Analysis of the Brownian Motion Approach for Ballistic Resistance Evaluation Using the Maximum Likelihood Inference

Abstract

Armor technologists’ improvement of protection systems led to the design of complex systems. Given the risk factor on human life, increasing requirements on the ballistic resistance evaluation are imposed. Consequently, an increased effort is dedicated to estimating the perforation probability curve as a function of the bullet impact velocity. The main limitation of methods that fits a normal law to perforation velocities is their purely statistical character. A Brownian-based approach that couples the system response variability and physics was proposed using the Chi-square and Kolmogorov-Smirnov criterion function for model parameters estimation. One major limitation of this inference approach is the large experimental database required for its execution. The contribution of this paper is the introduction of the maximum likelihood inference for parameters estimation of the Brownian-based approach. The agreement between the obtained results and the experimental ones confirms the appropriateness of the likelihood inference to solve the studied problem. Moreover, the estimations uncertainty was analyzed and compared to the existing method ones. It was observed that the proposed model reduces the confidence intervals on key velocity estimations. Accordingly, the present work encourages the adoption of this proposed methodology in a laboratory context with a restrained sample size.