Kronecker Product Formulation for System Identification of Discrete Convolution Filters

The following paper illustrates a mathematical framework for identifying discrete convolution filters and applies that framework to a time varying dynamic problem. Convolution matrices, formulated using Kronecker products, allow for least means squares solution of arbitrarily structured discrete convolution models. The framework exposes the convolution structure and the filter coefficients independently in order to solve for the time varying weights of a known model, or an unknown time varying filter. Transforms are shown to apply standard discrete spectral processing methods to this architecture. The identification methods were successfully applied to identify the stiffness-like and damping-like operating regimes of a typical viscous damper in a dynamic system subjected to periodic motion. The results show that discrete time varying system identification successfully predicts measured test data and provides intuitive results showing stiffness-like behavior at low force inputs and damping-like behavior for higher force inputs.