Stochastic Identification Using the Maximum Likelihood Method and a Statistical Reduction: Application to Drilling Dynamics

Abstract

A drill-string is a slender structure that drills rock to search for oil. The nonlinear interaction between the bit and the rock is of great importance for the drill-string dynamics. The interaction model has uncertainties, which are modeled using the nonparametric probabilistic approach. This paper deals with a procedure to perform the identification of the dispersion parameter of the probabilistic model of uncertainties of a bit-rock interaction model. The bit-rock interaction model is represented by a nonlinear constitutive equation, and the identification of the parameter of this probabilistic model is carried out using the Maximum Likelihood method together with a statistical reduction in the frequency domain using the Principal Component Analysis.