Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series
The article offers a regularization method for solving the polynomial integral Volterra equations of the first kind while solving the problem of restoration of the input signal of a nonlinear dynamic object determined by the integro-power Volterra series. The use of integro-power Volterra series mak...
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| Datum: | 2018 |
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Kamianets-Podilskyi National Ivan Ohiienko University
2018
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| Online Zugang: | http://mcm-tech.kpnu.edu.ua/article/view/140047 |
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| Назва журналу: | Mathematical and computer modelling. Series: Technical sciences |
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Mathematical and computer modelling. Series: Technical sciences| _version_ | 1856543220050165760 |
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| author | Ponedilok, Vadim Vitaliyovych |
| author_facet | Ponedilok, Vadim Vitaliyovych |
| author_sort | Ponedilok, Vadim Vitaliyovych |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-03-06T09:39:07Z |
| description | The article offers a regularization method for solving the polynomial integral Volterra equations of the first kind while solving the problem of restoration of the input signal of a nonlinear dynamic object determined by the integro-power Volterra series. The use of integro-power Volterra series makes it possible to simplify the primary nonlinear mathematical models of nonlinear dynamic objects turning them into quasi-linear ones. Polynomial Volterra equations of the first kind are solved by introducing the additional differential regularization operator. It is offered to solve the obtained integro-differential equations using quadrature algorithms by iterative methods. This approach allows makes it possible to increase the efficiency of the process of signals restoration on the input of nonlinear dynamic objects if there is noise. The efficiency of the offered algorithm is verified for the restoration of input signal of a nonlinear dynamic object given in the form of a sequential connection of linear and nonlinear parts. At the same time, the linear part is represented by an inertial joint, while the nonlinear is represented by polynomial dependence of the second kind. There are presented the results of solving of polynomial Volterra integral equations of the first kind in the presence of different noises on the input dependencies. Based on the described method, in Matlab / Simulink, there are created simulation models and software-based methods for solving inverse problems of signal restoration on the input of nonlinear dynamic objects. The results of computational experiments demonstrated that the offered regularization method for solving the polynomial Volterra integral equations of the first kind may be effectively used to restore the input signals of nonlinear dynamical systems being described by the integro-power Volterra series. |
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| format | Article |
| id | mcmtechkpnueduua-article-140047 |
| institution | Mathematical and computer modelling. Series: Technical sciences |
| language | English |
| last_indexed | 2025-07-17T10:13:43Z |
| publishDate | 2018 |
| publisher | Kamianets-Podilskyi National Ivan Ohiienko University |
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| spelling | mcmtechkpnueduua-article-1400472019-03-06T09:39:07Z Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series Ponedilok, Vadim Vitaliyovych The article offers a regularization method for solving the polynomial integral Volterra equations of the first kind while solving the problem of restoration of the input signal of a nonlinear dynamic object determined by the integro-power Volterra series. The use of integro-power Volterra series makes it possible to simplify the primary nonlinear mathematical models of nonlinear dynamic objects turning them into quasi-linear ones. Polynomial Volterra equations of the first kind are solved by introducing the additional differential regularization operator. It is offered to solve the obtained integro-differential equations using quadrature algorithms by iterative methods. This approach allows makes it possible to increase the efficiency of the process of signals restoration on the input of nonlinear dynamic objects if there is noise. The efficiency of the offered algorithm is verified for the restoration of input signal of a nonlinear dynamic object given in the form of a sequential connection of linear and nonlinear parts. At the same time, the linear part is represented by an inertial joint, while the nonlinear is represented by polynomial dependence of the second kind. There are presented the results of solving of polynomial Volterra integral equations of the first kind in the presence of different noises on the input dependencies. Based on the described method, in Matlab / Simulink, there are created simulation models and software-based methods for solving inverse problems of signal restoration on the input of nonlinear dynamic objects. The results of computational experiments demonstrated that the offered regularization method for solving the polynomial Volterra integral equations of the first kind may be effectively used to restore the input signals of nonlinear dynamical systems being described by the integro-power Volterra series. Kamianets-Podilskyi National Ivan Ohiienko University 2018-05-24 Article Article application/pdf http://mcm-tech.kpnu.edu.ua/article/view/140047 10.32626/2308-5916.2018-17.133-140 Mathematical and computer modelling. Series: Technical sciences; 2018: Mathematical and computer modelling. Series: Technical sciences. Issue 17; 133-140 Математичне та комп'ютерне моделювання. Серія: Технічні науки ; 2018: Математичне та комп'ютерне моделювання. Серія: Технічні науки. Випуск 17; 133-140 2308-5916 10.32626/2308-5916.2018-17 en http://mcm-tech.kpnu.edu.ua/article/view/140047/137087 Авторське право (c) 2021 Математичне та комп'ютерне моделювання. Серія: Технічні науки |
| spellingShingle | Ponedilok, Vadim Vitaliyovych Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series |
| title | Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series |
| title_full | Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series |
| title_fullStr | Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series |
| title_full_unstemmed | Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series |
| title_short | Regularization Method of Restoration of Input Signals of Nonlinear Dynamic Objects that Determined by Integro-Power Volterra Series |
| title_sort | regularization method of restoration of input signals of nonlinear dynamic objects that determined by integro-power volterra series |
| url | http://mcm-tech.kpnu.edu.ua/article/view/140047 |
| work_keys_str_mv | AT ponedilokvadimvitaliyovych regularizationmethodofrestorationofinputsignalsofnonlineardynamicobjectsthatdeterminedbyintegropowervolterraseries |