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Author (up) Dang, C.; Valdebenito, M.A.; Faes, M.G.R.; Wei, P.F.; Beer, M.
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.
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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.
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
Publisher Place of Publication Editor
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.
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
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:000809316300008 Approved
Call Number UAI @ alexi.delcanto @ Serial 1607
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Author (up) Faes, M.G.R.; Valdebenito, M.A.
Title Fully decoupled reliability-based optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables Type
Year 2021 Publication Mechanical Systems and Signal Processing Abbreviated Journal Mech. Syst. Sig. Process.
Volume 156 Issue Pages 107616
Keywords Linear structure; Gaussian loading; First excursion probability; Decoupling; Operator norm
Abstract Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even further enlarged when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of three examples.
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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 0888-3270 ISBN Medium
Area Expedition Conference
Notes WOS:000634833100004 Approved
Call Number UAI @ alexi.delcanto @ Serial 1364
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Author (up) Faes, M.G.R.; Valdebenito, M.A.; Yuan, X.K.; Wei, P.F.; Beer, M.
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
Publisher Place of Publication Editor
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) Ni, P.H.; Jerez, D.J.; Fragkoulis, V.C.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M.
Title Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading Type
Year 2022 Publication ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A-Civil Engineering Abbreviated Journal ASCE-ASME J. Risk Uncertain. Eng. Syst. A-Civ. Eng.
Volume 8 Issue 1 Pages 04021086
Keywords Uncertainty quantification; Imprecise probabilities; Operator norm theorem; Statistical linearization
Abstract This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to
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Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2376-7642 ISBN Medium
Area Expedition Conference
Notes WOS:000742414100022 Approved
Call Number UAI @ alexi.delcanto @ Serial 1550
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Author (up) Yuan, X.K.; Faes, M.G.R.; Liu, S.L.; Valdebenito, M.A.; Beer, M.
Title Efficient imprecise reliability analysis using the Augmented Space Integral Type
Year 2021 Publication Reliability Engineering & System Safety Abbreviated Journal Reliab. Eng. Syst. Saf.
Volume 210 Issue Pages 107477
Keywords Imprecise reliability analysis; Simulation-based method; Interval variable; Augmented space
Abstract This paper presents an efficient approach to compute the bounds on the reliability of a structure subjected to uncertain parameters described by means of imprecise probabilities. These imprecise probabilities arise from epistemic uncertainty in the definition of the hyper-parameters of a set of random variables that describe aleatory uncertainty in some of the structure's properties. Typically, such calculation involves the solution of a so-called double-loop problem, where a crisp reliability problem is repeatedly solved to determine which realization of the epistemic uncertainties yields the worst or best case with respect to structural safety. The approach in this paper aims at decoupling this double loop by virtue of the Augmented Space Integral. The core idea of the method is to infer a functional relationship between the epistemically uncertain hyper-parameters and the probability of failure. Then, this functional relationship can be used to determine the best and worst case behavior with respect to the probability of failure. Three case studies are included to illustrate the effectiveness and efficiency of the developed methods.
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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:000663909400008 Approved
Call Number UAI @ alexi.delcanto @ Serial 1432
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Author (up) Yuan, X.K.; Liu, S.L.; Valdebenito, M.A.; Faes, M.G.R.; Jerez, D.J.; Jensen, H.A.; Beer, M.
Title Decoupled reliability-based optimization using Markov chain Monte Carlo in augmented space Type
Year 2021 Publication Advances in Engineering Software Abbreviated Journal Adv. Eng. Softw.
Volume 157 Issue Pages 103020
Keywords Reliability-based design optimization; Markov chain simulation; Failure probability function; Bayes' theorem
Abstract An efficient framework is proposed for reliability-based design optimization (RBDO) of structural systems. The RBDO problem is expressed in terms of the minimization of the failure probability with respect to design variables which correspond to distribution parameters of random variables, e.g. mean or standard deviation. Generally, this problem is quite demanding from a computational viewpoint, as repeated reliability analyses are involved. Hence, in this contribution, an efficient framework for solving a class of RBDO problems without even a single reliability analysis is proposed. It makes full use of an established functional relationship between the probability of failure and the distribution design parameters, which is termed as the failure probability function (FPF). By introducing an instrumental variability associated with the distribution design parameters, the target FPF is found to be proportional to a posterior distribution of the design parameters conditional on the occurrence of failure in an augmented space. This posterior distribution is derived and expressed as an integral, which can be estimated through simulation. An advanced Markov chain algorithm is adopted to efficiently generate samples that follow the aforementioned posterior distribution. Also, an algorithm that re-uses information is proposed in combination with sequential approximate optimization to improve the efficiency. Numeric examples illustrate the performance of the proposed framework.
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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 0965-9978 ISBN Medium
Area Expedition Conference
Notes WOS:000653696200006 Approved
Call Number UAI @ alexi.delcanto @ Serial 1395
Permanent link to this record