Accuracy analysis of the Brownian motion approach for the ballistic resistance estimation: Comparison of numerical and experimental distributions

The ballistic resistance assessment is an active research field that deals with the estimation of the perforation probability of a given protection/bullet combination. The modelling challenge is to increase accuracy and precision of estimates based on a small sample of hidden penetration processes (limitation of experimental measurement tools due to the complexity of dynamic impact phenomenon). Actually, existing methods make use of the impacting bullet initial velocity and the protection response coded in a binary outcome (0 if perforation takes place and 1 if not). Recently, a Brownian motion approach has been proposed using the numerical integration of stochastic differential equations. This contribution analysis the sensitivity of the ballistic resistance estimations regarding the model parameters. To fulfil the desired goal, the numerical and experimental distribution of the estimates are compared. Available database allows the computation of a point estimation of the perforation probability at a given impact velocity. Statistical Bootstrap is performed to obtain the experimental distribution of the perforation probability in order to avoid costly experiments. In the other side, the model parameters uncertainty is propagated to the model estimations using Monte Carlo simulations. The resulted numerical distribution encompass the inherent stochastic model randomness and the model parameters uncertainty effect. Furthermore, the numerical experiments are generated as the experimental observations in the interest of a fair comparison. First, the numerical and experimental distributions are compared regarding the optimum values of the model parameters and randomly selected values over the tolerance intervals. It is concluded that the model presents a low sensitivity to the parameters estimation. Next, the experimental and numerical variance of the perforation probabilities are investigated. It is observed that the model estimations are in good agreement with the experimental one. Finally, the distribution of the mean difference between the numerical and experimental distributions is analysed as a function of the bullet impact velocity. Again, the model appears to have a low sensitivity to its parameters estimation uncertainty. Further-more, it is showed that the model performance depends on the bullet initial impact velocity. Therefore, it is suggested to further investigate the functional form of the stochastic differential equation coefficient in order to better estimate the perforation probability as a function of the initial impact velocity.