TY - JOUR

T1 - First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach

AU - Ding, Chen

AU - Dang, Chao

AU - Valdebenito, Marcos A.

AU - Faes, Matthias G.R.

AU - Broggi, Matteo

AU - Beer, Michael

N1 - Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2023/2/15

Y1 - 2023/2/15

N2 - First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed ‘fractional moments-based mixture distribution’, to address such challenge. This approach is implemented by capturing the extreme value distribution (EVD) of the system response with the concepts of fractional moment and mixture distribution. In our context, the fractional moment itself is by definition a high-dimensional integral with a complicated integrand. To efficiently compute the fractional moments, a parallel adaptive sampling scheme that allows for sample size extension is developed using the refined Latinized stratified sampling (RLSS). In this manner, both variance reduction and parallel computing are possible for evaluating the fractional moments. From the knowledge of low-order fractional moments, the EVD of interest is then expected to be reconstructed. Based on introducing an extended inverse Gaussian distribution and a log extended skew-normal distribution, one flexible mixture distribution model is proposed, where its fractional moments are derived in analytic form. By fitting a set of fractional moments, the EVD can be recovered via the proposed mixture model. Accordingly, the first-passage probabilities under different thresholds can be obtained from the recovered EVD straightforwardly. The performance of the proposed method is verified by three examples consisting of two test examples and one engineering problem.

AB - First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed ‘fractional moments-based mixture distribution’, to address such challenge. This approach is implemented by capturing the extreme value distribution (EVD) of the system response with the concepts of fractional moment and mixture distribution. In our context, the fractional moment itself is by definition a high-dimensional integral with a complicated integrand. To efficiently compute the fractional moments, a parallel adaptive sampling scheme that allows for sample size extension is developed using the refined Latinized stratified sampling (RLSS). In this manner, both variance reduction and parallel computing are possible for evaluating the fractional moments. From the knowledge of low-order fractional moments, the EVD of interest is then expected to be reconstructed. Based on introducing an extended inverse Gaussian distribution and a log extended skew-normal distribution, one flexible mixture distribution model is proposed, where its fractional moments are derived in analytic form. By fitting a set of fractional moments, the EVD can be recovered via the proposed mixture model. Accordingly, the first-passage probabilities under different thresholds can be obtained from the recovered EVD straightforwardly. The performance of the proposed method is verified by three examples consisting of two test examples and one engineering problem.

KW - Extreme value distribution

KW - First-passage probability

KW - Fractional moment

KW - Mixture distribution

KW - Stochastic dynamic system

UR - http://www.scopus.com/inward/record.url?scp=85139070346&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2022.109775

DO - 10.1016/j.ymssp.2022.109775

M3 - Article

AN - SCOPUS:85139070346

SN - 0888-3270

VL - 185

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

M1 - 109775

ER -