Proper orthogonal decomposition assisted multi-objective inverse design optimization method for the compressor cascade airfoil

The limited adoption of inverse design in engineering can be attributed to the challenges associated with predetermining optimal load distribution and the failure to consider aerodynamic performance under various operational conditions. The sparse polynomial combined with non-dominated sorting genetic algorithm-Ⅲ (NSGA3) is employed in this study to achieve the optimal load distribution under multiple operating conditions, which is utilized for inverse design. The introduction of proper orthogonal decomposition (POD) simultaneously aims to reduce the dimensionality of the static pressure distribution on the blade surface, thereby enhancing the accuracy of sparse polynomial representation. The results demonstrate that the optimized load distribution effectively shifts the maximum load towards the leading edge in comparison to the initial solution. The optimized blade profile also enhances the working range by 14.2% compared to the baseline blade profile.