Impact of normalization, standardization and pre-fit on the success rate of fitting in electrochemical impedance spectroscopy

Fitting the data of an electrochemical impedance spectroscopy (EIS) typically requires manual estimation of the initial values before regression algorithms such as complex nonlinear least squares (CNLS) can be applied. This makes the success rate of the fitting dependent on the user input. Furthermore, the Randles circuit consists of parameters with substantially differing magnitudes (e.g. capacitors and resistors), which can also strongly affect the success rate of the fitting due to numerical effects. The aim of this work is to investigate methods addressing the described limitations of fitting. Therefore, a Python implementation performing a fit for EIS is benchmarked with an equivalent open source library. The examined implementation optionally includes the normalization of the parameter values, the standardization of the impedances and a pre-fit. Applying the same equivalent circuit without additional signal processing steps and with fixed initial values defined by midpoints of the value ranges, both implementations were able to fit 46.50% of the simulated database with different spectra. Applying the normalization of the parameter values (76.25%) or the same method with additional pre-fit (97.75%) lead to a significant improvement of the success rate. The standardization of impedances did not affect the success rate.