Bayesian Inference of Constitutive Parameters of a Ball Material in an Oblique Collision

Abstract

The trajectory of a ball impacting with an angle on a rigid boundary is recorded with a high-speed camera and the dynamics is reconstructed in a computer. Several experiments are carried out in order to obtain statistical distributions of the trajectory. On the other hand, a simple model of a viscoelastic material ball simulates the experiment. If the values of the constitutive parameters (e.g. elastic and viscous modulus, friction coefficient, etc.) in the numerical model are correct, the simulated dynamics and the experimental data must be comparable. In this study, the Bayesian inference is applied to identify two constitutive parameters (the friction and viscous coefficients) through statistical measures. Furthermore and once the distributions of the stochastic parameters are available, a propagation of uncertainties is carried out to verify the experimental results and also, to obtain information about other variables of interest which experimental determination is not straightforward, such as contact forces, time of contact, etc.