Advances in Simulation-Based Uncertainty Quantification and Reliability Analysis

The special collection on Advances in Simulation-Based Uncertainty Quantification and Reliability Analysis is available in the ASCE Library (https://ascelibrary.org/page/ajrua6/simulation_based_uncertainty_quantification_reliability_analysis).

Simulations are increasingly being used in lieu of or to supplement physical testing in several major industries from civil structural analysis and design to the automotive, aircraft, and naval industries. Two critical aspects of simulation-based analysis and design are the rigorous quantification of uncertainty and the ability to rapidly and accurately assess reliability. Monte Carlo simulation is the most robust simulation-based approach for such problems and serves as a benchmark against which new methods can be compared. The well-known problem with Monte Carlo methods, especially for reliability assessment, is their large computational expense imposed by the requirement of running a very large number of simulations. In recent years, rapid advances that improve on classical Monte Carlo simulation, coupled with improvements in computational resources, have begun to usher in a new era of simulation-based uncertainty analysis such that modern challenges, e.g., uncertainty quantification (UQ) for very large (e.g., high-dimensional, computationally intensive) and complex (e.g., strongly nonlinear, multicomponent, multiscale, multiphysics) systems and inverse problems, are becoming increasingly tractable with a reasonable number of simulations. Examples of new methods include Markov chain Monte Carlo (MCMC) approaches such as subset simulations, sparse-grid stochastic collocation methods, Bayesian nested sampling, variance reduction techniques (i.e., Latin hypercube, importance sampling), and new adaptive Monte Carlo and quasi-Monte Carlo methods.

This special collection aims at exploring the latest methodological developments in simulation-based uncertainty quantification and reliability analysis. The genesis of this special collection was a series of minisymposia on the topic organized by the coeditors and colleagues held at the 2016 Probabilistic Mechanics and Reliability Conference, the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, and the 12th International Conference on Structural Safety and Reliability. These minisymposia saw a total of 39 speakers addressing some of the most pressing issues in computational uncertainty quantification and reliability analysis. Among these presenters, several authors were invited to contribute to this special collection as recognized leaders in the field of computational UQ and reliability analysis for civil engineering systems.

These invitations resulted in eight papers that cover four important research areas in simulation-based UQ and reliability analysis:

More specifically, Christou et al. (2018), Vlachos et al. (2018), and Suksuwan and Spence (2018) address issues related to seismic and wind hazards. Zhang and Taflanidis (2018), Moustapha et al. (2018), and Sundar and Shields (2019) discuss and compare approaches for surrogate model development—most notably Kriging- and support-vector-regression-based techniques. Naess and Bo (2018), Zhang and Taflanidis (2018), and Sundar and Shields (2019) further discuss issues related to sampling for Monte Carlo simulations or surrogate model development, while Christou et al. (2018) employs an optimal set of random field samples for hazard modeling. Lastly, Cai and Mahadevan (2018) discuss approaches to leverage big data for uncertainty quantification purposes.

With regard to seismic hazard modeling, Christou et al. (2018) propose a method called hazard quantization that models regional seismic intensity measures as two-dimensional, non-Gaussian, heterogeneous random fields, and present an optimal representation of these intensity measure maps through a process called functional quantization. Vlachos et al. (2018), meanwhile, present a stochastic method for generating nonstationary seismic acceleration time histories from a set of ground motion descriptors—the moment magnitude, rupture distance, and shear wave velocity—for a given site. The model is calibrated from existing ground motion data, validated against established ground motion prediction models, and employed for nonlinear time history analysis.

For the modeling of wind hazards, Suksuwan and Spence (2018) present an approach for reliability-based optimization of large structure systems subjected to wind excitations. The approach resolves the computational challenges of reliability-based optimization by decoupling the reliability problem and the optimization problem. Convergence properties of the proposed method are discussed and its efficiency demonstrated for large high-rise structural forms.

A dominant area of research in computational UQ over the past decade has been in the development of surrogate models that can be used to provide computationally inexpensive approximates of an expensive computer model. A surrogate modeling technique of particular interest is the Kriging (or Gaussian process) model that is studied extensively in this special collection. The paper by Moustapha et al. (2018) compares the Kriging model with support vector regression to assess their relative efficiency. In this comparison, the authors specifically uncover the importance of introducing anisotropy in the model hyperparameters through a carefully automated efficient global search algorithm. Along a similar line, Sundar and Shields (2019) explore the importance of the Kriging model form—in particular the form of the regressor used for the trend and the kernel used for the covariance. In this work, the authors show that the selection of the trend and kernel can play an important role in the estimation of reliability from a Kriging surrogate. In response to this, they propose the multimodel Kriging (MMK) approach in which an information theoretic criterion is used to combine multiple Kriging models based on model probabilities. This provides a level of robustness that is lost when assigning the trend and kernel arbitrarily.

Much of the recent research in Kriging model development has revolved around identifying the optimal sampling points at which to evaluate the expensive computational model. To this end, Zhang and Taflanidis (2018) propose the adaptive Kriging stochastic sampling and density (AK-SSD) approximation framework in which a Kriging model is progressively trained through a series of iterations aimed at producing an accurate metamodel from which to sample the probability density of the output. This AK-SSD framework is specifically explored for rare event simulation in which the identified density is used as an importance sampling density for reliability analysis. The work of Sundar and Shields (2019) similarly proposes a modified learning function for adaptive Kriging model development with their MMK surrogate.

In the context of Monte Carlo simulations, Naess and Bo (2018) propose a new method for efficiently calculating reliability for complex systems. This approach introduces a parameterized cascade of systems at known parameter values. Reliability of the original system can be obtained from Monte Carlo simulations with a greatly reduced number of samples from the parameterized systems by extrapolating a least-squares parametric curve fit to the simulation results.

Finally, data-driven techniques are growing increasingly important for UQ applications. Cai and Mahadevan (2018) propose a data-driven computational framework for diagnosis and prognosis of structural systems that integrates high volumes of sensor data and perform data analytics in parallel. For inverse UQ (diagnosis), the authors propose a Bayesian framework to parallelize the required numerical integrations. For uncertainty propagation (prognosis), the authors use Monte Carlo simulations.

Taken in total, these papers present a window into the leading approaches to simulation-based UQ and reliability analysis. They identify key challenges and propose novel solutions that will serve as benchmarks for continued evolution of the field.