Efficient multidimensional regularization for Volterra series estimation

• Published in: Mechanical systems and signal processing 2018-05, Vol.104, p.896-914
• Main Authors: Birpoutsoukis, Georgios, Csurcsia, Péter Zoltán, Schoukens, Johan
• Format: Article
• Language: English
• Subjects: Cascaded water tanks benchmark; Computer simulation; Estimating techniques; Impulse response; Kernel-based regression; Mathematical models; Nonlinear systems; Parameter estimation; Regularization; System dynamics; System identification; Time domain analysis; Time invariant systems; Transient elimination; Volterra series; Water tanks
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.10.007

•Regularized nonparametric estimation method for nonlinear systems is presented.•Modeling of nonlinearities by multidimensional Volterra kernels.•Inversion-free memory-saving algorithm for large number of parameters and/or data length.•Transient removal of nonparametric model by the use of regularization is proposed.•Methods applied and verified on the nonlinear benchmark problem of the cascaded water tanks. 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.