The method of statistical linearization for nonlinear stochastic vibrations. (English) Zbl 0663.73054

Kozin, F.

Nonlinear stochastic dynamic engineering systems, Proc. IUTAM Symp., Innsbruck/Igls/Austria 1987, 45-56 (1988).

[For the entire collection see Zbl 0658.00017.]
We discuss certain questions related to the method of statistical linearization as an approximation to the response of nonlinear systems. We discuss its second moment properties, its relationship to parameter estimation for linear systems as well as possible connections with recursive estimators. Finally, we show by example that for systems with randomly varying coefficients statistical linearization will yield sample properties that differ significantly from the sample solution properties of the original nonlinear system.

MSC:

74H50	Random vibrations in dynamical problems in solid mechanics
70Q05	Control of mechanical systems
93E12	Identification in stochastic control theory
70K40	Forced motions for nonlinear problems in mechanics

Keywords:

second moment properties; parameter estimation for linear systems; recursive estimators; randomly varying coefficients