Armor's ballistic resistance simulation using stochastic process modeling

For many years, ballistic performance evaluation of protection structures makes use of the estimation of the ballistic limit velocity V₅₀, the projectile impact velocity at which there is a 50 percent probability of perforation of the assessed structure. In recent years, enhancements to risk assessment required the estimation of the entire curve of the probability of perforation. Extreme values of complete perforation (partial penetration) at low (high) impact velocity are rare events of the studied system with binary response experiments. Existing methods have comparable accuracy in estimating the V₅₀ velocity, and use the normality assumption to estimate any percentile of interest V_x. This contribution proposes to model the projectile evolution into the target as a diffusion process using the Brownian motion process. A Chi-square and Kolmogorov–Smirnov goodness of fit test is applied to estimate the drift and diffusion coefficients of the developed stochastic differential equation based on the Monte Carlo simulated sample and the experimental one. Under the assumption of constant drift and diffusion coefficients, the estimated value of the projectile deceleration matches its analytically computed value depending on the system parameters and configuration. The established model presents a comparable predictive ability, as existing methods, of the V₅₀ with the advantage of defining a bounded velocity interval in which the perforation probability varies from zero to one in accordance with the physical behavior of the system. Furthermore, the fitted model provides the probability perforation of the structure at any impact velocity with an estimate of its variability.