account for the dependency between interval values of the Young's modulus at various locations by means of a deterministic symmetric non-negative function playing the same role of the autocorrelation function in random field theory. After performing a finite difference discretization of the interval ordinary differential equations of equilibrium, approximate closed-form expressions of the bounds of beam response are obtained. For validation purposes, numerical results concerning a simply supported Timoshenko beam are presented.

The present study focuses on the development of Nonlinear Interval Finite Elements (NIFEM) for beam and frame problems. Three constitutive models have been used in the present study viz. bilinear, Ramberg-Osgood, and cubic models, to illustrate the development of Nonlinear Interval Finite Elements (NIFEM). The Interval Finite Element Method (IFEM) has been developed to handle load, material, and geometric uncertainties that are introduced in a form of interval numbers defined by their lower and upper bounds. However, the scope of the previous methods was limited to linear problems. The present work introduces an IFEM formulation for problems involving material nonlinearity under interval loads. The algorithm is based on the previously developed high accuracy interval solutions. An iterative method that generates successive approximations to the secant stiffness is introduced. Examples are presented to illustrate the behavior of the formulation. It is shown that bounding the response of non-linear structures for a large number of load combinations can be computed at a reasonable computational cost.

Static analysis is an essential procedure to design a structure. Using static analysis, the structure's response to the applied external forces is obtained. Moreover, the static analysis is performed when the structure is subjected to external displacements, such as differential support settlements. The structure's response includes internal forces/moments and internal stresses that are used in the design process. In general, using a finite-element-based structural analysis scheme, first, the unknown displacements are obtained from equilibrium equations of an active system and then, the external and internal forces and stresses are calculated from structure's global equilibrium equations. However, for a structure subjected to external displacements, the prescribed displacements possess uncertainties because of limited information or measurement errors which alter the structure's response. One method to quantify the presence of these uncertainties is interval or unknown-but-bounded variables. Nevertheless, naïve implementation of intervals in a conventional finite-element scheme for this type of problem may cause errors and overestimations due to existing interval functional dependencies. In this work, a new method is developed that obtains the exact bounds on structure's static response of a structure subjected to interval displacements. This method combines the two steps of conventional analysis aforementioned into a single step, along with application of interval displacements, leading to direct determination of bounds of internal forces/moments and internal stresses. This approach removes the interval functional dependencies in calculations in order to attain exact results. A numerical example that shows the behavior of the developed method along with comparison to Monte-Carlo simulation results is presented. Using this method, it has shown that obtained bounds on static response of a structure subjected to interval displacements do not require an iterative procedure such as Monte-Carlo simulations.

This paper proposes a set-membership method to characterize a probabilistic set, i.e., a set enclosing the true value for the parameter vector of a parametric system with a given probability. The approach assumes that all errors are independent and an interval for the error is known. To each error interval, a probability to be an outlier is provided. It is shown that characterizing the probabilistic set is a set inversion problem. The main contribution of the paper is to provide a method to characterize the inner part of the probabilistic set. As an illustration, an application to the static localization of a mobile robot is considered.

With the enormous losses to society resulting from motor-vehicle crashes, traffic safety has become an increasing concern of transport agencies. The surrogate events, which are defined as measures of accident proximity, are recognised as an alternative instead of the accumulation of crashes in safety evaluation, by taking advantage of many merits. This paper briefly assesses the range of available events by analysing their strengths and weaknesses. By using an illustrative case study, the applicability and reliability of various surrogate events under different situations are discussed. While the introduction of surrogate events could potentially improve our understanding of the affecting factors for motor-vehicle crashes, it is the prospect of combining evolving methodologies with far more detailed vehicle crash data that holds the greatest promise for the future.

We consider a general transportation network where travelers are categorized into classes according to their value-of-time (VOTs). The travel demand of each class in each origin-destination (OD) pair is a known decreasing function of the generalized travel cost to reflect different values of the trips. We give an economic interpretation of elastic demand with user heterogeneity. We further consider the first-best pricing problem with elastic demand with heterogeneous users. We show that such a nonnegative toll always exists, and finding such a toll is simple in that only a convex optimization problem needs to be solved.

HCM 2000 model estimates entry capacity of roundabouts under an assumption of headway (time gaps) following an exponential distribution. Entry capacity is thus calculated by circulating flow, critical gap and follow-up time. This paper aims to analyse: (1) the actual distribution type of headway; and (2) the relative error resulting from the assumption. To this end, a simulation that simulates the real traffic operation is conducted based on survey data from an existing roundabout in Queensland, Australia. A comparative study is then carried out to compare the results from the HCM 2000 model and the simulation. It indicated that the HCM 2000 model is not appropriate to be established under an exponential distribution. Although HCM 2000 model over-estimated capacity in our case study, it is still an acceptable approximation. Results suggest that the relative error is 6% under the circulating flow of 468 vehicles/hour.

Park and Ride (P&R) is regarded as a means of encouraging car drivers to shift to public transport modes for part of their journey. Since the first siting of P&R in the 1930s, various levels of success have been experienced in different cities around the world. It has been well recognized that the location and the corresponding parking size are the key factors for the performance of the P&R system. This paper proposes a bi-level mathematical programming model which is a mathematical expression of Stackelberg duopolistic game to determine the best location for each P&R car park, with the objective of prompting the public transport mode share. In the model, the network users' route choice behavior is assumed to follow user equilibrium with elastic demand. A solution algorithm is proposed for solving this model.

This paper presents an extended risk assessment for a ship-ship collision where the struck ship is a RoPax vessel in an open sea area. The assessment combines state-of-the-art engineering models for assessing probabilities of events and their consequences in a Bayesian Belief Network (BBN). The overall model rationale is briefly outlined and abridged results are shown. The main focus of the paper, however, is the application of a relatively recently proposed uncertainty/bias-based risk perspective. In particular, special attention is given to the inadequacy of the BBN to express all decision-relevant uncertainty. The applied risk perspective highlights that probabilities do not fully account for uncertainty in terms of the strength of the knowledge base for making these probability statements, i.e. for evidential uncertainty. Furthermore, probabilities stemming from calculations using results of engineering models are conditional to the underlying assumptions and simplifications in these engineering models, which may be value-laden. This is reflected through a qualitative assessment of evidential biases. As a novelty, a qualitative analysis of evidential uncertainty and bias is proposed using a sensitivity-uncertainty-bias matrix triplet and an uncertainty-bias justification table, supplementing the BBN-based quantification of uncertainty.

Uncertainty is an essential factor in transportation. For example, one cannot predict exactly the travel time from home to work. Conventional transportation pedagogy is mainly focused on modeling deterministic situations because of the complex mathematics required for modeling uncertainty. We develop a framework for effectively teaching uncertainty modeling in transportation using the example of travel time uncertainty. The objective is for students to appreciate the significance of incorporating uncertainty in planning without resorting to lengthy and intimidating mathematics. The framework that is developed contains strategies for introducing travel time uncertainty, method for appreciating the impact of the uncertainty, approaches of modeling the uncertainty in planning problems, projects for students to practice, and assessment tasks.

This paper mainly addresses the optimal equity problem under cordon-based congestion pricing with distance toll. The distance tolls are firstly determined by nonlinear function with respect to the travel distance. A user equilibrium model with elastic demand is selected in this paper to evaluate each feasible toll-charge function. In addition, a network transformation technique is adopted to modify the Frank-Wolfe method for obtaining path flows in the pricing cordon. Equity issue under distance-based pricing scheme is considered as the objective function. One modified Gini coefficient is adopted to represent the equity impact. The toll design problem is formulated as the bi-level model, which is solved by the genetic algorithm and modified Frank-Wolfe method.

The liner shipping industry (LSI) is a complex and dynamic industry. With the era of unprecedented global changes, the LSI faces a variety of internal, as well as external, risks. Furthermore, the values of the liner shipping operators' performances and operational reliability are not fixed and change within different environments. As a result, an appropriate dynamic model for evaluation of environmental-based risks (EBRs), which is capable of dealing with the external risks, is needed. In this study, for assessment of the values of EBRs, a generic model is constructed and a combination of different decision-making techniques - such as analytical hierarchy process (AHP) and fuzzy set theory (FST) - are used. Furthermore, evidential reasoning (ER) is used to synthesize the belief values or degrees of linguistic variables of EBRs' criteria. Through the proposed methodology, a decision support framework is developed for the liner shipping operators, which enables them to assess the risk value of a country or a port of call prior to investment or strategic planning. In addition, with the help of the proposed methodology, the liner shipping operators will be able to assess the overall level of existing EBRs in order to proactively facilitate continuous improvement strategies.

The unsaturated soil hydraulic properties, i.e., soil-water characteristic curve (SWCC) and unsaturated permeability function (PF) are the most important soil properties to influence the pore-water pressure distribution in soil slopes under rainfall conditions. Estimation methods based on empirical pedotransfer functions (PTFs) have been developed as rapid and inexpensive ways to determine unsaturated soil hydraulic properties. In this study, more than 700 samples of measured SWCCs and PFs are selected from the database of UNSODA. The statistics and model error of the estimated van Genuchten and Mualem model, using PTFs, are analyzed. A parametric study of reliability analysis is conducted for a hypothetical slope which is subjected to heavy storm. The effects of both the uncertainties of soil hydraulic parameters and the model error on pore water pressure distribution and slope stability are investigated and discussed. It is shown the effect of the model error of PF estimation on variation of slope stability is smaller than the soil hydraulic parameters n and K0, but is similar to the effect of a and L. The reliability index of the slope is reduced when the prediction uncertainties of the estimation models are considered.

The main purpose of this research was to prepare a landslide susceptibility map of Deokjeok-ri Creek and validate the result by model replication in Karisan-ri Creek. The Index of Entropy (IoE) method was used to determine the relationship between landslide causative factors (CF) and landslide occurrence. To determine the effect of CFs on landslides, data layers of topographic, hydrological, soil, forest, and geological factors were analyzed in a geographic information system (GIS) environment. The landslide susceptibility of Karisan-ri Creek was prepared without any consideration of previous landslides occurrences. To assess its accuracy, instead of using new landslides of same area, landslides from a Karisan-ri Creek were selected for estimation of prediction rate. This study confirms that replication of landslide susceptibility analysis procedure is possible if the landslide distribution pattern and the causative factors used in the models are similar in nature and origin.

This research deals with a strategy for the maintenance of geotechnical structures such as earth-fill dams. Standard penetration test (SPT) N-values are frequently used to determine the soil parameters. Firstly, a statistical model for the N-values is determined from sounding test results. In this research, however, Swedish weight sounding (SWS) tests are employed as they are simpler than SPT. Secondly, an indicator simulation is conducted to interpolate the spatial distribution of the N-values, and the results are utilized to find degraded areas inside the embankments and to maintain the embankments. Based on the statistical model for the N-values, the shear strength parameters are derived through the empirical relationships. Then, a reliability analysis of the embankments is conducted considering the variability of the internal friction angle and the seismic hazard.

This paper compares two methods for geotechnical reliability code calibration, namely the well-known design value method (DVM) based on first-order reliability method and a recently developed method based on quantile, called the quantile value method (QVM). The feasibility of calibrating a single partial factor to cover the wide range of coefficients of variation (COVs) commonly encountered in geotechnical designs is studied. For analytical tractability, a simple design example consisting of one resistance random variable and one load random variable is first examined. A resistance factor is first calibrated using a single calibration case associated with a typical COV. The objective is to evaluate the departure from the target reliability index analytically when this calibrated resistance factor is applied to validation cases associated with a range of COVs. The results show that QVM is more robust than DVM in terms of achieving a more uniform reliability level over a range of COVs.

This paper presents a Bayesian approach to determine characteristic values of the undrained shear strength Su profile for geotechnical analysis and design, particularly those using probability-based design codes. The approach integrates systematically the prior knowledge (e.g., engineering judgment/local experience) and a limited number of project-specific liquidity index (LI) data under a Bayesian framework and transforms the integrated information into a large number, as many as needed, of equivalent samples of the Su profile using Markov Chain Monte Carlo simulation (MCMCS). Then, conventional statistical analysis is carried out to estimate statistics of the Su profile, and the characteristic values of the Su profile is determined accordingly. Equations are derived for the proposed Bayesian approach, and the approach is illustrated through a set of real-life data. It is shown that the approach effectively tackles the difficulty in generating meaningful statistics and probability distributions of soil properties from a usually limited number of soil property data obtained during geotechnical site investigation.

Many models have been proposed to estimate the Young's modulus, E, of intact rock based on its uniaxial compressive strength, UCS. Deere's model, i.e., E = M_R · UCS (where M_R is the modulus ratio), is the most accepted one. However, traditional models cannot provide uncertainty estimates of parameters and predictions. We present a novel approach, based on Bayesian theory, to estimate E of intact rock based on UCS. We develop three `rock specific' models (i.e., for basalt, limestone, and chalk) that account for the different sources of uncertainty. We also provide parameters to analytically approximate the posterior joint distribution of model parameters for the three rock types. An example illustrates that such `rock specific' models can be updated to incorporate new project-specific information, showing that the model uncertainty is reduced and that the predictive capability is improved through the updating process.

The first order reliability method (FORM) is applied to analyse the face stability of a circular tunnel driven by a pressurized shield, in a highly fractured rock mass characterized by the Hoek-Brown non-linear failure criterion. The collapse failure mode is studied in this paper. We employ a limit analysis approach with an advanced rotational failure mechanism. Rock mass parameters σ_ci, GSI and m_i are regarded as independent random variables with normal distributions. The reliability problem is solved numerically using FORM with an implicit limit-state function (LSF). A sensitivity analysis is conducted, as well. The results show that: (1) the reliability index increases with an increasing support pressure; (2) all three random variables considered are resistance variables; (3) σ_ci is found to be the most important variable with higher support pressures, whereas, GSI becomes the most influential variable with lower support pressures.

In this study, the derivation of semivariance function from a given database is first performed. After the semivariance function is determined, Krigging technique is employed with the semivariance function to simulate the distribution of SPT-N values in the construction site. The values of true data points and the estimated values were compared by Simple Krigging technique. Analysis results have shown that from Simple Krigging, the simulation can yield good results for the SPT-N values that are less than 30 blows. Finally, the simulation of SPT-N values across the whole construction site was also conducted to examine the distribution of SPT-N values. Spatial variability analysis with Krigging technique provided a means to estimate the required value and the contour map could be employed for further cost analysis regarding soil improvement methods or selections of foundation types.

The authors proposed a reliability analysis method for long continuous structures considering investigation sites to counter liquefaction failure. This method is characterized by continuously calculating the failure probability caused by liquefaction at an arbitrary point and quantifying the uncertainty concerning the investigation site. The purpose of this study is to verify its effectiveness based on application to an actual river dike that suffered liquefaction failure due to the 2011 earthquake off the Pacific coast of Tohoku.

The methodology in Eurocode 7 for addressing uncertainty and risk in geotechnical design is described. This includes the use of Geotechnical Categories with guidelines for appropriate geotechnical investigations, design procedures and expertise required, depending on the complexity of a geotechnical design. Checklists with factors to be considered in geotechnical design are an important part of Eurocode 7 to assist decision making and reduce risk, as is the requirement to prepare a geotechnical design report. Uncertainty in soil parameter values due to soil variability, limited test results and deficiencies in the test methods have resulted in a definition for the characteristic value of a soil parameter that differs from that for manufactured materials. Some statistical equations that may be used to select characteristic soil parameter values are presented. The use of consequences classes, with different partial factor values for design situations with different risk levels, that have been adopted by some countries is outlined.

A non-intrusive stochastic finite element method is proposed for reliability analysis of unsaturated slopes considering the spatial variability of hydraulic parameters and shear strength parameters. The Karhunen-Loève (KL) expansion technique is employed to discretize cross-correlated lognormal random fields. The factor of slope safety is explicitly expressed as input random parameters using the Hermite polynomial chaos expansion. The Latin hypercube sampling technique is used to calculate the unknown coefficients of polynomial chaos expansion. An example of reliability analysis of an unsaturated slope under the steady-state seepage flow is presented to demonstrate the validity of the proposed method. The results indicate that the proposed method can effectively evaluate the reliability of unsaturated slopes considering spatially varying soil properties. The polynomial chaos expansion combined with the Latin hypercube sampling technique can effectively estimate the probability of slope failure at a relatively low level.

The basal heave of excavation is generally evaluated with a factor of safety. In reality, the implementation of the probability analysis, in which the uncertainties of models and parameters can be adequately considered, is beneficial to the design of geotechnical engineering. Of various sources of uncertainties, the spatial variation of stratigraphy is a quite new research topic and its effect on the engineering behavior is still required further studied. This study aimed at investigating the effect of spatial variation on analysis of excavation basal heave in soft clay. The basal heave analysis proposed by the Taiwan building code, as well as the random field theory, is adopted to be capable of simultaneously considering the uncertainties and spatial variation of geomaterial in such analysis using Monte Carlo simulation. An actual excavation case history, in which the basal heave occurred, is used to conduct the intended analysis. Comparing with the conventional deterministic analysis method, the analysis results revealed that the probability of failure against basal heave would be reduced when the spatial variation is considered in the analysis.

This study presents a reliability-based design method for geotechnical structures based on the observational method, which can be used as a methodology for the performance verification of geotechnical structures. In the proposed method, the soil-water coupled finite element analysis is utilized as a performance-verification method, and stochastic uncertainties inherent in the geotechnical parameters are evaluated by a Monte Carlo simulation. The proposed method can select the optimum design/construction method from several design alternatives, from the viewpoint of Life Cycle Cost, and the predictions at the initial design stage are sequentially updated by the particle filter. The proposed method is applied to a numerical example of the construction problem of embankment specified quantitative performance criteria, such as allowable settlements and the probability of their exceedance, and the feasibility of the method is examined in this example.

Several existing dams worldwide have experienced rock foundation and downstream scouring/erosion caused by the large hydraulic power of impinging water jet resulting from overtopping during extreme floods. Hydrologic and geologic systems are dynamic and heterogeneous, but our knowledge of the parameters of these systems is often limited. This paper discusses the various uncertainties associated with dam erodibility analysis and utilizes a probabilistic approach to address the uncertainty issues. It particularly focuses on high concrete dams with unrecognized adverse rock conditions. Terrestial LiDAR and three-dimensional photogrammetry can be used to obtain high-resolution data for developing statistical rock joint parameters needed in analysis. The stability/erodibility of the rock foundation was evaluated based on Annandale's Erodibility Index method and Bolleart's Comprehensive Scour Model. Uncertainty of the Annandale's erosion criteria is addressed in the analysis. Dam erosion hazard curves can be developed considering the recurrence characteristics of extreme hydrologic events.

The evolution of geotechnical design codes, from traditional working stress design (factor of safety) to reliability-based design approaches, has been lagging well behind structural design codes. There is no question that this lag is due to the much larger uncertainty about the ground than exists with most other engineering materials. Nevertheless, significant efforts have been made in recent decades to provide insight into the probabilistic behaviour of the ground and allow for advances to be made in the development of reliability-based geotechnical design codes. This paper compares target reliability levels in existing codes from around the world and then presents the latest advances in consequence and resistance factors required for the design of both shallow and deep foundations which are scheduled to soon appear in Canadian geotechnical design codes.