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In this work, the Wiener-Hermite Expansion (WHE) is used in solving nonlinear differential equations with stochastic excitations. The generation of the equivalent set of deterministic integro-differential equations is described. A numerical Picard's successive algorithm is suggested to solve the resulting system. The suggested algorithm is applied on the 1D diffusion equation and the results are compared with the WHEP (WHE with perturbation) technique. The current work shows that the WHE solutions are the limit of the WHEP solutions with infinite number of corrections. The suggested algorithms are shown to be efficient in estimating the stochastic response of the nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper the uncertainty quantification of a 1-D beam deflection subjected to stochastic excitation, stochastic material property and mixed stochastic parameters is considered. A stochastic finite-volume solver based on the polynomial chaos expansion is developed and used to quantify the deflection in all cases. Monte Carlo simulations accelerated by a RBF neural network were used to verify the results. The RBF neural-network is trained with the dominant eigenpairs of the covariance kernel to reduce the dimensionality of the neural network. The mean and variance of the beam maximum deflection is quantified, compared and verified in all cases. [ABSTRACT FROM AUTHOR]