Studies On Distribution Of Relaxation Times From EIS Based On Feature Selection

Electrochemical impedance spectroscopy(EIS)is an important charactersation techniques in the field of electrochemistry.The distribution of relaxation times(DRT)is an effective method to analyze EIS.DRT is independent from models,and it can resolve peaks with different widths whose locations and numbers determine the characteristic time constants and the times of polarization processes occurring in the electrochemical system under study.However,deconvolution of DRT from EIS is typicall an inverse problem,which has an ill-posed problem and is particularly sensitive to experimental errors.The estimated DRT curve may be swinging with pseudo peaks,which would lead to errors in the diagnostic analysis of the electrochemical system.In the study,an analytical method based on feature selection for the distribution of relaxation times from EIS is proposed,in order to establish a correct electrochemical system model.Firstly,the DRT function is discretized by kernel density estimation,and then the experimental data set is obtained by Monte Carlo estimation through presetting the sampling points of frequency and relaxation time.In the study,the objective function is choosed to minimize the sum of squares of the errors between the measured values and the estimated values of the real-part of EIS impedance.Because of the DRT function is non-negative,solving the DRT becomes a constrained regression problem.Through the correlation analysis of the data set,it is found that the data set has multiple collinearity and the feature dimension is too high.If the regression problem is solved directly,it may lead to the instability of the DRT results and cause pseudo peaks.Secondly,a hybrid feature selection algorithm combining filter,embedding and wrapper is proposed to sparsely solve the DRT function.The variance selection method is used for preprocessing to filter out the features with minimal and meaningless variance after discretization to save the subsequent calculation cost.Then the elastic network regression is used to solve the problem of feature redundancy caused by multicollinearity of data set,while preserving the characteristics of DRT function curve smoothing.Eventually,the recursive feature elimination(RFE)algorithm is applied with the elastic network regression as the estimator for obtaining the optimal feature subset and the corresponding optimal solution,attempting to get a more stable and appropriate DRT function.Finally,four synthetic circuit models,a ZARC element,ZARC mixtures,a RC element and a fractal element,are used as experimental objects to verify the effectiveness and feasibility of the research method by comparing the accuracy of the estimation of ohmic resistance,polarization resistance,the corresponding relaxation time constant,and the degree of fitting the EIS to the DRT.From the results,using only elastic network regularization,although the ohmic and polarization resistances are estimated with high accuracy and the EIS is a good fit,pseudo-peaks appear in a ZARC element,ZARC mixtures and the fractal element circuit model.The results obtained after RFE optimization are suitable for DRT analysis,which is able to eliminate significantly pseudo-peaks and obtain the correct number of peaks and their approximate range.In practical applications,it is possible to reason about the electrochemical model of the battery,thus enabling battery diagnosis and dynamics analysis in the time domain.