A novel hybrid model for state of health prediction in lithium batteries based on non-stationary transformers optimized by tree-structured Parzen estimator considering health factors

Rui He, Tian Peng, Xinyu Zhang, Zhigang Chen, Junhao Yao, Muhammad Shahzad Nazir and Chu Zhang

Applied Energy, 2026, vol. 402, issue PC, No S030626192501760X

Abstract: Accurate prediction of State of Health (SOH) in lithium batteries is crucial for improving the performance, prolonging the service life, preventing failures, and ensuring the safe use of lithium batteries. This paper proposes a multivariate predictive correction model for lithium battery SOH based on Time-Varying Filter Empirical Mode Decomposition (TVFEMD), Pearson Correlation Coefficient (PCC), Kernel Principal Component Analysis (KPCA), improved Bayesian algorithm, Non-stationary Transformers (NSTransformers), and Regularized Online Sequential Extreme Learning Machine (ReOSELM). In order to reduce the complexity of lithium battery data and health factors and to fully extract the features, multiple methods are used for processing. Firstly, TVFEMD is used for the initial decomposition of lithium battery health state data, then KPCA is applied to downsize the decomposed data, and then PCC is selected for correlation analysis of the health factors to select features with high correlation. Next, the NSTransformers model is employed for predicting the lithium battery SOH, and a tree-structured Bayesian optimization algorithm, namely, Tree-structured Parzen Estimator (TPE) is used to optimize the important parameters of the NSTransformers model, enhancing the model's predictive performance. Finally, the ReOSELM model is used to correct the initial prediction errors, and the initial predicted values and error-corrected predicted values are summed to obtain the final lithium battery SOH prediction values. This paper compares the prediction results of the multivariate and univariate models. Compared with the other eight multivariate benchmark models, the MAE and RMSE of the TVFEMD-PCC-KPCA-TPE-NSTransformers-ReOSELM multivariate model proposed in this paper are reduced by about 0.1 %, and the R are increased by more than 1 %, which verifies the superiority of the multivariate model proposed in this paper in the prediction of lithium battery SOH.

Keywords: State of health of Lithium battery; TVFEMD; Tree-structured Parzen estimator; Non-stationary transformers; ReOSELM (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.apenergy.2025.127030

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