In this paper, the fractional-order modeling of multiple groups of lithium-ion batteries with different states is discussed referring to electrochemical impedance spectroscopy (EIS) analysis and iterative learning identification method. The structure and parameters of the presented fractional-order equivalent circuit model (FO-ECM) are determined by EIS from electrochemical test. Based on the working condition test, a P-type iterative learning algorithm is applied to optimize certain selected model parameters in FO-ECM affected by polarization effect. What’s more, considering the reliability of structure and adaptiveness of parameters in FO-ECM, a pre-tested nondestructive $1/f$ noise is superimposed to the input current, and the correlative information criterion (CIC) is proposed by means of multiple correlations of each parameter and confidence eigen-voltages from weighted co-expression network analysis method. The tested batteries with different state of health (SOH) can be successfully simulated by FO-ECM with rarely need of calibration when excluding polarization effect. Particularly, the small value of ${\mathrm{CIC}}_{\alpha }$ indicates that the fractional-order $\alpha$ is constant over time for the purpose of SOH estimation. Meanwhile, the time-varying ohmic resistance $R_0$ in FO-ECM can be regarded as a wind vane of SOH due to the large value of ${\mathrm{CIC}}_{R_0}$. The above analytically found parameter-state relations are highly consistent with the existing literature and empirical conclusions, which indicates the broad application prospects of this paper.

本文结合电化学阻抗谱（EIS）分析和迭代学习识别方法，讨论了多组状态不同的锂离子电池的分数阶建模。通过电化学测试的EIS确定了所提出的分数阶等效电路模型（FO-ECM）的结构和参数。基于工作条件测试，应用P型迭代学习算法优化受极化效应影响的FO-ECM中某些选定的模型参数。此外，考虑到FO-ECM（一种经过预先测试的无损检测）的结构可靠性和参数自适应性$\mathrm{1个}/F$将噪声叠加到输入电流上，并通过加权共表达网络分析方法通过每个参数与置信本征电压的多重相关性，提出了相关信息标准（CIC）。FO-ECM可以成功模拟具有不同健康状态（SOH）的被测试电池，并且在排除极化效应时很少需要校准。特别是${\mathrm{中投公司}}_{\alpha }$ 表示分数阶 $\alpha$为了进行SOH估算，它是随时间变化的常数。同时，时变欧姆电阻${\mathrm{[R}}_0$ 由于FO-ECM的巨大价值，可以将其视为SOH的风向标 ${\mathrm{中投公司}}_{{\mathrm{[R}}_0}$。以上分析发现的参数-状态关系与现有文献和经验结论高度吻合，表明了本文的广阔应用前景。