Details
| Original language | English |
|---|---|
| Article number | 103020 |
| Journal | Advances in Engineering Software |
| Volume | 157-158 |
| Early online date | 17 May 2021 |
| Publication status | Published - Jul 2021 |
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.
Keywords
- Bayes’ theorem, Failure probability function, Markov chain simulation, Reliability-based design optimization
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
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In: Advances in Engineering Software, Vol. 157-158, 103020, 07.2021.
Research output: Contribution to journal › Article › Research › peer review
}
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 - Funding Information: Xiukai Yuan would like to acknowledge financial support from NSAF (Grant No. U1530122), the Aeronautical Science Foundation of China (Grant No. ASFC-20170968002) and the Fundamental Research Funds for the Central Universities of China (XMU, 20720180072) and the funding of China Scholarship Council (CSC No. 201906315051). M.A. Valdebenito recognizes the support of ANID (National Agency for Research and Development, Chile) under its program FONDECYT, Grant No. 1180271. Matthias Faes acknowledges the financial support of the Research Foundation Flanders under Grant No. 12P3519N, as well as from the Humboldt Foundation. D.J. Jerez recognizes the support of ANID and DAAD (German Academic Exchange Service) under CONICYT-PFCHA/Doctorado Acuerdo Bilateral DAAD Becas Chile/2018-6218007. H.A. Jensen acknowledges the support of ANID under its program FONDECYT, Grant No. 1200087. Funding Information: Xiukai Yuan would like to acknowledge financial support from NSAF (Grant No. U1530122 ), the Aeronautical Science Foundation of China (Grant No. ASFC-20170968002 ) and the Fundamental Research Funds for the Central Universities of China (XMU, 20720180072 ) and the funding of China Scholarship Council (CSC No. 201906315051 ). M.A. Valdebenito recognizes the support of ANID (National Agency for Research and Development, Chile) under its program FONDECYT , Grant No. 1180271 . Matthias Faes acknowledges the financial support of the Research Foundation Flanders under Grant No. 12P3519N , as well as from the Humboldt Foundation . D.J. Jerez recognizes the support of ANID and DAAD (German Academic Exchange Service) under CONICYT-PFCHA /Doctorado Acuerdo Bilateral DAAD Becas Chile/ 2018-6218007 . H.A. Jensen acknowledges the support of ANID under its program FONDECYT, Grant No. 1200087 .
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
VL - 157-158
JO - Advances in Engineering Software
JF - Advances in Engineering Software
SN - 0965-9978
M1 - 103020
ER -