Abstract
Generalizations of the Gram—Charlier series of type A and C are used to approximate the probability density function (p.d.f.) of stochastic nonlinear dynamical systems under parametrical or external white noise excitation. By means of a Galerkin—technique for the Fokker—Planck equation, the expansion coefficients are obtained from a system of linear equations and a system of equations with a quadratic nonlinearity respectively. The coefficients of these systems of equations are expectations that depend on the system functions. If the system functions are at least piecewise polynomials, integral formulas can be used to evaluate the expectations. The approximations of the p.d.f. are compared and critical remarks concerning applicability are made.
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© 1998 Birkhäuser Boston
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Sobiechowski, C. (1998). Generalized Gram—Charlier Series A and C Approximation for Nonlinear Mechanical Systems. In: Kahle, W., von Collani, E., Franz, J., Jensen, U. (eds) Advances in Stochastic Models for Reliability, Quality and Safety. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2234-7_17
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DOI: https://doi.org/10.1007/978-1-4612-2234-7_17
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7466-7
Online ISBN: 978-1-4612-2234-7
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