TY - JOUR

T1 - Decoupled reliability-based optimization using Markov chain Monte Carlo in augmented space

AU - Yuan, Xiukai

AU - Liu, Shaolong

AU - Valdebenito, Marcos A.

AU - Faes, Matthias G.R.

AU - Jerez, Danko J.

AU - Jensen, Hector A.

AU - Beer, Michael

N1 - Publisher Copyright:
© 2021

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Bayes’ theorem

KW - Failure probability function

KW - Markov chain simulation

KW - Reliability-based design optimization

UR - http://www.scopus.com/inward/record.url?scp=85106247785&partnerID=8YFLogxK

U2 - 10.1016/j.advengsoft.2021.103020

DO - 10.1016/j.advengsoft.2021.103020

M3 - Article

AN - SCOPUS:85106247785

SN - 0965-9978

VL - 157-158

JO - Advances in Engineering Software

JF - Advances in Engineering Software

M1 - 103020

ER -