Making the Case for Geometric Identifiability in Electrochemical Impedance Spectroscopy

Electrochemical impedance spectroscopy (EIS) is a prevalent technique for battery characterization and testing. Despite recent advancements, EIS optimization remains a challenge faced by conventional EIS sampling techniques. One such example is the redundancy of samples. For instance, additional excitation frequencies are used to identify the parameters of a given equivalent circuit model (ECM), while this can be done with fewer excitation frequencies from a geometrical standpoint. In this brief, fundamentals of geometric identifiability of EIS ECMs are discussed and showcased for a framework formulated based on Fisher information matrix (FIM) optimization sampling. By using the geometric identifiability analysis, it is shown that the classic FIM EIS, optimizing the sensitivity of likelihood function to all the unknown parameters, leads to redundant samples. A geometric FIM EIS is then proposed, which reduces the number of sampling regions without compromising the estimation accuracy. It is yet shown that both the classic and the proposed geometric FIM EIS methods are suboptimal with respect to the geometric identifiability analysis. Both ordinary-order and factional-order ECMs are discussed, and simulation results are provided and compared against that of a conventional EIS implementation with uniform sampling.