Archive of Applied Mechanics

, Volume 81, Issue 11, pp 1541–1554 | Cite as

Application of inverse linear parametric models in the identification of rail track irregularities

  • Piotr CzopEmail author
  • Krzysztof Mendrok
  • Tadeusz Uhl


Requirements for current trains to be increasingly available have created the need to develop systems that can predict the quality of both trains and infrastructure components. The paper presents a new approach to the detection of rail truck irregularities, based on the measurements of bearing box acceleration during the operation of rail vehicles. The proposed procedure is based on an inverse problem solution, estimating track irregularities from measured acceleration of the applied model of vehicle dynamics. The simulation study of the proposed method, as well as its implementation, is presented. The method has been successfully applied for the identification of rail irregularities on a typical Polish railroad and vehicle.


Rail irregularities Linear model Inverse model Data-driven model 



Akaike’s information criterion


Akaike’s final prediction error


Linear and time-invariant model/system


AutoRegressive with eXogeneous input


AutoRegressive moving average with eXogeneous input




Prediction error method


Output error


Frequency response function


Single-input single-output

List of symbols


Discrete time

A, B, C, D, E, F

Polynomials used for the representation of the transfer function

nA, nB, nC, nE, nF

Order of polynomials used for the representation of the transfer function


Operator of the Z transformation


Disturbance variables in the model


Input variables in the model


Inverse input


Output variables in the model


Transfer function


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  1. 1.
    Allena M.S., Vehiclene T.G.: Delayed, Multi-step inverse structural filter for robust force identification. Mech. Syst. Signal Process. 22(5), 1036–1054 (2008)CrossRefGoogle Scholar
  2. 2.
    Bałuch H.: Diagnostics of the Railways (in Polish). Wydawnictwo Komunikacji i Łączności, Warsaw, Poland (1978)Google Scholar
  3. 3.
    Bracciali A., Cascini G.: High-frequency mobile input reconstruction algorithm (HF-MIRA) applied to forces acting on a damped linear mechanical system. Mech. Syst. Signal Process. 21(2), 255–268 (1998)CrossRefGoogle Scholar
  4. 4.
    Chan T.H.T., Law S.S., Chan T.H.T., Zeng Q.H.: Moving force identification: a time domain method. J. Sound Vib. 201, 1–22 (1997)CrossRefGoogle Scholar
  5. 5.
    Chen, T.C., Lee, M.H.: Research on moving force estimation of the bridge structure using the adaptive input estimation method. J. Struct. Eng. (8) (2008)Google Scholar
  6. 6.
    Elster C., Link A., Bruns T.: Analysis of dynamic measurements and determination of measurement uncertainty using a second-order model. Meas. Sci. Technol. 18, 3682–3697 (2007)CrossRefGoogle Scholar
  7. 7.
    Hollandsworth P.E., Busby H.R.: Impact force identification using the general inverse technique. Int. J. Impact Eng. 8, 315–322 (1989)CrossRefGoogle Scholar
  8. 8.
    Hundhausen, R.J., Adams, D.E., Derriso, M., Kukuchek, P., Alloway, R.: Transient loads identification for a standoff metallic thermal protection system panel. In: Proceedings of 23rd International, Modal Analysis Conference (IMAC XXIII). Orlando, Florida (2005)Google Scholar
  9. 9.
    Iwnicki S.: Handbook of Railway Vehicle Dynamics. CRC Press, Boca Raton (2006)CrossRefGoogle Scholar
  10. 10.
    Kammer D.C.: Input force reconstruction using a time domain technique. ASME J. Vib. Acoust. 120(4), 868–874 (1998)CrossRefGoogle Scholar
  11. 11.
    Ljung L.: System Identification—Theory for the User. Prentice-Hall, Englewood Cliffs, NJ (2009)Google Scholar
  12. 12.
    M. Software. ADAMS Multibody Simulation Software.
  13. 13.
    MATHWORKS Inc.: Matlab Signal Processing Toolbox Guide. The Mathowrks Inc., Natick, MA (2007)Google Scholar
  14. 14.
    MATHWORKS Inc.: Matlab System Identification Toolbox Guide. The Mathowrks Inc., Natick MA (2007)Google Scholar
  15. 15.
    Mendrok, K., Uhl, T.: Overview of modal model based damage detection methods. In: Proceedings of the 29th International Conference on Noise and Vibration Engineering (ISMA). Leuven, Belgium, pp. 561–576 (2004)Google Scholar
  16. 16.
    Moscinski, J., Ogonowski, Z. (eds): Advanced Control with MATLAB & SIMULINK. Ellis Horwood Ltd, UK (1995)Google Scholar
  17. 17.
  18. 18.
    Piazzi A., Visioli A.: Robust set-point constrained regulation via dynamic inversion. Int. J. Robust Nonlinear Control 11, 1–22 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Raath A.D., Van Waveren C.C.: A time domain approach to load reconstruction for durability testing. Eng. Fail. Anal. 4(1), 113–119 (1998)CrossRefGoogle Scholar
  20. 20.
  21. 21.
    Sang-Soo K., Choonsoo P., Young-Guk K., Chankyoung P.: Parameter characteristics of rail inspection measurement system of HSR-350x. J. Mech. Sci. Technol. 23, 1019–1022 (2009)CrossRefGoogle Scholar
  22. 22.
    Torfs, D., Swevers, J., De Schutter, J.: Quasi-perfect tracking control of non-minimal phase systems. In: Proceedings of the 30th Conference on Decision and Control Brighton, England, pp. 241–244 (1999)Google Scholar
  23. 23.
    Uhl, T., Mendrok, K., Chudzikiewicz, A.: Rail track and rail vehicle intelligent monitoring system, structural health monitoring 2009: from system integration to autonomous systems. In: Proceedings of the 7th International Workshop on Structural Health Monitoring. Stanford, CA, September 9–11, 2009, vol. 1, pp. 617–624 (2009)Google Scholar
  24. 24.
    Uhl T.: The inverse identification problem and its technical application. Arch. Appl. Mech. 77(5), 325–337 (2007)zbMATHCrossRefGoogle Scholar
  25. 25.
    VI-grade GmbH, VI-Rail Plugin for MSC.ADAMS.
  26. 26.
    Weston, P.F., Ling, C.S., Goodman, C.J., Roberts, C., Li, P., Goodall, R.M.: Monitoring lateral track irregularity from in-service railway vehicles. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 221, 89–100 (1/2007)Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Robotics and MechatronicsAGH University of Science and TechnologyKrakowPoland

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