Efficient Multidimensional Regularization for Volterra Series Estimation

TL;DR

This paper introduces an efficient nonparametric method for estimating truncated Volterra series models in nonlinear system identification, reducing memory needs and removing transient effects, with demonstrated effectiveness on a water tanks benchmark.

Contribution

It extends regularization techniques to Volterra series estimation, providing a practical gradient-based method and a novel transient removal approach for nonlinear system modeling.

Findings

Models accurately capture system dynamics.

Performance comparable to white-box models.

Effective transient removal improves model quality.

Abstract

This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. To avoid the excessive memory needs in case of long measurements or large number of estimated parameters, a practical gradient-based estimation method is also provided, leading to the same numerical results as the proposed Volterra estimation method. Moreover, the transient effects in the simulated output are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Combining the proposed methodologies, the nonparametric Volterra models of the cascaded water tanks benchmark are presented in this paper. The results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series with and without transient removal are compared and studied. It is clear that the obtained models capture the system dynamics when tested on a validation dataset, and their performance is comparable with the white-box (physical) models.