EXPLOITING SIMILARITY THEORY FOR CASE-BASED REASONING IN REAL-VALUED ENGINEERING DESIGN PROBLEMS PETER HERTKORN AND STEPHAN RUDOLPH Institute for Statics and Dynamics of Aerospace Structures

Abstract. The framework of dimensional analysis is used for case-based reasoning. For all case descriptions in engineering and physics consisting of real-valued quantities with physical units, the Pi-Theorem of Buckingham can be shown to derive appropriate similarity conditions and provide an appropriate case adaptation. The advantages of the Pi-Theorem are mainly based on the properties of the so-called dimensionless groups, which are associated with each case description and can be determined even if closed form analytical modeling knowledge is not known. In precisely defined situations (in so-called completely similar cases) the knowledge of the dimensionless groups turns out to be sufficient to guarantee the correct transformation and correct case adaptation of the old problem solution to the new problem solution. In cases where such a completely similar case is not known or available, a dimensionless function interpolation technique is used and its numerical performance is investigated and compared to a classical case interpolation technique.