Stochastic Structural Modal Analysis Involving Uncertain Parameters Using Generalized Polynomial Chaos Expansion

Abstract

In this paper, the application of generalized polynomial chaos expansion in stochastic structural modal analysis including uncertain parameters is investigated. We review the theory of polynomial chaos and relating error analysis. A general formulation for the representation of modal problems by the polynomial chaos expansion is derived. It shows how the modal frequencies and modal shapes are influenced by the parameter uncertainties. The key issues that arise in the polynomial chaos simulation of modal analysis are discussed for two examples: a discrete 2-DOF system and continuous model of a microsensor. In both cases, the polynomial chaos expansion is used for the approximation of uncertain parameters, eigenfrequencies and eigenvectors. We emphasize the accuracy and time efficiency of the method in estimation of the stochastic modal responses in comparison with the sampling techniques, such as the Monte Carlo simulation.

Spectral Representation of Uncertainty in Experimental Vibration Modal Data

“…in which E( ) = (1/ ) ∑ =1 is the mean value of samples. An error function based on the least-square criterion corresponding to the difference between the moments derived from (5) and (8) can be used to estimate the optimal coefficients . This leads to a minimization problem as follows:…”

“…Characterization of the stochastic response due to these uncertainties by stochastic methods has gained interest among researchers in past decades. Stochastic methods in conjunction with finite element method (FEM) have been widely used to quantify uncertainty in structural responses [1][2][3][4][5][6][7][8][9]. Two major issues have to be addressed regarding stochastic analysis of such structures under uncertainty: first, how the uncertainties can be efficiently identified and modeled in numerical simulations, particularly in finite element models and, secondly, how uncertainties affect the behavior of aforesaid structures.…”

Research on the Statistical Characteristics of Crosstalk in Naval Ships Wiring Harness Based on Polynomial Chaos Expansion Method

“…Polynomial chaos expansion method is a powerful and effective mehtod which is widely applied in numerous aspects such as industrial, material research and mathematical field [13][14][15][16][17][18]. The fundamentals of polynomial chaos expansion and uniform distribution will be briefly summarized here only to guide the audients and define units.…”

Stochastic collocation-based finite element of structural nonlinear dynamics with application in composite structures

“…The metha e-mail: k.sepahvand@tum.de ods are straightforward in application, but limited to the small range of uncertainty and very expensive in the term of computational costs. The non-sampling spectral methods, in contrast, are very efficient and exhibit the same level of accuracy sampling methods.The application of the methods is well known in linear structural dynamics [11][12][13][14][15][16] where random parameters are approximated by spectral expansions to give a complete characterization of the uncertain parameters. In this paper, the spectral stochastic finite element method (sSFEM) analysis of the nonlinear structural dynamics with parametric uncertainty is developed.…”