Space Infill Study of Kriging Meta-Model for Multi-Objective Optimization of an Engine Cooling Fan

Abstract

The meta-model based optimization is widely used in the aerodynamical design process for rotating machines, and the main industrial cost of such techniques comes from physical evaluations of answers, either by experimental or numerical means. Design of experiment (DoE) with Latin Hypercube sampling has been studied for the design of an automotive fan system for engine cooling. Surrogate models constructed with Kriging and Co-Kriging methods are estimated with the help of a reference numerical model. The objective of the present work is to assess the necessary number of sampling points for the initial DoE for this kind of meta-model method and to study the influence brought by the sample dispersion. The objective being to execute future aerodynamic optimizations at a reduced cost in term of timeframe and CPU effort. Two parameters, camber and chord length were used to investigate geometrical changes and they are completed with a physical parameter which is the flow rate. The optimization should lead to a higher level of performances with given constraints of rotational speed, torque and packaging. A criterion was defined for the initial necessary number of evaluations and the variances for different DoE design were controlled for the sake of comparison. Starting from an initial meta-model, a variance based method was used for further training with additional points. Uncertainties due to lack of information outside the domain led the model to regularly propose new points on the borders, yielding to high sample variance. A genetic-algorithm was employed to explore the final meta-model and to conduct a multi-objective optimization. Results are presented in terms of Pareto Front and are analysed with SOM to understand the relations between factors and objectives. A final optimal design was selected, and proposed to demonstrate the relevancy of the method.