Probabilistic analysis and control of uncertain dynamic systems: Generalized polynomial chaos expansion approaches

2012 ◽  
Author(s):  
Kwang Ki Kevin Kim ◽  
R. D. Braatz
Keyword(s):  
Dynamic Systems ◽  
Probabilistic Analysis ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Uncertain Dynamic Systems ◽  
Generalized Polynomial ◽  
And Control

STOCHASTIC STRUCTURAL MODAL ANALYSIS INVOLVING UNCERTAIN PARAMETERS USING GENERALIZED POLYNOMIAL CHAOS EXPANSION

2011 ◽  
Vol 03 (03) ◽  
pp. 587-606 ◽  
Author(s):  
K. SEPAHVAND ◽  
S. MARBURG ◽  
H.-J. HARDTKE
Keyword(s):  
Modal Analysis ◽  
Polynomial Chaos ◽  
Continuous Model ◽  
Polynomial Chaos Expansion ◽  
Uncertain Parameters ◽  
Chaos Expansion ◽  
Parameter Uncertainties ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
Key Issues

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.

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