Dynamic Analysis of Nonlinear Frames by Prandtl Neural Networks
Publication: Journal of Engineering Mechanics
Volume 134, Issue 11
Abstract
A new type of activation function, based on the use of the Prandtl–Ishlinskii operator, has been developed and used in the feed forward neural networks in order to improve their capabilities in learning to identify and analyze nonlinear structures subject to dynamic loading. The genetic algorithm has been used in its training. The neural network, which is referred to as the Prandtl neural network here, has been trained and used in the analysis of two shear frames, a single degree of freedom (SDOF) and a 3DOF, both subjected to earthquake excitations. To assess the capabilities of the Prandtl neural network under ideal situations, the data on the response of the frames have been obtained through the integration of their governing nonlinear equations of motion. The training has been based on the white noise while the strong earthquakes of 200% El Centro in 1940 and Gilroy have been used for testing. Results have shown the high precision of the Prandtl neural network in solving highly hysteretic problems. The issue is important for two main applications in structural dynamics and control: (1) analysis of highly nonlinear structures where it is desired to train a neural network to directly learn the behavior of a structure from experimental data; and (2) intelligent active control of structures where neural network emulators are designed to provide as precise predictions about the future response of the structures as possible, in order to be used in the determination of the required control forces.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers would like to thank the Office of the Deputy of Higher Education of Sharif University of Technology, Tehran, Iran for partially supporting this study.
References
Bani-Hani, K., and Ghaboussi, J. (1998). “Nonlinear structural control using neural networks.” J. Eng. Mech., 124(3), 319–327.
Bouc, R. (1967). “Forced vibration of mechanical systems with hysteresis.” Proc., 4th Conf. on Nonlinear Oscillation, Prague, Czechoslovakia.
Brokate, M., and Sprekels, J. (1996). Hysteresis and phase transitions, Springer, New York.
Chen, H. M., Qi, G. Z., Yang, J. C. S., and Amini, F. (1995a). “Neural network for structural dynamic model identification.” J. Eng. Mech., 121(12), 1377–1381.
Chen, H. M., Tsai, K. H., Qi, G. Z., Yang, J. C. S., and Amini, F. (1995b). “Neural network for structure control.” J. Comput. Civ. Eng., 9(2), 168–176.
Ghaboussi, J., Garret, J. H., Jr., and Wu, X. (1991). “Knowledge-based modeling of material behavior with neural networks.” J. Eng. Mech., 117(1), 132–153.
Ghaboussi, J., and Joghataie, A. (1995). “Active control of structures using neural networks.” J. Eng. Mech., 121(4), 555–567.
Goldberg, D. E. (1989). Genetic algorithm in search, optimization and machine learning, Addison-Wesley, Reading, Mass.
Joghataie, A., and Vahidi, A. (2000). “Designing a general neurocontroller for water towers.” J. Eng. Mech., 126(6), 582–587.
Kosmatopoulos, E. B., Smyth, A. W., Masri, S. F., and Chassiakos, A. G. (2001). “Robust adaptive neural estimation of restoring forces in nonlinear structures.” J. Appl. Mech., 68, 880–893.
Masri, S. F., Chassiakos, A. G., and Caughy, T. K. (1993). “Identification of nonlinear dynamic systems using neural networks.” J. Appl. Mech., 60, 123–133.
Mayergoyz, I. D. (1991). Mathematical models of hysteresis, Springer, New York.
Mukherjee, A. (1997). “Self-organizing neural network for identification of natural modes.” J. Comput. Civ. Eng., 11(1), 74–77.
Nelles, O. (2001). Nonlinear systems identification from classical approaches to neural networks and fuzzy models, Springer, Berlin.
Serpico, C., and Visone, C. (1998). “Magnetic hysteresis modeling via feed-forward neural networks.” IEEE Trans. Magn., 34(3), 623–628.
Shin, H. S., and Pande, G. N. (2000). “On self-learning finite element codes based on monitored response of structures.” Comput. Geotech., 27, 161–178.
Visintin, A. (1994). Differential models of hysteresis, Springer, New York.
Wen, Y. K. (1976). “Method for random vibration of hysteretic systems.” J. Engrg. Mech. Div., 102(2), 249–263.
Wen, Y. K. (1989). “Methods of random vibration for inelastic structures.” Appl. Mech. Rev., 42(2), 39–52.
Zhang, A., and Zhang, L. (2004). “RBF neural networks for the prediction of building interference effects.” Comput. Struct., 82(27), 2333–2339.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 11 • November 2008
Pages: 961 - 969
Copyright
© 2008 American Society of Civil Engineers.
History
Received: Mar 28, 2006
Accepted: Apr 25, 2008
Published online: Nov 1, 2008
Published in print: Nov 2008
Notes
Note. Associate Editor: Lambros S. Katafygiotis
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.