An identifying function approach for determining structural identifiability of parameter learning machines

Structural identifiability (SI) is a fundamental prerequisite for system modeling and parameter estimation. It concerns theoretical uniqueness of model parameters determined from ideal model structure and error-free input-output observations. In this work, we present an identifying function (IF) approach for examining SI of parameter learning machines with the help of Rank Theorem in Riemann geometry. The resulting theorem works by checking the rank of the derivative matrix (DM) of IF. Further, based on the DM, an analytic method for constructing identifiable independent parametric functions is presented. The relationship of structural nonidentifiability, parameter redundancy and parameter dependence is therefore clarified. Several model examples from the literature are presented to examine their identifiability property.