Advertisement

Archive of Applied Mechanics

, Volume 77, Issue 5, pp 325–337 | Cite as

The inverse identification problem and its technical application

  • Tadeusz Uhl
Original

Abstract

This paper presents an overview of a loading force identification technique. Load identification methods are based on the solution of the inverse identification problem. Many different approaches for linear systems have been developed in this area. For both linear and nonlinear systems, methods based on the minimization of assumed objective functions are formulated. The least square error between the simulated and measured system responses is mainly used as the objective function. The dynamic programming optimization method formulated by Bellman is commonly used for the minimization of the objective function to estimate the excitation forces. The inverse identification problem in most practical cases is ill-posed because not all the state variables or initial conditions are known. Ill-posed inverse identification problems can be solved using several techniques, the most useful of which are: the generalized cross-validation method, the dynamic programming technique and Tikhonov’s method. This article presents the theoretical background and main limits to the application of inverse identification methods. Numerical and experimental tests on a laboratory rig were made to verify the formulated procedures. The method is applied to the identification of wheel–rail contact forces during rail vehicle operation. The method can be applied for indirect measurements of contact forces in railway equipment testing.

Keywords

Load identification problem Inverse identification method Rail vehicle testing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allemang, R.J., Brown, D.L., Fludang, W.: Modal parameter estimation: unified matrix polynomial approach, Proceedings of the 12th IMAC, pp. 501–514 (1994)Google Scholar
  2. 2.
    Anger G. (1990) Inverse problems in differential equations. Plenum, New YorkGoogle Scholar
  3. 3.
    Bracciali A., Cascini G. (2000) Rolling contact force energy reconstruction, J. Sound Vib. 236(2): 185–192CrossRefGoogle Scholar
  4. 4.
    Busby H.R., Trujillo D.M. (1986) Solution of an inverse dynamics problem using an eigenvalue reduction technique, Comput. Struct. 25(1):123–136Google Scholar
  5. 5.
    Cannon J.R., Hornung U. (1986) Inverse Problems. Birkhauser Verlag, VauserzbMATHGoogle Scholar
  6. 6.
    Chudzikiewicz A. (1991) Selected elements of the contact problems necessary for investigating the rail vehicle system. In: Kisilowski J., Knothe K. (eds) Advanced railway vehicle system dynamics. WNT, WarszawaGoogle Scholar
  7. 7.
    Chudzikiewicz, A.: Elements of vehicle diagnostics, (in Polish) ITE, Radom (2002)Google Scholar
  8. 8.
    Czop, P., Uhl, T.: Load identification methods based on parametric models for mechanical structures, In: 8th IEEE international conference on methods and models in automation and robotics, Szczecin, pp. 203–209 (2002)Google Scholar
  9. 9.
    Dobson B.J., Rider E. (1990) A review of the indirect calculation of excitation forces from measured structural response data. J. Mech. Eng. Sci. 204, 69–75Google Scholar
  10. 10.
    Giergiel J., Uhl T. (1989) Identification of impact forces in mechanical systems. Arch. Mach. Des. 36(2–3): 321–336Google Scholar
  11. 11.
    Giergiel J., Uhl T. (1989) Identification of the input excitation forces in mechanical structures. Arch. Transp. 1(1): 8–24Google Scholar
  12. 12.
    Golub G.H., van Loan C.F. (1996) Matrix Computations. John Hopkins University Press, BaltimorezbMATHGoogle Scholar
  13. 13.
    Góral, G., Zbydoń, K., Uhl, T.: Intelligent transducers of in-operational loads in construction fatigue monitoring. Mach. Dyn. Probl. 2–3, 73–88 (2002)Google Scholar
  14. 14.
    Hadamard J. (1923) Lectures on Coughy’s Problem in Linear Partial Differential Equations. Yale University Press, New HavenGoogle Scholar
  15. 15.
    Hansel E. (1991) Inverse Theory and Applications for Engineers. Prentice Hall, Englewood CliffsGoogle Scholar
  16. 16.
    Inoue H., Ishida K., Kishimoto T. Shibuya (1991) Measurements of impact load by using an inverse analysis technique. JSME Int. J. series I 34(4): 453–458Google Scholar
  17. 17.
    Kanehara, H., et al.: Study on online measurement of longitudinal creep force of railway vehicles, In: Proceedings of the conference J-Rail’98, November, Tokyo, pp. 457–469 (1998)Google Scholar
  18. 18.
    Kanehara H., Fujioka T. (2002) Measuring rail/wheel contact points of running railway vehicles. Wear 253, 275–283CrossRefGoogle Scholar
  19. 19.
    Lechowicz, S., Hunt, C.: Monitoring and managing wheel condition and loading. In: Proceeding of International Symposium for transportation recorders, Arlington, pp. 205–239 (1999)Google Scholar
  20. 20.
    Li, J.: Application of mutual energy theorem for determining unknown force sources, Proceeding Of Internoise 88, Avignion, pp. 245–263 (1988)Google Scholar
  21. 21.
    Liu G.R., Han X. (2003) Computational Inverse techniques in nondestructive evaluation. CRC Press, Boca RatonzbMATHGoogle Scholar
  22. 22.
    Meirovitch L., Baruch H. (1982) Control of self-adjoint distributed-parameter systems. J. Guid. Control Dyn. 5, 60–66zbMATHCrossRefGoogle Scholar
  23. 23.
    Mendrok, K.: Identification of loads in mechanical systems, Ph.D. Thesis, University of Science and Technology, Krakow (2003)Google Scholar
  24. 24.
    Nielsen, J., Johansson, A.: Out of round railway wheels—literature survey, In: Proceedings Of the Institute of Mechanical Engineers – part F, vol. 214, pp. 79–91 (2002)Google Scholar
  25. 25.
    Philips D.L. (1962) A technique for the numerical solution of certain equations of the first kind. J. ACM 9: 84–97CrossRefGoogle Scholar
  26. 26.
    Simonian S.S. (1981) Inverse problems in structural dynamics. Int. J. Numer. Methods Eng. 17, 357–365zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Tikhonov A.N., Arsenin V.Y. (1977) Solution of Ill-Possed Problems. Winston and Sons, Washington, DCGoogle Scholar
  28. 28.
    Trujillo D.M. (1987) Application of dynamic programming to the general inverse problem. Int. J. Numer. Methods Eng. 23, 613–624Google Scholar
  29. 29.
    Trujillo D.M., Busby H.R. (1997) Practical Inverse Engineering. CRC Press, LondonzbMATHGoogle Scholar
  30. 30.
    Uhl T. (1998) Computer Assisted Identification of Mechanical Structures (in Polish). WNT, WarszawaGoogle Scholar
  31. 31.
    Uhl T. (2002) Identification of loads in mechanical structures – helicopter case study Comput. Assist. Mech. Eng. Sci. 9, 151–160zbMATHGoogle Scholar
  32. 32.
    Uhl T., Pieczara J. (2003) Identification of operational loading forces for mechanical structures, Arch. Transp. 16(2): 109–126Google Scholar
  33. 33.
    Uhl T., Mendrok K. (2005) Inverse Identification Problems: Theory and Practical Applications (in Polish). ITE Press, KrakówGoogle Scholar
  34. 34.
    Zhang, Q., Allemang, R.J., Brown, D.L.: Modal filter: concept and applications. In: Proceeding of 8th IMAC, pp. 487–496 (1990)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.University of Science and TechnologyKrakowPoland

Personalised recommendations