Data Fitting of EIS

The rapid development of computer technology has yielded powerful tools that make it possible for modem EIS analysis software not only to optimize an equivalent circuit, but also to produce much more reliable system parameters. For most EIS data analysis software, a non-linear least squares fitting method, developed by Marquardt and Levenberg, is commonly used. The NLLS Levenberg-Marquardt algorithm has become the basic engine of several data analysis programs. 

The core of the NLLS Levenberg-Marquardt algorithm is the use of the chi-squared parameter, %2, which is defined as follows 

For the complex non-linear least squares (CNLS) method, the object function, S, is defined as [5, 6] 

ak) = Zre(a)i,ak) +jZim(cai,ak) is the model function, which can be altered using the adjustable parameters the model function can often be presented by an equivalent circuit, involving such elements as resistance, capacitance, and Warburg in series and/or in parallel  

Other parameters, such as CNLS-fit residuals (Are and Ajm), also indicate the goodness of fit . They are defined as 

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