Records 
Author 
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 semianalytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel AdaptiveBayesian Failure Probability Learning (PABFPL) method is proposed within the Bayesian framework. In the PABFPL method, a varianceamplified 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 PABFPL 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 
01674730 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000837863500001 
Approved 

Call Number 
UAI @ alexi.delcanto @ 
Serial 
1637 
Permanent link to this record 



Author 
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 socalled 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. 
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 
09659978 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000649550900002 
Approved 

Call Number 
UAI @ alexi.delcanto @ 
Serial 
1378 
Permanent link to this record 



Author 
Fina, M.; Lauff, C.; Faes, M.G.R.; Valdebenito, M.A.; Wagner, W.; Freitag, S. 
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 doubleloop approach for coping with imprecise failure probabilities. In fact, the proposed framework allows to decouple the propagation of aleatoric and epistemic uncertainty. 
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 
01674730 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000899856800006 
Approved 

Call Number 
UAI @ alexi.delcanto @ 
Serial 
1712 
Permanent link to this record 



Author 
Valdebenito, M.A.; Wei, P.F.; Song, J.W.; Beer, M.; Broggi, M. 
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 
09518320 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000663910500016 
Approved 

Call Number 
UAI @ alexi.delcanto @ 
Serial 
1430 
Permanent link to this record 



Author 
Yuan, X.K.; Liu, S.L.; Valdebenito, M.A.; Faes, M.G.R.; Jerez, D.J.; Jensen, H.A.; Beer, M. 
Title 
Decoupled reliabilitybased 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 
Reliabilitybased design optimization; Markov chain simulation; Failure probability function; Bayes' theorem 
Abstract 
An efficient framework is proposed for reliabilitybased 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 reuses information is proposed in combination with sequential approximate optimization to improve the efficiency. Numeric examples illustrate the performance of the proposed framework. 
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 
09659978 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000653696200006 
Approved 

Call Number 
UAI @ alexi.delcanto @ 
Serial 
1395 
Permanent link to this record 