Metamodelling approach using radial basis functions, stochastic search algorithm and CFD – application to blade cascade design

Abstract

This paper discusses the viability of using a metamodelling technique in conjunction with a controlled random search algorithm (CRSA) for global optimisation of costly functions. CRSA is a stochastic, population-set based algorithm, capable of performing global optimisation tasks efficiently. The metamodel technique is based on the iterative construction of response surfaces with radial basis functions (inverse multiquadrics) using the points exactly evaluated during the optimisation process. Cyclic search patterns for metamodel constrained optimisations are iteratively used for determining candidate points using CRSA. The methodology is tested on some Dixon-Szegö functions for evaluating its efficiency and robustness. For illustrative purposes, a simple case of blade cascade optimisation with profiles of NACA65 family is also presented. The maximisation of the lift-to-drag ratio is taken as objective with airfoil camber and pitch as design variables. The CFD software FLUENT is used for the flow calculations so representing the costly objective function model.