Dimensional Analysis in Case-Based Reasoning

Case-based reasoning is a method intended to develop knowledge based systems by imitating the behavior of human experts. Compared to classical rule-based reasoning, case-based reasoning attempts to solve new problems by using previous cases from a case base and adapting the solution of a similar problem according to the parameters of the new situation. In case-based systems, the quality of the solutions depends mainly on the similarity measure that is used to retrieve similar cases and on the adaptation rules to modify a solution of a similar case appropriately if there is no exact case in the case base available. For all case descriptions in physics and engineering consisting of real-valued quantities with physical units, it is shown how the pi-theorem of Buckingham can be used to derive appropriate similarity conditions and to provide an appropriate case adaptation. An application of the case-based reasoning technique based on dimensionless groups is demonstrated and compared to a conventional approach.