Direct Frequency Domain Identification of Time Varying Systems

The following paper presents a frequency domain method to perform time varying linear identification of deterministic non-linear systems and provides an empirical example to illustrate the application of the method for a nonlinear structural dynamic system. The proposed method employs the Kronecker product form of convolution matrices to enable the least mean squares solution of arbitrarily structured cross frequency coupled responses. The mathematical framework allows for solution of different parts of the time varying frequency response depending upon information known about the system. Definitions of time varying coherence, cross and autospectra are derived, and are shown to be equivalent to conventional definitions when simplified to the linear time invariant form. These methods are applied to a physical beam damper system with observed nonlinear behavior tested at the University of Connecticut in order to identify an accurate time varying frequency domain model of the nonlinear system. The new model shows improved coherence relative to a standard linear time invariant model.