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1

Bandwidth selection for kernel generalized regression neural networks in identification of hammerstein systems

Lv Jiaqing, Pawlak Mirosław

Journal of Artificial Intelligence and Soft Computing Research

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2021

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Vol. 11, No. 3

181--194

EN

This paper addresses the issue of data-driven smoothing parameter (bandwidth) selection in the context of nonparametric system identification of dynamic systems. In particular, we examine the identification problem of the block-oriented Hammerstein cascade system. A class of kernel-type Generalized Regression Neural Networks (GRNN) is employed as the identification algorithm. The statistical accuracy of the kernel GRNN estimate is critically influenced by the choice of the bandwidth. Given the need of data-driven bandwidth specification we propose several automatic selection methods that are compared by means of simulation studies. Our experiments reveal that the method referred to as the partitioned cross-validation algorithm can be recommended as the practical procedure for the bandwidth choice for the kernel GRNN estimate in terms of its statistical accuracy and implementation aspects.

2

Nonparametric instrumental variables for identification of block-oriented systems

Mzyk G.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 3

521--537

EN

A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.

3

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

Śliwiński P., Hasiewicz Z., Wachel P.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 3

507--520

EN

A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewise-Lipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output data are presented and discussed to illustrate the applicability of the routine.

4

On-line wavelet estimation of Hammerstein system nonlinearity

Śliwiński P.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 3

513-523

EN

A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlinearities and the rate of this convergence are both established.

5

Generalized kernel regression estimate for the identification of Hammerstein systems

Mzyk G.

International Journal of Applied Mathematics and Computer Science

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2007

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Vol. 17, no 2

189-197

EN

A modified version of the classical kernel nonparametric identification algorithm for nonlinearity recovering in a Hammerstein system under the existence of random noise is proposed. The assumptions imposed on the unknown characteristic are weak. The generalized kernel method proposed in the paper provides more accurate results in comparison with the classical kernel nonparametric estimate, regardless of the number of measurements. The convergence in probability of the proposed estimate to the unknown characteristic is proved and the question of the convergence rate is discussed. Illustrative simulation examples are included.