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1

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.

2

Identyfikacja złożonego układu napędowego jako systemu Wienera

Lis J., Orłowska-Kowalska T.

Elektrotechnika i Elektronika

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2006

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T. 25, z. 2

172-176

PL

Artykuł dotyczy identyfikacji części mechanicznej napędu dwumasowego z silnikiem indukcyjnym. W procesie identyfikacji uwzględniono występowanie w układzie trudno modelowanych zjawisk nieliniowych, takich jak luzy i tarcie suche, co spowodowało, że realizowano identyfikację nieliniowego obiektu dynamicznego. W niniejszej pracy zaproponowano identyfikację według koncepcji systemów blokowo zorientowanych, przy zastosowaniu systemu Wienera. Liniowy podsystem dynamiczny układu napędowego identyfikowano parametrycznie, za pomocą metody zmiennych instrumentalnych, natomiast trudno modelowalne nieliniowości identyfikowano nieparametrycznie, przy zastosowaniu estymatora regresji jądrowej. W procesie identyfikacji zastosowano metodę odsprzęgania podsystemu liniowego i nieliniowego, wykorzystującą właściwości pobudzenia typu PRBS.

EN

The paper deals with the identification of the mechanical part of a two-mass drive system. The system nonlinearities were taken into account and thus the dynamical nonlinear system was identified. The identification approach took advantage of the block oriented systems theory. A block oriented Wiener system was used, which consists of the dynamic linear subsystem and the static nonlinear subsystem, connected in series. Both parametric and non-parametric identification algorithms were applied to solve the problem of Wiener system identification. The static nonlinearity was identified nonparametrically by means of the kernel regression estimate, while the dynamic linear subsystem was identified parametrically by means of the instrumental variables estimate. The method for decoupling the systems nonlinearities using the PRBS input was also applied to the identification procedure. Good results have been obtained.

3

Recursive Identification of Wiener Systems

Greblicki W.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 4

977-991

EN

A Wiener system, i.e. a cascade system consisting of a linear dynamic subsystem and a nonlinear memoryless subsystem is identified. The a priori information is nonparametric, i.e. neither the functional form of the nonlinear characteristic nor the order of the dynamic part are known. Both the input signal and the disturbance are Gaussian white random processes. Recursive algorithms to estimate the nonlinear characteristic are proposed and their convergence is shown. Results of numerical simulation are also given. A known algorithm recovering the impulse response of the dynamic part is presented in a recursive form.