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Dang, C.; Valdebenito, M.A.; Faes, M.G.R.; Wei, P.F.; Beer, M. |
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Title |
Structural reliability analysis: A Bayesian perspective |
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2022 |
Publication |
Structural Safety |
Abbreviated Journal |
Struct. Saf. |
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Volume |
99 |
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102259 |
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Keywords |
Failure probability; Bayesian inference; Gaussian process; Numerical uncertainty; Parallel computing |
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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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0167-4730 |
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WOS:000837863500001 |
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UAI @ alexi.delcanto @ |
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1637 |
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Author |
Dang, C.; Wei, P.F.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M. |
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Title |
Interval uncertainty propagation by a parallel Bayesian global optimization method |
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2022 |
Publication |
Applied Mathematical Modelling |
Abbreviated Journal |
Appl. Math. Model. |
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108 |
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220-235 |
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Keywords |
Interval uncertainty propagation; Bayesian global optimization; Gaussian process; Infill sampling criterion; Parallel computing |
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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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0307-904X |
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WOS:000830573400001 |
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UAI @ alexi.delcanto @ |
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1625 |
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Author |
Dang, C.; Wei, P.F.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M. |
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Title |
Parallel adaptive Bayesian quadrature for rare event estimation |
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2022 |
Publication |
Reliability Engineering & System Safety |
Abbreviated Journal |
Reliab. Eng. Syst. Saf. |
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225 |
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108621 |
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Reliability analysis; Gaussian process; Numerical uncertainty; Bayesian quadrature; Parallel computing |
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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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0951-8320 |
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WOS:000809316300008 |
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UAI @ alexi.delcanto @ |
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1607 |
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Author |
Morales-Onate, V.; Crudu, F.; Bevilacqua, M. |
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Title |
Blockwise Euclidean likelihood for spatio-temporal covariance models |
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2021 |
Publication |
Econometrics and Statistics |
Abbreviated Journal |
Econ. Stat. |
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20 |
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176-201 |
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Composite likelihood; Euclidean likelihood; Gaussian random fields; Parallel computing; OpenCL |
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A spatio-temporal blockwise Euclidean likelihood method for the estimation of covariance models when dealing with large spatio-temporal Gaussian data is proposed. The method uses moment conditions coming from the score of the pairwise composite likelihood. The blockwise approach guarantees considerable computational improvements over the standard pairwise composite likelihood method. In order to further speed up computation, a general purpose graphics processing unit implementation using OpenCL is implemented. The asymptotic properties of the proposed estimator are derived and the finite sample properties of this methodology by means of a simulation study highlighting the computational gains of the OpenCL graphics processing unit implementation. Finally, there is an application of the estimation method to a wind component data set. (C) 2021 EcoSta Econometrics and Statistics. Published by Elsevier B.V. All rights reserved. |
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2468-0389 |
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WOS:000689351000012 |
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UAI @ alexi.delcanto @ |
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1460 |
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