Volterra Black-Box Models Identification Methods: Direct Collocation vs. Least Squares

Denis Sidorov (), Aleksandr Tynda, Vladislav Muratov and Eugeny Yanitsky
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Denis Sidorov: Applied Mathematics Department, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, Irkutsk 664003, Russia
Aleksandr Tynda: Higher and Applied Mathematics Department, Penza State University, Penza 440026, Russia
Vladislav Muratov: Institute of Mathematics and Information Technologies, Irkutsk State University, Irkutsk 664003, Russia
Eugeny Yanitsky: Intermediate Radio Frequency Lab, Huawei Russian Research Institute, Moscow 121096, Russia

Mathematics, 2024, vol. 12, issue 2, 1-13

Abstract: The Volterra integral-functional series is the classic approach for nonlinear black box dynamical system modeling. It is widely employed in many domains including radiophysics, aerodynamics, electronic and electrical engineering and many others. Identifying the time-varying functional parameters, also known as Volterra kernels, poses a difficulty due to the curse of dimensionality. This refers to the exponential growth in the number of model parameters as the complexity of the input-output response increases. The least squares method (LSM) is widely acknowledged as the standard approach for tackling the issue of identifying parameters. Unfortunately, the LSM suffers with many drawbacks such as the sensitivity to outliers causing biased estimation, multicollinearity, overfitting and inefficiency with large datasets. This paper presents an alternative approach based on direct estimation of the Volterra kernels using the collocation method. Two model examples are studied. It is found that the collocation method presents a promising alternative for optimization, surpassing the traditional least squares method when it comes to the Volterra kernels identification including the case when input and output signals suffer from considerable measurement errors.

Keywords: Volterra series; collocation method; kernels identification; Chebyshev polynomials; memory effects (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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