Nonparametric Volterra Series Estimate of the Cascaded Water Tanks Using Multidimensional Regularization

This paper presents an efficient nonparametric time domain nonlinear system identification method applied to the measurement benchmark data of the cascaded water tanks. In this work a method to estimate efficiently finite Volterra kernels without the need of long records is presented. This work is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. Due to the limited number of available data samples, the highest considered Volterra order is limited. In the paper the results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series are compared and studied. In each case, the transients are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Using the proposed methodologies, the nonparametric Volterra models provide a very good data-fit, and their performance is comparable with the white-box (physical) models.