Modeling gunshot bruises in soft body armor with an adaptive fuzzy system

Gunshots produce bruise patterns on persons who wear soft body armor when shot even though the armor stops the bullets. An adaptive fuzzy system modeled these bruise patterns based on the depth and width of the deformed armor given a projectile's mass and momentum. The fuzzy system used rules with sinc-shaped if-part fuzzy sets and was robust against random rule pruning: Median and mean test errors remained low even after removing up to one fifth of the rules. Handguns shot different caliber bullets at armor that had a 10%-ordnance gelatin backing. The gelatin blocks were tissue simulants. The gunshot data tuned the additive fuzzy function approximator. The fuzzy system's conditional variance V[Y/X = x] described the second-order uncertainty of the function approximation. Handguns with different barrel lengths shot bullets over a fixed distance at armor-clad gelatin blocks that we made with Type 250 A Ordnance Gelatin. The bullet-armor experiments found that a bullet's weight and momentum correlated with the depth of its impact on armor-clad gelatin (R2 = 0.881 and p-value < 0.001 for the null hypothesis that the regression line had zero slope). Related experiments on plumber's putty showed that highspeed baseball impacts compared well to bullet-armor impacts for large-caliber handguns. A baseball's momentum correlated with its impact depth in putty (R2 = 0.93 and p-value < 0.001). A bullet's momentum similarly correlated with its armor-impact in putty (R2 = 0.97 and p-value < 0.001). A Gujarati-Chow test showed that the two putty-impact regression lines had statistically indistinguishable slopes for p-value = 0.396. Baseball impact depths were comparable to bullet-armor impact depths: Getting shot with a .22 caliber bullet when wearing soft body armor resembles getting hit in the chest with a 40-mph baseball. Getting shot with a .45 caliber bullet resembles getting hit with a 90-mph baseball.