Identifiability: from qualitative analysis to model structure approximation

Abstract The question whether a physical model structure is identifiable is usually considered in a qualitative way, i.e. it is answered with a yes/no answer. However when considering parameters in large scale (nonlinear) physical models it is relevant to raise the question how the notion of identifiability can be quantified. This implies addressing the question how the model structure can be approximated so as to achieve identifiability, while retaining the interpretation of the physical parameters. In this paper this problem is addressed in a prediction error setting, and it is shown how the construction of best locally identifiable model structure approximations relates to notions of controllability and observability. Additionally the analysis in terms of an prediction error approach relates to iterative optimization algorithms (like Gauss-Newton and Steepest-Descent) and to Bayesian parameter estimation.