The drill-string dynamics is difficult to predict due to the nonlinearities and uncertainties involved in the problem. In this paper a stochastic computational model is proposed to model uncertainties in the bit-rock interaction model. To do so, a new strategy that uses the nonparametric probabilistic approach is developed to take into account model uncertainties in the bitrock nonlinear interaction model. The mean model considers the main forces applied to the column such as the bit-rock interaction, the fluid-structure interaction and the impact forces. The nonlinear Timoshenko beam theory is used and the nonlinear dynamical equations are discretized by means of the finite element method.

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One of the main features of electromechanical systems is the mutual influence between electrical and mechanical parts. This interaction characterizes coupling. Each part of the system affects the behavior of the other. To properly represent the dynamics of a coupled system, it is necessary to properly characterize how is this interaction between the parts. Any change in model of the interaction affects the behavior of the entire system. Typically, the coupling between electrical and mechanical parts is expressed by a set of coupled differential equations. The dynamics of the coupled system is given by an initial value problem comprising this set of coupled differential equations. Some references in the literature claim that it is possible to reduce the number of equations in initial value problem without changing the interaction between the electrical and mechanical parts. They assume a hypothesis that a term in the equations can be neglected in a way that the coupling between the parts becomes a linear algebraic relationship. This hypothesis reduces the number of equations to be integrated, however it is a pitfall! It implies the decoupling of the motor-cart system, misleading the results as it is shown in this paper.

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This paper is devoted to the construction of a stochastic nonlinear dynamical system for signal generation such as the production of voiced sounds. The dynamical system is highly nonlinear, and the output signal generated is very sensitive to a few parameters of the system. In the context of the production of voiced sounds the measurements have a significant variability. We then propose a statistical treatment of the experiments and we developed a probability model of the sensitive parameters in order that the stochastic dynamical system has the capability to predict the experiments in the probability distribution sense. The computational nonlinear dynamical system is presented, the Maximum Entropy Principle is used to construct the probability model and an experimental validation is shown.