Interval uncertain optimization for interior ballistics based on Chebyshev surrogate model and affine arithmetic

Abstract

This article proposes an interior ballistic interval optimization method with the consideration of parameter uncertainty. Interior ballistic parameters such as charge mass, web thickness, powder aperture and chamber volume are considered as design variables and described by interval number. A one-dimensional two-phase interior ballistic model is constructed, and the MacCormack scheme is used to calculate the interior ballistic parameters. A Chebyshev surrogate model is constructed to replace the one-dimensional two-phase interior ballistic model and applied to the optimization process. For each set of design variables, affine arithmetic is introduced to calculate the interval bounds of the performance index of the interior ballistic, avoiding nested double-loop optimization and improving computational efficiency. The Pareto-optimal solution is searched for by an improved non-dominant sorting genetic algorithm. An example is given to demonstrate the effectiveness of the proposed method.