State variable and optimization potential-based multi-objective optimization method and application in compressor blade airfoil design

To improve the optimization accuracy and efficiency, state variable and optimization potential-based multi-objective optimization (MOP) method is introduced. State variable records whether the simulation failed, which caused by ill geometry and mismatched predetermined boundary condition, and is consequently incorporated into objective function through weighted average method to improve the accuracy of surrogate model and optimization. Optimization potential, which represents the difference between present performance and ideal optimal objective, can be used to direct MOP and avoids the manual selection of weight vectors. Four optimization cases, including traditional weighted optimization, state variable based optimization, optimization potential based optimization, and the optimization combined presented two methods, are applied to optimize a typical compressor blade airfoil and demonstrate the proposed optimization method. Results show that the combination of these two methods produces the best optimization result. In which the state variable method generates most of improvement in optimal performance and the optimization potential method notably improves optimal performance under large incidences. The introduction of state variable excludes the invalid objective values at one sample point rather than directly removing or keeping, so that the accuracy of surrogate model is significantly improved and obtains better optimal results. The distribution of optimization potential among each incidence is similar to that of weight vector. Using its summation to construct objective function can be deemed as automatically assigning a preferable weight vector and the optimal result consequently presents slight preferable performance.