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Prediction of state of health (SOH), a crucial aspect of battery management systems, necessitates accurate and reliable estimations for lithium-ion batteries. However, achieving high-precision SOH estimation using the deep extreme learning machine (DELM) in complex environments is challenging due to the instability caused by its random key parameters. To address this, we propose a novel approach that combines the improved bald eagle search (IBES) algorithm with DELM. By utilizing the IBES algorithm, we can extract highly relevant health indicators from the battery's parameter curve during charging and discharging, as well as the incremental capacity curve. These indicators serve as inputs to the constructed estimation model, which predicts SOH under different working conditions. The proposed method has been validated using publicly available experimental data, with an overall error in SOH estimation of less than 1%. In comparison to the existing model, the proposed method achieves RMSE, MAE, and MAPE values lower than 0.35%, 0.26%, and 0.21%, respectively. These findings demonstrate that the proposed method excels in terms of both the speed and accuracy of SOH estimation, showcasing its enhanced robustness and reliability. [ABSTRACT FROM AUTHOR]