Hybrid Simulation of a Frame Equipped with MR Damper by Utilizing Least Square Support Vector Machine

Document Type : Research


1 Ph.D. Candidate, Civil Engineering Department, K. N. Toosi University of Technology, Tehran, Iran.

2 Associate Professor, Civil Engineering Department, K. N. Toosi University of Technology, Tehran, Iran

3 Assistant Professor, Aerospace Engineering Department, K. N. Toosi University of Technology, Tehran, Iran.


In hybrid simulation, the structure is divided into numerical and physical substructures to achieve more accurate responses in comparison to a full computational analysis. As a consequence of the lack of test facilities and actuators, and the budget limitation, only a few substructures can be modeled experimentally, whereas the others have to be modeled numerically. In this paper, a new hybrid simulation has been introduced utilizing Least Square Support Vector Machine (LS-SVM) instead of physical substructures. With the concept of overcoming the hybrid simulation constraints, the LS-SVM is utilized as an alternative to the rate-dependent physical substructure. A set of reference data is extracted from appropriate test (neumerical test) as the input-output data for training LS-SVM. Subsequently, the trained LS-SVM performs the role of experimental substructures in the proposed hybrid simulation. One-story steel frame equipped with Magneto-Rheological (MR) dampers is analyzed to examine the ability of LS-SVM model. The proposed hybrid simulation verified by some numerical examples and  results demonstrate the capability and accuracy of  this new hybrid simulation.


1. Ahmadizadeh, M. Real-time seismic hybrid simulation procedures for reliable structural performance testing (PhD Dissertation), 2007. State University of New York at Buffalo.
2. Ahmadizadeh, M. and Mosqueda, G., "Online energy-based error indicator for the assessment of numerical and experimental errors in a hybrid simulation." Engineering Structures, vol. 31(9), 2009, p. 1987-1996. [DOI:10.1016/j.engstruct.2009.03.002]
3. Boser, B.E., Guyon, I.M. and Vapnik, V.N., "A training algorithm for optimal margin classifiers", In Proceedings of the fifth annual workshop on Computational learning theory, 1992, p. 144-152). ACM. [DOI:10.1145/130385.130401]
4. Brokate, M. and Sprekels, J., "Hysteresis and Phase Transitions", vol. 121, 1996, Springer Science & Business Media. [DOI:10.1007/978-1-4612-4048-8]
5. Cortes, C. and Vapnik, V., Lucent Technologies Inc, Soft margin classifier. U.S. 1997, Patent 5,640,492. [DOI:10.1016/S1353-4858(97)89868-6]
6. De Brabanter, K., Karsmakers, P., Ojeda, F., Alzate, C., De Brabanter, J., Pelckmans, K., De Moor, B., Vandewalle, J. and Suykens, J.A., "LS-SVMlab toolbox user's guide: version 1.7", 2010, Katholieke Universiteit Leuven.
7. Elanwar, H.H. and Elnashai, A.S., "Framework for online model updating in earthquake hybrid simulations", Journal of Earthquake Engineering, vol. 20 (1), 2016, p. 80-100. [DOI:10.1080/13632469.2015.1051637]
8. Farrokh, M., "Hysteresis Simulation Using Least-Squares Support Vector Machine", Journal of Engineering Mechanics, vol. 144(9), 2018, p.04018084. [DOI:10.1061/(ASCE)EM.1943-7889.0001509]
9. Farrokh, M., Dizaji, M.S. and Joghataie, A., "Modeling hysteretic deteriorating behavior using generalized Prandtl neural network", Journal of Engineering Mechanics, vol. 141(8), 2015, p.04015024. [DOI:10.1061/(ASCE)EM.1943-7889.0000925]
10. Friedman, A.J., Zhang, J., Phillips, B.M., Jiang, Z., Agrawal, A., Dyke, S.J., Ricles, J.M., Spencer, B.F., Sause, R. and Christenson, R., "Accommodating MR damper dynamics for control of large scale structural systems",In Proceedings of the Fifth World Conference on Structural Control and Monitoring, vol. 5, 2010, p. 10075).
11. Hakuno, M., Shidawara, M. and Hara, T., "Dynamic destructive test of a cantilever beam, controlled by an analog-computer", In Proceedings of the Japan Society of Civil Engineers vol. 1969 (171), 1969, p. 1-9. [DOI:10.2208/jscej1969.1969.171_1]
12. Jiang, Z. and Christenson, R.E., "A fully dynamic magneto-rheological fluid damper model", Smart Materials and Structures, vol. 21(6), 2012, p.065002. [DOI:10.1088/0964-1726/21/6/065002]
13. Joghataie, A. and Farrokh, M., "Dynamic analysis of nonlinear frames by Prandtl neural networks", Journal of engineering mechanics, vol. 134(11), 2008, p. 961-969. [DOI:10.1061/(ASCE)0733-9399(2008)134:11(961)]
14. Kwon, O.S., Nakata, N., Park, K.S., Elnashai, A. and Spencer, B., "User manual and examples for UI-SIMCOR v2. 6.", 2007, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign. Urbana, IL.
15. Mahin, S.A., Shing, P.S.B., Thewalt, C.R. and Hanson, R.D., "Pseudodynamic test method-Current status and future directions", Journal of Structural Engineering, vol. 115(8), 1989, p. 2113-2128. [DOI:10.1061/(ASCE)0733-9445(1989)115:8(2113)]
16. Mayergoyz, I.D., "Mathematical Models of Hysteresis", 1991, Springer. New York. [DOI:10.2172/6911694]
17. Murphy, K. P. (2012). "Machine learning: a probabilistic perspective." MIT Press, Cambridge, MA.
18. Nelder, J.A. and Mead, R., "A simplex method for function minimizaion", The computer journal, vol. 7(4), 1965, p.308-313. [DOI:10.1093/comjnl/7.4.308]
19. Sapiński, B. and Filuś, J., "Analysis of parametric models of MR linear damper", Journal of Theoretical and Applied Mechanics, vol. 41(2), 2003, p.215-240.
20. Spencer Jr, B.F., Dyke, S.J., Sain, M.K. and Carlson, J., "Phenomenological model for magnetorheological dampers", Journal of engineering mechanics, vol. 123(3), 1997, p.230-238. [DOI:10.1061/(ASCE)0733-9399(1997)123:3(230)]
21. Suykens, J.A. and Vandewalle, J., "Least squares support vector machine classifiers", Neural processing letters, vol. 9(3), 1999, p. 293-300. [DOI:10.1023/A:1018628609742]
22. Suykens, J.A., Van Gestel, T. and De Brabanter, J., "Least squares support vector machines", 2002, World Scientific. [DOI:10.1142/5089]
23. Takanashi, K. and Nakashima, M., "Japanese activities on on-line testing", Journal of Engineering Mechanics, vol. 113 (7), 1987, p. 1014-1032. [DOI:10.1061/(ASCE)0733-9399(1987)113:7(1014)]
24. Vapnik, V., Golowich, S. E and Smola, A. J., "Support vector method for function approximation, regression estimation and signal processing", Advances in neural information processing systems, 1997.
25. Visintin, A, "Differential models of hysteresis", 1994, Springer Berlin. [DOI:10.1007/978-3-662-11557-2]
26. Wu, B., Chen, Y., Xu, G., Mei, Z., Pan, T. and Zeng, C., "Hybrid simulation of steel frame structures with sectional model updating Earthquake Engineering & Structural Dynamics, 45(8), 2016, p. 1251-1269. [DOI:10.1002/eqe.2706]
27. Xavier-de-Souza, S., Suykens, J.A., Vandewalle, J. and Bollé, D., "Coupled simulated annealing", IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 40(2), 2010, p. 320-335. [DOI:10.1109/TSMCB.2009.2020435]
28. Yang, W.J. and Nakano, Y., "Substructure online test by using real-time hysteresis modeling with a neural network", Advances in Experimental Structural Engineering, vol. 38, 2005, p. 267-274.
29. Yang, Y.S., Tsai, K.C., Elnashai, A.S. and Hsieh, T.J., "An online optimization method for bridge dynamic hybrid simulations", Simulation Modelling Practice and Theory, vol. 28, 2012, p. 42-54. [DOI:10.1016/j.simpat.2012.06.002]
30. Yun, G.J., Ghaboussi, J. and Elnashai, A.S., "A new neural network‐based model for hysteretic behavior of materials" International Journal for Numerical Methods in Engineering, vol. 73(4), 2008, p. 447-469. [DOI:10.1002/nme.2082]
31. Zavala, C., Ohi, K. and Takanashi, K., "Neuro-Hybrid Substructuring On-Line Test on Moment Resistant Frames", In Proceedings of 11th World Conference on Earthquake Engineering, 1996, paper No. 1387.