Crossing Rate Analysis of NonGaussian Response of Linear Systems

Abstract

A method is presented for estimating mean crossing rates for the stationary response of linear systems to non-normal excitation modeled by polynomials of Gaussian processes. Information about the non-Gaussian system response is derived in terms of statistical moments that are accurately calculated from a closed system of linear algebraic equations. This information is used to construct the most unbiased response distribution using the maximum entropy principle, a consistent method of inductive inference. Mean crossing rates are then estimated by mapping a standard Gaussian process into the nonGaussian response and by using the property that the two processes have nearly equal crossing rates. The proposed method is applied to compute mean crossing rates and probability density functions for the response of a simple oscillator to the following types of excitation processes: the square of the Ornstein-Uhlenbeck process, and third degree polynomials of Gaussian processes.