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

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Chen Ding
  • Chao Dang
  • Marcos A. Valdebenito
  • Matthias G.R. Faes
  • Matteo Broggi
  • Michael Beer

Externe Organisationen

  • Universidad Adolfo Ibanez
  • Technische Universität Dortmund
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer109775
FachzeitschriftMechanical Systems and Signal Processing
Jahrgang185
Frühes Online-Datum30 Sept. 2022
PublikationsstatusVeröffentlicht - 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.

ASJC Scopus Sachgebiete

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First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach. / Ding, Chen; Dang, Chao; Valdebenito, Marcos A. et al.
in: Mechanical Systems and Signal Processing, Jahrgang 185, 109775, 15.02.2023.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Ding C, Dang C, Valdebenito MA, Faes MGR, Broggi M, Beer M. First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach. Mechanical Systems and Signal Processing. 2023 Feb 15;185:109775. Epub 2022 Sep 30. doi: 10.15488/12761, 10.1016/j.ymssp.2022.109775
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title = "First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach",
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 {\textquoteleft}fractional moments-based mixture distribution{\textquoteright}, 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.",
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note = "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.",
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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.

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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.

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