TY - JOUR

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

T2 - I. Performance estimation

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 Aerospace Science and Technology Foundation of China . The first author is also supported by the Top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University. The first and third authors are both supported by the Alexander von Humboldt Foundation of Germany . The second author is supported by the program of China Scholarships Council (CSC) . Part of this work is supported by the National Natural Science Foundation of China (Grant No. U1530122 ). The authors are thankful for all these grants.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - Uncertainty propagation through the simulation models is critical for computational mechanics engineering to provide robust and reliable design in the presence of polymorphic uncertainty. This set of companion papers present a general framework, termed as non-intrusive imprecise stochastic simulation, for uncertainty propagation under the background of imprecise probability. This framework is composed of a set of methods developed for meeting different goals. In this paper, the performance estimation is concerned. The local extended Monte Carlo simulation (EMCS) is firstly reviewed, and then the global EMCS is devised to improve the global performance. Secondly, the cut-HDMR (High-Dimensional Model Representation) is introduced for decomposing the probabilistic response functions, and the local EMCS method is used for estimating the cut-HDMR component functions. Thirdly, the RS (Random Sampling)-HDMR is introduced to decompose the probabilistic response functions, and the global EMCS is applied for estimating the RS-HDMR component functions. The statistical errors of all estimators are derived, and the truncation errors are estimated by two global sensitivity indices, which can also be used for identifying the influential HDMR components. In the companion paper, the reliability and rare event analysis are treated. The effectiveness of the proposed methods are demonstrated by numerical and engineering examples.

AB - Uncertainty propagation through the simulation models is critical for computational mechanics engineering to provide robust and reliable design in the presence of polymorphic uncertainty. This set of companion papers present a general framework, termed as non-intrusive imprecise stochastic simulation, for uncertainty propagation under the background of imprecise probability. This framework is composed of a set of methods developed for meeting different goals. In this paper, the performance estimation is concerned. The local extended Monte Carlo simulation (EMCS) is firstly reviewed, and then the global EMCS is devised to improve the global performance. Secondly, the cut-HDMR (High-Dimensional Model Representation) is introduced for decomposing the probabilistic response functions, and the local EMCS method is used for estimating the cut-HDMR component functions. Thirdly, the RS (Random Sampling)-HDMR is introduced to decompose the probabilistic response functions, and the global EMCS is applied for estimating the RS-HDMR component functions. The statistical errors of all estimators are derived, and the truncation errors are estimated by two global sensitivity indices, which can also be used for identifying the influential HDMR components. In the companion paper, the reliability and rare event analysis are treated. The effectiveness of the proposed methods are demonstrated by numerical and engineering examples.

KW - Aleatory and epistemic uncertainties

KW - High-dimensional model representation

KW - Imprecise probability models

KW - Imprecise stochastic simulation

KW - Sensitivity analysis

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85061312016&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2019.01.058

DO - 10.1016/j.ymssp.2019.01.058

M3 - Article

AN - SCOPUS:85061312016

VL - 124

SP - 349

EP - 368

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

ER -