Estimating Initial Values for EIS Analysis by Complex Nonlinear Least Squares Fitting

Abstract With the advent of digital frequency response analyzers, the measurement of electrochemical impedance spectra (EIS) has become relatively straight-forward, and as a result, large amounts of such spectra are generated. The perhaps more complex task then is the development of physically useful equivalent circuits, and the estimation of the circuit parameters. In many cases, the software used to drive present day EIS measurement systems comes complete with tools to perform complex non-linear least squares (CNLS) fitting in order to estimate the equivalent circuit characteristic parameters. For most such CNLS packages it is necessary to provide an initial estimate of the parameter value in order for the fitted model to converge to a suitable local minimum. The paper provides a review of a number of different techniques that can be used to generate reasonable initial estimates for parameter values. A system of X65 carbon steel corroding in a CO2 saturated environment undergoing iron carbonate (FeCO3) formation is used as a case study to show how to readily estimate parameter values for R-C networks, constant phase elements, R-L networks, and Warburg diffusion processes.