Experimental and physics-guided modeling of perforation transition and residual velocity in an insert plate–gelatin impact system

The ballistic insert plate–gelatin configuration is a hard–soft coupled terminal-ballistic system for evaluating perforation resistance and post-perforation residual threat, but reliable prediction remains difficult because real ballistic tests are costly, sparse, and limited in test conditions. Objective: This study aims to develop a physics-guided small-sample modelling framework for jointly characterizing perforation probability, mass-dependent 50% perforation velocity, and residual velocity in tungsten-alloy fragment impact tests. Methods: Based on 21 impact tests, including 11 perforation cases, a continuous-mass logistic model was established to describe perforation probability as a function of impact velocity and projectile mass. The estimated mass-dependent 50% perforation velocity was used as the threshold anchor of a physics-based residual-velocity backbone, and four residual-learning models were introduced to correct the remaining prediction error. Their outputs were integrated using a reliability-gated ensemble determined by leave-one-out cross-validation errors. Results: The continuous-mass formulation enabled information sharing between two neighboring projectile-mass groups of approximately 3.5 g and 4.1 g. With feasible-domain constraints, the fitted backbone parameters were 3.912 and 0.663. For the present dataset, the integrated model achieved a root mean square error of approximately 31 m/s and a coefficient of determination of approximately 0.60, while physics-constrained data augmentation was used only for training regularization. Conclusions: The proposed framework provides an interpretable and experimentally constrained approach for small-sample insert–gelatin ballistic data, although broader validation with additional projectile masses, insert materials, gelatin conditions, and impact velocities is still required.