{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T01:44:53Z","timestamp":1772502293647,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T00:00:00Z","timestamp":1690761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"College of Engineering, American University of Sharjah, Sharjah, UAE"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This study presents hybrid particle swarm optimization with quasi-Newton (HPSO-QN), a hybrid optimization method for accurately identifying mechanical parameters in two-mass model (2MM) systems. These systems are commonly used to model and control high-performance electric drive systems with elastic joints, which are prevalent in modern industrial production. The proposed method combines the global exploration capabilities of particle swarm optimization (PSO) with the local exploitation abilities of the quasi-Newton (QN) method to precisely estimate the motor and load inertias, shaft stiffness, and friction coefficients of the 2MM system. By integrating these two optimization techniques, the HPSO-QN method exhibits superior accuracy and performance compared to standard PSO algorithms. Experimental validation using a 2MM system demonstrates the effectiveness of the proposed method in accurately identifying and improving the mechanical parameters of these complex systems. The HPSO-QN method offers significant implications for enhancing the modeling, performance, and stability of 2MM systems and can be extended to other systems with flexible shafts and couplings. This study contributes to the development of accurate and effective parameter identification methods for complex systems, emphasizing the crucial role of precise parameter estimation in achieving optimal control performance and stability.<\/jats:p>","DOI":"10.3390\/a16080371","type":"journal-article","created":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T10:00:15Z","timestamp":1690797615000},"page":"371","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Identification of Mechanical Parameters in Flexible Drive Systems Using Hybrid Particle Swarm Optimization Based on the Quasi-Newton Method"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6887-0972","authenticated-orcid":false,"given":"Ishaq","family":"Hafez","sequence":"first","affiliation":[{"name":"Mechatronics Graduate Program, College of Engineering, American University of Sharjah, Sharjah 26666, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5040-6947","authenticated-orcid":false,"given":"Rached","family":"Dhaouadi","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, American University of Sharjah, Sharjah 26666, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"212","DOI":"10.20965\/jrm.2023.p0212","article-title":"Identification of Shaft Stiffness and Inertias in Flexible Drive Systems","volume":"35","author":"Dhaouadi","year":"2023","journal-title":"J. Robot. Mechatron."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hafez, I., and Dhaouadi, R. (2022, January 17\u201320). Application of Particle Swarm Optimization for the Identification of Two-Mass Electric Drive Systems. Proceedings of the 2022 8th International Conference on Control, Decision and Information Technologies (CoDIT), Istanbul, Turkey.","DOI":"10.1109\/CoDIT55151.2022.9804056"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hafez, I., and Dhaouadi, R. (2021, January 27\u201328). Parameter Identification of DC Motor Drive Systems using Particle Swarm Optimization. Proceedings of the 2021 International Conference on Engineering and Emerging Technologies (ICEET), Istanbul, Turkey.","DOI":"10.1109\/ICEET53442.2021.9659664"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1177\/0142331218765614","article-title":"Mechanical parameter identification of two-mass drive system based on variable forgetting factor recursive least squares method","volume":"41","author":"Ke","year":"2019","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"92","DOI":"10.18201\/ijisae.2019252787","article-title":"Neural Network Based Control of a Two-Mass Drive System","volume":"7","author":"Korkmaz","year":"2019","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Saarakkala, S.E., Leppinen, T., Hinkkanen, M., and Luomi, J. (2012, January 25\u201327). Parameter estimation of two-mass mechanical loads in electric drives. Proceedings of the 2012 12th IEEE International Workshop on Advanced Motion Control (AMC), Sarajevo, Bosnia and Herzegovina.","DOI":"10.1109\/AMC.2012.6197104"},{"key":"ref_7","unstructured":"Dhaouadi, R., and Kubo, K. (1996, January 18\u201321). Transfer function and parameters identification of a motor drive system using adaptive filtering. Proceedings of the 4th IEEE International Workshop on Advanced Motion Control\u2014AMC \u201996-MIE, Mie, Japan."},{"key":"ref_8","unstructured":"Sadovoy, O.V., Nazarova, O.S., Bondarenko, V.I., Pirozhok, A.V., Hutsol, T.D., Nurek, T., and Glowacki, S. (2020). Modeling and Research of Electromechanical Systems of Cold Rolling Mills, Traicon."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"053127","DOI":"10.1063\/1.4934581","article-title":"Modeling and control of variable speed wind turbine using laboratory simulator","volume":"7","author":"Bajpai","year":"2015","journal-title":"J. Renew. Sustain. Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0967-0661(02)00114-4","article-title":"Closed-loop identification of an industrial robot containing flexibilities","volume":"11","author":"Gunnarsson","year":"2003","journal-title":"Control Eng. Pract."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1109\/TIA.2005.844383","article-title":"Evaluation of torsional oscillations in paper machine sections","volume":"41","author":"Valenzuela","year":"2005","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_12","unstructured":"Ryu, H.M., Kim, S.J., Sul, S.K., Kwon, T.S., Kim, K.S., Shim, Y.S., and Seok, K.R. (2002, January 2\u20135). Dynamic load simulator for high-speed elevator system. Proceedings of the Power Conversion Conference\u2014Osaka 2002 (Cat. No. 02TH8579), Osaka, Japan."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4633","DOI":"10.1109\/TPEL.2020.3024914","article-title":"An Overview of Artificial Intelligence Applications for Power Electronics","volume":"36","author":"Zhao","year":"2021","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"41246","DOI":"10.1109\/ACCESS.2021.3064360","article-title":"Deep Learning for Fault Diagnostics in Bearings, Insulators, PV Panels, Power Lines, and Electric Vehicle Applications\u2014The State-of-the-Art Approaches","volume":"9","author":"Sundaram","year":"2021","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mukhamediev, R.I., Popova, Y., Kuchin, Y., Zaitseva, E., Kalimoldayev, A., Symagulov, A., Levashenko, V., Abdoldina, F., Gopejenko, V., and Yakunin, K. (2022). Review of Artificial Intelligence and Machine Learning Technologies: Classification, Restrictions, Opportunities and Challenges. Mathematics, 10.","DOI":"10.3390\/math10152552"},{"key":"ref_16","first-page":"1173603","article-title":"Reconstruct fingerprint images using deep learning and sparse autoencoder algorithms","volume":"Volume 11736","author":"Kehtarnavaz","year":"2021","journal-title":"Real-Time Image Processing and Deep Learning 2021"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Venkatesh, G.S., Steven Gray, W., and Duffaut Espinosa, L.A. (2019, January 11\u201313). Combining Learning and Model Based Multivariable Control. Proceedings of the 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France.","DOI":"10.1109\/CDC40024.2019.9028944"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"637","DOI":"10.20965\/jaciii.2013.p0637","article-title":"Nonlinear Friction Estimation in Elastic Drive Systems Using a Dynamic Neural Network-Based Observer","volume":"17","author":"Jafari","year":"2013","journal-title":"J. Adv. Comput. Intell. Intell. Inform."},{"key":"ref_19","unstructured":"Pham, M., Gautier, M., and Poignet, P. (2002, January 11\u201315). Accelerometer based identification of mechanical systems. Proceedings of the 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292), Washington, DC, USA."},{"key":"ref_20","unstructured":"Kara, T., and Eker, I. (2003, January 25). Experimental nonlinear identification of a two mass system. Proceedings of the 2003 IEEE Conference on Control Applications, Istanbul, Turkey."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"\u0141uczak, D., and Nowopolski, K. (2014, January 3\u20135). Identification of multi-mass mechanical systems in electrical drives. Proceedings of the 16th International Conference on Mechatronics\u2014Mechatronika 2014, Brno, Czech Republic.","DOI":"10.1109\/MECHATRONIKA.2014.7018271"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Petrea, R.A.B., and Oboe, R. (2022, January 11\u201315). A DOB-based Parameter Identification method for Series Elastic Actuators without Load-Side Encoder. Proceedings of the 2022 IEEE\/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Sapporo, Japan.","DOI":"10.1109\/AIM52237.2022.9863413"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1109\/TIE.2007.909753","article-title":"Application of the Welch-Method for the Identification of Two- and Three-Mass-Systems","volume":"55","author":"Villwock","year":"2008","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Nowopolski, K., and Wicher, B. (2017, January 11\u201314). Parametric identification of electrical drive with complex mechanical structure utilizing Particle Swarm Optimization method. Proceedings of the 2017 19th European Conference on Power Electronics and Applications (EPE\u201917 ECCE Europe), Warsaw, Poland.","DOI":"10.23919\/EPE17ECCEEurope.2017.8099375"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"157","DOI":"10.3390\/make1010010","article-title":"Particle Swarm Optimization: A Survey of Historical and Recent Developments with Hybridization Perspectives","volume":"1","author":"Sengupta","year":"2019","journal-title":"Mach. Learn. Knowl. Extr."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Li, G., Wang, T., Chen, Q., Shao, P., Xiong, N., and Vasilakos, A. (2022). A Survey on Particle Swarm Optimization for Association Rule Mining. Electronics, 11.","DOI":"10.3390\/electronics11193044"},{"key":"ref_27","unstructured":"Robinson, J., Sinton, S., and Rahmat-Samii, Y. (2002, January 16\u201321). Particle swarm, genetic algorithm, and their hybrids: Optimization of a profiled corrugated horn antenna. Proceedings of the IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No. 02CH37313), San Antonio, TX, USA."},{"key":"ref_28","unstructured":"Shi, X., Lu, Y., Zhou, C., Lee, H., Lin, W., and Liang, Y. (2003, January 8\u201312). Hybrid evolutionary algorithms based on PSO and GA. Proceedings of the 2003 Congress on Evolutionary Computation, Canberra, ACT, Australia."},{"key":"ref_29","unstructured":"Yang, B., Chen, Y., and Zhao, Z. (June, January 30). A Hybrid Evolutionary Algorithm by Combination of PSO and GA for Unconstrained and Constrained Optimization Problems. Proceedings of the 2007 IEEE International Conference on Control and Automation, Guangzhou, China."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Valdez, F., Melin, P., and Castillo, O. (2009, January 20\u201324). Evolutionary method combining particle swarm optimization and genetic algorithms using fuzzy logic for decision making. Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, Jeju, Republic of Korea.","DOI":"10.1109\/FUZZY.2009.5277165"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.jocs.2017.07.009","article-title":"A hybrid optimizer based on firefly algorithm and particle swarm optimization algorithm","volume":"26","author":"Xia","year":"2018","journal-title":"J. Comput. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Huang, D.S., Zhang, X.P., and Huang, G.B. (2005). Advances in Intelligent Computing, Springer.","DOI":"10.1007\/11538059"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Singh, A., Sharma, A., Rajput, S., Bose, A., and Hu, X. (2022). An Investigation on Hybrid Particle Swarm Optimization Algorithms for Parameter Optimization of PV Cells. Electronics, 11.","DOI":"10.3390\/electronics11060909"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s10845-020-01559-0","article-title":"Estimation of tool wear and optimization of cutting parameters based on novel ANFIS-PSO method toward intelligent machining","volume":"32","author":"Xu","year":"2021","journal-title":"J. Intell. Manuf."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"dos Santos Coelho, L., and Mariani, V.C. (2006, January 8\u201311). Particle Swarm Optimization with Quasi-Newton Local Search for Solving Economic Dispatch Problem. Proceedings of the 2006 IEEE International Conference on Systems, Man and Cybernetics, Taipei, Taiwan.","DOI":"10.1109\/ICSMC.2006.384593"},{"key":"ref_36","unstructured":"Wang, Y.J., Zhang, J.S., and Zhang, Y.F. (2005, January 18\u201321). A fast hybrid algorithm for global optimization. Proceedings of the 2005 International Conference on Machine Learning and Cybernetics, Guangzhou, China."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1109\/28.245715","article-title":"Two-degree-of-freedom robust speed controller for high-performance rolling mill drives","volume":"29","author":"Dhaouadi","year":"1993","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1109\/TEC.2010.2090155","article-title":"Nonlinear Control of a Variable-Speed Wind Turbine Using a Two-Mass Model","volume":"26","author":"Boukhezzar","year":"2011","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Kabzi\u0144ski, J., and Mosio\u0142ek, P. (2021). Integrated, Multi-Approach, Adaptive Control of Two-Mass Drive with Nonlinear Damping and Stiffness. Energies, 14.","DOI":"10.3390\/en14175475"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1186\/s41601-022-00257-8","article-title":"Drive-train torsional vibration suppression of large scale PMSG-based WECS","volume":"7","author":"Zhou","year":"2022","journal-title":"Prot. Control Mod. Power Syst."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Montavon, G., Orr, G.B., and M\u00fcller, K.R. (2012). Neural Networks: Tricks of the Trade: Second Edition, Springer.","DOI":"10.1007\/978-3-642-35289-8"},{"key":"ref_42","unstructured":"Nocedal, J., and Wright, S.J. (2006). Numerical Optimization, Springer. [2nd ed.]."},{"key":"ref_43","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_44","unstructured":"Kennedy, J. (2006). Handbook of Nature-Inspired and Innovative Computing, Springer."},{"key":"ref_45","unstructured":"Shi, Y., and Eberhart, R. (1998, January 4\u20139). A modified particle swarm optimizer. Proceedings of the 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence (Cat. No. 98TH8360), Anchorage, AK, USA."},{"key":"ref_46","unstructured":"Eberhart, S.Y. (2001, January 27\u201330). Particle swarm optimization: Developments, applications and resources. Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No. 01TH8546), Seoul, Republic of Korea."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s10898-007-9149-x","article-title":"A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm","volume":"39","author":"Karaboga","year":"2007","journal-title":"J. Glob. Optim."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/EVCO_r_00180","article-title":"Particle Swarm Optimization for Single Objective Continuous Space Problems: A Review","volume":"25","author":"Bonyadi","year":"2017","journal-title":"Evol. Comput."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Yang, X.S., and Deb, S. (2009, January 9\u201311). Cuckoo Search via L\u00e9vy flights. Proceedings of the 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), Coimbatore, India.","DOI":"10.1109\/NABIC.2009.5393690"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"10031","DOI":"10.1109\/ACCESS.2022.3142859","article-title":"Particle Swarm Optimization: A Comprehensive Survey","volume":"10","author":"Shami","year":"2022","journal-title":"IEEE Access"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1016\/j.cor.2011.09.026","article-title":"Multiobjective cuckoo search for design optimization","volume":"40","author":"Yang","year":"2013","journal-title":"Comput. Oper. Res."},{"key":"ref_52","unstructured":"Shi, Y., and Eberhart, R. (1999, January 6\u20139). Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), Washington, DC, USA."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","article-title":"The particle swarm\u2014Explosion, stability, and convergence in a multidimensional complex space","volume":"6","author":"Clerc","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_54","unstructured":"Nocedal, J., and Wright, S.J. (2006). Numerical Optimization, Springer International Publishing."},{"key":"ref_55","unstructured":"Nocedal, J., and Wright, S.J. (2006). Numerical Optimization, Springer International Publishing."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Arora, J. (2004). Introduction to Optimum Design, Elsevier.","DOI":"10.1016\/B978-012064155-0\/50012-4"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Zhao, S.Z., Liang, J.J., Suganthan, P.N., and Tasgetiren, M.F. (2008, January 1\u20136). Dynamic multi-swarm particle swarm optimizer with local search for Large Scale Global Optimization. Proceedings of the 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), Hong Kong, China.","DOI":"10.1109\/CEC.2008.4631320"},{"key":"ref_58","unstructured":"MathWorks Inc (2023). MATLAB, MathWorks Inc."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Arora, J.S. (2004). Introduction to Optimum Design, Academic Press. [2nd ed.].","DOI":"10.1016\/B978-012064155-0\/50012-4"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Tan, Y., Shi, Y., Buarque, F., Gelbukh, A., Das, S., and Engelbrecht, A. (2015). Advances in Swarm and Computational Intelligence, Springer International Publishing.","DOI":"10.1007\/978-3-319-20472-7"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.asoc.2011.08.037","article-title":"A new gradient based particle swarm optimization algorithm for accurate computation of global minimum","volume":"12","author":"Noel","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1109\/19.863938","article-title":"A measurement procedure for viscous and coulomb friction","volume":"49","author":"Kelly","year":"2000","journal-title":"IEEE Trans. Instrum. Meas."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/8\/371\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:23:17Z","timestamp":1760127797000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/8\/371"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,31]]},"references-count":62,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["a16080371"],"URL":"https:\/\/doi.org\/10.3390\/a16080371","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,31]]}}}