Comparison study of parameter estimation techniques for rock failure-criterion models

This paper presents a comparative study of parameter estimation of rock failure criteria using different statistical methods, such as the least squares, least median squares, and reweighted least squares. The Mises-Schleicher and Drucker-Prager unified (MSDPu) failure criterion, a nonlinear polyaxial failure criterion suitable for different rock strength data, has been considered for this study. The procedure for determining model parameters from scattered data using the least median squares method is presented, and the methods of identifying the scattered data are discussed. The use of the reweighted least squares method for improving statistical performance of model parameter estimation from scattered data is presented. Using the variable transformation technique, the parameter estimation problem has been formulated as an unconstrained minimization problem. Here, both traditional nonlinear programming techniques and recently developed evolutionary optimization algorithms have been employed, and a comparative study of their relative efficacy is presented. Of several traditional nonlinear unconstrained minimization techniques, only the Hooke-Jeeves method could be used to find the optimum value, but its robustness is much lower than that of evolutionary algorithms. Evolutionary algorithms can be applied to find the optimal solution for cases with a high degree of robustness.