Lithium-ion Battery SOH Estimation Based on the Fractional-order Learnable Activation Function FO-KAN

To address the "black-box" nature of lithium-ion battery state-of-health (SOH) estimation and the inability of traditional models to capture internal physical effects—such as nonlinearity—this paper proposes a physics-informed "white-box" estimation method (FO-KAN) that integrates fractional-order calculus dynamics with Kolmogorov-Arnold Networks (KAN). Departing from traditional B-spline functions, this method employs fractional-order Chebyshev polynomials—which incorporate long-memory effects—as the learnable activation functions within the KAN. An adaptive update algorithm treats the fractional order as a learnable parameter during backpropagation, enabling the identification of the equivalent fractional-order system's order and indirectly characterizing the anomalous diffusion trends caused by porous electrode degradation. Following a rigorous selection of health features based on correlation coefficients, the method was validated using NASA and CALCE datasets. The results demonstrate that FO-KAN offers high accuracy and robustness, achieving a root mean square error (RMSE) as low as 0.0040 on the NASA B0005 test set. With a 60% training ratio, the minimum RMSE and MAE reached 0.0049 and 0.0054, respectively; the model's performance metrics significantly outperformed advanced benchmarks such as TCN and BiLSTM. The adaptively learned fractional order exhibits a monotonic decay consistent with physical phenomena like the non-uniform growth of the solid electrolyte interphase (SEI) layer, offering a novel paradigm for "white-box" battery state diagnosis.