Response probability estimation for randomly excited quasi-linear systems using a neural network approach

A quasi-linear system is referred to as a system linear in properties and subjected to multiplicative random excitations appearing also in the linear terms. It is known that exact solutions for the stationary moments can be obtained analytically for such a quasi-linear system if the excitations are Gaussian white noises. However, the exact response probability, which is non-Gaussian, is not obtainable analytically. In this paper, a neural network approach is proposed to evaluate the stationary response probability for quasi-linear systems under both additive and multiplicative excitations of Gaussian white noises based on the obtained exact statistical moments. Numerical examples show that the procedure yields accurate results if an appropriate form is assumed for the probability density function. The accuracy of the results is substantiated by comparing them with those obtained from Monte Carlo simulations.