The True Linearization Coefficients for Nonlinear Systems Under Parametric White Noise Excitations

[+] Author and Article Information
Giovanni Falsone

Dipartmento di Ingegneria Civile (DIC), Università di Messina, Salita Sperone, 31, Vill. S. Agata, 198166 Messina, Italy

J. Appl. Mech 74(1), 161-163 (Dec 02, 2004) (3 pages) doi:10.1115/1.1940665 History: Received June 20, 2003; Revised December 02, 2004

In this paper some properties of the stochastic linearization method applied to nonlinear systems excited by parametric Gaussian white noises are discussed. In particular, it is shown that the linearized quantities, obtained by the author in another paper by linearizing the coefficients of the Ito differential rule related to the original system, show the same properties found by Kozin with reference to nonlinear system excited by external white noises. The first property is that these coefficients are the true linearized quantities, in the sense that their exact values are able to give the first two statistical moments of the true response. The second property is that, in the stationary case and in the field of the parameter estimation theory, they represent the maximum likelihood estimates of the linear model quantities fitting the original nonlinear response.

Copyright © 2007 by American Society of Mechanical Engineers
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