Structural Identifiability of Impedance Spectroscopy Fractional-Order Equivalent Circuit Models With Two Constant Phase Elements

TL;DR

This paper addresses the challenge of determining whether fractional-order impedance models with two CPEs are structurally identifiable, introducing a novel algebraic method for analysis and applying it to battery models.

Contribution

It presents a new computational algebraic approach for the structural identifiability analysis of fractional-order impedance models with two CPEs, filling a gap in existing theoretical proofs.

Findings

The proposed method successfully analyzes a battery impedance model.

Matlab codes are provided for reproducibility.

The analysis confirms the models' structural identifiability.

Abstract

Structural identifiability analysis of fractional-order equivalent circuit models (FO-ECMs), obtained through electrochemical impedance spectroscopy (EIS) is still a challenging problem. No peer-reviewed analytical or numerical proof does exist showing that whether impedance spectroscopy FO-ECMs are structurally identifiable or not, regardless of practical issues such as measurement noises and the selection of excitation signals. By using the coefficient mapping technique, this paper proposes novel computationally-efficient algebraic equations for the numerical structural identifiability analysis of a widely used FO-ECM with Gr\"{u}nwald-Letnikov fractional derivative approximation and two constant phase elements (CPEs) including the Warburg term. The proposed numerical structural identifiability analysis method is applied to an example from batteries, and the results are discussed. Matlab codes are available on github.