Multiresolution Wavelet Method for Trend Removal in Electrochemical Noise Data From LiFePO₄ Batteries

Electrochemical potential noise signals from LiFePO4 batteries often contain a slowly varying trend component that overlaps with and distorts the intrinsic low-frequency electrochemical noise. This component must therefore be removed to enable reliable downstream analysis. To address this issue, this work presents a new segment-wise wavelet-based detrending (SWBD) method for electrochemical noise signals measured in commercial rechargeable LiFePO4/graphite batteries during discharge. The approach combines signal segmentation, dyadic discrete wavelet decomposition, and joint optimization of the mother wavelet and decomposition level under a regularized SNR&#x2013;RMSE&#x2013;parsimony criterion. It is validated against widely used detrending methods, including high-order polynomial fitting, Empirical Mode Decomposition (EMD), and fixed-wavelets configurations. Quantitative evaluation across discharge segments shows that SWBD achieves higher signal-to-trend ratios and lower reconstruction errors, resulting in improved temporal and spectral fidelity. Power spectral density (PSD) analysis shows that SWBD produces a smooth and continuous spectral slope with <inline-formula> <tex-math notation="LaTeX">$\alpha \approx ~1$ </tex-math></inline-formula>, consistent with 1/<inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula>-type electrochemical noise. Shannon energy analysis confirms a uniform and gradual multiscale energy distribution, indicating effective energy dispersion across scales. Overall, the results demonstrate that SWBD provides a robust framework for adaptive trend removal by preserving the intrinsic stochastic dynamics of electrochemical fluctuations and enabling accurate spectral and statistical characterization in lithium-ion energy storage systems.