Research on Metamodel-Based Global Design Optimization and Data Mining Methods

Abstract

The turbomachinery cascades design is a typical high dimensional computationally expensive and black box problem, thus a metamodel-based design optimization and data mining method is proposed and programed in this work, which is intended to gain knowledge of design space except for optimal solutions. The method combines a Kriging-based global algorithm with data mining techniques of self-organizing map (SOM), analysis of variance (ANOVA), and parallel axis. NACA Rotor 37, a typical axial transonic rotor blade, is selected for the research. Through SOM analysis, the overall changing trend of performance indicators like isentropic efficiency, total pressure ratio, and so on for the rotor blade is nearly consistent; therefore, a single-objective design for maximizing isentropic efficiency of the rotor blade with constraints prescribed on total pressure ratio and mass flow rate is carried out. The computational fluid dynamics (CFD) evaluations needed for the Kriging-based optimization process amount to only 1/5 of that required when employing a modified differential evolution (DE) algorithm as the optimizer. The isentropic efficiency of related optimal solution is 1.74% higher than the reference design. Then, the interactions among design variables and critical performance indicators as well as common features of better solutions are analyzed via ANOVA and parallel axis. Particularly, an ANOVA-based optimization is tried, which can validate the detected significant variables and gain knowledge of subspace with minimum cost. By integrating data mining results with practical knowledge of aerodynamics, it is confirmed that the shock wave has the most significant influence on the aerodynamic performance of transonic rotor blades. The sweep in tip section is found to be responsible for slight tradeoff relation between isentropic efficiency and total pressure ratio. The combinations of forward lean, thinner section profile near the blade leading edge, and compound sweep are favorable to get better aerodynamic performance, which is validated by the configuration of optimal solution obtained by MBGO algorithm.