Finding the Optimal Regularization Parameter in Distribution of Relaxation Times Analysis

The distribution of relaxation times (DRT) method allows the direct interpretation of electrochemical impedance data, yielding an increased resolution in the frequency domain. Calculating the DRT from experimental impedance spectra, however, is an intrinsically ill-posed problem requiring special mathematical treatments such as, for example, the Tikhonov regularization. In this study, we propose a new approach for finding optimal regularization parameters in the Tikhonov regularization. The new test function is based on repetitive impedance measurements and a simple data resampling with a subsequent variance investigation. Furthermore, our new approach is combined with already published procedures considering the determination of best regularization parameters. Here, the combination of several tests enables a clear assignment of an upper and a lower boundary for suitable regularization parameters. Finally, both tests were applied to simulated as well as to experimental impedance data for validation. To analyze the sensitivity of the approach, varying error extent was generated to the synthetic and experimental measurements.