Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes

Abstract

This paper concerns the statistical characterization of the non-Gaussian response of non-linear systems excited by polynomial forms of filtered Gaussian processes. The non-Gaussianity requires the computation of moments of any order. The problem is solved profiting from both the stochastic equivalent linearization (EL), and the moment equation approach of Itô’s stochastic differential calculus through a procedure divided into two parts. The first step requires the linearization of the system, while retaining the non-linear excitation; the response statistical moments are calculated exactly, and constitute a first estimate of the moments of the actual non-linear system. In the second step, the moment equations of the non-linear system are considered, which form an infinite hierarchy so that a closure method is necessary. The moment equations are closed by giving the values previously obtained for the linearized system to the hierarchical moments present in them. Performing iterations the solution is improved. The method is applicable to both scalar and vector dynamical systems, and the filter from which stems the primary excitation may be of an order whichever provided that it is linear. The comparisons of the results with Monte Carlo simulation give good or acceptable matching.