Details
| Original language | English |
|---|---|
| Article number | 109775 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 185 |
| Early online date | 30 Sept 2022 |
| Publication status | Published - 15 Feb 2023 |
Abstract
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.
Keywords
- Extreme value distribution, First-passage probability, Fractional moment, Mixture distribution, Stochastic dynamic system
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 185, 109775, 15.02.2023.
Research output: Contribution to journal › Article › Research › peer review
}
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 - Funding Information: Chen Ding is grateful for the support by the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie project GREYDIENT – Grant Agreement n°955393. Chao Dang is mainly supported by the China Scholarship Council (CSC). Marcos Valdebenito acknowledges the support of ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271.
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 - 10.15488/12761
DO - 10.15488/12761
M3 - Article
AN - SCOPUS:85139070346
VL - 185
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 109775
ER -