FIR Model Identification: Achieving Parsimony through Kernel Compression with Wavelets

Although finite impulse response (FIR) models are nonparsimonious, they are frequently used in model predictive control (MPC) systems because they can fit arbitrarily complex stable linear dynamics. However, identification of FIR models from experimental data may result in data-overfitting and high modeling uncertainty. To overcome this, FIR models may be determined by (a) regularization-based least squares, and (b) indirectly after prior identification of other parametric models such as ARX. In both cases, some prior knowledge about the model is essentially assumed to be known. ARX models, although parsimonious in terms of the number of identified parameters, perform poorly for bad choices of model structure and order. In this paper we propose a methodology for the identification of parsimonious FIR models. In this way, most advantages of the FIR structure are retained, without its disadvantages. The idea relies in the effective use of some prior information about the model, through wavelet-based signal compression. The proposed methodology is compared with other FIR identification methodologies, on the basis of the closeness of the identified FIR to the true FIR, steady state gain estimation, and analysis of the prediction residuals on a cross validation set of fresh data. Simulation studies on a single-input-single-output (SISO) process show that the proposed methodology performs very well in all tests considered. Certain industrial practices are shown to be special cases of the proposed formalism.