The Preisach hysteresis model: Error bounds for numerical identification and inversion

Pavel Krejčí

doi:10.3934/dcdss.2013.6.101

Article Contents

2013, Volume 6, Issue 1: 101-119. Doi: 10.3934/dcdss.2013.6.101

This issue Previous Article Computational aspects of quasi-static crack propagation Next Article Local minimality and crack prediction in quasi-static Griffith fracture evolution

The Preisach hysteresis model: Error bounds for numerical identification and inversion

Pavel Krejčí^1,

1.
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Praha 1

Received: March 2011

Revised: July 2011

Published: February 2013

Abstract Related Papers Cited by

Abstract

A structure analysis of the Preisach model in a variational setting is carried out by means of an auxiliary hyperbolic equation with memory variable playing the role of time, and amplitude of cycles as spatial variable. Using this representation, we propose an algorithm and derive error estimates for the identification of the Preisach density function and for an approximate inversion of the Preisach operator.

Keywords:

Mathematics Subject Classification: Primary: 34C55; Secondary: 65L70, 65Q99.

Citation:

Related Papers

Cited by

References

[1]	M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,'' Appl. Math. Sci., 121, Springer-Verlag, New York, 1996.
[2]	M. Brokate and A. Visintin, Properties of the Preisach model for hysteresis, J. Reine Angew. Math., 402 (1989), 1-40.
[3]	D. Davino, A. Giustiniani and C. Visone, Fast inverse Preisach models in algorithms for static and quasistatic magnetic-field computations, IEEE Transactions on Magnetics, 44 (2008), 862-865.
[4]	K. H. Hoffmann and G. H. Meyer, A least squares method for finding the Preisach hysteresis operator from measurements, Numer. Math., 55 (1989), 695-710.
[5]	S. K. Hong, H. K. Jung and H. K. Kim, Analytical formulation for the Everett function, Journal of Magnetics, 2 (1997), 105-109.
[6]	M. A. Krasnosel'skii and A. V. Pokrovskii, "Systems with Hysteresis,'' Nauka, Moscow, 1983 (in Russian, English edition Springer 1989).
[7]	P. Krejčí, Hysteresis and periodic solutions of semilinear and quasilinear wave equations, Math. Z, 193 (1986), 247-264.
[8]	P. Krejčí, On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case, Apl. Math., 34 (1989), 364-374.
[9]	P. Krejčí, Hysteresis memory preserving operators, Appl. Math., 36 (1991), 305-326.
[10]	P. Krejčí, "Hysteresis, Convexity and Dissipation in Hyperbolic Equations,'' Gakuto Int. Ser. Math. Sci. Appl., 8, Gakkōtosho, Tokyo, 1996.
[11]	P. Krejčí, Kurzweil integral and hysteresis, Journal of Physics: Conference Series, 55 (2006), 144-154.
[12]	F. Preisach, Über die magnetische Nachwirkung, Z. Physik, 94 (1935), 277-302.doi: 10.1007/BF01349418.
[13]	A. Visintin, "Differential Models of Hysteresis,'' Springer, Berlin-Heidelberg, 1994.
[14]	C. Visone and M. Sjöström, Exact invertible hysteresis models based on play operators, Physica B, 343 (2004), 148-152.