Guaranteed estimation of electrochemical parameters by set inversion using interval analysis
Résumé
The bounded-error approach to parameter estimation, mainly developed in the context of control and signal processing, is applied in the electrochemistry field in order to obtain reliable estimates for kinetic parameters. The method is based on the assumption that an uncertainty bar is available for each measurement. A set guaranteed to contain all values of the parameter vector that lead to model outputs consistent with these error bars is then computed, based on interval analysis and set inversion. The resulting technique is applied on simulated and experimental data for several classical electrochemical models. Its merits are compared to those of a more traditional approach based on least square estimation by iterative local optimization. A first obvious difference is that the point estimate provided by the latter method may or may not belong to the set estimated by the former, because it does not take the bounds on the uncertainty into account. Moreover, as our approach is global, it escapes the difficult problem of initialization encountered with iterative optimization methods. Finally, the set obtained is a natural characterization of the uncertainty on the estimated parameters.