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Author (up) Dang, C.; Valdebenito, M.A.; Faes, M.G.R.; Wei, P.F.; Beer, M. doi  openurl
  Title Structural reliability analysis: A Bayesian perspective Type
  Year 2022 Publication Structural Safety Abbreviated Journal Struct. Saf.  
  Volume 99 Issue Pages 102259  
  Keywords Failure probability; Bayesian inference; Gaussian process; Numerical uncertainty; Parallel computing  
  Abstract Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0167-4730 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000837863500001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1637  
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Author (up) Dang, C.; Wei, P.F.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M. doi  openurl
  Title Interval uncertainty propagation by a parallel Bayesian global optimization method Type
  Year 2022 Publication Applied Mathematical Modelling Abbreviated Journal Appl. Math. Model.  
  Volume 108 Issue Pages 220-235  
  Keywords Interval uncertainty propagation; Bayesian global optimization; Gaussian process; Infill sampling criterion; Parallel computing  
  Abstract This paper is concerned with approximating the scalar response of a complex computational model subjected to multiple input interval variables. Such task is formulated as finding both the global minimum and maximum of a computationally expensive black-box function over a prescribed hyper-rectangle. On this basis, a novel non-intrusive method, called `triple-engine parallel Bayesian global optimization', is proposed. The method begins by assuming a Gaussian process prior (which can also be interpreted as a surrogate model) over the response function. The main contribution lies in developing a novel infill sampling criterion, i.e., triple-engine pseudo expected improvement strategy, to identify multiple promising points for minimization and/or maximization based on the past observations at each iteration. By doing so, these identified points can be evaluated on the real response function in parallel. Besides, another potential benefit is that both the lower and upper bounds of the model response can be obtained with a single run of the developed method. Four numerical examples with varying complexity are investigated to demonstrate the proposed method against some existing techniques, and results indicate that significant computational savings can be achieved by making full use of prior knowledge and parallel computing.  
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  Corporate Author Thesis  
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  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0307-904X ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000830573400001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1625  
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Author (up) Dang, C.; Wei, P.F.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M. doi  openurl
  Title Parallel adaptive Bayesian quadrature for rare event estimation Type
  Year 2022 Publication Reliability Engineering & System Safety Abbreviated Journal Reliab. Eng. Syst. Saf.  
  Volume 225 Issue Pages 108621  
  Keywords Reliability analysis; Gaussian process; Numerical uncertainty; Bayesian quadrature; Parallel computing  
  Abstract Various numerical methods have been extensively studied and used for reliability analysis over the past several decades. However, how to understand the effect of numerical uncertainty (i.e., numerical error due to the discretization of the performance function) on the failure probability is still a challenging issue. The active learning probabilistic integration (ALPI) method offers a principled approach to quantify, propagate and reduce the numerical uncertainty via computation within a Bayesian framework, which has not been fully investigated in context of probabilistic reliability analysis. In this study, a novel method termed `Parallel Adaptive Bayesian Quadrature' (PABQ) is proposed on the theoretical basis of ALPI, and is aimed at broadening its scope of application. First, the Monte Carlo method used in ALPI is replaced with an importance ball sampling technique so as to reduce the sample size that is needed for rare failure event estimation. Second, a multi-point selection criterion is proposed to enable parallel distributed processing. Four numerical examples are studied to demonstrate the effectiveness and efficiency of the proposed method. It is shown that PABQ can effectively assess small failure probabilities (e.g., as low as 10(-7)) with a minimum number of iterations by taking advantage of parallel computing.  
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  Corporate Author Thesis  
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  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0951-8320 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000809316300008 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1607  
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Author (up) Faes, M.G.R.; Valdebenito, M.A.; Yuan, X.K.; Wei, P.F.; Beer, M. doi  openurl
  Title Augmented reliability analysis for estimating imprecise first excursion probabilities in stochastic linear dynamics Type
  Year 2021 Publication Advances in Engineering Software Abbreviated Journal Adv. Eng. Softw.  
  Volume 155 Issue Pages 102993  
  Keywords FAILURE PROBABILITY; SYSTEMS SUBJECT; INTERVAL; QUANTIFICATION; DESIGN  
  Abstract Imprecise probability allows quantifying the level of safety of a system taking into account the effect of both aleatory and epistemic uncertainty. The practical estimation of an imprecise probability is usually quite demanding from a numerical viewpoint, as it is necessary to propagate separately both types of uncertainty, leading in practical cases to a nested implementation in the so-called double loop approach. In view of this issue, this contribution presents an alternative approach that avoids the double loop by replacing the imprecise probability problem by an augmented, purely aleatory reliability analysis. Then, with the help of Bayes' theorem, it is possible to recover an expression for the failure probability as an explicit function of the imprecise parameters from the augmented reliability problem, which ultimately allows calculating the imprecise probability. The implementation of the proposed framework is investigated within the context of imprecise first excursion probability estimation of uncertain linear structures subject to imprecisely defined stochastic quantities and crisp stochastic loads. The associated augmented reliability problem is solved within the context of Directional Importance Sampling, leading to an improved accuracy at reduced numerical costs. The application of the proposed approach is investigated by means of two examples. The results obtained indicate that the proposed approach can be highly efficient and accurate.  
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  Corporate Author Thesis  
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  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0965-9978 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000649550900002 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1378  
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Author (up) Song, J.W.; Wei, P.F.; Valdebenito, M.A.; Faes, M.; Beer, M. doi  openurl
  Title Data-driven and active learning of variance-based sensitivity indices with Bayesian probabilistic integration Type
  Year 2021 Publication Mechanical Systems and Signal Processing Abbreviated Journal Mech. Syst. Sig. Process.  
  Volume 163 Issue Pages 108106  
  Keywords Variance-based sensitivity; Gaussian process regression; Bayesian probabilistic integration; Data-driven; Adaptive experiment design; Posterior variance contribution  
  Abstract Variance-based sensitivity indices play an important role in scientific computation and data mining, thus the significance of developing numerical methods for efficient and reliable estimation of these sensitivity indices based on (expensive) computer simulators and/or data cannot be emphasized too much. In this article, the estimation of these sensitivity indices is treated as a statistical inference problem. Two principle lemmas are first proposed as rules of thumb for making the inference. After that, the posterior features for all the (partial) variance terms involved in the main and total effect indices are analytically derived (not in closed form) based on Bayesian Probabilistic Integration (BPI). This forms a data-driven method for estimating the sensitivity indices as well as the involved discretization errors. Further, to improve the efficiency of the developed method for expensive simulators, an acquisition function, named Posterior Variance Contribution (PVC), is utilized for realizing optimal designs of experiments, based on which an adaptive BPI method is established. The application of this framework is illustrated for the calculation of the main and total effect indices, but the proposed two principle lemmas also apply to the calculation of interaction effect indices. The performance of the development is demonstrated by an illustrative numerical example and three engineering benchmarks with finite element models.  
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  Corporate Author Thesis  
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  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0888-3270 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000687134700006 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1458  
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Author (up) Valdebenito, M.A.; Wei, P.F.; Song, J.W.; Beer, M.; Broggi, M. doi  openurl
  Title Failure probability estimation of a class of series systems by multidomain Line Sampling Type
  Year 2021 Publication Reliability Engineering & System Safety Abbreviated Journal Reliab. Eng. Syst. Saf.  
  Volume 213 Issue Pages 107673  
  Keywords Line sampling; Multidomain; Linear performance function; Failure probability; Series system  
  Abstract This contribution proposes an approach for the assessment of the failure probability associated with a particular class of series systems. The type of systems considered involves components whose response is linear with respect to a number of Gaussian random variables. Component failure occurs whenever this response exceeds prescribed deterministic thresholds. We propose multidomain Line Sampling as an extension of the classical Line Sampling to work with a large number of components at once. By taking advantage of the linearity of the performance functions involved, multidomain Line Sampling explores the interactions that occur between failure domains associated with individual components in order to produce an estimate of the failure probability. The performance and effectiveness of multidomain Line Sampling is illustrated by means of two test problems and an application example, indicating that this technique is amenable for treating problems comprising both a large number of random variables and a large number of components.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0951-8320 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000663910500016 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1430  
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