Systematic method to identify patterns in engineering data

In physics and engineering, data is represented as attribute-value pairs with corresponding measurement units. Due to the functional model building process in the natural sciences, any functional relationship with measurement units based on a dimensions concept can be written in terms of dimensionless groups. This is guaranteed by the Pi-Theorem of Buckingham which is based on the condition of dimensional homogeneity. These dimensionless groups are determined in the model building process by selecting the relevant problem variables and applying the Pi-Theorem. The Pi-Theorem helps in some cases to check whether the relevance list is formally complete and whether there are variables contained which are not relevant for the problem. This work focuses on the transformation of engineering data with dimensionless groups leading to a dimensionality reduction. The application of dimensionless groups to data mining problems has been observed to lead to improved results. It is shown that the similarity transformations map all physically completely similar data onto the very same point in the dimensionless space and represents a whole class of data. Using this property, the patterns found by a data mining algorithm can be verified by the physically completely similar data of an attribute-value pair in the database. An application of the knowledge discovery in database process based on dimensionless groups is demonstrated. The limitations and underlying assumptions of the approach are enumerated and discussed.