State of health estimation of lithium batteries based on a transformer with physical constraints and multidimensional feature fusion

Abstract

To address the key bottlenecks in the state of health prediction of lithium-ion batteries under random variable load conditions, such as poor physical consistency, insufficient feature representation, and non-physical fluctuations in the prediction curves, this paper proposes a high-precision state of health prediction model that combines physical information constraints and multi-dimensional features, aiming to enhance the safety and long-term reliability of the battery management system. A neural network-transformer framework based on physical information was constructed, converting the consistency laws of irreversible battery aging into regularization loss terms in the training process to ensure physical rationality. Multi-dimensional coupled features including voltage, current, and cycle count were extracted to characterize the aging characteristics of the battery, and Bayesian optimization was applied to adaptively adjust key hyperparameters. Experimental results show that this model outperforms the comparison models in terms of MAE, RMSE, and R² metrics, effectively suppressing non-physical fluctuations, balancing high prediction accuracy and physical rationality, and providing technical support for the full life cycle health management and safe operation of lithium-ion batteries.

Graphical abstract

Keywords

lithium-ion battery / state of health / physics-informed neural network / multi-dimensional feature fusion / bayesian optimization

References

[1] Yi Z X , Chen Z L , Yin K , Wang L C , Wang K . Sensing as the key to the safety and sustainability of new energy storage devices. Protection and Control of Modern Power Systems, 2023, 8: 27

[2] Lei M F , Zhang M , Wang K . Research on bidding optimization strategy for virtual power plants with wind–solar–storage systems based on IGDT-DRO. Electrical Engineering, 2026, 108(3): 208

[3] Jiang W , Deng Y Y , Li W T , Song J L , Che S T , Wang K . Research progress of noninvasive magnetic resonance imaging in lithium-ion battery detection. Coatings, 2026, 16(4): 453

[4] Jiang W , Tan C C , Su E Q , Lu J Y , Shi H L , Wang Y , Song J L , Wang K . Advanced electronic materials for liquid thermal management of lithium-ion batteries: mechanisms, materials and future development directions. Coatings, 2026, 16(1): 59

[5] Li S , Du X , Gao Y , Fan A H , Zhao Y Y , Du H L . Enhanced energy storage performance by stabilizing antiferroelectric phase through high-entropy engineering of NaNbO₃. Journal of Materials Science: Materials in Electronics, 2026, 37(12): 888

[6] Gao Y , Du X , Li Z , Wang L H , Tian B , Tian R X , Du H L . Enhanced VOCs degradation performance of TiO₂-OV/NH₂-MIL-125 by synergistic modulation of oxygen vacancy and heterojunction. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2026, 741: 140318

[7] Wu L , Hu Y X , Du X , Lu J , Li Z , Cao N , Zhang S R , Du H L . Movable SiO₂ reinforced polymethyl methacrylate dual network coating for highly stable zinc anodes. Journal of Energy Storage, 2025, 132: 117752

[8] Lv X , Cui S H , Wang Y , Lu J Y , Yu P M , Wang K . Patch time series transformer-based short-term photovoltaic power prediction enhanced by artificial fish. Energies, 2026, 19(1): 284

[9] Zhu X S , Xu C Q , Song T B , Huang Z , Zhang Y . Sparse self-attentive transformer with multiscale feature fusion on long-term SOH forecasting. IEEE Transactions on Power Electronics, 2024, 39(8): 10399–10408

[10] Zhu B , Jia L , Pan Q K , Zhang H . Cross-domain battery SOH and RUL estimation via domain-adaptive transformer. Energy, 2025, 341: 139288

[11] Liu Z Y , Liu Y N , Zhang Y , Wu C Q , Zhang S F , Sun C . Data-driven lithium-ion battery SOH prediction: a novel SHMM-transformer-BiGRU hybrid neural network method. Measurement, 2026, 257: 118579

[12] Hu Y X , Du H L , Lu J , Zhang H , Li S , Du X . Interface synergistic stabilization of zinc anodes via polyacrylic acid doped polyvinyl alcohol ultra-thin coating. Journal of Energy Storage, 2024, 87: 111444

[13] Chen Y , Huang X H , He Y G , Zhang S Y , Cai Y J . Edge-cloud collaborative estimation lithium-ion battery SOH based on MEWOA-VMD and Transformer. Journal of Energy Storage, 2024, 99: 113388

[14] Shi M J , Xu J , Lin C P , Mei X S . A fast state-of-health estimation method using single linear feature for lithium-ion batteries. Energy, 2022, 256: 124652

[15] Xian Y H , Li M Y , Huang J Y . A lithium-ion batteries SOH estimation method based on extracting new features during the constant voltage charging stage and improving BPNN. PLoS One, 2025, 20(5): e0324868

[16] Su Z P , Lai J D , Su J H , Zhou C G , Shi Y , Xie B . Modeling and health feature extraction method for lithium-ion batteries state of health estimation by distribution of relaxation times. Journal of Energy Storage, 2024, 90: 111770

[17] Obregon J , Han Y R , Ho C W , Mouraliraman D , Lee C W , Jung J Y . Convolutional autoencoder-based SOH estimation of lithium-ion batteries using electrochemical impedance spectroscopy. Journal of Energy Storage, 2023, 60: 106680

[18] Li M , Hong J C , Shen Y H , Ma F , Liang F W , Zhang L , Zhang H Q , Zhang C , Wang J G , Xu Q . et al. Research on safety management strategy for the whole-life-cycle of power batteries in electric vehicles. Journal of Cleaner Production, 2025, 490: 144804

[19] Li Q W , Song R J , Wei Y Q . A review of state-of-health estimation for lithium-ion battery packs. Journal of Energy Storage, 2025, 118: 116078

[20] Chen Y J , Lu J Y , Tang Z , Zhu J H , Wang S , Dong H J , Wang K . Recent progress in the physics-constrained state of health estimation for lithium-ion batteries. Energies, 2026, 19(8): 1920

[21] Jiang W , Wang J C , Guo R , Wang J W , Song J L , Wang K . Electrode materials and prediction of cycle stability and remaining service life of supercapacitors. Coatings, 2026, 16(1): 41

[22] Lou C , Zhang J H , Mu X M , Zeng F P , Wang K . Innovative deep learning method for predicting the state of health of lithium-ion batteries based on electrochemical impedance spectroscopy and attention mechanisms. Frontiers of Chemical Science and Engineering, 2025, 19(6): 52

[23] Li L , Li Y J , Mao R Z , Li L , Hua W B , Zhang J L . Remaining useful life prediction for lithium-ion batteries with a hybrid model based on TCN-GRU-DNN and dual attention mechanism. IEEE Transactions on Transportation Electrification, 2023, 9(3): 4726–4740

[24] Jia C Y , Tian Y K , Shi Y H , Jia J F , Wen J , Zeng J C . State of health prediction of lithium-ion batteries based on bidirectional gated recurrent unit and transformer. Energy, 2023, 285: 129401

[25] Li Z X , Yang Y , Li L W , Wang D Q . A weighted Pearson correlation coefficient based multi-fault comprehensive diagnosis for battery circuits. Journal of Energy Storage, 2023, 60: 106584

[26] Zheng Y S , Che Y H , Hu X S , Sui X , Stroe D I , Teodorescu R . Thermal state monitoring of lithium-ion batteries: progress, challenges, and opportunities. Progress in Energy and Combustion Science, 2024, 100: 101120

[27] Ravishankar S , Battineni G . A survey on recent advancements in auto-machine learning with a focus on feature engineering. Journal of Computational and Cognitive Engineering, 2025, 4(1): 56–63

[28] Almomani O , Alsaaidah A , Abu-Shareha A A , Alzaqebah A , Amin Almaiah M , Shambour Q . Enhance URL defacement attack detection using particle swarm optimization and machine learning. Journal of Computational and Cognitive Engineering, 2025, 4(3): 296–308

[29] Dalal S , Rani U , Lilhore U K , Dahiya N , Batra R , Nuristani N , Le D N . Optimized XGBoost model with whale optimization algorithm for detecting anomalies in manufacturing. Journal of Computational and Cognitive Engineering, 2025, 4(4): 413–423

[30] Zhang C L , Luo L J , Yang Z , Zhao S S , He Y G , Wang X , Wang H X . Battery SOH estimation method based on gradual decreasing current, double correlation analysis and GRU. Green Energy and Intelligent Transportation, 2023, 2(5): 100108

[31] Peng S M , Wang Y J , Tang A H , Jiang Y X , Kan J R , Pecht M . State of health estimation joint improved grey wolf optimization algorithm and LSTM using partial discharging health features for lithium-ion batteries. Energy, 2025, 315: 134293

[32] Wang S Q , Xia P , Gong F Y , Zhao Y X , Lin P . A Bayesian-physical informed conditional tabular generative adversarial network framework for low-carbon concrete data augmentation and hyperparameter optimization. Engineering Applications of Artificial Intelligence, 2025, 152: 110811

[33] Li S H , Jiang Z L , Zhu Z W , Jiang W H , Ma Y , Sang X , Yang S Y . A framework of joint SOC and SOH estimation for lithium-ion batteries: using BiLSTM as a battery model. Journal of Power Sources, 2025, 635: 236342

[34] Wang S L , Ma C , Gao H Y , Deng D , Fernandez C , Blaabjerg F . Improved hyperparameter Bayesian optimization-bidirectional long short-term memory optimization for high-precision battery state of charge estimation. Energy, 2025, 328: 136598

[35] Hanifi S , Cammarono A , Zare-Behtash H . Advanced hyperparameter optimization of deep learning models for wind power prediction. Renewable Energy, 2024, 221: 119700

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Higher Education Press