International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.8, No.7, Jul. 2016

Structural Identification of Dynamic Systems with Hysteresis

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Nikolay Karabutov

Index Terms

Structural identification;structure;secant;framework;coefficient of structural properties system;structurally-frequency method hysteresis


The method of structural identification dynamic systems with a hysteresis in the conditions of uncertainty is developed. The method is based on selection of the special set containing the information on properties of a nonlinear part system. The virtual structure (VS) which allows the make the decision about hysteresis structure is offered. The concept of structural identifiability of nonlinear dynamic systems is introduced. Structural identifiability is a necessary condition of obtaining the original form of hysteresis. The criterion of structural identifiability is proposed. The solution of a problem selection the class of the functions belonging to hysteresis to nonlinearities is given.
The procedure of structural identification of hysteresis functions is developed. Procedure realization is based on the phenomenological analysis of structure VS. Defini-tion of features and properties of the VS is the goal of phenomenological analysis. Each non-linearity introduces the features in the behavior of the system. Therefore, their detection gives only the concrete analysis of VS.
Algorithms of estimation structural parameters the hysteresis in the conditions of uncertainty are offered. They analyze the data in special structural space and are based on the application of secant method VS. Such approach gives adequate estimations of parameters hysteresis. The method of the structurally-frequency analysis is offered for check of the obtained results and estimations. It is based on the analysis of fragments VS in two planes. Such analysis allows the make a decision about hysteresis structure. We show that the offered methodology is applicable to unstable dynamic systems. Results of the computer simulation are given.

Cite This Paper

Nikolay Karabutov,"Structural Identification of Dynamic Systems with Hysteresis", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.7, pp.1-13, 2016. DOI: 10.5815/ijisa.2016.07.01


[1]V.G. Shashiashvili, “Structural identification of nonlinear dynamic systems on set of the continuous block-oriented models,” in XII All-Russia conference on problems of con-trol ARCPC-2014. Moscow on June, 16-19th, 2014. Mos-cow: V.A. Trapeznikov Institute of Control Sciences, 2014, pp. 3018-3028.

[2]T.H.Van Pelt, and D.S. Bernstein, “Nonlinear system iden-tification using Hammerstein and non-linear feedback models with piecewise linear static maps,” International journal control, 2001. vol. 74, no. 18, pp. 1807–1823.

[3]W.J. Rugh, Nonlinear system theory: The Volterra/Wiener approach, The Johns Hopkins University Press, 1981. 

[4]G. Dimitriadis, Investigation of nonlinear aeroelastic systems. Thesis of degree the doctor of philosophy, Uni-versity of Manchester, 2001.

[5]G. Kerschen, K. Worden, A. Vakakis, and J. Golinval, “Past, present and future of nonlinear system identification in structural dynamics,” Mechanical systems and signal processing,  2006, vol. 20, pp. 505–592.

[6]R. Lin, and D.J. Ewins, “Location of localized stiffness non-linearity using measured modal data,” Mechanical systems and signal processing, 1995, vol. 9,pp. 329–339.

[7]C.P. Fritzen, “Damage detection based on model updating methods,” Mechanical systems and signal processing, 1998, vol. 12, pp. 163–186.

[8]R. Pascual, I. Trendafilova, J.C. Golinval, and W. Heylen, “Damage detection using model updating and identification techniques,” in Proceedings of the second international conference on identification in engineering systems, Swansea, 1999.

[9]I. Trendafilova, V. Lenaerts, G. Kerschen, J.C. Golinval, and H. Van Brussel, “Detection, localization and identifi-cation of nonlinearities in structural dynamics,” in Pro-ceedings of the international seminar on modal analysis (ISMA), Leuven, 2000.

[10]K. Worden, and G. Tomlinson, Nonlinearity in Structural Dynamics. Detection, Identification and Modelling, Insti-tute of Physics Publishing, Bristol and Philadelphia, 2001.

[11]J.S. Bendat, and A.G. Piersol, Random Data: Analysis and measurement procedures, third ed., Wiley Interscience, New York, 2010. 

[12]G. Kerschen, J.C. Golinval, and F.M. Hemez, “Bayesian model screening for the identification of non-linear me-chanical structures,” Journal of vibration and acoustics, 2003, vol. 125, pp. 389–397.

[13]Y. Fan, and C.J. Li, “Non-linear system identification using lumped parameter models with embedded feedforward neural networks,” Mechanical systems and signal processing, 2002, vol. 16, pp. 357–372.

[14]M. Peifer, J. Timmer, and H.U. Voss, “Nonparametric identification of nonlinear oscillating systems,” Journal of sound and vibration, 2003, vol. 267, pp. 1157–1167.

[15]H. Yu, J. Peng, and Y. Tang, “Identification of Nonlinear Dynamic Systems Using Hammerstein-Type Neural Net-work,” Mathematical problems in engineering, vol. 2014, article ID 959507, 9 p.

[16]A.W. Smith, S.F. Masri, E.B. Kosmatopoulos, A.G. Chas-siakos, and T.K. Caughey, “Development of adaptive modeling techniques for non-linear hysteretic systems,” International journal of non-linear mechanics, 2002, vol. 37, is. 8, pp. 1435-1451.

[17]J. Vörös, “Modeling and identification of hysteresis using special forms of the Coleman–Hodgdon model,” Journal of electrical engineering, 2009, vol. 60, no. 2, pp. 100–105.

[18]K. Worden, and G. Manson, “On the identification of hysteretic systems, Part I: an Extended Evolutionary Scheme,” in Proceedings of the IMAC-XXVIII February 1–4, 2010, Jacksonville, Florida USA, 2010, 9p.

[19]M. Peimani, M.J. Yazdanpanah, and N. Khaji, “Parameter estimation in hysteretic systems based on adaptive least-squares,” Journal of information systems and telecommu-nication, 2013, vol. 1, no. 4, pp. 217-221.

[20]Y. Tan, R. Dong, H. Chen, and H. He, “Neural network based identification of hysteresis in human meridian sys-tems,” Int. J. Appl. Math. Comput. Sci., 2012, vol. 22, no. 3, pp. 685–694.

[21]Y. Ding, B.Y. Zhao, and B. Wu, “Structural system iden-tification with extended Kalman filter and orthogonal de-composition of excitation,” Mathematical problems in en-gineering, 2014, Vol. 2014, article ID 987694, 10 p.

[22]K. Kuhnen, “Modeling, Identification and Compensation of Complex Hysteretic Nonlinearities: A Modified Prandtl-Ishlinskii Approach,” European journal of control, 2003, vol. 9, pp. 407-418.

[23]T. Furukawa, M. Ito, K. Izaw, and M.N. Noori, “System identification of base-isolated building using seismic response data,” Journal of engineering mechanics, 2005. vol. 131, pp. 268-275.

[24]Y. Ding, B.Y. Zhao, and B.Wu, “Structural system identi-fication with extended Kalman filter and orthogonal de-composition of excitation,” Mathematical problems in en-gineering, 2014, vol. 2014, pp. 1-10.

[25]N.N. Karabutov, Structural identification of static plants: Fields, structures, methods, URRS/Book house "Libro-kom", Moscow, 2011.

[26]N.N. Karabutov. “Structural identification of static pro-cesses with hysteresis nonlinearities in civil engineering,” Journal of civil engineering and science, 2012, vol. 1, no. 4, pp.22-29.

[27]I.Е. Kazakov, and B.G. Doctupov, Statistical dynamics of nonlinear automatic systems, Fizmatgiz, Moscow, 1962.

[28]V.D. Furasov, Stability of motion, estimation and stabili-zation, Nauka, Moscow, 1977.

[29]N.N. Karabutov, Structural identification of systems: the analysis of informational structures, URRS/Book house "Librokom", Moscow, 2009.

[30]N.N. Karabutov, “Structural identification of nonlinear static system on basis of analysis sector sets,” International journal of intelligent systems and applications, 2014, vol. 6, no. 1, pp. 1-10.

[31]G. Choquet, L'enseignement de la geometrie, Hermann, Paris, 1964.

[32]N.N. Karabutov, “Structural identification of nonlinear dynamic systems,” International journal of intelligent sys-tems and applications, 2015,vol. 7, no. 9, pp. 1-11.

[33]L. Acho, “Hysteresis modeling and synchronization of a class of RC-OTA hysteretic-jounce-chaotic oscillators,” Universal journal of applied mathematics, 2013, vol. 1, no. 2, pp. 82-85.