ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

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The treatment of uncertainty using extra-probabilistic approaches, like intervals or p-boxes, allows for a clear separation between epistemic uncertainty and randomness in the results of risk assessments. This can take the form of an interval of failure probabilities; the interval width W being an indicator of “what is unknown.” In some situations, W is too large to be informative. To overcome this problem, we propose to reverse the usual chain of treatment by starting with the targeted value of W that is acceptable to support the decision-making, and to quantify the necessary reduction in the input p-boxes that allows achieving it. In this view, we assess the feasibility of this procedure using two case studies (risk of dike failure, and risk of rupture of a frame structure subjected to lateral loads). By making the link with the estimation of excursion sets (i.e., the set of points where a function takes values below some prescribed threshold), we propose to alleviate the computational burden of the procedure by relying on the combination of Gaussian process (GP) metamodels and sequential design of computer experiments. The considered test cases show that the estimates can be achieved with only a few tens of calls to the computationally intensive algorithm for mixed aleatory/epistemic uncertainty propagation. This article is available in the ASME Digital Collection at .

Reliability analysis evaluates the failure probability of structures considering random variables of a system. Existing methods such as first-order reliability method (FORM) and second-order reliability method (SORM) are difficult to predict the failure probability of implicit functions in mechanical structures. Monte Carlo simulation (MCS) can predict the failure probability with high accuracy, but it is time-consuming. Agent-based methods such as the Kriging model have the approved performance to predict the failure probability in both efficiency and accuracy. An active method is proposed in this paper to improve the efficiency of predicting the probability of failures by combining the Kriging model and MCS, using a new learning function and its stopping condition. A representative selection strategy is developed based on spectral clustering to decide sample points in the design of experiments (DoEs). The new learning function integrates uncertainty and similarity of predicted Kriging values to search the next best sample point for updating the initial DoE. The learning process is terminated based on the stopping condition for a given accuracy of predicted probability of failures. Four case studies are conducted to validate the proposed method. Results show that the proposed method can predict the probability of failures with improved accuracy and reduced time. This article is available in the ASME Digital Collection at .

The Bhattacharyya distance has been developed as a comprehensive uncertainty quantification metric by capturing multiple uncertainty sources from both numerical predictions and experimental measurements. This work pursues a further investigation of the performance of the Bhattacharyya distance in different methodologies for stochastic model updating, and thus to prove the universality of the Bhattacharyya distance in various currently popular updating procedures. The first procedure is the Bayesian model updating where the Bhattacharyya distance is utilized to define an approximate likelihood function and the transitional Markov chain Monte Carlo algorithm is employed to obtain the posterior distribution of the parameters. In the second updating procedure, the Bhattacharyya distance is utilized to construct the objective function of an optimization problem. The objective function is defined as the Bhattacharyya distance between the samples of numerical prediction and the samples of the target data. The comparison study is performed on a four degrees-of-freedom mass-spring system. A challenging task is raised in this example by assigning different distributions to the parameters with imprecise distribution coefficients. This requires the stochastic updating procedure to calibrate not the parameters themselves, but their distribution properties. The second example employs the GARTEUR SM-AG19 benchmark structure to demonstrate the feasibility of the Bhattacharyya distance in the presence of practical experiment uncertainty raising from measuring techniques, equipment, and subjective randomness. The results demonstrate the Bhattacharyya distance as a comprehensive and universal uncertainty quantification metric in stochastic model updating. This article is available in the ASME Digital Collection at .

This contribution proposes a strategy for performing fuzzy analysis of linear static systems applying α-level optimization. In order to decrease numerical costs, full system analyses are replaced by a reduced order model that projects the equilibrium equations to a small-dimensional space. The basis associated with the reduced order model is constructed by means of a single analysis of the system plus a sensitivity analysis. This reduced basis is enriched as the α-level optimization strategy progresses in order to protect the quality of the approximations provided by the reduced order model. A numerical example shows that with the proposed strategy, it is possible to produce an accurate estimate of the membership function of the response of the system with a limited number of full system analyses. This article is available in the ASME Digital Collection at .

In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional (1D) consolidation problems. A possibility distribution is the one-point coverage function of a random set and is viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on the transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problem. This article is available in the ASME Digital Collection at .

This paper studies the propagation of uncertainties on serviceability assessment of footbridges in unrestricted traffic condition based on a nondeterministic approach. Multipedestrian loading is modeled as a stationary Gaussian random process through the equivalent spectral model which yields analytical expressions of the spectral moments of the footbridge dynamic response. The uncertain pedestrian-induced loading parameters and structural dynamic properties are modeled as interval variables. An approximate analytical procedure, based on the improved interval analysis, is introduced as an efficient alternative to classical optimization in order to propagate interval uncertainties. The presented procedure allows us to derive closed-form expressions of the bounds of the spectral moments of the response, as well as of the expected value and cumulative distribution function of the maximum footbridge acceleration. Two strategies are proposed to assess footbridges' serviceability. The first one leads to the definition of a range of comfort classes. The second strategy enables us to estimate an interval of probability of reaching at least a suitable comfort level. This article is available in the ASME Digital Collection at .

The well-known standardized plant analysis risk-human reliability (SPAR-H) methodology is widely used for analysis of human reliability in complex technological systems. It allows assessing the human error probability taking into account eight important groups of performance shaping factors. Application of this methodology to practical problems traditionally involves assumptions which are difficult to verify under the conditions of uncertainty. In particular, it introduces only two possible values of the nominal human error probabilities (for diagnosis and for actions) which do not cover the whole spectrum of the tasks within operator's activity. In addition, although the traditional methodology considers the probabilities of human errors as the random variables, it operates only on a single predefined type of distribution for these variables and does not deal with the real situations in which the type of distribution remains uncertain. The paper proposes modification to the classical approach to enable more adequate modeling of real situations with the lack of available information. The authors suggest usage of the interval-valued probability technique and of the expert judgment on the maximum probability density for actual probabilities of human errors. Such methodology allows obtaining generic results that are valid for the entire set of possible distributions (not only for one of them). The modified methodology gives possibility to derive final assessments of human reliability in interval form indicating “the best case” and “the worst case.” A few numerical examples illustrate the main stages of the suggested procedure. This article is available in the ASME Digital Collection at .

In this article, a method is proposed to conduct a global sensitivity analysis of epistemic uncertainty on both system input and system structure, which is very common in early stage of system development, using Dempster-Shafer theory (DST). In system reliability assessment, the input corresponds to component reliability and system structure is given by system reliability function, cut sets, or truth table. A method to propagate real-number mass function through set-valued mappings is introduced and applied on system reliability calculation. Secondly, we propose a method to model uncertain system with multiple possible structures and how to obtain the mass function of system level reliability. Finally, we propose an indicator for global sensibility analysis. Our method is illustrated, and its efficacy is proved by numerical application on two case studies. This article is available in the ASME Digital Collection at .

In a probabilistic design approach for cylindrical shells, Gaussian random fields are used to simulate geometric imperfections. The shape of imperfections depends, among others, on the autocorrelation properties of the random field. Underlying uncertainties such as a small sample size or imprecise measurements make it practically impossible to define a crisp correlation function. For a more realistic description of the imprecise correlation structure, the classical probabilistic approach is extended to a fuzzy stochastic approach. More exactly, the polymorphic uncertainty approach is used taking into account natural variability and incompleteness. Consequently, geometric imperfections are represented as fuzzy probability based random fields. Therefore, the required correlation parameters are described as polymorphic uncertain parameters. The quantification of uncertainties is demonstrated on real data. Furthermore, the polynomial chaos surrogate model is used for the alpha-level optimization in the fuzzy analysis. The sensitivity indices as a by-product of the surrogate model show the influence of the input parameters on the statistical parameters of the critical buckling load factor. The main purpose of this paper is to show how the presented methods can support the design process of cylindrical shells. This article is available in the ASME Digital Collection at .

Multiplying the capacity of communication links by using the multiple-input multiple-output (MIMO) mechanism has become an essential part of various wireless standards. In this paper, we focus on the bit error ratio (BER) in such systems and consider its optimization under parameter uncertainty from a formal point of view (including methods with result verification). The theoretical results are demonstrated using a close-to-life application. This article is available in the ASME Digital Collection at .

This paper presents a novel methodology to solve an inverse uncertainty quantification problem where only the variation of the system response is provided by a small set of experimental data. Furthermore, the method is extended for cases where the uncertainty of the response quantities is given by an incomplete set of statistical moments. For both cases, the uncertainty on the output space is represented by a minimum volume enclosing ellipsoid (MVEE). The actual inverse uncertainty quantification is conducted by identifying also a hyper-ellipsoid for the input parameters, which has an image on the output space that matches the MVEE as close as possible. Hence, the newly introduced approach is a contribution to the field of nonprobabilistic uncertainty quantification methods. Compared to literature, the new approach has often superior accuracy and especially an improved efficiency for high-dimensional problems. The method is validated first by an analytical test case and subsequently applied to a jet engine performance model, where this type of inverse uncertainty quantification has to be solved to allow for a consistent and integrated solution procedure. In both cases, the results are compared with an inverse method where the variability on the input side is quantified by a multidimensional interval. It can be shown that the hyper-ellipsoid approach is superior with respect to the computation time in high-dimensional problems encountered not only in jet engine design. This article is available in the ASME Digital Collection at .

A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures. This article is available in the ASME Digital Collection at .

Deterministic design and a priori parameters are used in traditional optimization approaches. The material characteristics of solid wood are not deterministic in reality. Hence, realistic optimization and simulation methods need to take the uncertainties of parameters into account. The uncertainty characteristics of wood are mainly originated in natural variation. In addition to this, incertitudes from lack of knowledge are inherent. Accordingly, the aleatoric approach of randomness can be expanded to a polymorphic uncertainty model. Fuzzy probability-based randomness is used in this work. Therefore, the epistemic approach of fuzziness is taken into account. The distribution functions of random variables are parametrized by fuzzy variables. So coupling of both, aleatoric and epistemic uncertainties, is involved. Interactions of fuzzy variables and crosscorrelations of random variables are considered among and within the parameters. Crosscorrelated random fields are used to represent spatial variation of material parameters. The autocovariance structures are modeled structurally dependent on the tree trunk axes. Finite element method is applied as deterministic basic solution of a loaded timber structure. A local orthotropic material formulation with respect to specifically located tree trunk axes is used. The optimal positions of the tree trunk axes for each wooden log are examined as design parameters. Polymorphic uncertainty is used to describe a priori parameters. The developed methods for uncertainty analysis are embedded in an automated and parallelized optimization processing. An analysis of a two-tier glulam beam, according to a purlin of a timber roof construction, is shown as numerical example for the optimization framework. This article is available in the ASME Digital Collection at .

The use of evidence theory in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes (i) an introduction to evidence theory, (ii) definition of two WLs and two SLs used for illustration, (iii) belief and plausibility for the occurrence of LOAS for a one WL/two SL system, and (iv) a sampling-based procedure for the verification of belief and plausibility calculations. The presented results can be generalized to systems with more than one WL and two SLs. This article is available in the ASME Digital Collection at .

The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) time at which LOAS occurs for a one WL/two SL system, (ii) time at which a two-link system fails, (iii) temperature at which a two-link system fails, and (iv) temperature at which LOAS occurs for a one WL/two SL system. The presented results can be generalized to systems with more than one WL and two SLs. This article is available in the ASME Digital Collection at .

The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of time and temperature margins associated with loss of assured safety (LOAS) for one weak link (WL)/two strong link (SL) systems is illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) SL/WL failure time margins defined by (time at which SL failure potentially causes LOAS) − (time at which WL failure potentially prevents LOAS), (ii) SL/WL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) − (the temperature at which WL failure potentially prevents LOAS), and (iii) SL/SL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) − (the temperature of SL whose failure potentially causes LOAS at the time at which WL failure potentially prevents LOAS). This article is available in the ASME Digital Collection at .

In heavy rotating machines and assembly lines, bearing failure in any one of them may result in shut down and affects the overall cost and quality of the product. Condition monitoring of bearing systems avoids breakdown and saves time and cost of preventive and corrective maintenance. This research paper proposes advanced fault detection strategies for taper rolling bearings. In this, a mathematical model using dimension analysis by matrix method (DAMM) and support vector machine (SVM) is developed to predict the vibration characteristic of the rotor-bearing system. Various types of defects created using an electric discharge machine (EDM) are analyzed by correlating dependent and independent parameters. Experiments were performed to classify the rotor dynamic characteristic of the bearings and validated the models developed using DAMM and SVM. Results showed the potential of DA and SVM to predict the dynamic response and contribute to the service life extension, efficiency improvement, and reduce failure of bearings. Thus, the automatic online diagnosis of bearing faults is possible with a developed model-based by DAMM and SVM. This article is available in the ASME Digital Collection at .

The demand of steam in process industries is increasing rapidly, and this demand can be met by increasing the capacity utilization of steam boilers. Many of the process industries depend on industrial steam boilers as a vital component for their operation. The availability of the boiler can be improved by identifying critical mechanical subsystems/components concerning failure frequency, reliability, and maintainability and minimizing their likelihood of occurrences. The selection of appropriate technique for data collection and reliability analysis is essential. The time between failure (TBF) and time to repair (TTR) of all components and subsystems were collected to carry out reliability, availability, and maintainability (RAM) analysis. The best-fit distribution and distribution parameters were calculated using reliasoft software weibull++10 after performing trend testing. The preventive maintenance intervals of all components and subsystems and the availability of the system were evaluated. The analysis reveals that the combustion system, feed-water system, and blow-down system are the critical subsystems from a reliability perspective and are still the biggest reasons for the boiler downtime. The research study also showed that TTR was longer for the combustion system than the other subsystems, and thus, to enhance its availability, it is suggested that maintenance resources should be allocated at the appropriate moment to the combustion system. The study also shows the usage of RAM analysis in deciding the preventive maintenance intervals of components/subsystems of the boiler. It also provides a reference for the preparation of the maintenance plan for the boiler system. This article is available in the ASME Digital Collection at .

The performance of a mechanical or structural system can be improved through a proper selection of its design parameters such as the geometric dimensions, external actions (loads), and material characteristics. The computation of the reliability of a system, in general, requires a knowledge of the probability distributions of the parameters of the system. It is known that for most practical systems, the exact probability distributions of the parameters are not known. However, the first few moments of the parameters of the system may be readily available in many cases from experimental data. The determination of the reliability and the sensitivity of reliability to variations or fluctuations in the parameters of the system starts with the establishment of a suitable limit state equation. This work presents an approximate reliability analysis for mechanical and structural systems using the fourth-order moment function for approximating the first four moments of the limit state function. By combining the fourth-order moment function with the probabilistic perturbation method, numerical methods are developed for finding the reliability and sensitivity of reliability of the system. An automobile brake and a power screw are considered for demonstrating the methodology and effectiveness of the proposed computational approach. The results of the automobile brake are compared with those given by the Monte Carlo method. This article is available in the ASME Digital Collection at .

Military operations in Iraq and Afghanistan have resulted in the increased exposure of military personnel to explosive threats. Combat-related pelvic fractures are a relatively new battlefield injury that poses a serious threat to military personnel. Injury prediction for these events continues to be a challenge due to the limited availability of blast-specific test studies and the use of established automotive-based injury criteria that do not directly translate to combat-related exposures. The objective of this study is to evaluate the pelvic response of the global human body models consortium (GHBMC) 50th percentile detailed male model (v4.3) in under body blast (UBB) loading scenarios. Nine simulations were conducted with mild or enhanced threat levels, and nominal or obtuse occupant positions. Cross-sectional force outputs from the superior pubic ramus (SPR), ilium, and sacroiliac (SI) regions were evaluated using previously developed injury risk curves (IRC). Additionally, maximum principal strain (MPS) data were extracted from the pelvic cortical bone elements. Results showed that shear force was the best predictor of fracture for the ischial and SI regions, while axial force was the best predictor for the SPR region. These outcomes were consistent with the load path of the simulated UBB events. The obtuse posture had higher peak force values for injurious and noninjurious outcomes for the SPR and SI region. The nominal posture had higher peak force values for noninjurious outcomes in the ischial region. These outcomes were supported by the MPS response present in these postures. This article is available in the ASME Digital Collection at .