The standard stochastic linearization method applied to a nonlinear dynamic system is based on a mean square deviation measure to derive the "equivalent" linear parameters. Experience indicates that the resulting "equivalent" linear system may have approximately the same mean square response as the original nonlinear system. For predicting extreme response, however, this procedure is not equally suitable. In the case of strong nonlinearities in the dynamic model, application of the standard method of stochastic linearization may lead to significant overestimation of extreme responses. In the present paper are described some initial efforts to develop stochastic linearization methods applicable for prediction of extreme response levels.
The problem of estimating the response statistics of nonlinear dynamic systems has been a subject of research for several decades. Considerable progress has been made, but from a practical point of view the general results are still too weak to provide accurate estimates of exceedance probabilities for use m the design process of nonlinear structures subjected to random excitation. A number of simplified procedures have been proposed for estimating specific response quantities of nonlinear systems. In particular, the method of stochastic linearization is extensively used. The attractive feature of this type of procedure is to replace the initial nonlinear dynamic system by a linear one. The general experience indicates that the standard method of stochastic linearization leads to estimates of the response variance that is often fairly accurate. Hence, for the purposes of design, the standard method of stochastic linearization is not adequate. Since the feature of replacing nonlinear equations of motion by linear equations is very attractive, it is appropriate to ask the question whether a linearization procedure can be established such that the resulting extreme response predictions are in agreement with those of the original nonlinear dynamic system.