Structural identifiability of impedance spectroscopy fractional-order equivalent circuit models with two constant phase elements

Abstract

Structural identifiability analysis of fractional-order equivalent circuit models (FO-ECMs) obtained through electrochemical impedance spectroscopy (EIS) remains as a challenging problem. Aside from practical challenges such as measurement noise and the selection of excitation signals, no widely accepted analytical or numerical proof addressing the structural identifiability of impedance spectroscopy FO-ECMs exists. Through the use of coefficient mapping technique, this paper proposes novel computationally-efficient algebraic equations for numerical structural identifiability analysis of a widely used FO-ECM with Grünwald–Letnikov fractional derivative approximation and two constant phase elements (CPEs) including the Warburg term. The effects of the length of the data and sampling time on the proposed method for the structural identifiability analysis of the two-CPE FO-ECMs are discussed along with two examples and a discussion of the results.