Efficient Shape Optimization Using Polynomial Chaos Expansion and Local Sensitivities

This paper presents an efficient shape optimization technique based on stochastic response surfaces (polynomial chaos expansion) constructed using performance and local sensitivity data at heuristically selected collocation points. The cited expansion uses Hermite polynomial bases for the space of square-integrable probability density functions and provides a closed form solution of the performance. The focus is on calculating the uncertainty propagation using less number of function evaluations since the response surface needs to be reconstructed at each design cycle. Due to the continuum-based sensitivity analysis, the gradient information of performance is efficiently calculated and used in constructing the stochastic response surface. The efficiency and convergence of the proposed approach are demonstrated using a reliabilitybased shape optimization of a well-known structural problem.