A study of equivalent electrical circuit fitting to electrochemical impedance using a stochastic method

Modeling electrochemical impedance spectroscopy is usually done using equivalent electrical circuits. These circuits have parameters that need to be estimated properly in order to make possible the simulation of impedance data. Despite the fitting procedure is an optimization problem solved recurrently in the literature, rarely statistical significance of the estimated parameters is evaluated. In this work, the optimization process for the equivalent electrical circuit fitting to the impedance data is detailed. First, a mathematical development regarding the minimization of residual least squares is presented in order to obtain a statistically valid objective function of the complex nonlinear regression problem. Then, the optimization method used in this work is presented, the Differential Evolution, a global search stochastic method. Furthermore, it is shown how a population-based stochastic method like this can be used directly to obtain confidence regions to the estimated parameters. A sensitivity analysis was also conducted. Finally, the equivalent circuit fitting is done to model synthetic experimental data, in order to demonstrate the adopted procedure.