Uncertainty quantification in multibody dynamics – Application to the PKM Exechon robust dynamic analysis

In many cases, when we want to study the dynamic behavior of complex mechanical systems that are subjected to large displacements and rotations, the resulting equation of motion is nonlinear. Therefore, the mathematical model is too complex to provide an analytical solution. Nowadays the dynamic of complex systems it is usually studied with multi-body codes through numerical integration of the equations. High-performance mechanical system requires a compromise between efficiency and effectiveness. The mathematical model as well as the parameters of the model are contaminated with uncertainties, therefore to improve the predictability of the model uncertainties must be take into account. The aim of the project is to show through an industrial application, how to take into account all the possible source of uncertainties that may arise in a multi-body (MB) system and a flexible MB system, in order to increase the robustness of the numerical model. This project will particularly focus on uncertainties related to (1) the inertial properties of the bodies, (2) the placement of sensor and actuators during experiments, (3) Controllers parameters and (4) joints friction and (5) uncertainties related to the stiffness matrices of flexible parts of a flexible multi-body system. Through the Maximum Entropy Principle the prior probability distribution of the random variable are constructed, then the stochastic dynamical equation are solved through the Monte Carlo simulation method, which will allow us through mathematical statistics, to obtain a confidence region of the response of the system. These sensitivity analysis will be useful to understand (1) how these uncertainty affect the response of the system and (2) which parameters influence the most the system.