Using mutual information to pre-process input data for a virtual sensor

Mutual information can be used to determine appropriate input signals and input transformations for a black-box model that represents a virtual sensor. Mutual information is a measure of the strength of the input-output relationship, and can be computed without any assumptions about the linearity of the input-output process. The power of the method is demonstrated with an incompressible flow process. Results using mutual information clearly show that all three input signals are necessary to capture the input-output mapping. In addition, nonlinear transformations, such as raising each input to a power, can be evaluated by checking the corresponding mutual information. Results show that raising two of the inputs to the exponent ½ gives the highest mutual information, which is consistent with the governing equation