To reduce huge computation of the traditional stochastic optimization methods for engineering optimization

approximation model methods with acceptable accuracy for engineering design are developed based on the statistical theory. Especially

the approximation model methods can be applied to the aerodynamic optimization design instead of the time-consuming computational fluid dynamics(CFD)analysis to shorten the design process and reduce the computational cost. In the aerodynamic optimization design of turbomachine

the approximation model methods enable to balance the computational cost and accuracy

whose successful applications in centrifugal compressor impeller

diffuser

and mixed-flow pump impeller designs are introduced to show a wide engineering foreground. An optimization design system has been constructed and practically used for centrifugal compressor components and mixed-flow pump impeller.