Archive of Applied Mechanics

, Volume 81, Issue 11, pp 1621–1637 | Cite as

A novel method to estimate derailment probability due to track geometric irregularities using reliability techniques and advanced simulation methods

  • Saeed Mohammadzadeh
  • Manie Sangtarashha
  • Habibollah Molatefi
Original

Abstract

Track irregularities have a dramatic impact on the response and vibration of a railway vehicle and on the interaction between wheel and rail. The random nature of the track structure and constituent materials and the effects of other factors such as maintenance conditions and transit traffic give rise to the random nature of track irregularities. This research provides a method to estimate the derailment probability of a railway vehicle where track irregularities are assumed to be random, and the interaction of the track and the moving train is considered using advanced dynamic analysis. For this purpose, the limit state function of derailment was estimated using the response surface method and advanced simulation. The probability of derailment was then estimated using a Level 3 reliability method.

Keywords

Estimation of derailment Response surface method Derailment Saturated design method Track–rail interaction SIMPACK Importance sampling method 

List of symbols

fx (x)

Joint probability distribution function for n-dimensional vector of base variables

Gi (x)

Limit state function

Y

Wheel flange force

Q

Instantaneous load of wheel

β

Wheel flange angle

μ

Coefficient of friction between flange rim and rail

N

Total number of tests for Monte Carlo analysis

k

Number of observations for G(x) ≤ 0

G(x)

Real limit state function of derailment

G*(x)

Approximate limit state function of derailment (response surface function)

a, b, c, d

Coefficients of response surface function

xi

Random variables representing track geometric parameters

n

Total number of random variables

hv(vi)

Joint probability density function of importance sampling

fx(vi)

Main joint density function of random variables

I(vi)

Indicator function with a value of one if x is located in failure region and zero if x is located in safe region

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References

  1. 1.
    Yadav, R.K.: The Investigation of Derailments, 3rd edn. Indian Railways Institute of Civil Engineering (2007)Google Scholar
  2. 2.
    Wu H., Wilson N.: Railway vehicle derailment and prevention. In: Inwicki, S. (ed.) Handbook of Railway Vehicle Dynamics, pp. 209–238. Taylor & Francis, UK (2006)CrossRefGoogle Scholar
  3. 3.
    Elkins, J., Wu, H.: New criteria for flange climb derailment. In: Proceedings of 2000 IEEE/ASME Joint Railroad Conference, Newark, NJ, April 4–6, 2000Google Scholar
  4. 4.
    Nadal, M.J.: Locomotives a Vapeur, Collection Encyclopedie Scientifique, Biblioteque de Mecanique Appliquee et Genie, vol. 186, Paris (1908)Google Scholar
  5. 5.
    Weinstock, H.: Wheel-climb derailment criteria for evaluation of rail vehicle safety, ASME Winter Annual Meeting, Paper no. 84-WA/RT-1, November 1984Google Scholar
  6. 6.
    Wu, H., Elkins, J.: Investigation of wheel flange climb derailment criteria. Association of American railroad report R-931, July 1999Google Scholar
  7. 7.
    Karmel A., Sweet L.M.: Evaluation of time-duration dependent wheel load criteria for wheel climb derailment. ASME J. Dyn. Syst. Meas. Control 103, 219–227 (1981)CrossRefGoogle Scholar
  8. 8.
    Karmel A., Sweet L.M.: Wheelset mechanics during wheel climb derailment. Trans. ASME J. Appl. Mech. 51, 680–686 (1984)CrossRefGoogle Scholar
  9. 9.
    Gilchrist A.O., Brickle B.V.: A re-examination of the proneness to derailment of a running wheelset. J. Mech. Eng. Sci. 18(3), 131–141 (1976)CrossRefGoogle Scholar
  10. 10.
    Barbosa R.S.: A 3D contact safety criterion for flange climb derailment of a railway wheel. Veh. Syst. Dyn. 42(5), 289–300 (2004)CrossRefGoogle Scholar
  11. 11.
    Kik W., Menssen R., Moelle D., Bergerder B.: Comparison of Results of Calculations and Measurements of DYSAF-tests, A research project to investigate safety limits of derailment at high speeds. Veh. Syst. Dyn. 37(Suppl.), 543–553 (2002)Google Scholar
  12. 12.
    Magel E., Tajaddinib A., Trosinoc M., Kalousekd J.: Traction, forces, wheel climb and damage in high-speed railway operations. Wear 265, 1446–1451 (2008)CrossRefGoogle Scholar
  13. 13.
    Takai, H., Uchida, M., Muramatsu, H., Ishida, H.: Derailment safety evaluation by analytic equations. Japan National Railway, RTRI. Q. Rep. Jpn, 43(3), (2002)Google Scholar
  14. 14.
    Ishida, H., Miyamoto, T., Maebashi, E., Doi, H.: Safety assessment for flang climb derailment of trains running at low speeds on sharp curves. Q R RTRI 47(2), (2006)Google Scholar
  15. 15.
    Anderson, R.T., Barkan, C.P.L.: Derailment probability analyses and modeling of mainline freight trains. In: Proceedings of the 8th International Heavy Haul Conference, Rio de Janiero, pp. 491–497 (2005)Google Scholar
  16. 16.
    Investigation of Train Accident on 22 july 2004 Near Pamukova, Turkey. Esveld consulting Services BV(ECS), final report, (2004)Google Scholar
  17. 17.
    Power spectral density of track irregularities. ORE Rep. Question C116(1), Offc. for Res. and Experiments of the Int. Union of Railways (UTRECHT), The therlands (1971)Google Scholar
  18. 18.
    Balzer L.A.: High speed ground transportation- stochastic model of track roughness and misalignment. J. Mech. Eng. Sci. 20(3), 143–148 (1978)CrossRefGoogle Scholar
  19. 19.
    Iyengar R.N., Jaiswal O.R.: Random field modeling of railway track irregularities. J. Transp. Eng. 121(4), 303–308 (1995)CrossRefGoogle Scholar
  20. 20.
    Nowak A.S., Collins K.R.: Reliability of Structures. McGraw Hill, New York (2000)Google Scholar
  21. 21.
    Ranganathan R.: Reliability Analysis and Design of Structures. TATA McGraw Hill, New Delhi (1990)Google Scholar
  22. 22.
    Choi S., Grandhi R., Canfield R.: Reliability-based Structural Design. Springer, London (2006)Google Scholar
  23. 23.
    Tichy M.: Applied Methods of Structural Reliability, pp. 168–170. Kluwer Academic Publisher, The Netherlands (1993)MATHCrossRefGoogle Scholar
  24. 24.
    Ditlevsen O., Madsen H.O.: Structural Reliability Method. John Wiley & Sons, Chichester, UK (1996)Google Scholar
  25. 25.
    Melchers R.E.: Structural Reliability: Analysis and Prediction. Ellis Horwood Ltd., Chichester, UK (1987)Google Scholar
  26. 26.
    Zhao Y.G., Ono T.: A general procedure for first/second order reliability method (Form/Sorm). Struct. Saf. 21, 95–112 (1999)CrossRefGoogle Scholar
  27. 27.
    Union Internationale des Chemins de Fer, UIC CODE 518, Sec. 10-1-1-1, second edn., (2003)Google Scholar
  28. 28.
    EN 14363: Railway Applications, Testing for the Acceptance of Running Characteristics of Railway Vehicles, Testing of Running Behaviour and Stationary Tests, CEN, Brussels, June 2005Google Scholar
  29. 29.
    Veneziano, D., Casciati, F., Faravelli, L.: Methods of seismic fragility for complicated systems. In: Proceedings of Second Committee on the Safety of Nuclear Installations, Specialist Meeting on Probabilistic Methods in Seismic Risk Assessment for NPP, Livermore, California (1983)Google Scholar
  30. 30.
    Fravelli L.: Response-surface approach for reliability analysis. ASCE J. Eng. Mech. 115(12), 2763–2768 (1989)CrossRefGoogle Scholar
  31. 31.
    Huh J.: Reliability analysis of nonlinear structural systems using response surface method. KSCE J. Civil Eng. 4(3), 119–166 (2000)CrossRefGoogle Scholar
  32. 32.
    Bucher C., Macke M.: Response surface methodology. In: Nikolaidis, E., Ghiocel, D.M., Singhal, S. (eds) Structural Reliability Handbook, CRC Press, Boca Raton (2005)Google Scholar
  33. 33.
    Bucher C.G., Bourgund U.: A fast and efficient response surface approach for structural reliability problems. Struc. Saf. 7, 57–66 (1990)CrossRefGoogle Scholar
  34. 34.
    Wong F.S.: Slope reliability and response surface method. ASCE J. Geotech. Eng. 111, 32–53 (1985)CrossRefGoogle Scholar
  35. 35.
    Wong F.S.: Uncertainty in dynamic soil-structure interaction. ASCE J. Eng. Mech. 110, 308–324 (1984)CrossRefGoogle Scholar
  36. 36.
    Bucher, C.G., Chen, Y.M., Scholar, G.I.: Time variant reliability analysis utilizing response surface approach, reliability and optimization of structural systems ‘88. In: Proceedings of Second IFIP WG7.5 Conference, pp. 1–14. Springer, Berlin (1988)Google Scholar
  37. 37.
    Rajashekar M.R., Ellingwood B.R.: A new look at the response surface approach for reliability analysis. Struc. Saf. 12, 205–220 (1993)CrossRefGoogle Scholar
  38. 38.
    Shinozuka M.: Basic analysis of structural safety. J. Struct. Div. ASCE 109(ST-3), 721–740 (1983)CrossRefGoogle Scholar
  39. 39.
    Xia F., True H.: The dynamics of the three-piece-freight truck. J. Veh. Syst. Dyn. 41, 212–221 (2004)Google Scholar
  40. 40.
    Karamchandani A., Bjerager P., Cornell C.A.: Adaptive importance sampling. In: Ang, M., Shinozuka, G.I. (eds) Proceedings of ICOSSAR 89, pp. 855–862. A.H.S., Schueller, New York (1989)Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Saeed Mohammadzadeh
    • 1
  • Manie Sangtarashha
    • 1
  • Habibollah Molatefi
    • 1
  1. 1.School of Railway EngineeringIran University of Science and TechnologyTehranIran

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