The Buckingham's $π$, theorem has been recently introduced in the context of Non destructive Testing \& Evaluation (NdT\&E) , giving a theoretical basis for developing simple but effective methods for multi-parameter estimation via dimensional analysis. Dimensional groups, or $π-$groups, allow for the reduction of the number of parameters affecting the dimensionless measured quantities. In many real-world applications, the main interest is in estimating only a subset of the variables affecting the measurem…