Identification of parameters of interval nonlinear models of static systems using multidimensional optimization
| dc.citation.epage | 13 | |
| dc.citation.issue | 2 | |
| dc.citation.journalTitle | Обчислювальні проблеми електротехніки | |
| dc.citation.spage | 5 | |
| dc.contributor.affiliation | Western Ukrainian National University | |
| dc.contributor.author | Дивак, Микола | |
| dc.contributor.author | Манжула, Володимир | |
| dc.contributor.author | Дивак, Тарас | |
| dc.contributor.author | Dyvak, Mykola | |
| dc.contributor.author | Manzhula, Volodymyr | |
| dc.contributor.author | Dyvak, Taras | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-06T07:20:21Z | |
| dc.date.created | 2022-02-28 | |
| dc.date.issued | 2022-02-28 | |
| dc.description.abstract | Запропоновано підхід до параметричної ідентифікації інтервальних нелінійних моделей статичних систем на основі стандартної задачі мінімізації середньоквадратичного відхилення між значеннями модельованої характеристики статичного об’єкта та значеннями, які належать до експериментальних інтервалів. Внаслідок розширення простору параметрів нелінійних моделей за рахунок введення додаткових коефіцієнтів для узгодження прогнозованих та експериментальних значень у функцію мети отримано задачу багатовимірної оптимізації з нелінійною багатоекстремальною функцією мети. В роботі досліджено характеристики функції мети та конвергенцію її оптимізації. Виконано компаративний аналіз відомих засобів глобальної оптимізації з метою вибору оптимального методу розв’язування оптимізаційної задачі ідентифікації параметрів інтервальних нелінійних моделей статичних систем. | |
| dc.description.abstract | The article proposes an approach to parametric identification of interval nonlinear models of static systems based on the standard problem of minimizing the root mean square deviation between the values of the modeled characteristics of the static object and the values belonging to the experimental intervals. As a result of expanding the parameter space of nonlinear models by introducing additional coefficients to match the predicted and experimental values into the objective function, a multidimensional optimization problem with a nonlinear multiextremal objective function is obtained. The paper examines the characteristics of the objective function and the convergence of its optimization. | |
| dc.format.extent | 5-13 | |
| dc.format.pages | 9 | |
| dc.identifier.citation | Dyvak M. Identification of parameters of interval nonlinear models of static systems using multidimensional optimization / Mykola Dyvak, Volodymyr Manzhula, Taras Dyvak // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 12. — No 2. — P. 5–13. | |
| dc.identifier.citationen | Dyvak M. Identification of parameters of interval nonlinear models of static systems using multidimensional optimization / Mykola Dyvak, Volodymyr Manzhula, Taras Dyvak // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 12. — No 2. — P. 5–13. | |
| dc.identifier.doi | doi.org/10.23939/jcpee2022.02.005 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63933 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Обчислювальні проблеми електротехніки, 2 (12), 2022 | |
| dc.relation.ispartof | Computational Problems of Electrical Engineering, 2 (12), 2022 | |
| dc.relation.references | [1] M. P. Dyvak, Problems of mathematical modeling of static systems with interval data: monograph, T.: Econom. TNEU opinion, 2011 (in Ukrainian). | |
| dc.relation.references | [2] M. P. Dyvak, N. P. Porplitsia, and T. M. Dyvak, Identification of discrete models of systems with distributed parameters based on the analysis of interval data [Text]: monograph, Ternopil: Economic Opinion TNEU, 2018 (in Ukrainian). | |
| dc.relation.references | [3] R. E. Moore, Interval analysis, Englewood Cliffs: Prentice Hall, 1966. | |
| dc.relation.references | [4] R. E. Moore, Methods and applications of interval analysis, Philadelphia: SIAM, 1979. | |
| dc.relation.references | [5] R. E. Moore, Reliability in computing: the role of interval methods in scientific computing, Elsevier, 2014. | |
| dc.relation.references | [6] M. P. Dyvak, A. V. Pukas, N. P. Porplitsia, and A. M. Melnyk, Applied problems of structural and parametric identification of interval models of complex objects: monograph, Ternopil: University Opinion, 2021 (in Ukrainian). | |
| dc.relation.references | [7] N. P. Dyvak and V. I. Manzhula, “Structural Identification of Interval Models of the Static Systems”, Journal of Automation and Information Sciences, vol. 40, no. 4, pp. 49–61, 2008. | |
| dc.relation.references | [8] M. Dyvak, V. Manzhula, A. Melnyk, and A. Pukas, “Method of structural identification of nonlinear interval models of static objects”, Information technologies and computer engineering, vol. 54, no. 2, p. 103–114, June 2022. (in Ukrainian) | |
| dc.relation.references | [9] M. Dyvak, “Parameters Identification Method of Interval Discrete Dynamic Models of Air Pollution Based on Artificial Bee Colony Algorithm”, in Proc. 10th International Conference on Advanced Computer Information Technologies (ACIT), pp. 130–135, Deggendorf, Germany, 13–15 May 2020. | |
| dc.relation.references | [10] N. Porplytsya, M. Dyvak, I. Spivak, and I. Voytyuk, “Mathematical and algorithmic foundations for implementation of the method for structure identification of interval difference operator based on functioning of bee colony”, in Proc. 13th International Conference on the Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), pp. 196–199, Lviv, Ukraine, February 24–27, 2015. | |
| dc.relation.references | [11] N.P. Porplitsia and M.P. Dyvak, “Implementation of the method of structural identification of interval difference operators based on the bee colony behavior algorithm”, Bulletin of Mykhailo Ostrogradsky National University of Kremenchug, vol. 93, no. 4, pp. 34–40, 2015 (in Ukrainian). | |
| dc.relation.references | [12] V. Manzhula, “Genetic algorithm of structural identification of interval models of static systems”, in Proc. Third Workshop IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005, pp. 524–526, Sofia, Bulgaria, 2005. | |
| dc.relation.references | [13] A. Petrowski and S. Ben-Hamida, Evolutionary Algorithms (Computer Engineering: Metaheuristics Book 9), 1st ed. Wiley-ISTE: Hoboken, NJ, USA, 2017. | |
| dc.relation.references | [14] I. T. Christou, W. L. Darrell, K. De Long, and W. Martin, Evolutionary Algorithms”, SpringerVerlag: New York, NY, USA, 2021. | |
| dc.relation.references | [15] A. Kumar, G. Negi, S. Pant, M. Ram, and S. C. Dimri, “Availability-Cost Optimization of Butter Oil Processing System by Using Nature Inspired Optimization Algorithms”, Reliab. Theory Appl., SI 2, 188–200, 2021. | |
| dc.relation.references | [16] S. Katoch, S. S. Chauhan, V. Kumar, “A review on genetic algorithms: Past, present, and future”, Multimed. Tools Appl., 80, 8091–8126, 2021 [CrossRef] [PubMed]. | |
| dc.relation.references | [17] A. Ivakhnenko and G. Ivakhnenko, “The Review of Problems Solvable by Algorithms of the Group Method of Data Handling (GMDH)”, Pattern Recognition and Image Analysis, vol. 5, no. 4, pp. 527–535, 1995. | |
| dc.relation.references | [18] A. Slowik, Swarm Intelligence Algorithms: Modification and Applications, 1st ed.; CRC Press: Boca Raton, FL, USA, 2020. | |
| dc.relation.references | [19] A. Abraham, R.K. Jatoth, and A. Rajasekhar, “Hybrid differential artificial bee colony algorithm”, J. Comput. Theor. Nanosci., no. 9, pp. 249–257, 2012 [CrossRef]. | |
| dc.relation.references | [20] S. Alshattnawi, L. Afifi, A.M. Shatnawi, and M. M. Barhoush, “Utilizing Genetic Algorithm Mykola Dyvak, Volodymyr Manzhula, Taras Dyvak 12 and Artificial Bee Colony Algorithm to Extend the WSN Lifetime”, Int. J. Comput., no. 21, pp. 25–31, 2022 [CrossRef]. | |
| dc.relation.references | [21] M. Dyvak, A. Pukas, A. Melnyk, I. Voytyuk, S. Valchyshyn, and I. Romanets, “Software Architecture for Modeling the Interval Static and Dynamic Objects”, in Proc. 11th International Conference on Advanced Computer Information Technologies (ACIT'2021), pp. 572–575, Deggendorf, Germany, 2021. | |
| dc.relation.references | [22] B. Akay, D. Karaboga, B. Gorkemli, and E. Kaya, “A survey on the artificial bee colony algorithm variants for binary, integer and mixed integer programming problems”, Appl. Soft Comput., 106, 107351, 2021 [CrossRef]. | |
| dc.relation.references | [23] Y. Kedrin, M. Dyvak, A. Pukas, I. Voytyuk, Y. Maslyiak, and O. Papa, “Features of artificial bee colony based algorithm realization for parametric identification method of the interval discrete dynamic models”, in Proc. 10th International Conference on Advanced Computer Information Technologies (ACIT), pp. 239–245, Deggendorf Germany, 2020. | |
| dc.relation.references | [24] B. Akay and D. Karaboga, “A survey on the applications of artificial bee colony in signal, image, and video processing”, Signal Image Video Process, no. 9, pp. 967–990, 2015. [CrossRef] | |
| dc.relation.references | [25] M. Dyvak, N. Porplytsya, Y. Maslyiak, and N. Kasatkina, “Modified artificial bee colony algorithm for structure identification of models of objects with distributed parameters and control”, in Proc. 14th International Conference The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), pp. 50–54, Lviv, 2017. | |
| dc.relation.references | [26] A. Beck, Introduction to nonlinear optimization: Theory, algorithms, and applications with MATLAB, Society for Industrial and Applied Mathematics, 2014. | |
| dc.relation.references | [27] M. Dyvak, V. Manzhula, and O. Kozak, “New method tolerance estimation of the parameters set of interval model based on saturated block of ISLAE”, in Proc. IX-th International Conference CADSM'2007, pp. 376–379, Lviv–Polyana, 2007. | |
| dc.relation.references | [28] M. Dyvak, A. Pukas, I. Oliynyk, and A. Melnyk, “Selection of the “Saturated” Block from Interval System of Linear Algebraic Equations for Recurrent Laryngeal Nerve Identification”, in Proc. IEEE Second International Conference on Data Stream Mining & Processing (DSMP), pp. 444–448, Lviv, Ukraine, August 21–25, 2018. | |
| dc.relation.references | [29] M. Dyvak, N. Porplytsya, I. Borivets, and M. Shynkaryk, “Improving the computational implementation of the parametric identification method for interval discrete dynamic models”, in Proc. 12th International Conference on International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT), pp. 533–536, Lviv, Ukraine, September 5–8, 2017. | |
| dc.relation.references | [30] M. Dyvak, I. Spivak, A. Melnyk, V. Manzhula, T. Dyvak, A. Rot, and M. Hernes, “Modeling Based on the Analysis of Interval Data of Atmospheric Air Pollution Processes with Nitrogen Dioxide due to the Spread of Vehicle Exhaust Gases”, Sustainability, vol. 15, no. 3, p. 2163, 2023. https://doi.org/10.3390/su15032163. | |
| dc.relation.references | [31] V. Manzhula and M. Dyvak, “Interval nonlinear model of information signal amplitude distribution in the problem of detection and localization of the recurrent laryngeal nerve during surgical operations”, Opt-el. inf-energy tech., vol. 43, issue 1, pp. 65–75, December 2022 (in Ukrainian). | |
| dc.relation.references | [32] “Global Optimization Toolbox”, www.mathworks.com/help/gads/index.html | |
| dc.relation.references | [33] R.W. Garden and A.P Engelbrecht, “Analysis and classification of optimization benchmark functions and benchmark suites,” in Proc. IEEE CEC, pp. 1641–1649, 2014. | |
| dc.relation.references | [34] A. Forsgren, P. Gill, M. Wright, “Interior methods for nonlinear optimization”, SIAM review, 44.4, pp. 525–597, 2002. | |
| dc.relation.referencesen | [1] M. P. Dyvak, Problems of mathematical modeling of static systems with interval data: monograph, T., Econom. TNEU opinion, 2011 (in Ukrainian). | |
| dc.relation.referencesen | [2] M. P. Dyvak, N. P. Porplitsia, and T. M. Dyvak, Identification of discrete models of systems with distributed parameters based on the analysis of interval data [Text]: monograph, Ternopil: Economic Opinion TNEU, 2018 (in Ukrainian). | |
| dc.relation.referencesen | [3] R. E. Moore, Interval analysis, Englewood Cliffs: Prentice Hall, 1966. | |
| dc.relation.referencesen | [4] R. E. Moore, Methods and applications of interval analysis, Philadelphia: SIAM, 1979. | |
| dc.relation.referencesen | [5] R. E. Moore, Reliability in computing: the role of interval methods in scientific computing, Elsevier, 2014. | |
| dc.relation.referencesen | [6] M. P. Dyvak, A. V. Pukas, N. P. Porplitsia, and A. M. Melnyk, Applied problems of structural and parametric identification of interval models of complex objects: monograph, Ternopil: University Opinion, 2021 (in Ukrainian). | |
| dc.relation.referencesen | [7] N. P. Dyvak and V. I. Manzhula, "Structural Identification of Interval Models of the Static Systems", Journal of Automation and Information Sciences, vol. 40, no. 4, pp. 49–61, 2008. | |
| dc.relation.referencesen | [8] M. Dyvak, V. Manzhula, A. Melnyk, and A. Pukas, "Method of structural identification of nonlinear interval models of static objects", Information technologies and computer engineering, vol. 54, no. 2, p. 103–114, June 2022. (in Ukrainian) | |
| dc.relation.referencesen | [9] M. Dyvak, "Parameters Identification Method of Interval Discrete Dynamic Models of Air Pollution Based on Artificial Bee Colony Algorithm", in Proc. 10th International Conference on Advanced Computer Information Technologies (ACIT), pp. 130–135, Deggendorf, Germany, 13–15 May 2020. | |
| dc.relation.referencesen | [10] N. Porplytsya, M. Dyvak, I. Spivak, and I. Voytyuk, "Mathematical and algorithmic foundations for implementation of the method for structure identification of interval difference operator based on functioning of bee colony", in Proc. 13th International Conference on the Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), pp. 196–199, Lviv, Ukraine, February 24–27, 2015. | |
| dc.relation.referencesen | [11] N.P. Porplitsia and M.P. Dyvak, "Implementation of the method of structural identification of interval difference operators based on the bee colony behavior algorithm", Bulletin of Mykhailo Ostrogradsky National University of Kremenchug, vol. 93, no. 4, pp. 34–40, 2015 (in Ukrainian). | |
| dc.relation.referencesen | [12] V. Manzhula, "Genetic algorithm of structural identification of interval models of static systems", in Proc. Third Workshop IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005, pp. 524–526, Sofia, Bulgaria, 2005. | |
| dc.relation.referencesen | [13] A. Petrowski and S. Ben-Hamida, Evolutionary Algorithms (Computer Engineering: Metaheuristics Book 9), 1st ed. Wiley-ISTE: Hoboken, NJ, USA, 2017. | |
| dc.relation.referencesen | [14] I. T. Christou, W. L. Darrell, K. De Long, and W. Martin, Evolutionary Algorithms", SpringerVerlag: New York, NY, USA, 2021. | |
| dc.relation.referencesen | [15] A. Kumar, G. Negi, S. Pant, M. Ram, and S. C. Dimri, "Availability-Cost Optimization of Butter Oil Processing System by Using Nature Inspired Optimization Algorithms", Reliab. Theory Appl., SI 2, 188–200, 2021. | |
| dc.relation.referencesen | [16] S. Katoch, S. S. Chauhan, V. Kumar, "A review on genetic algorithms: Past, present, and future", Multimed. Tools Appl., 80, 8091–8126, 2021 [CrossRef] [PubMed]. | |
| dc.relation.referencesen | [17] A. Ivakhnenko and G. Ivakhnenko, "The Review of Problems Solvable by Algorithms of the Group Method of Data Handling (GMDH)", Pattern Recognition and Image Analysis, vol. 5, no. 4, pp. 527–535, 1995. | |
| dc.relation.referencesen | [18] A. Slowik, Swarm Intelligence Algorithms: Modification and Applications, 1st ed.; CRC Press: Boca Raton, FL, USA, 2020. | |
| dc.relation.referencesen | [19] A. Abraham, R.K. Jatoth, and A. Rajasekhar, "Hybrid differential artificial bee colony algorithm", J. Comput. Theor. Nanosci., no. 9, pp. 249–257, 2012 [CrossRef]. | |
| dc.relation.referencesen | [20] S. Alshattnawi, L. Afifi, A.M. Shatnawi, and M. M. Barhoush, "Utilizing Genetic Algorithm Mykola Dyvak, Volodymyr Manzhula, Taras Dyvak 12 and Artificial Bee Colony Algorithm to Extend the WSN Lifetime", Int. J. Comput., no. 21, pp. 25–31, 2022 [CrossRef]. | |
| dc.relation.referencesen | [21] M. Dyvak, A. Pukas, A. Melnyk, I. Voytyuk, S. Valchyshyn, and I. Romanets, "Software Architecture for Modeling the Interval Static and Dynamic Objects", in Proc. 11th International Conference on Advanced Computer Information Technologies (ACIT'2021), pp. 572–575, Deggendorf, Germany, 2021. | |
| dc.relation.referencesen | [22] B. Akay, D. Karaboga, B. Gorkemli, and E. Kaya, "A survey on the artificial bee colony algorithm variants for binary, integer and mixed integer programming problems", Appl. Soft Comput., 106, 107351, 2021 [CrossRef]. | |
| dc.relation.referencesen | [23] Y. Kedrin, M. Dyvak, A. Pukas, I. Voytyuk, Y. Maslyiak, and O. Papa, "Features of artificial bee colony based algorithm realization for parametric identification method of the interval discrete dynamic models", in Proc. 10th International Conference on Advanced Computer Information Technologies (ACIT), pp. 239–245, Deggendorf Germany, 2020. | |
| dc.relation.referencesen | [24] B. Akay and D. Karaboga, "A survey on the applications of artificial bee colony in signal, image, and video processing", Signal Image Video Process, no. 9, pp. 967–990, 2015. [CrossRef] | |
| dc.relation.referencesen | [25] M. Dyvak, N. Porplytsya, Y. Maslyiak, and N. Kasatkina, "Modified artificial bee colony algorithm for structure identification of models of objects with distributed parameters and control", in Proc. 14th International Conference The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), pp. 50–54, Lviv, 2017. | |
| dc.relation.referencesen | [26] A. Beck, Introduction to nonlinear optimization: Theory, algorithms, and applications with MATLAB, Society for Industrial and Applied Mathematics, 2014. | |
| dc.relation.referencesen | [27] M. Dyvak, V. Manzhula, and O. Kozak, "New method tolerance estimation of the parameters set of interval model based on saturated block of ISLAE", in Proc. IX-th International Conference CADSM'2007, pp. 376–379, Lviv–Polyana, 2007. | |
| dc.relation.referencesen | [28] M. Dyvak, A. Pukas, I. Oliynyk, and A. Melnyk, "Selection of the "Saturated" Block from Interval System of Linear Algebraic Equations for Recurrent Laryngeal Nerve Identification", in Proc. IEEE Second International Conference on Data Stream Mining & Processing (DSMP), pp. 444–448, Lviv, Ukraine, August 21–25, 2018. | |
| dc.relation.referencesen | [29] M. Dyvak, N. Porplytsya, I. Borivets, and M. Shynkaryk, "Improving the computational implementation of the parametric identification method for interval discrete dynamic models", in Proc. 12th International Conference on International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT), pp. 533–536, Lviv, Ukraine, September 5–8, 2017. | |
| dc.relation.referencesen | [30] M. Dyvak, I. Spivak, A. Melnyk, V. Manzhula, T. Dyvak, A. Rot, and M. Hernes, "Modeling Based on the Analysis of Interval Data of Atmospheric Air Pollution Processes with Nitrogen Dioxide due to the Spread of Vehicle Exhaust Gases", Sustainability, vol. 15, no. 3, p. 2163, 2023. https://doi.org/10.3390/su15032163. | |
| dc.relation.referencesen | [31] V. Manzhula and M. Dyvak, "Interval nonlinear model of information signal amplitude distribution in the problem of detection and localization of the recurrent laryngeal nerve during surgical operations", Opt-el. inf-energy tech., vol. 43, issue 1, pp. 65–75, December 2022 (in Ukrainian). | |
| dc.relation.referencesen | [32] "Global Optimization Toolbox", www.mathworks.com/help/gads/index.html | |
| dc.relation.referencesen | [33] R.W. Garden and A.P Engelbrecht, "Analysis and classification of optimization benchmark functions and benchmark suites," in Proc. IEEE CEC, pp. 1641–1649, 2014. | |
| dc.relation.referencesen | [34] A. Forsgren, P. Gill, M. Wright, "Interior methods for nonlinear optimization", SIAM review, 44.4, pp. 525–597, 2002. | |
| dc.relation.uri | https://doi.org/10.3390/su15032163 | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2022 | |
| dc.subject | interval analysis | |
| dc.subject | interval nonlinear model | |
| dc.subject | static system | |
| dc.subject | parametric identification | |
| dc.subject | multidimensional optimization | |
| dc.subject | objective function | |
| dc.subject | convergence | |
| dc.title | Identification of parameters of interval nonlinear models of static systems using multidimensional optimization | |
| dc.title.alternative | Ідентифікація параметрів інтервальних нелінійних моделей статичних систем із застосуванням багатовимірної оптимізації | |
| dc.type | Article |
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