Adaptive Reduction of Design Variables Using Global Sensitivity in Reliability-Based Optimization

This paper presents an efficient shape optimization technique based on stochastic response surfaces (SRS) and adaptive reduction of random variables using global sensitivity information. Each SRS is a polynomial chaos expansion that uses Hermite polynomial bases and provides a closed form solution of the model output from a significant lower number of model simulations than those required by conventional methods such as modified Monte Carlo Methods and Latin Hypercube Sampling. Random variables are adaptively fixed before constructing the SRS if their corresponding global sensitivity indices calculated using low-order SRS are below a certain threshold. Using SRS and adaptive reduction of random variables, reliability-based optimization problems can be solved with a reasonable amount of computational cost. The efficiency and convergence of the proposed approach are demonstrated using a benchmark case and an industrial reliability-based design optimization problem (automotive part).