Consider ing the structural analysis problem of systems properties with Bouc- Wen hysteresis (BWH) , various approaches are proposed for the identification of BWH parameters. The applied methods and algorithms are based on the design of parametric models and consider a priori information and the results of data analysis. Structural changes in the BWH form a priori. Methods for the Bouc-Wen model (BWM) identification and its structure esti mation are not considered under uncertainty. The study ’ s purpose is the analysis the structural problems of the Bouc-Wen hysteresis identification. The analysis base is the application of geometric frameworks (GF) under uncertainty. Methods for adaptive estimation parameters and structural of BWM were proposed. The adaptive system stability is proved based on vector Lyapunov functions. An approach is proposed to estimate the identifiability and structure of the system with BWH. The method for estimating the identifiability degree based on the analysis of GF is considered. BWM modifications are proposed to guarantee the system ’s stability and simplify its description.
Krasnosel’skii, M.A. and Pokrovskii, A.V. (1989) Systems with Hysteresis. Springer-Verlag, Berlin, Heidelberg.
Bouc, R. (1967) Forced Vibrations of a Mechanical System with Hysteresis. Proceedings of the 4th Conference on Nonlinear Oscillations, Prague, 5-9 September 1967, 315-321.
Wen, Y.K. (1976) Method for Random Vibration of Hysteretic Systems. Journal of the Engineering Mechanics Division, 102, 246-263.
Ismail, M. (2009) The Hysteresis Bouc-Wen Model, a Survey. Archives of Computational Methods in Engineering, 16, 161-188. https://doi.org/10.1007/s11831-009-9031-8
Ismail, M. and Rodellar, J. (2007) Systems with Hysteresis: Analysis, Identification and Control Using the Bouc-Wen Model. Wiley & Sons Ltd., Hoboken.
Smyth, A.W., Masri, S.F., Kosmatopoulos, E.B., Chassiakos, A.G. and Caughey, T.K. (2007) Development of Adaptive Modeling Techniques for Non-Linear Hysteretic Systems. International Journal of Non-Linear Mechanics, 37, 1435-1451. https://doi.org/10.1016/S0020-7462(02)00031-8
Leenen, R. (2002) The Modelling and Identification of a Hysteretic System: The Wire as a Nonlinear Shock Vibration Isolator. (DCT Reported; 2002.072). Technische Universiteit Eindhoven, Eindhoven.
Chassiakos, G., Masri, S.F., Smyth, A.W. and Caughy, T.K. (1998) Online Identification of Hysteretic Systems. Journal of Applied Mechanics, 65, 194-203. https://doi.org/10.1115/1.2789025
Smith, A.W., Masri, S.F., Chassiakos, A.G. and Caughey, T.K. (1999) Online Parametric Identification of MDOF Nonlinear Hysteretic Systems, Journal of Engineering Mechanics, 125, 133-142. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:2(133)
Ioannou, P.A. and Sun, J. (1996) Robust Adaptive Control. Prentice Hall, New York.
Lin, J.W., Betti, R., Smyth, A.W. and Longman, R.W. (2001) On-Line Identification of Nonlinear Hysteretic Structural Systems Using a Variable Trace Approach. Earthquake Engineering and Structural Dynamics, 30, 1279-1303. https://doi.org/10.1002/eqe.63
Shih, M., Sung, W. and Go, C. (2004) Investigation of Newly Developed Added Damping and Stiffness Device with Low Yield Strength Steel. Journal of Zhejiang University—Science A: Applied Physics & Engineering, 5, 326-334.
Karabutov, N.N. (2019) Identification of System with Bouc-Wen Hysteresis. EPJ Web of Conferences, 224, Article No. 1003. https://doi.org/10.1051/epjconf/201922401003 https://www.epj-conferences.org/articles/epjconf/abs/2019/29/epjconf_mnps2018_01003/epjconf_mnps2018_01003.html
Charalampakis, A.E. and Dimou, C.K. (2010) Identification of Bouc-Wen Hysteretic Systems Using Particle Swarm Optimization. Computers and Structures, 88, 1197-1205. https://doi.org/10.1016/j.compstruc.2010.06.009
Ikhouane, F. and Rodellar, J. (2007) Systems with Hysteresis: Analysis, Identification and Control Using the Bouc-Wen Model. John Wiley & Sons Ltd., Koboken.
Talatahari, S., Kaveh, A. and Rahbari, N.M. (2012) Parameter Identification of Bouc-Wen Model for MR Fluid Dampers Using Adaptive Charged System Search Optimization. Journal of Mechanical Science and Technology, 26, 2523-2534. https://doi.org/10.1007/s12206-012-0625-y
Nguyen, X.B., Komatsuzaki, T., Hoa, T. and Truong, H. (2021) Adaptive Parameter Identification of Bouc-Wen Hysteresis Model for a Vibration System Using Magnetorheological Elastomer. International Journal of Mechanical Sciences, 213, Article ID: 106848. https://doi.org/10.1016/j.ijmecsci.2021.106848
Danilin, A.N., Kuznetsova, E.L., Kurdumov, N.N., Rabinsky, L.N. and Tarasov, S.S. (2016) A Modified Bouc-Wen Model to Describe the Hysteresis of Non-Stationary Processes. PNRPU Mechanics Bulletin, 4, 187-199.
Ikhouane, F., Hurtado, J.E. and Rodellar, J. (2007) Variation of the Hysteresis Loop with the Bouc-Wen Model Parameters. Nonlinear Dynamics, 48, 361-380. https://doi.org/10.1007/s11071-006-9091-3
Zhang, J. and Sato, T. (2006) Non-Linear Hysteretic Structural Identification by Utilizing On-Line Support Vector Regression. Structural Engineering/Earthquake Engineering, 23, 45s-55s. https://doi.org/10.2208/jsceseee.23.45s
Li, S.J., Suzuki, Y. and Noori, M. (2004) Identification of Hysteretic Systems with Slip Using Bootstrap Filter. Mech. Systems and Signal Processing, 18, 781-795. https://doi.org/10.1016/j.ymssp.2003.08.001
Karabutov, N.N. (2020) Structural Approach to Identification of Nonlinear Manufacturing Systems. In: Mellal, M.A., Ed., Book Manufacturing Systems Recent Progress and Future Directions, Nova Science Publishers, Hauppauge, 121-153.
Karabutov, N. (2018) Structural-Parametrical Design Method of Adaptive Observers for Nonlinear Systems. International Journal of Intelligent Systems and Applications, 10, 1-16. https://doi.org/10.5815/ijisa.2018.02.01
Karabutov, N. (2020) Parameters Adaptive Identification of Bouc-Wen Hysteresis. IFAC-Papersonline, 53, 3971-3976. https://doi.org/10.1016/j.ifacol.2020.12.1339
Gantmakher, F.R. (1959) Theory of Matrices. Chelsea Pub. Co., New York.
Karabutov, N. (2015) Structural Methods of Estimation Lyapunov Exponents Linear Dynamic System. International Journal of Intelligent Systems and Applications, 7, 1-11. https://doi.org/10.5815/ijisa.2015.10.01
Chang, C.-M., Strano, S. and Terzo, M. (2016) Modelling of Hysteresis in Vibration Control Systems by Means of the Bouc-Wen Model. Shock and Vibration, 2016, Article ID: 3424191. https://doi.org/10.1155/2016/3424191
Fujii, F., Tatebatake, K., Morita, K. and Shiinoki, T. (2018) A Bouc-Wen Model-Based Compensation of the Frequency-Dependent Hysteresis of a Piezoelectric Actuator Exhibiting Odd Harmonic Oscillation. Actuators, 7, Article No. 37. https://doi.org/10.3390/act7030037
Kwok, N., Ha, Q., Nguyen, M., Li, J. and Samali, B. (2007) Bouc-Wen Model Parameter Identification for a MR Fluid Damper Using Computationally Efficient GA. ISA Transactions, 46, 167-179. https://doi.org/10.1016/j.isatra.2006.08.005
Dong, H., Han, Q. and Du, X. (2019) Application of an Extended Bouc-Wen Model for Hysteretic Behaviour of the RC Structure with SCEBs. Structural Engineering and Mechanics, 71, 683-697.
Karabutov, N.N. (2020) Structural Analysis and Modifications of System with Bouc-Wen Hysteresis. Bulletin of the Voronezh State Technical University, 16, 57-64.
Van Pelt, T.H. and Bernstein, D.S. (2001) Nonlinear System Identification Using Hammerstein and Non-Linear Feedback Models with Piecewise Linear Static Maps. International Journal Control, 74, 1807-1823. https://doi.org/10.1080/00207170110089798
Lin, R. and Ewins, D.J. (1995) Location of Localized Stiffness Non-Linearity Using Measured Modal Data. Mechanical Systems and Signal Processing, 9, 329-339. https://doi.org/10.1006/mssp.1995.0027
Trendafilova, I., Lenaerts, V., Kerschen, G., Golinval, J.C. and Van Brussel, H. (2000) Detection, Localization and Identification of Nonlinearities in Structural Dynamics. Proceedings of the International Seminar on Modal Analysis (ISMA), Leuven, 13-15 September 2000, 1-8.
Worden, K. and Tomlinson, G. (2001) Nonlinearity in Structural Dynamics. Detection, Identification and Modelling, Institute of Physics Publishing, Bristol and Philadelphia.
Kerschen, G., Golinval, J.C. and Hemez, F.M. (2003) Bayesian Model Screening for the Identification of Non-Linear Mechanical Structures. Journal of Vibration and Acoustics, 125, 389-397. https://doi.org/10.1115/1.1569947
Karabutov, N. (2015) Structural Identification of Nonlinear Dynamic Systems. International Journal of Intelligent Systems and Applications, 7, 1-11. https://doi.org/10.5815/ijisa.2015.09.01
Kazakov, I.Е. and Doctupov, B.G. (1962) Statistical Dynamics of Nonlinear Automatic Systems. Russia Fizmatgiz, Moscow.
Karabutov, N.N. (2011) Structural Identification of Static Plants: Fields, Structures, Methods. URRS/Book House “Librokom”, Moscow.
Karabutov, N.N. (2009) Structural Identification of Systems: The Analysis of Informational Structures. URRS/Book House “Librokom”, Moscow.
Jauberthie, C., Travé-Massuyès, L. and Verdière, N. (2016) Set-Membership Identifiability of Nonlinear Models and Related Parameter Estimation Properties. International Journal of Applied Mathematics and Computer Science, 26, 803-813. https://doi.org/10.1515/amcs-2016-0057
Karabutov, N. (2018) About Structural Identifiability of Nonlinear Dynamic Systems under Uncertainty. Global Journal of Science Frontier Research: A Physics and Space Science, 18, 51-61.
Karabutov N.N. (2020) S-Synchronization Structural Identifiability and Identification of Nonlinear Dynamic Systems. Mekhatronika, Avtomatizatsiya, Upravlenie, 21, 323-336. https://doi.org/10.17587/mau.21.323-336
Karabutov, N.N. (2018) Frameworks in Identification Problems: Design and Analysis. URSS/Lenand, Moscow.
Karabutov, N. (2017) Structural Methods of Design Identification Systems. In: Uvarova, L., Nadykto, A.B. and Latyshev, A.V., Ed., Nonlinearity: Problems, Solutions and Applications. Vol. 1, Nova Science Publishers Inc., Hauppauge, 233-274.