Estimating the parameters of a fatigue model using Benders' decomposition Articles uri icon

publication date

  • November 2013

start page

  • 309

end page

  • 331


  • 1


  • 210

International Standard Serial Number (ISSN)

  • 0254-5330

Electronic International Standard Serial Number (EISSN)

  • 1572-9338


  • This paper shows how Benders decomposition can be used for estimating the parameters of a fatigue model. The objective function of such model depends on five parameters of different nature. This makes the parameter estimation problem of the fatigue model suitable for the Benders decomposition, which allows us to use well-behaved and robust parameter estimation methods for the different subproblems. To build the Benders cuts, explicit formulas for the sensitivities (partial derivatives) are obtained. This permits building the classical iterative method, in which upper and lower bounds of the optimal value of the objective function are obtained until convergence. Two alternative objective functions to be optimized are the likelihood and the sum of squares error functions, which relate to the maximum likelihood and the minimum error principles, respectively. The method is illustrated by its application to a real-world problem.


  • Chemistry
  • Materials science and engineering


  • benders' decomposition; fatigue; least-squares; linear optimization; maximum likelihood; sensitivity analysis