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A least squares method for finding the preisach hysteresis operator from measurements

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Summary

A finite element like least squares method is introduced for determining the density function in the Preisach hysteresis model from overdeterined measured data. It is shown that the least squares error depends on the quality of the data and the best approximations to the analytic density. For consistent data criteria are given for convergence of the approximate density and Preisach operator with increasing measurements.

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References

  1. Biorci, G., Pescetti, D.: Analytical theory of the behaviour of ferromagnetic materials. II Nuovo Cimento7, 829–839 (1958)

    Google Scholar 

  2. Biorci, G., Pescetti, D.: Some consequences of the analytical theory of the ferromagnetic hysteresis. J. Phys. Radium20, 233–236 (1959)

    Google Scholar 

  3. Biorci, G., Pescetti, D.: Some remarks on Hysteresis. J. Appl. Phys.37, 425–427 (1966)

    Google Scholar 

  4. Brokate, M.: Optimale Steuerung von gewöhnlichen Differentialgleichungen mit Nichtlinearitäten vom Hysteresis-Typ. Frankfurt: Lang 1987

    Google Scholar 

  5. Hoffmann, K.-H., Sprekels, J., Visintin, A.: Identification of hysteresis loops. J. Comput. Phys. (to appear) 1989

  6. Kádár, G., Della Torre, E.: Determination of the bilinear product Preisach function. J. Appl. Phys.8, 3001–3004 (1988)

    Article  Google Scholar 

  7. Krasnosel'skii, M.A., Pokrovskii, A.V.: Systems with Hysteresis. Nauka, Moscow, 1983 English Translation in press)

    Google Scholar 

  8. Quarteroni, A.: Approximation theory and analysis of spectral methods. In: Schempp, W., Zeller, K. (eds.): Multivariate approximation theory III, 1985

  9. Verdi, C., Visintin, A.: Numerical approximation of the Preisach model for hysteresis. IMA J. Num. Anal. (to appear)

  10. Visintin, A.: On the Preisach model for hysteresis. Nonlinear Analysis8, 977–996 (1984)

    Article  Google Scholar 

  11. Woodward, J.G., Della Torre, E.: Particle interaction in magnetic recording tapes. J. Appl. Phys.31, 56–62 (1960)

    Google Scholar 

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Authors and Affiliations

  1. Institute for Mathematics, University of Augsburg, Memminger Strasse 6, D-8900, Augsburg, Federal Republic of Germany

    K. -H. Hoffmann

  2. School of Mathematics, Georgia Technology, 30332, Atlanta, GA, USA

    G. H. Meyer

Authors
  1. K. -H. Hoffmann
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  2. G. H. Meyer
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Dedicated to Günther Hämmerlin on the occasion of his 60th birthday

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Hoffmann, K.H., Meyer, G.H. A least squares method for finding the preisach hysteresis operator from measurements. Numer. Math. 55, 695–710 (1989). https://doi.org/10.1007/BF01389337

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  • DOI: https://doi.org/10.1007/BF01389337

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