Identification of nonlinear systems through statistical analysis of the dynamic response

In this paper an extension to the method for the identification of mechanical parameters of nonlinear systems proposed in Breccolotti and Materazzi (2007) for MDoF systems is presented. It can be used for damage identification purposes when damage modifies the linear characteristics of the investigated structure. It is based on the following two main features: the solution of the Fokker-Planck equation that describes the response probabilistic properties of the system when it is excited by external Gaussian loads; and a model updating technique that minimizes the differences between the response of the actual system and that of a parametric system used to identify the unknown parameters. Numerical analysis, that simulate virtual experimental tests, are used in the paper to show the capabilities of the method and to analyse the conditions required for its application.