PSI - Issue 44

ScienceDirect Structural Integrity Procedia 00 (2022) 000–000 Structural Integrity Procedia 00 (2022) 000–000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceD rect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 44 (2023) 1680–1687

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy. Abstract This study presents a reliability analysis of stochastic system using the probability density evolution method (PDEM). The PDEM is formulated according to the principle of probability conservation where generalized density evolution equations (GDEEs) are completely decoupled. To estimate the probability density function accurately, a set of representative points of random variables are generated using the GF-discrepancy scheme. A large number of representative points is needed to obtain satisfactory accuracy, which becomes computationally expensive. To reduce the computation burden, a stochastic spectral embedding (SSE) is used as a surrogate model which approximates the original response surface. To illustrate the proposed SSE-based PDEM, two numerical examples are investigated, including the reliability analysis of four-branch problem, and the reliability-based design optimization of a shape memory alloy based damped outrigger tall timber building. Numerical results show that the proposed SSE-based PDEM can estimate failure probability using a very small number of representative points without compromising accuracy compared with Monte Carlo simulation, which leads to a reduction in computational costs. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy Keywords: Probability Density Evolution Method ; Stochastic Spectral Embedding ; Reliability Analysis 1. Introduction Reliability analysis is an established method to compute probability of failure of structures under structural system and external excitation uncertainties. The reliability analysis methods can be categorized into four sub-groups, i.e., analytical-approximation method, numerical-sampling-based method, surrogate-based method, and numerical- XIX ANIDIS Conference, Seismic Engineering in Italy Reliability Analysis of Stochastic System using Stochastic Spectral Embedding based Probability Density Evolution Method Sourav Das a , Solomon Tesfamariam b * a School of Engineering, The University of British Columbia, Okanagan Campus,3333 University Way, Kelowna, V1V1V7, BC, Canada Abstract This study presents a reliability analysis of stochastic system using the probability density evolution method (PDEM). The PDEM is form lated according to the principle prob bility conservation where generalized density evolution equations (GDEEs) are completely ecoupled. T estimate the probability density function accu ately, a set of representative points of random variables are generate using the GF-discrepancy scheme. A large number f representative points is n eded to obtai atisf ct ry accuracy, which becomes computationally xpensive. To reduce the computation burden, a st cha tic spectral embedding (SSE) is used s a surrogat model which pproximates the original response surface. To illustrate the proposed SSE-based PDEM, two n merical examples are investigated, including the reliability analy is of our-branch problem, and the reliability-based design ptimization of shape m mory alloy based damped outr gger tall timber building. Numerical results show that the propose SSE-based PDEM can estimate failure pr bability using a very small number of representative points without compromising accuracy compared with Monte Carlo simulation, wh ch leads to a eductio in computational costs. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review under responsibility of the scientific committee of the XIX ANIDIS C nference, Seismic Engineering in Italy K ywords: Probability Density Evolution Method ; Stochastic Spectral Embedding ; Reliability Analysis 1. Introduction Reliability analysis is an established method to compute probability of failure of structures under structural system and xternal excitation unc rtaint es. The reliability analysis methods can be catego ized into four sub-groups, i.e., alytical- pproximation me hod, num rical-sampling-based method, surrog t -base meth d, and numerical- XIX ANIDIS Conference, Seismic Engineering in Italy Reliability Analysis of Stochastic System using Stochastic Spectral Embedding based Probability Density Evolution Method Sourav Das a , Solomon Tesfamariam b * a School of Engineering, The University of British Columbia, Okanagan Campus,3333 University Way, Kelowna, V1V1V7, BC, Canada

* Corresponding author. Tel.: +1-250-807-8185 E-mail address: solomon.tesfamariam@ubc.ca * Corresponding author. Tel.: +1-250-807-8185 E-mail address: sol mon.tesfamariam@ubc.ca

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy. 10.1016/j.prostr.2023.01.215