Bayesian inference of constitutive parameters from video data of the impact dynamics of a ball

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 continuum 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 should match. In this study, the Bayesian inference is applied to identify two constitutive parameters (the friction and viscous coefficients) through statistical measures. The methodology shows to provide a useful tool to solve an inverse problem with a stochastic approach which allows to reference the results in a statistic frame starting from indirect and sparse information.