519.87
Doi: 10.31772/2587-6066-2020-21-2-195-200
E. D. Mikhov
Siberian Federal University
79, Svobodnii Av., 660041, Krasnoyarsk, Russian Federation
In this research the issue of inertialess processes modeling is under study. The main modeling algorithm is the non-parametric recovery algorithm of the regression function. The algorithm allows to build a process model under conditions of low a priori information. This feature may be particularly important in modeling processes of large dimensions prevailing in the space industry. One important feature of the algorithm for nonparametric estimation of the regression function is that the accuracy of modeling using this algorithm highly depends on the quality of the observations sample. Due to the fact that in processes with large dimensions of input and output variable vectors observation sampling
elements are in most cases unevenly distributed, the development of modifications to improve the quality of mod-eling
is relevant.
The modification of the nonparametric dual algorithm based on piecewise approximations has been devel-oped.
According to the proposed modification, the process area is divided into sub-areas and a non-parametric esti-mate of the regression function for each of these sub-areas is recovered. The proposed modification reduces the impact of some observation sampling features, such as sparseness or voids in observation samples on the quality of the built model.
The computational experiments were carried out, during which a comparison was made between the classical algorithm of non-parametric estimation of regression function and the developed modification. As the computa-tional experiments have shown, with uniform distribution of the sample elements of observations, the developed modification does not lead to the improvement of the quality of modeling. With a substantial uneven distribution of the observations sample elements, the developed modification resulted in a 2-fold improvement in the quality of the simulation. The results suggest that the proposed modification can be used to model complex technologi-cal processes, including those in the space industry.
Keywords: identification, nonparametric estimation of the regression function, piecewise approximation.
1. Medvedev A. V., Mihov E. D., Ivanov
N. D. Identification of multidimensional technological processes with dependent
input variables. Journal of the Siberian Federal University.
Series: Mathematics and Physics. 2018, Vol. 11, No. 5, P. 649–658.
2. Kornet M. E.,
Shishkina A. V. About the identification of dynamic systems under nonparametric
uncertainty. Aspire to Science. 2018,
P. 166–170.
3. Lapko A. V.,
Lapko V. A. Multilevel nonparametric information processing systems. Krasnoyarsk :
SibGAU,
2013. 270 p. (In
Russ.)
4. Medvedev A.
V. Some remarks on the theory of non-parametric systems. Applied Methods of Statistical Analysis. 2017, P. 72–81.
5. Medvedev A.
V., Raskina A. V., Chzhan E. A., Korneeva A. A., Videnin C. A. Determination of
the order of stochastically linear dynamic systems by using non-parametric
estimation of a regression function. Journal
of Physics: Conference Series. Krasnoyarsk
Science and Technology City Hall of the Russian Union of Scientific and
Engineering Associations; Polytechnical Institute of Siberian Federal
University. Bristol, United
Kingdom. 2019, P. 1–8.
6. Reisinger C.,
Forsyth P. A. Piecewise constant policy approximations to
Hamilton–Jacobi–Bellman equations. Applied
Numerical Mathematics. 2016, Vol. 103,
P. 27–47.
7. Gaudioso M.,
Giallombardo G., Miglionico G., Bagirov A. M. Minimizing nonsmooth DC functions
via successive DC piecewise-affine approximations. Journal of Global Optimization. 2018, Vol. 71, P 37–55.
8. Liu J., Bynum
M., Castillo A., Watsonb J., Lairda C. D. A multitree approach for global
solution of ACOPF problems using piecewise outer approximations.
Computers & Chemical Engineering. 2018,
Vol. 114,
P. 145–157.
9. Medvedev
A. V., Meleh D. A., Sergeeva N. A., Chubarova O. V. [On the problem of
classifying objects by data with gaps]. Information
Technology and Mathematical Modeling (ITMM-2019). P. 146–151 (In Russ.).
10. Chzhan E. A.,
Medvedev A. V., Kukartsev V. V. Nonparametric modelling of multidimensional
technological processes with dependent variables. IOP Conference Series: Earth and Environmental Science. 2018,
P. 1–5.
11. Paul S.,
Shankar S. On estimating efficiency
effects in a stochastic frontier model. European
Journal of Operational Research. 2018, Vol. 271, Iss. 2,
P. 769–774.
12. Mikhov
E. D. [Core blur coefficient optimization in nonparametric modeling]. Vestnik SibGAU. 2015, Vol. 16, No. 2, P. 338–342 (In Russ.).
13. Medvedev A.
V., Chzhan E. A. [Modeling of multidimensional H-processes]. Information and mathematical technologies in
science and management. 2018,
No. 1 (9), P. 99–105
(In Russ.).
14. Simar L., Keilegom I.,
Zelenyuk V. Nonparametric least squares methods for stochastic frontier
models. Journal of Productivity Analysis.
2017, Vol. 47, P. 189–204.
15. Zhang C.,
Travis D. Gaps‐fill
of SLC‐off
Landsat ETM+ satellite image using a geostatistical approach. International Journal of Remote Sensing.
2007, Vol.
28, Iss. 22, P. 5103–5122.