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


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.


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


Wheel flange force


Instantaneous load of wheel


Wheel flange angle


Coefficient of friction between flange rim and rail


Total number of tests for Monte Carlo analysis


Number of observations for G(x) ≤ 0


Real limit state function of derailment


Approximate limit state function of derailment (response surface function)

a, b, c, d

Coefficients of response surface function


Random variables representing track geometric parameters


Total number of random variables


Joint probability density function of importance sampling


Main joint density function of random variables


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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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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