Probability density estimation of polynomial chaos and its application in structural reliability analysis

IF 9.4 1区 工程技术 Q1 ENGINEERING, INDUSTRIAL
Ye-Yao Weng, Teng Liu, Xuan-Yi Zhang, Yan-Gang Zhao
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引用次数: 0

Abstract

Polynomial chaos expansion (PCE) is a widely used approach for establishing the surrogate model of a time-consuming performance function for the convenience of uncertainty quantification of a stochastic structure. However, it remains difficult to calculate the probability density function (PDF) of the PCE accurately for general cases, though the PDF, as a complete representation of a random variable, is often required in some uncertainty problems. To address this problem, this paper proposes a semi-analytical method to compute the PDF of a PCE. This method derives the closed-form solutions of characteristic functions (CFs) of the first- and second-order PCEs, while an equivalent parabolization technique is proposed to provide the approximate solutions of CFs of higher-order PCEs. Then, the PDF of the PCE can be obtained by the Fourier transform of the resulting CF. Three numerical examples are investigated to demonstrate the accuracy, applicability, and efficiency of the proposed method for probability density estimation of PCE in structural reliability analysis.
多项式混沌的概率密度估计及其在结构可靠性分析中的应用
多项式混沌扩展(PCE)是一种广泛使用的方法,用于建立耗时性能函数的替代模型,以方便对随机结构进行不确定性量化。然而,尽管在某些不确定性问题中经常需要 PCE 的概率密度函数(PDF)作为随机变量的完整表示,但在一般情况下仍难以准确计算 PCE 的概率密度函数。为了解决这个问题,本文提出了一种计算 PCE 的 PDF 的半解析方法。该方法推导出了一阶和二阶 PCE 的特征函数 (CF) 的闭式解,同时提出了一种等效抛物线技术来提供高阶 PCE CF 的近似解。然后,PCE 的 PDF 可以通过所得到的 CF 的傅立叶变换得到。研究了三个数值示例,以证明所提方法在结构可靠性分析中用于 PCE 概率密度估计的准确性、适用性和高效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Reliability Engineering & System Safety
Reliability Engineering & System Safety 管理科学-工程:工业
CiteScore
15.20
自引率
39.50%
发文量
621
审稿时长
67 days
期刊介绍: Elsevier publishes Reliability Engineering & System Safety in association with the European Safety and Reliability Association and the Safety Engineering and Risk Analysis Division. The international journal is devoted to developing and applying methods to enhance the safety and reliability of complex technological systems, like nuclear power plants, chemical plants, hazardous waste facilities, space systems, offshore and maritime systems, transportation systems, constructed infrastructure, and manufacturing plants. The journal normally publishes only articles that involve the analysis of substantive problems related to the reliability of complex systems or present techniques and/or theoretical results that have a discernable relationship to the solution of such problems. An important aim is to balance academic material and practical applications.
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