Polynomial chaos expansion with random and fuzzy variables

被引：44

作者：

Jacquelin, E. ^{[1
,2
,3
]}

Friswell, M. I. ^{[4
]}

Adhikari, S. ^{[4
]}

Dessombz, O. ^{[5
]}

Sinou, J. -J. ^{[5
,6
]}

机构：

[1] Univ Lyon, F-69622 Lyon, France

[2] Univ Lyon 1, F-69622 Villeurbanne, France

[3] IFSTTAR, UMR T9406, LBMC, F-69675 Bron, France

[4] Swansea Univ, Coll Engn, Swansea SA2 8PP, W Glam, Wales

[5] Ecole Cent Lyon, LTDS, CNRS, UMR 5513, F-69134 Ecully, France

[6] Inst Univ France, F-75005 Paris, France

来源：

MECHANICAL SYSTEMS AND SIGNAL PROCESSING | 2016年 / 75卷

关键词：

Random systems; Structural dynamics; Polynomial chaos expansion; Fuzzy variables; Random variables; Steady-state response; FREQUENCY-RESPONSE FUNCTIONS; FINITE-ELEMENT PROCEDURE; DAMPED STRUCTURES; UNCERTAINTY;

D O I：

10.1016/j.ymssp.2015.12.001

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：41 / 56

页数：16

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