Concept Identification for Complex Engineering Datasets

Finding meaningful concepts in engineering application datasets which allow for a sensible grouping of designs is very helpful in many contexts. It allows for determining different groups of designs with similar properties and provides useful knowledge in the engineering decision making process. Also, it opens the route for further refinements of specific design candidates which exhibit certain characteristic features. In this work, an approach to define meaningful and consistent concepts in an existing engineering dataset is presented. The designs in the dataset are characterized by a multitude of features such as design parameters, geometrical properties or performance values of the design for various boundary conditions. In the proposed approach the complete feature set is partitioned into several subsets called description spaces. The definition of the concepts respects this partitioning which leads to several desired properties of the identified concepts, which cannot be achieved with state-of-the-art clustering or concept identification approaches. A novel concept quality measure is proposed, which provides an objective value for a given definition of concepts in a dataset. The usefulness of the measure is demonstrated by considering a realistic engineering dataset consisting of about 2500 airfoil profiles where the performance values (lift and drag) for three different operating conditions were obtained by a computational fluid dynamics simulation. A numerical optimization procedure is employed which maximizes the concept quality measure, and finds meaningful concepts for different setups of the description spaces while also incorporating user preference. It is demonstrated how these concepts can be used to select archetypal representatives of the dataset which exhibit characteristic features of each concept.