Polynomial chaos expansion based robust design optimization

In this paper, we present the polynomial chaos expansion (PCE) approach as a rigorous method for uncertainty propagation and further extend its use to robust design optimization. Thus a PCE based robust design optimization approach is developed. The mathematical background of PCE is introduced, where techniques of full factorial numerical integration (FFNI) and sparse grid numerical integration (SGNI) are proposed to estimate the PCE coefficients for low and high dimensional cases, respectively. Through a rocket design example, it is shown that the robustly optimized designs of the rocket are significantly less sensitive to the input variations compared to the deterministic oneS, which demonstrates the effectiveness of the proposed PCE based robust design procedure in the designs involving varying random dimensions. Specifically, the curse of dimensionality is significantly alleviated for high-dimension problems by SGNI, which indicates the high efficiency of our approach.