Multidimensional Solution Clustering and Its Application to the Coolant Passage Optimization of a Turbine Blade

Abstract

Data clustering methods can be a useful tool for engineering design that is based on numerical optimization. The clustering method is an effective way of producing representative designs, or clusters, from a large set of potential designs. These methods have recently been applied to the clustering of Pareto-optimal solutions from multi-objective optimization. The results presented here focus on the application of clustering to single objective optimization results. In the case of single objective optimization, the method is used to determine the clusters in a set of quasi-optimal feasible solutions generated by an optimizer. A data clustering procedure based on an evolutionary method is briefly described. The number of clusters is determined automatically and need not be known a priori. The method is demonstrated by application to the results of a turbine blade coolant passage shape optimization problem. The solutions are transformed to a lower-dimensional space for better understanding of their variance and character. Engineering information, such as the shapes and locations of the internal passages, is supported by the visualization of clustered solutions. The clustering, transformation, and visualization methods presented in this study might be applicable to the increasing interpretation demands of design optimization.

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