TY - JOUR

T1 - Fuzzy failure probability estimation applying intervening variables

AU - Valdebenito, Marcos A.

AU - Beer, Michael

AU - Jensen, Héctor A.

AU - Chen, Jianbing

AU - Wei, Pengfei

N1 - Funding Information:
This research is partially supported by CONICYT (National Commission for Scientific and Technological Research) under Grant No. 1180271 and Universidad Tecnica Federico Santa Maria under its program PAC (Programa Asistente Cientifico 2017). The first author developed this work during a research stay at the Institute for Risk and Reliability (IRZ) of the Leibniz Universität Hannover, Germany. Both the first and fifth authors conducted this research under the auspice of the Alexander von Humboldt Foundation. This support is gratefully acknowledged by the authors.
Funding Information:
This research is partially supported by CONICYT (National Commission for Scientific and Technological Research) under Grant No. 1180271 and Universidad Tecnica Federico Santa Maria under its program PAC (Programa Asistente Cientifico 2017). The first author developed this work during a research stay at the Institute for Risk and Reliability (IRZ) of the Leibniz Universität Hannover, Germany. Both the first and fifth authors conducted this research under the auspice of the Alexander von Humboldt Foundation. This support is gratefully acknowledged by the authors.
Publisher Copyright:
© 2019 Elsevier Ltd

PY - 2020/3

Y1 - 2020/3

N2 - Fuzzy probability offers a framework for taking into account the effects of both aleatoric and epistemic uncertainty on the performance of a system, quantifying its level of safety, for example, in terms of a fuzzy failure probability. However, the practical application of fuzzy probability is often challenging due to increased numerical efforts arising from the need to propagate both types of uncertainties. Hence, this contribution proposes an approach for approximate calculation of fuzzy failure probabilities for a class of problems that involve moderately nonlinear performance functions, where uncertain input parameters of a model are characterized as random variables while their associated distribution parameters (for example, mean and standard deviation) are described as fuzzy variables. The proposed approach is cast as a post-processing step of a standard (yet advanced) reliability analysis. The key issue for performing an approximate calculation of the fuzzy failure probabilities is extracting probability sensitivity information from the reliability analysis stage as well as the introduction of intervening variables that capture – to some extent – the nonlinear relation between distribution parameters and the failure probability. A series of relatively simple illustrative examples demonstrate the capabilities of the proposed approach, highlighting its numerical advantages, as it comprises a single standard reliability analysis plus some additional system analyses.

AB - Fuzzy probability offers a framework for taking into account the effects of both aleatoric and epistemic uncertainty on the performance of a system, quantifying its level of safety, for example, in terms of a fuzzy failure probability. However, the practical application of fuzzy probability is often challenging due to increased numerical efforts arising from the need to propagate both types of uncertainties. Hence, this contribution proposes an approach for approximate calculation of fuzzy failure probabilities for a class of problems that involve moderately nonlinear performance functions, where uncertain input parameters of a model are characterized as random variables while their associated distribution parameters (for example, mean and standard deviation) are described as fuzzy variables. The proposed approach is cast as a post-processing step of a standard (yet advanced) reliability analysis. The key issue for performing an approximate calculation of the fuzzy failure probabilities is extracting probability sensitivity information from the reliability analysis stage as well as the introduction of intervening variables that capture – to some extent – the nonlinear relation between distribution parameters and the failure probability. A series of relatively simple illustrative examples demonstrate the capabilities of the proposed approach, highlighting its numerical advantages, as it comprises a single standard reliability analysis plus some additional system analyses.

KW - Fuzzy probability

KW - Intervening variables

KW - Probability sensitivity analysis

KW - Reliability analysis

UR - http://www.scopus.com/inward/record.url?scp=85075989265&partnerID=8YFLogxK

U2 - 10.1016/j.strusafe.2019.101909

DO - 10.1016/j.strusafe.2019.101909

M3 - Article

AN - SCOPUS:85075989265

SN - 0167-4730

VL - 83

JO - Structural Safety

JF - Structural Safety

M1 - 101909

ER -