阻抗谱分数阶等效电路模型的结构可辨识性
Structural Identifiability of Impedance Spectroscopy Fractional-Order Equivalent Circuit Models With Two Constant Phase Elements
摘要：
通过电化学阻抗谱（EIS）获得的分数阶等效电路模型（FO-ECMs）的结构可辨识性分析仍然是一个具有挑战性的问题。没有同行评审的分析或数值证据表明阻抗谱FO-ECM是否在结构上可识别，无论测量噪声和激励信号的选择等实际问题如何。利用系数映射技术，提出了一种新的计算效率高的代数方程，用于一种广泛使用的FO-ECM的数值结构可识别性分析，该方程采用Grünwald-Letnikov分数阶导数近似和两个包含Warburg项的常相位元素（CPE）。将所提出的数值结构可识别性分析方法应用于蓄电池的一个实例，并对结果进行了讨论。Matlab代码可以在github上找到。
英文摘要：
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 Grünwald-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.
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