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

Ruijing Zhang and Hongzhe Dai

Reliability Engineering and System Safety, 2022, vol. 221, issue C

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.

Keywords: Non-Gaussian model; Limited observations; Fractional moments; Bootstrapping; Karhunen-Loève expansion; Polynomial chaos (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:221:y:2022:i:c:s0951832022000059

DOI: 10.1016/j.ress.2022.108323

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