On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects
Under consideration there is a compliance with observed data and nonlinear models of monitoring. These models are based on superposition of oscillators with free parameters. Optimal estimation of free parameters of model which enter into model both linearly and nonlinearly, we shall consider as a pr...
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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | rus |
| Опубліковано: |
Subbotin Institute of Geophysics of the NAS of Ukraine
2012
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| Онлайн доступ: | https://journals.uran.ua/geofizicheskiy/article/view/116626 |
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| Назва журналу: | Geofizicheskiy Zhurnal |
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journalsuranua-geofizicheskiy-article-1166262020-10-07T12:21:24Z On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects Mostovoy, V. S. Mostovoy, S. V. Under consideration there is a compliance with observed data and nonlinear models of monitoring. These models are based on superposition of oscillators with free parameters. Optimal estimation of free parameters of model which enter into model both linearly and nonlinearly, we shall consider as a problem of nonlinear regression. The optimality is understood in sense of a global minimum of an objective functional. The point in space of possible values of free parameters of model in which criterion has a global minimum is accepted as the optimal solution of a problem. For the chosen nonlinear mathematical models it is necessary to find out the questions connected with existence of the solution, its uniqueness, and stability of the solution depending on initial data. The last circumstance is especially important, as the algorithms constructed on the basis of these models, are concentrated on direct processing of field supervision. It means dependence on characteristics of the measuring equipment, errors of measurement and to accompanying by background noises. Separation of linear and nonlinear parameters with the purpose of calculation process optimization is offered for construction of optimal estimations model parameters. By search quasi-optimal solutions such division allows to use for the Monte-Carlo technique simulation only nonlinear parameters. Linearly entering parameters are defined by the solution of system of the linear equations. Thus, dimension of a search problem of optimal estimations is decreased on a size of a linear parameters vector dimension. Subbotin Institute of Geophysics of the NAS of Ukraine 2012-04-01 Article Article application/pdf https://journals.uran.ua/geofizicheskiy/article/view/116626 10.24028/gzh.0203-3100.v34i2.2012.116626 Geofizicheskiy Zhurnal; Vol. 34 No. 2 (2012); 140-143 Геофизический журнал; Том 34 № 2 (2012); 140-143 Геофізичний журнал; Том 34 № 2 (2012); 140-143 2524-1052 0203-3100 rus https://journals.uran.ua/geofizicheskiy/article/view/116626/110660 Copyright (c) 2020 Geofizicheskiy Zhurnal https://creativecommons.org/licenses/by/4.0 |
| institution |
Geofizicheskiy Zhurnal |
| collection |
OJS |
| language |
rus |
| format |
Article |
| author |
Mostovoy, V. S. Mostovoy, S. V. |
| spellingShingle |
Mostovoy, V. S. Mostovoy, S. V. On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects |
| author_facet |
Mostovoy, V. S. Mostovoy, S. V. |
| author_sort |
Mostovoy, V. S. |
| title |
On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects |
| title_short |
On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects |
| title_full |
On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects |
| title_fullStr |
On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects |
| title_full_unstemmed |
On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects |
| title_sort |
on correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects |
| description |
Under consideration there is a compliance with observed data and nonlinear models of monitoring. These models are based on superposition of oscillators with free parameters. Optimal estimation of free parameters of model which enter into model both linearly and nonlinearly, we shall consider as a problem of nonlinear regression. The optimality is understood in sense of a global minimum of an objective functional. The point in space of possible values of free parameters of model in which criterion has a global minimum is accepted as the optimal solution of a problem. For the chosen nonlinear mathematical models it is necessary to find out the questions connected with existence of the solution, its uniqueness, and stability of the solution depending on initial data. The last circumstance is especially important, as the algorithms constructed on the basis of these models, are concentrated on direct processing of field supervision. It means dependence on characteristics of the measuring equipment, errors of measurement and to accompanying by background noises. Separation of linear and nonlinear parameters with the purpose of calculation process optimization is offered for construction of optimal estimations model parameters. By search quasi-optimal solutions such division allows to use for the Monte-Carlo technique simulation only nonlinear parameters. Linearly entering parameters are defined by the solution of system of the linear equations. Thus, dimension of a search problem of optimal estimations is decreased on a size of a linear parameters vector dimension. |
| publisher |
Subbotin Institute of Geophysics of the NAS of Ukraine |
| publishDate |
2012 |
| url |
https://journals.uran.ua/geofizicheskiy/article/view/116626 |
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