A spectral projection approach for fuzzy uncertainty propagation in structural dynamics

Adhikari, S. (2012) A spectral projection approach for fuzzy uncertainty propagation in structural dynamics. In: 25th International Conference on Noise and Vibration engineering, ISMA2012 in conjunction with the 4th International Conference on Uncertainty in Structural Dynamics, USD 2012, Leuven. Belgium, 17-19 Sept 2012, pp. 4745-4759. ISBN 9781622768257

Abstract

Propagation of uncertainties in complex engineering dynamical systems is receiving increasing attention. When uncertainties are modelled by fuzzy variables, the equations of motion of discretised dynamical systems can be expressed by coupled ordinary differential equations with fuzzy coefficients. This paper proposes a Polynomial Chaos type of spectral approach based on orthogonal function expansion. A fuzzy variable is represented as a set of interval variables via the membership function. The intervals variables are further transformed into the standard interval [-1,1]. Smooth nonlinear functions of standard interval variables are projected in the basis of Legendre polynomials by exploiting its orthogonal properties over the interval [-1,1]. The coefficients associated with the basis functions are obtained by a Galerkin type of error minimisation. The method is first illustrated using scalar functions of multiple fuzzy variables. Later the method is proposed for linear dynamic problems where the technique is extended to vector valued functions with multiple fuzzy variables. The response of such systems can be expressed in the complete basis of multivariate Legendre polynomials. The coefficients, obtained by Galerkin type of error minimisation, can be calculated from the solution of an extended set of linear algebraic equations. A numerical example of axial vibration of a rod with fuzzy axial stiffness is considered to illustrate the proposed methods. The results are compared with direct numerical simulation results to investigate the accuracy of the proposed method.

• Item Type: Conference Proceedings
• Additional Information: Volume 6, 2012, pages 4745-4759.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Adhikari, Professor Sondipon
• Authors: Adhikari, S.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Conference on Noise and Vibration Engineering 2012, ISMA 2012, including USD 2012: International Conference on Uncertainty in Structure Dynamics
• ISBN: 9781622768257

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