Application of heuristic methods to identification of the parameters of discrete-continuous models

• Autorzy: Cekus Dawid , Kwiatoń Paweł , Šofer Michal , Šofer Pavel

Identyfikatory

DOI

10.24425/bpasts.2022.140150

• Języki publikacji: EN

Abstrakty

EN

The article presents the process of identifying discrete-continuous models with the use of heuristic algorithms. A stepped cantilever beam was used as an example of a discrete-continuous model. The theoretical model was developed based on the formalism of Lagrange multipliers and the Timoshenko theory. Based on experimental research, the theoretical model was validated and the optimization problem was formulated. Optimizations were made for two algorithms: genetic (GA) and particle swarm (PSO). The minimization of the relative error of the obtained experimental and numerical results was used as the objective function. The performed process of identifying the theoretical model can be used to determine the eigenfrequencies of models without the need to conduct experimental tests. The presented methodology regarding the parameter identification of the beams with the variable cross-sectional area (according to the Timosheno theory) with additional discrete components allows us to solve similar problems without the need to exit complex patterns.

Słowa kluczowe

EN

discrete-continuous model; experimental modal analysis; optimalization; identification; vibrations

PL

model dyskretno-ciągły; eksperymentalna analiza modalna; optymalizacja; identyfikacja; wibracje

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2022
• Tom: Vol. 70, nr 1
• Strony: art. no. e140150
• Opis fizyczny: Bibliogr. 31 poz., rys., tab.

Twórcy

autor

Cekus Dawid

• Department of Mechanics and Machine Design Fundamentals, Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, 42-201 Częstochowa, Poland

• https://orcid.org/0000-0002-5551-1153

autor

Kwiatoń Paweł

• Department of Mechanics and Machine Design Fundamentals, Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, 42-201 Częstochowa, Poland

• https://orcid.org/0000-0002-0067-0384

autor

Šofer Michal

• Department of Applied Mechanics, Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, 17. listopadu 15/2127, 708 33 Ostrava-Poruba, Czech Republic

• https://orcid.org/0000-0002-9253-5760

autor

Šofer Pavel

• Department of Control Systems and Instrumentation, Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, 17. listopadu 15/2127, 708 33 Ostrava-Poruba, Czech Republic

• https://orcid.org/0000-0003-0182-1487

Bibliografia

• [1] D. Cekus, B. Posiadała, and P. Warys, “Integration of modeling in SolidWorks and Matlab/Simulink environments,” Arch. Mech. Eng., vol. 61, no. 1, pp. 57–74, 2014, doi: 10.2478/meceng-2014-0003.
• [2] K. Kuli ́nski and J. Przybylski, “Stability and vibrations control of a stepped beam using piezoelectric actuation,” MATEC Web Conf., vol. 157, p. 08004, 2018, doi: 10.1051/matecconf/201815708004.
• [3] S.A. Moezi, E. Zakeri, A. Zare, and M. Nedaei, “On the application of modified cuckoo optimization algorithm to the crack detection problem of cantilever Euler–Bernoulli beam,” Comput. Struct., vol. 157, pp. 42–50, 2015, doi: 10.1016/j.compstruc.2015.05.008.
• [4] P.K. Jena and D.R. Parhi, “A modified particle swarm optimization technique for crack detection in cantilever beams,” Arabian J. Sci Eng., vol. 40, no. 11, pp. 3263–3272, 2015, doi: 10.1007/s13369-015-1661-6.
• [5] X.-L. Li, R. Serra, and O. Julien, “Effects of the Particle Swarm Optimization parameters for structural dynamic monitoring of cantilever beam,” in Surveillance, Vishno and AVE conferences. Lyon, France: INSA-Lyon, Université de Lyon, 2019. Available: https://hal.archives-ouvertes.fr/hal-02188562.
• [6] S. Das, S. Mondal, and S. Guchhait, “Particle swarm optimization-based characterization technique of nonproportional viscous damping parameter of a cantilever beam,” J. Vib. Control, p. 107754632110105, 2021, doi: 10.1177/10775463211010526.
• [7] J. Zolfaghari, “Optimization of dynamic response of cantilever beam by genetic algorithm,” in Nonlinear Approaches in Engineering Applications. Springer International Publishing, 2019, pp. 403–448, doi: 10.1007/978-3-030-18963-1_10.
• [8] M.A. Wahab, I. Belaidi, T. Khatir, A. Hamrani, Y.-L. Zhou, and M.A. Wahab, “Multiple damage detection in composite beams using particle swarm optimization and genetic algorithm,” Mechanics, vol. 23, no. 4, 2017, doi: 10.5755/j01.mech.23.4.15254.
• [9] Z. Xia, K. Mao, S. Wei, X. Wang, Y. Fang, and S. Yang, “Application of genetic algorithm-support vector regression model to predict damping of cantilever beam with particle damper,” J. Low Freq. Noise Vibr. Act. Control, vol. 36, no. 2, pp. 138–147, 2017, doi: 10.1177/0263092317711987.
• [10] M. Friswell and J. Mottershead, Finite Element Model Updating in Structural Dynamics, Springer, Dordrecht, 1995.
• [11] S. Garus and W. Sochacki, “Structure optimization of quasi one-dimensional acoustic filters with the use of a genetic algorithm,” Wave Motion, vol. 98, p. 102645, 2020, doi: 10.1016/j.wavemoti.2020.102645.
• [12] S. Mirjalili, “Genetic algorithm,” in Studies in Computational Intelligence. Springer, Cham, 2018, pp. 43–55, doi: 10.1007/978-3-319-93025-1_4.
• [13] W. Sochacki, J. Garus, J. Szmidla, M. Nabiałek, K. Błoch, P. Kwiatoń, B. Jeż, K. Jeż, and S. Garus, “Designing two-band mechanical wave filters using genetic algorithm,” Acta Phys. Pol. A, vol. 139, no. 5, pp. 479–482, May 2021, doi: 10.12693/aphyspola.139.479.
• [14] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95 – International Conference on Neural Networks. IEEE, 1995, doi: 10.1109/icnn.1995.488968.
• [15] D. Skrobek and D. Cekus, “Optimization of the operation of the anthropomorphic manipulator in a three-dimensional working space,” Eng. Optim., vol. 51, no. 11, pp. 1997–2010, 2019, doi: 10.1080/0305215x.2018.1564919.
• [16] P. Dziwi ́nski, Ł. Bartczuk, and J. Paszkowski, “A new auto adaptive fuzzy hybrid particle swarm optimization and genetic algorithm,” J. Artif. Intell. Soft Comput. Res., vol. 10, no. 2, pp. 95–111, Mar. 2020, doi: 10.2478/jaiscr-2020-0007.
• [17] S. Timoshenko, “On the transverse vibrations of bars of uniform cross section,” Philos. Mag., vol. 43, no. 253, pp. 125–131, Jan. 1922, doi: 10.1080/14786442208633855.
• [18] W. Sochacki, “The dynamic stability of a stepped cantilever beam with attachments,” J. Vibroeng., vol. 15, no. 1, pp. 280–290, 2013.
• [19] M.H. Korayem and A. Nahavandi, “Analyzing the effect of the forces exerted on cantilever probe tip of atomic force microscope with tapering-shaped geometry and double piezoelectric extended layers in the air and liquid environments,” J. Sound Vib., vol. 386, pp. 251–264, 2017, doi: 10.1016/j.jsv.2016. 08.031.
• [20] B. Posiadała, “Use of lagrange multiplier formalism to analyze free vibrations of combined dynamical systems,” J. Sound Vib., vol. 176, no. 4, pp. 563–572, Sep. 1994, doi: 10.1006/jsvi.1994.1396.
• [21] R. Pytlarz, “Experimental modal analysis of the beam with the help of non-contact vibration measurement method,” Master’s thesis, Czestochowa University of Technology, Częstochowa, 2008.
• [22] Z. Abo-Hammour, O.A. Arqub, O. Alsmadi, S. Momani, and A. Alsaedi, “An optimization algorithm for solving systems of singular boundary value problems,” Appl. Math. Inf. Sci., vol. 8, no. 6, pp. 2809–2821, 2014, doi: 10.12785/amis/080617.
• [23] I. Rejer, “Classic genetic algorithm vs. genetic algorithm with aggressive mutation for feature selection for a brain-computer interface,” Przegl ̨ad Elektrotechniczny, vol. 1, no. 2, pp. 100–104, 2015, doi: 10.15199/48.2015.02.24.
• [24] M. Nikoo, M. Hadzima-Nyarko, E.K. Nyarko, and M. Nikoo, “Determining the natural frequency of cantilever beams using ANN and heuristic search,” Appl. Artif. Intell, vol. 32, no. 3, pp. 309–334, Mar. 2018, doi: 10.1080/08839514.2018.1448003.
• [25] A. Mayer, “A genetic algorithm with randomly shifted gray codes and local optimizations based on quadratic approximations of the fitness,” in Proceedings of the Genetic and Evolutionary Computation Conference Companion. ACM, 2017, doi: 10.1145/3067695.3075968.
• [26] B. Ufnalski and L. Grzesiak, “Particle swarm optimization of artificial-neural-network-based on-line trained speed controller for battery electric vehicle,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 60, no. 3, pp. 661–667, 2012, doi: 10.2478/v10175-012-0059-9.
• [27] M. Szczepanik and T. Burczyński, “Swarm optimization of stiffeners locations in 2-d structures,” Bull. Pol. Acad. Sci. Tech. Sci.,, vol. 60, no. 2, pp. 241–246, 2012, doi: 10.2478/v10175-012-0032-7.
• [28] J.C. Bansal, “Particle swarm optimization,” in Studies in Computational Intelligence. Springer, Cham, 2018, pp. 11–23, doi: 10.1007/978-3-319-91341-4_2.
• [29] D. Cekus and P. Warys, “Identification of parameters of discretecontinuous models,” in AIP Conference Proceedings. AIP Publishing LLC, 2015, doi: 10.1063/1.4913110.
• [30] D. Cekus and D. Skrobek, “The influence of inertia weight on the particle swarm optimization algorithm,” J. Appl. Math. Comput. Mech., vol. 17, no. 4, pp. 5–11, Dec. 2018, doi: 10.17512/jamcm.2018.4.01.
• [31] A.R. Jordehi and J. Jasni, “Parameter selection in particle swarm optimisation: a survey,” J. Exp. Theor. Artif. Intell., vol. 25, no. 4, pp. 527–542, Dec. 2013, doi: 10.1080/0952813x.2013.782348.