System Identification Techniques for Mixed Responses Using the Proper Orthogonal Decomposition

The Proper Orthogonal Decomposition (POD) is a method that may be applied to linear and nonlinear structures for extracting important information from a measured structural response. The POD is often applied for model reduction of linear and nonlinear systems and recently in system identification. Although methods have previously been developed to identify reduced-order predictive models for simple linear and nonlinear structures using the POD of a measured structural response, the application of these methods has been limited to cases where the excitation is either an initial condition or an applied load but not a combination of the two. This paper presents a method for combining the POD-based identification techniques for strictly free or strictly forced systems to identify predictive models for a system when only mixed response data are available, i.e. response data resulting from initial conditions and loads that are applied together. This method extends the applicability of POD-based identification techniques to operational data acquired outside of a controlled laboratory setting. The method is applied to finite element models of simple linear and nonlinear beams and is shown to identify an accurate predictive model for each beam when compared with results obtained by the finite element method.