UDK 519.87 Vestnik SibGAU. 2014, No. 3(55), P. 107–113
A. V. Medvedev [1], E. D. Mihov [2]
1Siberian State Aerospace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation 2 Siberian Federal University 79, Svobodnyi prosp., Krasnoyarsk, 660041, Russian Federation E-mail: Saor_medvedev@sibsau.ru; edmihov@mail.ru
A modeling of discrete-continuous processes with “tubular” structure in space “input – output” variables is consid-ered. Moreover general scheme of the test process, including not only the input-output variables but also intermediate is discussed. Attention is drawn to the essential factor which shows that a change of input variables carries out through various time intervals. This is due to various output variables controlled by electrical means, as a result of chemical analysis and physico-mechanical tests. In this regard the various component models for different process output are given. The question is analyzed in the identification of “narrow” and “broad” sense. Recursive algorithm provides estimates of the parameters of adaptive models based on stochastic approximation method. Modelling of processes of this class differs significantly from conventional parametric models representing the surface in the same space. When constructing students’ parametric models “tubular” processes require the use of appropriate non-parametric indicators. The recurrent algorithms estimate the parameters that take into account the relevant indicators in parametric models are also given. It may be noted that the H-pattern is more common in comparison with conventional. That is, if the test process does not have “tubular” structure, then H-model in this case, goes to the class of well-known models of free-wheeling systems. Thus, the adaptive models freewheeling processes change somewhat, unlike conventional. Some special examples of modeling “tubular” processes, from which it follows that the “tubular” processes take place in the space of fractional dimension. We present the case of functions of several variables and analyzed the situation where, over time these variables can “disappear” and “occur” again. Statistical modeling method, has been carried out numerical study of H-models with different sample sizes measuring input-output variables and different levels of noise. As a result of this study shows that the dimension of the space in which the process takes place, not only fractionally, but also changing. It turns out that the calculation of fractional dimension space can be done in different ways.
a priori information, identification, nonparametric model, nonparametric algorithms, H-model, fractional dimension space.

1. Medvedev A. V. [Some notes on H-models for non-inertis systems with a delay]. Vestnik SibGAU. 2014,
no. 2 (54), p. 24–34. (In Russ.)

2. Medvedev A. V. [Analysis of the data in the problem identification]. Computer analysis of simulation data. 1995, Vol. 2, p. 201–206. (In Russ.)

3. Medvedev A.V. [H-model for non-inertia systems with delay]. Vestnik SibGAU. 2012, no. 5 (45), p. 84–89. (In Russ.)

4. Mondelbrot B. Fraktalnaya geometriya prirody [Fractal Geometry of Nature]. Moscow – Izhevsk, Institute of Computer Science, NITS “Regular and Chaotic Dynamicsˮ Publ., 2010, 656 p.

5. Arnold V. I. Teoriya katastrof [Catastrophe
Theory]. Moscow, Nauka Publ., 1990, 128 p.

Medvedev Alexander Vasil'yevich – Doctor of Engineering Science, Professor of Siberian State Aerospace University named after academician M.F. Reshetnev. E-mail: Saor_medvedev@sibsau.ru.

Mihov Eugene Dmitriyevich – engineer, Siberian Federal University. E-mail: edmihov@mail.ru