Reliable Discrimination of Models Based on EIS Data

Abstract

We present a test to discriminate equivalent electrical models via electrochemical impedance spectroscopy ͑EIS͒ data collected on a frequency response analyzer ͑FRA͒. Derived in the set-membership framework, this test is an interesting alternative to classical estimators, as it does not rely on statistical thresholding and bypasses many numerical limitations ͑initialization, convergence͒ of nonlinear least-squares methods. Models are systematically discarded when their associated impedance is proved not to satisfy both the experimental data and the uncertainty range of the FRA. In this paper, we detail the methodology adapted to FRA measurements and apply the test on known electrical circuits to evaluate the required uncertainty ranges of different commercial impedance meters.The expansion of lithium-metal and lithium-ion batteries as highenergy-density storage devices ͑portable equipment, electrical or hybrid vehicles, microelectronics, etc.͒ is currently being slowed down in the industrial market by the aging and degradation of the electrode materials upon cycling. These degradation mechanisms depend on numerous factors, several of which are still to be determined, so that they are not well understood and not brought under control yet. Modelling the kinetic reactions involved is then required to determine these parameters and quantify their respective influence. Two approaches coexist in the electrochemical literature. Either one builds a behavioral ͑or measurement͒ model from the experimental data that is later interpreted in terms of reaction mechanisms. Differential impedance analysis, for instance, does not require any prior hypothesis and builds a model from the local properties of the data. 1 Or, one tests a theoretical hypothesis by facing the associated ͑knowledge-based or process͒ model to the experimental data. For instance, a Randles-based model derived from the assumption of the electroinsertion of lithium in the cathode 2 has been proven irrelevant with data collected on cathodes like LiCoO 2 and LiNiO 2 , which suggests that other physical and chemical phenomena take place at the electrolyte/electrode interface. 3,4 Many candidates can be proposed that are much harder to discriminate with classical tools. Indeed, the quality of the decision then relies on two main issues: ͑i͒ controlling the error due to the parameter estimation process and ͑ii͒ defining a reliable condition to reject a model. As the condition usually relies on "the goodness-of-fit," when dealing with competing models it is crucial to obtain accurate estimates, because this procedure can invalidate a mechanism to the benefit of another one.Electrochemical impedance spectroscopy ͑EIS͒ is an in situ technique that aims at discriminating all electrochemical processes that occur at the electrolyte/electrode interface by their time constant. This is of particular interest because this nondestructive investigation method is easy to perform on classical electrochemical cells and can also give access to several electrochemical parameters ...