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Wiener-Hermite functional representation of nonlinear stochastic systems
Abstract In this paper functionals of the vector Wiener process W(t) are defined, from the perspective of representing the response of nonlinear stochastic systems described by Itô stochastic differential equations. Wiener kernels are found in closed form for the class of bilinear systems. The general case of nonlinear, analytic systems is studied through the use of Carleman linearization process, whereby the original system is converted into a bilinear one of infinite dimension. Wiener kernels and transfer functions are found by the application of a perturbation method. The case of the Duffing oscillator is studied, and the results obtained by the present analytical technique are compared with those obtained by Gaussian closure and digital simulations.
Wiener-Hermite functional representation of nonlinear stochastic systems
Abstract In this paper functionals of the vector Wiener process W(t) are defined, from the perspective of representing the response of nonlinear stochastic systems described by Itô stochastic differential equations. Wiener kernels are found in closed form for the class of bilinear systems. The general case of nonlinear, analytic systems is studied through the use of Carleman linearization process, whereby the original system is converted into a bilinear one of infinite dimension. Wiener kernels and transfer functions are found by the application of a perturbation method. The case of the Duffing oscillator is studied, and the results obtained by the present analytical technique are compared with those obtained by Gaussian closure and digital simulations.
Wiener-Hermite functional representation of nonlinear stochastic systems
Valéry Roy, R. (author) / Spanos, Pol D. (author)
Structural Safety ; 6 ; 187-202
1989-01-01
16 pages
Article (Journal)
Electronic Resource
English
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