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.
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January 2007
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The True Linearization Coefficients for Nonlinear Systems Under Parametric White Noise Excitations
Giovanni Falsone
Giovanni Falsone
Dipartmento di Ingegneria Civile (DIC),
Università di Messina
, Salita Sperone, 31, Vill. S. Agata, 198166 Messina, Italy
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Giovanni Falsone
Dipartmento di Ingegneria Civile (DIC),
Università di Messina
, Salita Sperone, 31, Vill. S. Agata, 198166 Messina, ItalyJ. Appl. Mech. Jan 2007, 74(1): 161-163 (3 pages)
Published Online: December 2, 2004
Article history
Received:
June 20, 2003
Revised:
December 2, 2004
Citation
Falsone, G. (December 2, 2004). "The True Linearization Coefficients for Nonlinear Systems Under Parametric White Noise Excitations." ASME. J. Appl. Mech. January 2007; 74(1): 161–163. https://doi.org/10.1115/1.1940665
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