TY - JOUR

T1 - Non-intrusive stochastic analysis with parameterized imprecise probability models

T2 - II. Reliability and rare events analysis

AU - Wei, Pengfei

AU - Song, Jingwen

AU - Bi, Sifeng

AU - Broggi, Matteo

AU - Beer, Michael

AU - Lu, Zhenzhou

AU - Yue, Zhufeng

N1 - Funding Information: This work is supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JQ1007) and the Aerospace Science and Technology Foundation of China. The first and third authors are both supported by the Alexander von Humboldt Foundation of Germany. The first author is also supported by the Top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University. The second author is supported by the program of China Scholarships Council (CSC). The authors are thankful for all these grants. The authors would also like to thank Prof. Hongshuang Li for providing the Matlab code of subset simulation, Dr. Xiaojing Wu for providing the wing flutter model and the two anonymous reviewers for helpful comments.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Structural reliability analysis for rare failure events in the presence of hybrid uncertainties is a challenging task drawing increasing attentions in both academic and engineering fields. Based on the new imprecise stochastic simulation framework developed in the companion paper, this work aims at developing efficient methods to estimate the failure probability functions subjected to rare failure events with the hybrid uncertainties being characterized by imprecise probability models. The imprecise stochastic simulation methods are firstly improved by the active learning procedure so as to reduce the computational costs. For the more challenging rare failure events, two extended subset simulation based sampling methods are proposed to provide better performances in both local and global parameter spaces. The computational costs of both methods are the same with the classical subset simulation method. These two methods are also combined with the active learning procedure so as to further substantially reduce the computational costs. The estimation errors of all the methods are analyzed based on sensitivity indices and statistical properties of the developed estimators. All these new developments enrich the imprecise stochastic simulation framework. The feasibility and efficiency of the proposed methods are demonstrated with numerical and engineering test examples.

AB - Structural reliability analysis for rare failure events in the presence of hybrid uncertainties is a challenging task drawing increasing attentions in both academic and engineering fields. Based on the new imprecise stochastic simulation framework developed in the companion paper, this work aims at developing efficient methods to estimate the failure probability functions subjected to rare failure events with the hybrid uncertainties being characterized by imprecise probability models. The imprecise stochastic simulation methods are firstly improved by the active learning procedure so as to reduce the computational costs. For the more challenging rare failure events, two extended subset simulation based sampling methods are proposed to provide better performances in both local and global parameter spaces. The computational costs of both methods are the same with the classical subset simulation method. These two methods are also combined with the active learning procedure so as to further substantially reduce the computational costs. The estimation errors of all the methods are analyzed based on sensitivity indices and statistical properties of the developed estimators. All these new developments enrich the imprecise stochastic simulation framework. The feasibility and efficiency of the proposed methods are demonstrated with numerical and engineering test examples.

KW - Aleatory uncertainty

KW - Epistemic uncertainty

KW - Failure probability

KW - High-dimensional model representation

KW - Imprecise probability

KW - Imprecise stochastic simulation

KW - Sensitivity analysis

KW - Subset simulation

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85061803582&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2019.02.015

DO - 10.1016/j.ymssp.2019.02.015

M3 - Article

AN - SCOPUS:85061803582

VL - 126

SP - 227

EP - 247

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

ER -