Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion

Abstract

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.

Keywords: Correlative information criterion; Electrochemical impedance spectroscopy; Fractional-order modeling; Iterative learning identification; Weighted co-expression network analysis.