The design of turbomachinery cascades is a typical high dimensional and computationally expensive problem, a metamodel-based global optimization and data mining method is proposed to solve it. A modified Efficient Global Optimization (EGO) algorithm named Multi-Point Search based Efficient Global Optimization (MSEGO) is proposed, which is characterized by adding multiple samples at per iteration. By testing on typical mathematical functions, MSEGO outperforms EGO in accuracy and convergence rate. MSEGO is used for the optimization of a turbine vane with non-axisymmetric endwall contouring (NEC), the total pressure coefficient of the optimal vane is increased by 0.499%. Under the same settings, another two optimization processes are conducted by using the EGO and an Adaptive Range Differential Evolution algorithm (ARDE), respectively. The optimal solution of MSEGO is far better than EGO. While achieving similar optimal solutions, the cost of MSEGO is only 3% of ARDE. Further, data mining techniques are used to extract information of design space and analyze the influence of variables on design performance. Through the analysis of variance (ANOVA), the variables of section profile are found to have most significant effects on cascade loss performance. However, the NEC seems not so important through the ANOVA analysis. This is due to the fact the performance difference between different NEC designs is very small in our prescribed space. However, the designs with NEC are always much better than the reference design as shown by parallel axis, i.e., the NEC would significantly influence the cascade performance. Further, it indicates that the ensemble learning by combing results of ANOVA and parallel axis is very useful to gain full knowledge from the design space.
An efficient global optimization algorithm based on augmented radial basis function
