Rigorous model-based uncertainty quantification with application to terminal ballistics, part I: Systems with controllable inputs and small scatter
This work is concerned with establishing the feasibility of a data-on-demand (DoD) uncertainty quantification (UQ) protocol based on concentration-of-measure inequalities. Specific aims are to establish the feasibility of the protocol and its basic properties, including the tightness of the predictions afforded by the protocol. The assessment is based on an application to terminal ballistics and a specific system configuration consisting of 6061-T6 aluminum plates struck by spherical S-2 tool steel projectiles at ballistic impact speeds. The system's inputs are the plate thickness and impact velocity and the perforation area is chosen as the sole performance measure of the system. The objective of the UQ analysis is to certify the lethality of the projectile, i.e., that the projectile perforates the plate with high probability over a prespecified range of impact velocities and plate thicknesses. The net outcome of the UQ analysis is an M/U ratio, or confidence factor, of 2.93, indicative of a small probability of no perforation of the plate over its entire operating range. The high-confidence (>99.9%) in the successful operation of the system afforded the analysis and the small number of tests (40) required for the determination of the modeling-error diameter, establishes the feasibility of the DoD UQ protocol as a rigorous yet practical approach for model-based certification of complex systems.
© 2011 Elsevier Ltd. Received 23 August 2011. Revised 1 December 2011. Accepted 3 December 2011. Available online 9 December 2011. The authors gratefully acknowledge the support of the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials.