Adaptive reduction of random variables using global sensitivity in reliability-based optimisation

This paper presents an efficient shape optimisation technique based on Stochastic Response Surfaces (SRS) and adaptive reduction of random variables using global sensitivity information. The SRS is a polynomial chaos expansion that uses Hermite polynomial bases and provides a closed form solution of the model output from a significantly lower number of model simulations than those required by conventional methods such as the Monte Carlo simulations and Latin Hypercube sampling. Random variables are adaptively fixed before constructing the SRS if their corresponding Global Sensitivity Indices (GSI) calculated using the low-order SRS are below a certain threshold. It has been shown that the GSI can be calculated analytically because the SRS employs the Hermite polynomials as bases. Using SRS and adaptive reduction of random variables, reliability-based optimisation problems are solved with a significant reduction in computational cost. The efficiency and convergence of the proposed approach is demonstrated using a benchmark case and an industrial Reliability-Based Design Optimisation (RBDO) problem.