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Author 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 (up)  
  Call Number UAI @ alexi.delcanto @ Serial 1378  
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Author Yuan, X.K.; Liu, S.L.; Valdebenito, M.A.; Faes, M.G.R.; Jerez, D.J.; Jensen, H.A.; Beer, M. doi  openurl
  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  
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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:000653696200006 Approved (up)  
  Call Number UAI @ alexi.delcanto @ Serial 1395  
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Author 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.  
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  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0951-8320 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000663910500016 Approved (up)  
  Call Number UAI @ alexi.delcanto @ Serial 1430  
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Author 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.  
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  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 (up)  
  Call Number UAI @ alexi.delcanto @ Serial 1637  
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Author Fina, M.; Lauff, C.; Faes, M.G.R.; Valdebenito, M.A.; Wagner, W.; Freitag, S. doi  openurl
  Title Bounding imprecise failure probabilities in structural mechanics based on maximum standard deviation Type
  Year 2023 Publication Structural Safety Abbreviated Journal Struct. Saf.  
  Volume 101 Issue Pages 102293  
  Keywords Linear structures; Gaussian loading; Standard deviation; Failure probability; Aleatoric uncertainty; Epistemic uncertainty  
  Abstract This paper proposes a framework to calculate the bounds on failure probability of linear structural systems whose performance is affected by both random variables and interval variables. This kind of problems is known to be very challenging, as it demands coping with aleatoric and epistemic uncertainty explicitly. Inspired by the framework of the operator norm theorem, it is proposed to consider the maximum standard deviation of the structural response as a proxy for detecting the crisp values of the interval parameters, which yield the bounds of the failure probability. The scope of application of the proposed approach comprises linear structural systems, whose properties may be affected by both aleatoric and epistemic uncertainty and that are subjected to (possibly imprecise) Gaussian loading. Numerical examples indicate that the application of such proxy leads to substantial numerical advantages when compared to a traditional double-loop approach for coping with imprecise failure probabilities. In fact, the proposed framework allows to decouple the propagation of aleatoric and epistemic uncertainty.  
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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 0167-4730 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000899856800006 Approved (up)  
  Call Number UAI @ alexi.delcanto @ Serial 1712  
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