Cumulants of Stochastic Response for Linear Systems

Abstract

The magnitudes of response cumulants are investigated for linear systems excited by stochastic inputs. This extension of the classical study of mean and covariance (i.e., first and second cumulants), provides basic information regarding the non‐normality of a response process. The dependence of the response cumulants on the parameters of the linear system is emphasized, as are approximations and order‐of‐magnitude results which reveal the nature of this dependence without numerical computation of response values. New information is provided regarding the phenomenon of a linear system having a nearly normal response to a non‐normal excitation. Conditions are determined under which a complicated stochastic excitation may be adequately approximated by a process which is delta correlated and a numerical example is given to illustrate one particular situation. Conditions are also derived under which a stationary process may adequately approximate an excitation that is nonstationary.