Application Study Of Co-Kriging Surrogate Model In Compressor Cascade Aerodynamic Optimization

The continuous improvement of aero-engine performance puts forward higher requirements for the study of advanced and efficient aerodynamic optimization design methods.Among them,the optimization design method based on surrogate model plays an important role in aerodynamic optimization.At present,the agent model is mainly constructed with high-confidence samples.The acquisition of expensive samples takes a lot of time and computation,especially for the complex problems of multi-variables.It is inefficient to construct the model with expensive samples,which makes the whole optimization process inefficient.Therefore,it is of great engineering significance to use a large number of cheap samples with small calculations and a small number of expensive sample points to build models for optimization.For a high subsonic compressor cascade,we construct a Co-Kriging surrogate model using expensive and cheap samples.The cascade is aerodynamically optimized with the total pressure loss coefficient as the target parameter,and the flow field performance in the cascade before and after optimization is analyzed.At the same time,combined with the optimization results of Kriging model,we deeply analyze the advantages of Co-Kriging proxy model in aerodynamic optimization.Firstly,we clarify the basic theory and core idea of Co-Kriging surrogate model.According to the mathematical deduction process of Kriging model,the pre-estimation formula of Co-Kriging agent model is deduced.In view of the single and bivariate functions and the mathematical characteristics of the high subsonic compressor cascade studied in this paper,the Co-Kriging proxy model is successfully constructed by using the programming language of matlab.Then,we use the univariate and bivariate test functions to verify the influence of the number of expensive samples and the number of cheap samples on the prediction accuracy of the Co-Kriging surrogate model.The results show that the Co-Kriging surrogate model is not sensitive to the number of expensive samples,but highly sensitive to the number of cheap samples.The Co-Kriging model can maintain sufficient accuracy only if the number of cheap samples is sufficient and the distribution trend of real functions can be predicted.In this paper,we use the RAE2822 airfoil optimization example to compare the surface pressure and the lift and drag coefficients of the airfoil before and after optimization,which ensures the feasibility of the surrogate model in the field of aerodynamic optimization design.Finally,we take the high subsonic compressor cascade as the research object and use the cubic B-spline curve to parameterize the blade profile.We take the control vertex ordinate as the design variable,and establish Co-Kriging proxy model in two different ways(dense grid,Euler equation and N-S equation).We use the model to optimize the design of the cascade.the optimization results are compared with the original cascade and Kriging model to optimize the performance of the cascade.Compared with the Kriging model,the Co-Kriging proxy model constructed by sparse grid can significantly improve the optimization efficiency,and the total optimization time is reduced by 26.74%.The total pressure loss of the optimized cascade is reduced by 8.96% compared with the prototype.The result of optimization is less than 1% different from that of Kriging model constructed with high reliability samples.Therefore,the Co-Kriging agent model constructed by sparse grids has higher efficiency in aerodynamic optimization and can meet the needs of engineering optimization design.