Efficient Multidimensional Regularization for Volterra Series Estimation
| Autor: | Joannes Schoukens, Georgios Birpoutsoukis, Péter Zoltán Csurcsia |
|---|---|
| Přispěvatelé: | Electricity, Faculty of Engineering, Engineering Technology, Thermodynamics and Fluid Mechanics Group |
| Rok vydání: | 2018 |
| Předmět: |
Signal processing
0209 industrial biotechnology Finite impulse response Cascaded water tanks benchmark Volterra series Aerospace Engineering 02 engineering and technology Systems and Control (eess.SY) Regularization (mathematics) LTI system theory 020901 industrial engineering & automation Control theory 0202 electrical engineering electronic engineering information engineering FOS: Electrical engineering electronic engineering information engineering Applied mathematics Time domain Impulse response Mathematics Civil and Structural Engineering Kernel-based regression Nonlinear system identification Mechanical Engineering 020208 electrical & electronic engineering Nonparametric statistics Computer Science Applications regularization Transient elimination Control and Systems Engineering Computer Science - Systems and Control |
| DOI: | 10.48550/arxiv.1804.10026 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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