Article

### Cover

### Title

Optimization of the core smooth coefficient in the problem of the nonparametric identification### Authors

^{}E.D. Mikhov,

^{}N.D. Ivanov

### Organization

Siberian Federal UniversityKrasnoyarsk, Russian Federation

### Abstract

The problem of modeling discrete-continuous processes is investigated. The general scheme of the investigated process is considered. The considered scheme includes input, output intermediate variables. The issue of identification in the «narrow» and «broad» sense. Analyzed Briefly. A recurrent algorithm for estimating the parameters of adaptive models based on the method of stochastic approximations. The vector of the blurring coefficients of the nucleus is an important parameter when constructing an object model using nuclear estimates. The quality of the constructed model depends on the selected vector of the blur factor. The blurring factor determines the degree of participation of the sampling elements in the evaluation. Researchers often face the task of optimizing this vector, since the vector of the kernel blur factor affects the quality of the constructed model. Algorithms for optimizing the vector of the kernel blur coefficients are considered in the article. The following algorithms for optimization are considered: the method of search, the method of a deformable polyhedron and the genetic algorithm. The root-mean-square error of the constructed model was chosen as an optimization criterion. The root-mean-square error was calculated using a sliding exam. The table in which the accuracy of the constructed model is displayed after the optimization of the vector of the kernel blur factors (for each input effect), and also after optimization of one common blur factor of the kernel, which is assigned to all input variables, is presented.### Keywords

nonparametric model, nonparametric algorithms, core smooth coefficient, optimization### References

[1] Tweedle V., Smith R. A mathematical model of Bieber Fever // Transworld Research Network, 2012, vol. 37/661, no. 2, pp. 157–177.

[2] Antonov A.V. Sistemnyj analiz [The system analysis]. Moscow, Higher School, 2004, 454 p. (In Russian)

[3] Trusov P. V. Vvedenie v matematicheskoe modelirovanie [Introduction to mathematical modeling]. Moscow, Logos, 2005, 440 p. (In Russian)

[4] Medvedev A. V. Analiz dannyh v zadache identifikacii [Analysis of data in the identification problem] // International conference «Computer-aidd data analysis and modeling», 1995, Vol. 2, pp. 201–207. (In Russian)

[5] Sovetov B. Ya., Yakovlev S. A. Modelirovanie sistem [Modeling of systems]. Moscow, Higher School, 2001, 343 p. (In Russian)

[6] Tirsina A. N. Teoriya sistem i sistemnyj analiz [Theory of systems and systems analysis]. Chelyabinsk, Znanie, 2002, 128 p. (In Russian)

[7] Medvedev A. V. Nekotorye zamechaniya k N-modelyam bezynercionnyh processov s zapazdyvaniem [Some remarks to the H-models of inertial-free processes with delay] // Bulletin of Siberian State University of Economics, 2014, no. 2 (54), pp. 24–34. (In Russian)

[8] Ruban A. I. Metody analiza dannyh [Methods of data analysis]. Krasnoyarsk, IPC KSTU, 2004, 319 p. (In Russian)

[9] Kureichik V. M, Lebedev B. K., Lebedev O.K. Poiskovaya adaptaciya: teoriya i praktika [Search adaptation: theory and practice]. Moscow, Fizmatlit, 2006, 272 p. (In Russian)

[10] Kumsawat P. A Genetic Algorithm Optimization Technique for Multiwavelet – Based Digital Audio Watermarking // EURASIP Journal on Advances in Signal Processing, 2010, vol. 1, pp.15–25.