### Numerical analysis of structural identifiability of electrochemical systems

Vikhansky, A *(QMUL)*

Friday 16 December 2011, 09:00-09:30

Seminar Room 1, Newton Institute

#### Abstract

Development of an experiment-based model often encounters so-called identifiability problem. Namely, if there is a system of (e.g., differential) equations at our disposal and a set of experiments to perform, the question arises whether the planned experiments allow for reliable identification of the parameters of the model, such as reaction rates or diffusivities? Since in many cases the initial answer is negative, one has to modify the experimental design. In the present research we considered identifiability of a system of reaction-diffusion equations and explicitly calculate the experimental conditions, which allows for the most reliable identification of the model’s parameters. According to our approach solution of the identifiability problem requires finding of the global maximum of a specially designed function and it is shown that the identifiability criterion is equal to the ratio of the parameters’ uncertainty to the experimental error under worst-case scenario, i.e., it characterizes the precision of the identification procedure. Since the outcome of our identifiability test is not simply “yes” or “no”, but a number, one can modify the experimental conditions in order to minimize the uncertainty.

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