Optimization procedures for the inversion of impedance spectra to the distribution of relaxation times

Tikhonov regularization technology has been applied to solve the ill-posed inversion problem of electrochemical impedance spectra inversion to the distribution of relaxation times (DRT). However, the parameters contributing to the accuracy of the DRT obtained by this method, including types of the EIS data, regularization matrixes, regularization parameters, and shape factors, need sophisticated adjustment. In this work, the influences of these parameters were discussed in detail, and the results showed that the effects of some process parameters on the DRT worked complementarily. Therefore, the DRT inversion program with the particle swarm optimization algorithm (PSO), a multi-objective global optimization algorithm, was developed. It was demonstrated the accuracy, feasibility, and reliability of the proposed DRT program. The program was also applied to separate and quantify the electrochemical processes of the commercial LIBs.