TY - JOUR

T1 - Non-intrusive imprecise stochastic simulation by line sampling

AU - Song, Jingwen

AU - Valdebenito, Marcos

AU - Wei, Pengfei

AU - Beer, Michael

AU - Lu, Zhenzhou

N1 - Funding Information: This work is supported by National Natural Science Foundation of China (NSFC) under grant number 51905430 . The first author is supported by the program of China Scholarship Council (CSC). The second and third authors are both supported by the Alexander von Humboldt Foundation of Germany. The second author also acknowledges the support by CONICYT ( National Commission for Scientific and Technological Research ) under grant number 1180271 .

PY - 2020/5

Y1 - 2020/5

N2 - The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the requirement of performing optimization analysis on the response functions can be elegantly avoided. However, for rare failure events, the current NISS methods are still computationally expensive. In this paper, the classical line sampling developed for precise stochastic simulation is injected into the NISS framework, and two different imprecise line sampling (ILS) methods are developed based on two different interpretations of the classical line sampling procedure. The first strategy is devised based on the set of hyperplanes introduced by the line sampling analysis, while the second strategy is developed based on an integral along each individual line. The truncation errors of both methods are measured by sensitivity indices, and the variances of all estimators are derived for indicating the statistical errors. A test example and three engineering problems of different types are introduced for comparing and demonstrating the effectiveness of the two ILS methods.

AB - The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the requirement of performing optimization analysis on the response functions can be elegantly avoided. However, for rare failure events, the current NISS methods are still computationally expensive. In this paper, the classical line sampling developed for precise stochastic simulation is injected into the NISS framework, and two different imprecise line sampling (ILS) methods are developed based on two different interpretations of the classical line sampling procedure. The first strategy is devised based on the set of hyperplanes introduced by the line sampling analysis, while the second strategy is developed based on an integral along each individual line. The truncation errors of both methods are measured by sensitivity indices, and the variances of all estimators are derived for indicating the statistical errors. A test example and three engineering problems of different types are introduced for comparing and demonstrating the effectiveness of the two ILS methods.

KW - Aleatory uncertainty

KW - Epistemic uncertainty

KW - Imprecise probability models

KW - Line sampling

KW - Sensitivity analysis

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85078907328&partnerID=8YFLogxK

U2 - 10.1016/j.strusafe.2020.101936

DO - 10.1016/j.strusafe.2020.101936

M3 - Article

AN - SCOPUS:85078907328

VL - 84

JO - Structural Safety

JF - Structural Safety

SN - 0167-4730

M1 - 101936

ER -