Knowledge discovery in scientific data using hierarchical modeling in dimensional analysis

In the automotive and the aerospace industry large amounts of expensively gathered experimental data are stored in huge databases. The real worth of these databases lies not only in easy data access, but also in the additional possibility of extracting the engineering knowledge implicitly contained in these data. As analytical modeling techniques in engineering are usually limited in model complexity, data driven techniques gain more and more importance in this kind of modeling. Using additional engineering knowledge such as dimensional information, the data driven modeling process has a great potential for saving modeling as well as experimental effort and may therefore help to generate financial benefit. In a technical context, knowledge is often represented as numerical attribute-value pairs with corresponding measurement units. The database fields form the so-called relevance list which is the only information needed to find the set of dimensionless parameters for the problem. The Pi-Theorem of Buckingham guarantees that for each complete relevance list a set of dimensionless groups exists. The number of these dimensionless parameters is less than the number of dimensional parameters in the dimensional formulation, thus a dimensionality reduction can easily be accomplished. Additionally. dimensional analysis allows a hierarchical modeling technique, first creating models of subsystems and then aggregating them consecutively into the overall model using coupling numbers. This paper gives a brief introduction into dimensional analysis and then shows the procedure of hierarchical modeling, its implications, as well, as its application to knowledge discovery in scientific data. The proposed method is illustrated in a simplified example from the aerospace industry.