Accurate state of health prediction is critical for the safe operation and maintenance of lithium-ion batteries in electric vehicles and energy storage systems. However, under random variable load conditions, existing methods often suffer from poor physical consistency, insufficient feature representation, and non-physical fluctuations in prediction curves. In a study published in ENG. Chem. Eng. , researchers at Qingdao University and collaborators propose a physics-informed neural network-transformer model that addresses these challenges by embedding physical constraints into the deep learning framework.
The model was evaluated on the NASA random load battery aging dataset, which contains multiple battery cells with cycle counts greater than 100. Three multidimensional features were extracted: voltage drop, average current, and cycle count. Pearson correlation analysis confirmed strong correlations with SOH, with absolute correlation coefficients exceeding 0.95 for all three features.
The model architecture combines a Transformer backbone with physical information constraints. The Transformer's self-attention mechanism captures long-term dependencies in battery degradation sequences. The physical constraint enforces the monotonic degradation law of battery capacity: as cycles increase, remaining capacity strictly decreases. This prior knowledge is incorporated as a regularization loss term. If a predicted value shows a rebound, the physical loss generates a positive penalty, forcing the optimizer to adjust parameters to comply with physical laws.
Bayesian optimization using the Tree-structured Parzen Estimator algorithm was employed for hyperparameter tuning. After 50 iterations, the optimal learning rate was determined as 1.94 × 10⁻³, the physical constraint weight as 0.668, and the Transformer feature mapping dimension as 64.
Experimental results on the validation set demonstrated that the PINN-Transformer model achieved an R² of 0.98973, significantly outperforming LSTM with an R² of 0.90078, GRU with an R² of 0.90133, and TSMixer with an R² of 0.90078. The average MAE and RMSE were reduced by 0.00932 and 0.01028 respectively compared to the suboptimal TSMixer model. The predicted SOH values showed good agreement with actual measured values, with R² consistently above 0.985 across all test cases.
Ablation experiments further validated the contribution of each component. The complete model with both physical constraints and hyperparameter optimization achieved an R² of 0.98611. Removing the physical constraint caused a significant decline in R² to 0.80945 and resulted in unphysical rebound phenomena in the later aging stage. Using default hyperparameters while retaining physical constraints yielded an R² of 0.94657, confirming that Bayesian optimization further enhances performance.
Compared with single-feature input models, the fusion of multiple features fully represents the coupled evolution laws of battery aging, significantly enhancing the model's anti-interference ability against complex working condition noise. The physical constraints ensure that the predicted trajectory complies with the irreversible aging law, completely eliminating physical violations such as prediction rebound.
This work provides a reliable and interpretable solution for battery state assessment under complex random loads, with strong potential for practical engineering applications in battery management systems.
ENGINEERING Chemical Engineering
Experimental study
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State of health estimation of lithium batteries based on a transformer with physical constraints and multidimensional feature fusion
14-Jul-2026