TY - JOUR

T1 - Active learning line sampling for rare event analysis

AU - Song, Jingwen

AU - Wei, Pengfei

AU - Valdebenito, Marcos

AU - Beer, Michael

N1 - Funding Information: This work is supported by the National Natural Science Foundation of China (NSFC 51905430 ) and ANID (Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271. The first author is supported by the program of China Scholarships Council (CSC). The second and third authors are both supported by the Alexander von Humboldt Foundation of Germany. The second author is also supported by the Top International University Visiting Program for Outstanding Young Scholars of Northwestern Polytechnical University. We would also like to thank our colleague Dr. Matteo Broggi for his strong support on COSSAN.

PY - 2021/1/15

Y1 - 2021/1/15

N2 - Line Sampling (LS) has been widely recognized as one of the most appealing stochastic simulation algorithms for rare event analysis, but when applying it to many real-world engineering problems, improvement of the algorithm with higher efficiency is still required. This paper aims to improve both the efficiency and accuracy of LS by active learning and Gaussian process regression (GPR). A new learning function is devised for informing the accuracy of the calculation of the intersection points between each line associated with LS and the failure surface. Then, an adaptive algorithm, with the learning function as an engine and a stopping criterion, is developed for adaptively training a GPR model to accurately estimate the intersection points for all lines in LS scheme, and the number of lines is actively increased if it is necessary for improving the accuracy of failure probability estimation. By introducing this adaptive GPR model, the number of required function calls has been largely reduced, and the accuracy for estimation of the intersection points has been largely improved, especially for highly nonlinear problems with extremely rare events. Numerical test examples and engineering applications show the superiority of the developed algorithm over the classical LS algorithm and some other active learning schemes.

AB - Line Sampling (LS) has been widely recognized as one of the most appealing stochastic simulation algorithms for rare event analysis, but when applying it to many real-world engineering problems, improvement of the algorithm with higher efficiency is still required. This paper aims to improve both the efficiency and accuracy of LS by active learning and Gaussian process regression (GPR). A new learning function is devised for informing the accuracy of the calculation of the intersection points between each line associated with LS and the failure surface. Then, an adaptive algorithm, with the learning function as an engine and a stopping criterion, is developed for adaptively training a GPR model to accurately estimate the intersection points for all lines in LS scheme, and the number of lines is actively increased if it is necessary for improving the accuracy of failure probability estimation. By introducing this adaptive GPR model, the number of required function calls has been largely reduced, and the accuracy for estimation of the intersection points has been largely improved, especially for highly nonlinear problems with extremely rare events. Numerical test examples and engineering applications show the superiority of the developed algorithm over the classical LS algorithm and some other active learning schemes.

KW - Active learning

KW - Adaptive experiment design

KW - Gaussian process regression

KW - Learning function

KW - Line sampling

KW - Rare failure event

UR - http://www.scopus.com/inward/record.url?scp=85088126114&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2020.107113

DO - 10.1016/j.ymssp.2020.107113

M3 - Article

AN - SCOPUS:85088126114

VL - 147

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 107113

ER -