Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model

This work proposes a strategy for the robust optimization of the nonlinear dynamics of a drill-string, which is a structure that rotates and digs into the rock to search for oil. The nonparametric probabilistic approach is employed to model the uncertainties of the structure as well as the uncertainties of the bit-rock interaction model. This paper is particularly concerned with the robust optimization of the rate of penetration of the column, i.e., we aim to maximize the mathematical expectation of the mean rate of penetration, respecting the integrity of the system. The variables of the optimization problem are the rotational speed at the top and the initial reaction force at the bit; they are considered deterministic. The goal is to find the set of variables that maximizes the expected mean rate of penetration, respecting, vibration limits, stress limit and fatigue limit of the dynamical system.