Fast State-of-Health Estimation of Lithium-Ion Batteries Using Short-Term Relaxation-Voltage Features Integrated with a Differential Evolution-Optimized Extreme Learning Machine Algorithm

Accurate and rapid state-of-health (SOH) estimation is important for lithium-ion battery management, but many existing methods require complete charge–discharge curves or long static-rest measurements. This study develops a SOH estimation method that combines short-term relaxation-voltage features with a differential evolution-optimized extreme learning machine (DE-ELM). After the initial relaxation transient, the apparent time-varying relaxation descriptor follows an approximately linear trend over the selected fitting interval; its fitted slope and intercept, together with the finite-time relaxation voltage (quasi-OCV), are used as health indicators. Differential evolution optimizes the ELM parameters and reduces dependence on random initialization. The method was tested on one lithium iron phosphate (LFP) battery module and one nickel–cobalt–aluminum (NCA) cylindrical cell under the investigated laboratory protocols and training-set ratios. The relaxation descriptors and quasi-OCV showed overall, chemistry- and direction-dependent associations with SOH rather than a universally monotonic relationship. In the reported experiments, the mean absolute percentage error did not exceed 0.411% when 5 min of post-charge or post-discharge relaxation data were used. Under the reported test protocol, DE-ELM achieved an RMSE of 0.335%, MAE of 0.231%, MAPE of 0.275%, and R2 of 0.9938. It was competitive with the four benchmark machine-learning models and yielded lower errors in several settings. These findings provide preliminary evidence that short-term relaxation-voltage data can support rapid and data-efficient SOH estimation for scheduled or opportunistic battery diagnostics.