Adaptive Modeling of Highly Nonlinear Hysteresis Using Preisach Neural Networks
Publication: Journal of Engineering Mechanics
Volume 140, Issue 4
Abstract
In this paper, a new type of multilayer feedforward neural network has been proposed based on inspiration from the Preisach model, which has been called the Preisach neural network (Preisach-NN). It is comprised of input, output, and two hidden layers. The input and output layers contain linear neurons, whereas the first hidden layer incorporates neurons called stop neurons, whose activation function represents a stop operator. The second hidden layer includes sigmoidal neurons. The subgradient optimization method with space dilatation has been adopted for training of the Preisach-NN as a nonsmooth problem. Although the proposed Preisach-NN could be mathematically identical to the Preisach model, tuning of the Preisach-NN is easier and also more general than that of the model. To assess their capability, Preisach-NNs are used to model two different types of hysteretic behaviors of Masing and non-Masing problems. The results presented and discussed in this paper show that the neural networks have been capable of learning the material behaviors successfully and with high precision.
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References
Brokate, M., and Sprekels, J. (1996). Hysteresis and phase transitions, Springer, New York.
Ewing, A. L. (1885). “Experimental researches in magnetism.” Philos. Trans. R. Soc. Lond., 176, 523–640.
Flynn, D. (2004). “Application of the Preisach model in soil-moisture hysteresis.” M.S. thesis, Univ. College Cork, Cork, Ireland.
Guyer, R. A., McCall, K. R., and Boitnott, G. N. (1995). “Hysteresis, discrete memory, and nonlinear wave propagation in rock: A new paradigm.” Phys. Rev. Lett., 74(17), 3491–3494.
Haykin, S. (1994). Neural networks: A comprehensive foundation, Macmillan, New York.
Joghataie, A., and Farrokh, M. (2008). “Dynamic analysis of nonlinear frames by Prandtl neural networks.” J. Eng. Mech., 961–969.
Joghataie, A., and Farrokh, M. (2011). “Matrix analysis of nonlinear trusses using Prandtl-2 neural networks.” J. Sound Vibrat., 330(20), 4813–4826.
Masing, G. (1926). “Eigenspannungen und verfestigung beim messing [Self stretching and hardening for brass].” Proc., 2nd Int. Congress for Applied Mechanics, Orell Füssli Verlag, Zürich, Switzerland, 332–335 (in German).
Mayergoyz, I. D. (1986). “Mathematical models of hysteresis.” Phys. Rev. Lett., 56(15), 1518–1521.
Mayergoyz, I. D. (2003). Mathematical models of hysteresis and their applications, Elsevier Science, New York.
Morris, K. A. (2012). “What is hysteresis?” Appl. Mech. Rev., 64(5), 050801.
Ortin, J. (1992). “Preisach modeling of hysteresis for a pseudoelastic Cu-Zn-Al single crystal. ” J. Appl. Phys., 71(3), 1454–1461.
Preisach, F. (1935). “Uber dei magnetische nachwirkung [On magnetic aftereffect].” Z. Phys., 94(5–6), 277–302 (in German).
Serpico, C., and Visone, C. (1998). “Magnetic hysteresis modeling via feed-forward neural networks.” IEEE Trans. Magn., 34(3), 623–628.
Shor, N. Z., Zhurbenko, N. G., Likhod, A. P., and Stetsyuk, P. I. (2003). “Algorithms of nondifferentiable optimization: Development and application.” Cybern. Syst. Anal., 39(4), 537–548.
Zakerzadeh, M. R., Firouzi, M., Sayyaadi, H., and Shouraki, S. B. (2010). “Hysteresis identification of shape memory alloy actuators using a novel artificial neural network based Presiach model.” Proc., ASME 2010 Conf. on Smart Materials, Adaptive Structures and Intelligent Systems, Vol. 1, ASME, New York, 653–660.
Zhou, A. G., Basu, S., Friedman, G., Finkel, P., Yeheskel, O., and Barsoum, M. W. (2010). “Hysteresis in kinking nonlinear elastic solids and the preisach-mayergoyz model.” Phys. Rev. B, 82(9), 094105.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 4 • April 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 14, 2013
Accepted: Aug 15, 2013
Published online: Aug 19, 2013
Published in print: Apr 1, 2014
Discussion open until: Jun 10, 2014
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