Advertisement

Numerische Mathematik

, Volume 55, Issue 6, pp 695–710 | Cite as

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

  • K. -H. Hoffmann
  • G. H. Meyer
Article

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.

Subject Classifications

AMS(MOS): 65D10 CR:G1.2 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Biorci, G., Pescetti, D.: Analytical theory of the behaviour of ferromagnetic materials. II Nuovo Cimento7, 829–839 (1958)Google Scholar
  2. 2.
    Biorci, G., Pescetti, D.: Some consequences of the analytical theory of the ferromagnetic hysteresis. J. Phys. Radium20, 233–236 (1959)Google Scholar
  3. 3.
    Biorci, G., Pescetti, D.: Some remarks on Hysteresis. J. Appl. Phys.37, 425–427 (1966)Google Scholar
  4. 4.
    Brokate, M.: Optimale Steuerung von gewöhnlichen Differentialgleichungen mit Nichtlinearitäten vom Hysteresis-Typ. Frankfurt: Lang 1987Google Scholar
  5. 5.
    Hoffmann, K.-H., Sprekels, J., Visintin, A.: Identification of hysteresis loops. J. Comput. Phys. (to appear) 1989Google Scholar
  6. 6.
    Kádár, G., Della Torre, E.: Determination of the bilinear product Preisach function. J. Appl. Phys.8, 3001–3004 (1988)CrossRefGoogle Scholar
  7. 7.
    Krasnosel'skii, M.A., Pokrovskii, A.V.: Systems with Hysteresis. Nauka, Moscow, 1983 English Translation in press)Google Scholar
  8. 8.
    Quarteroni, A.: Approximation theory and analysis of spectral methods. In: Schempp, W., Zeller, K. (eds.): Multivariate approximation theory III, 1985Google Scholar
  9. 9.
    Verdi, C., Visintin, A.: Numerical approximation of the Preisach model for hysteresis. IMA J. Num. Anal. (to appear)Google Scholar
  10. 10.
    Visintin, A.: On the Preisach model for hysteresis. Nonlinear Analysis8, 977–996 (1984)CrossRefGoogle Scholar
  11. 11.
    Woodward, J.G., Della Torre, E.: Particle interaction in magnetic recording tapes. J. Appl. Phys.31, 56–62 (1960)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • K. -H. Hoffmann
    • 1
  • G. H. Meyer
    • 2
  1. 1.Institute for MathematicsUniversity of AugsburgAugsburgFederal Republic of Germany
  2. 2.School of MathematicsGeorgia TechnologyAtlantaUSA

Personalised recommendations