Details

Autor(en) / Beteiligte

• Zhang, Ruijing
• Dai, Hongzhe

Titel

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

Ist Teil von

• Reliability engineering & system safety, 2022-05, Vol.221, p.108323, Article 108323

Ort / Verlag

Barking: Elsevier Ltd

Erscheinungsjahr

2022

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• •A unified non-Gaussian stochastic model from limited observations is developed.•The developed model is based on polynomial chaos (PC) and fractional moments.•The developed model can be embedded into PC framework for stochastic propagation.•Two numerical examples demonstrate the developed model. 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.