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A non-Gaussian stochastic model from limited observations using polynomial chaos and fractional moments

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  • Zhang, Ruijing
  • Dai, Hongzhe

Abstract

The reasonable representation of input random fields is the key element in the reliability analysis of practical engineering systems. In most engineering applications, the characterization of a random field often relies on limited measurements. Although the simulation of random fields with complete probabilistic information has been quite well-established, reconstructing a random field from limited observations is still a challenging task. In this paper, we develop a methodology for constructing non-Gaussian random model from limited observations based on polynomial chaos (PC) and fractional moments for real-life problems. Our method begins with the reduce-order representation of measurements by Karhunen-Loève (KL) expansion, followed by the PC representation of KL coefficients. The PC coefficients are further modeled as random variables, whose distributions are determined by a modified maximum entropy principle with fractional moments (ME-FM) procedure and a ME-FM-based bootstrapping. In this way, the developed non-Gaussian model enables to quantify the inherent randomness and the statistical uncertainty of the observed non-Gaussian field simultaneously. Since the developed non-Gaussian model is embedded into the well-established PC framework, our method facilitates the implementation of PC-based stochastic analysis in practical engineering applications, in which only limited probabilistic measures are available. Two numerical examples demonstrate the application of the developed method.

Suggested Citation

  • Zhang, Ruijing & Dai, Hongzhe, 2022. "A non-Gaussian stochastic model from limited observations using polynomial chaos and fractional moments," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
  • Handle: RePEc:eee:reensy:v:221:y:2022:i:c:s0951832022000059
    DOI: 10.1016/j.ress.2022.108323
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    References listed on IDEAS

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    6. Zhao, Tengyuan & Wang, Yu, 2020. "Non-parametric simulation of non-stationary non-gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo (MCMC) simulation," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
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    9. Salomon, Julian & Winnewisser, Niklas & Wei, Pengfei & Broggi, Matteo & Beer, Michael, 2021. "Efficient reliability analysis of complex systems in consideration of imprecision," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
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    Cited by:

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    6. Xu, Jun & Song, Jinheng & Yu, Quanfu & Kong, Fan, 2023. "Generalized distribution reconstruction based on the inversion of characteristic function curve for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).

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