REVERSE ENGINEERING OF NONLINEAR SYSTEMS USING ANALYTICAL NETWORKS

Authors

  • Rovinskyi V.A.
  • Yevchuk O.V

DOI:

https://doi.org/10.31471/1993-9981-2020-2(45)-109-118

Keywords:

analytical network, genetic algorithm, neural network, electronic system

Abstract

 using their known input and output signals taken synchronously is proposed. The functioning of the proposed analytical networks is based on the use of a modified genetic algorithm and a library of blocks of constant functionality. Genotype structure and mutation algorithms are proposed for describing an analytical network. In addition, methods for modeling complex non-linear systems using the Volterra, Wiener-Hammerstein series, adaptive filters, non-linear model of an autoregressive moving average with exogenous inputs, neural networks and genetic algorithms are considered, and the main problems that arise when using these models are identified. A practical example of the possibility of using the analytical network is shown on the example of the resynthesis of a sound synthesizer. A typical diagram of such a synthesizer is described. A possible scheme of a re-synthesized system based on an analytical network that is functionally as similar as possible to desired system is considered. The possibility of automatically constructing a numerical model of the reaction of a nonlinear mechanical system to input disturbances using known input and output signals recorded synchronously is shown. The main difficulties of the resynthesis of complex systems for sound reproduction are considered - the influence of psychoacoustic phenomena on the perception of synthesis results and the need to ensure high fidelity for obtaining adequate results are shown. The structure of typical blocks of the analytical network is proposed, which should include typical conversions used in digital signal processing, arithmetic and logical operations, correlation and comparison blocks, hysteresis components, and in addition, typical possible standard blocks of a system that undergoes resynthesis.

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References

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Literature

Billings S.A. "Identification of Nonlinear Systems: A Survey". IEE Proceedings Part D 127(6), 272–285,1980

Rugh W.J. "Nonlinear System Theory – The Volterra Wiener Approach". Johns Hopkins Univer-sity Press,1981

Billings S.A. "Identification of Nonlinear Systems: A Survey". IEE Proceedings Part D 127(6), 272–285,1980

Haber R., Keviczky L "Nonlinear System Identification-Input Output Modeling Approach". Vols I & II, Kluwer,1980

M.Poluektov and A.Polar. Modelling non-linear control systems using the discrete urysohn op-erator. 2018. Submitted arXiv:1802.01700.

A.Polar. http://ezcodesample.com/urysohn/urysohn.html

M.Poluektov and A.Polar. Urysohn Adaptive Filter. 2019.

Haykin S. "Neural Networks: A Comprehensive Foundation". McMillan,1999

Warwick K, Irwin G.W., Hunt K.J. "Neural Networks for Control and Systems". Peter Pere-grinus, 1992

Lennart., Ljung (1999). System identification : theory for the user (2nd ed.). Upper Saddle River, NJ: Prentice Hall PTR. ISBN 978-0136566953. OCLC 38884169.

Schön, Thomas B.; Lindsten, Fredrik; Dahlin, Johan; Wågberg, Johan; Naesseth, Christian A.; Svensson, Andreas; Dai, Liang (2015). "Sequential Monte Carlo Methods for System Identi-fica-tion**This work was supported by the projects Learning of complex dynamical systems (Con-tract number: 637-2014-466) and Probabilistic modeling of dynamical systems (Con-tract num-ber: 621-2013-5524), both funded by the Swedish Research Council". IFAC-PapersOnLine. 48 (28): 775–786. arXiv:1503.06058. doi:10.1016/j.ifacol.2015.12.224.

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Published

2021-04-12

How to Cite

Ровінський В. А., & Євчук О. В. (2021). REVERSE ENGINEERING OF NONLINEAR SYSTEMS USING ANALYTICAL NETWORKS. METHODS AND DEVICES OF QUALITY CONTROL, (2(45). https://doi.org/10.31471/1993-9981-2020-2(45)-109-118

Issue

Section

MATHEMATICAL MODELLING FOR THE UNDESTROYED CONTROL PROBLEMS