Parameter Optimization of Rock Failure Criterion Using Error-in-Variables Approach

Abstract

Parameters of rock failure criteria are estimated using an optimization procedure based on appropriate objective function. In the development of objective function, it is assumed that the independent variables are free from errors. But, as measurement error is attributed to equipment and random testing effects, all the measuring variables may have some error. In such cases, a statistical approach known as error-in-variables (EIVs) method has been proposed in literature. In EIV, the parameter vectors and reconciled values of the measured variables are estimated. The parameter estimation of such problem is associated with increase in dimensions of the optimization problems, and due to chosen nonlinear models, the resulting optimization problem is generally nonconvex. In the present study, the EIV approach has been applied for estimation of rock strength parameter for multiaxial rock failure criteria using evolutionary optimization algorithms. The rock strength parameters and the mean square error values so obtained have been compared with that obtained from least square and reweighted least-square methods.