鋰離子電池因具有高能量密度、高功率密度、低自回充、壽命長等優點，被廣泛應用到電動車以及其他攜帶式裝置上，然而鋰離子電池在充放電的過程中會產生固態電解質膜，導致電解質降解、電池內阻增加、電池最大電容量下降，電池的健康狀態為當前最大電容量相對於額定最大電容量的百分比，電動車用電池的產品壽命結束通常為健康狀態衰退到70%~80%，而距離電池到達產品壽命結束的充放電循環次數則是電池的剩餘使用壽命，本文將建立一個電池健康狀態與剩餘使用壽命的預測模型，預測電動車電池的最大電容量衰退，及時維護或是更換電池，線性降維主要成分分析(Principal component analysis, PCA)與非線性降維拉普拉斯特徵映射(Laplacian eigenmaps, LE)將被應用到對電池資料降維得到特徵，訓練閘門循環單元遞迴類神經網路模型預測電池狀態與剩餘使用壽命，實驗結果顯示LE可以彌補PCA局部特徵的不足，結合PCA與LE可以降低預測誤差。LE與PCA作為向量特徵尚不充足，在加入了純量特徵平均值之後整體的預測誤差大幅下降。

Lithium-ion batteries are widely used in electric vehicles (EV) and other portable devices due to their high energy density, high power density, low self-recharge, and long life. However, solid electrolyte interphase (SEI) formed during the charging and discharging process of lithium-ion batteries result in electrolyte decomposition, increased battery internal resistance, and decreased battery capacity. State-of-health (SOH) is the percentage of the current maximum capacity relative to the rated maximum capacity. The end of life (EOL) of an EV battery is usually when the SOH decays to 70%~80%, and the charge-discharge cycles before the battery reaches EOL is the remain using life (RUL) of EV battery. This thesis proposes a prediction model for SOH and RUL of lithium-ion batteries to predict the capacity decline of EV batteries for timely maintain or replacing the batteries. The features are extracted by linear dimensionality reduction, principal component analysis (PCA), and nonlinear dimensionality reduction, Laplacian eigenmaps (LE). Train the gated recurrent unit (GRU) recurrent neural network (RNN) model with the features to predict lithium-ion battery SOH and RUL. The experimental results show that LE can make up for the lack of local features of PCA, and combining PCA with LE can reduce the prediction error. The overall prediction error is greatly reduced after vector features, LE and PCA, combining with the scalar feature, average value.

[1] M. Muratori, M. Alexander, D. Arent, M. Bazilian, P. Cazzola, E. M. Dede, J. Farrell, C. Gearhart, D. Greene, A. Jenn, M. Keyser, T. Lipman, S. Narumanchi, A. Pesaran, R. Sioshansi, E. Suomalainen, G. Tal, K. Walkowicz, & J. Ward, “The Rise of Electric vehicles—2020 Status and Future Expectations,” Progress in Energy, vol. 3, no. 2, p. 022002, Mar. 2021.
[2] X. Chen, W. Shen, T. T. Vo, Z. Cao, & A. Kapoor, “An overview of lithium-ion batteries for electric vehicles,” 2012 10th International Power & Energy Conference (IPEC), pp. 230-235, Dec. 2012, doi: https://doi.org/10.1109/asscc.2012.6523269.
[3] N. Takenaka, A. Bouibes, Y. Yamada, M. Nagaoka, and A. Yamada, “Frontiers in Theoretical Analysis of Solid Electrolyte Interphase Formation Mechanism,” Advanced Materials, vol. 33, no. 37, p. 2100574, Aug. 2021, doi: https://doi.org/10.1002/adma.202100574.
[4] K. S. Ng, C.-S. Moo, Y.-P. Chen, and Y.-C. Hsieh, “Enhanced Coulomb Counting Method for Estimating state-of-charge and state-of-health of lithium-ion Batteries,” Applied Energy, vol. 86, no. 9, pp. 1506–1511, Sep. 2009, doi: https://doi.org/10.1016/j.apenergy.2008.11.021.
[5] D. Saji, P. S. Babu, and K. Ilango, “SoC Estimation of Lithium Ion Battery Using Combined Coulomb Counting and Fuzzy Logic Method,” IEEE Xplore, pp. 948–952, May 2019, doi: https://doi.org/10.1109/RTEICT46194.2019.9016956.
[6] S. Zhang, X. Guo, X. Dou, and X. Zhang, “A Rapid Online Calculation Method for State of Health of lithium-ion Battery Based on Coulomb Counting Method and Differential Voltage Analysis,” Journal of Power Sources, vol. 479, p. 228740, Dec. 2020, doi: https://doi.org/10.1016/j.jpowsour.2020.228740.
[7] H. He, R. Xiong, and J. Fan, “Evaluation of Lithium-Ion Battery Equivalent Circuit Models for State of Charge Estimation by an Experimental Approach,” Energies, vol. 4, no. 4, pp. 582–598, Mar. 2011, doi: https://doi.org/10.3390/en4040582.
[8] B. Long, W. Xian, L. Jiang, and Z. Liu, “An Improved Autoregressive Model by Particle Swarm Optimization for Prognostics of lithium-ion Batteries,” Microelectronics Reliability, vol. 53, no. 6, pp. 821–831, Jun. 2013, doi: https://doi.org/10.1016/j.microrel.2013.01.006.
[9] L. Zhang, Z. Mu, and C. Sun, “Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Exponential Model and Particle Filter,” IEEE Access, vol. 6, pp. 17729–17740, 2018, doi: https://doi.org/10.1109/access.2018.2816684.
[10] W. Xian, B. Long, M. Li, and H. Wang, “Prognostics of Lithium-Ion Batteries Based on the Verhulst Model, Particle Swarm Optimization and Particle Filter,” IEEE Transactions on Instrumentation and Measurement, vol. 63, no. 1, pp. 2–17, Jan. 2014, doi: https://doi.org/10.1109/tim.2013.2276473.
[11] M. A. Patil, P. Tagade, K. S. Hariharan, S. M. Kolake, T. Song, T. Yeo, and S. Doo, “A Novel Multistage Support Vector Machine Based Approach for Li Ion Battery Remaining Useful Life Estimation,” Applied Energy, vol. 159, pp. 285–297, Dec. 2015, doi: https://doi.org/10.1016/j.apenergy.2015.08.119.
[12] D. Liu, J. Zhou, D. Pan, Y. Peng, and X. Peng, “Lithium-ion Battery Remaining Useful Life Estimation with an Optimized Relevance Vector Machine Algorithm with Incremental Learning,” Measurement, vol. 63, pp. 143–151, Mar. 2015, doi: https://doi.org/10.1016/j.measurement.2014.11.031.
[13] H. Pan, Z. Lü, H. Wang, H. Wei, and L. Chen, “Novel Battery state-of-health Online Estimation Method Using Multiple Health Indicators and an Extreme Learning Machine,” Energy, vol. 160, pp. 466–477, Oct. 2018, doi: https://doi.org/10.1016/j.energy.2018.06.220.
[14] R. R. Richardson, M. A. Osborne, and D. A. Howey, “Gaussian Process Regression for Forecasting Battery State of Health,” Journal of Power Sources, vol. 357, pp. 209–219, Jul. 2017, doi: https://doi.org/10.1016/j.jpowsour.2017.05.004.
[15] Akram Eddahech, Olivier Briat, N. Bertrand, Jean-Yves Deletage, and Jean-Michel Vinassa, “Behavior and state-of-health Monitoring of Li-ion Batteries Using Impedance Spectroscopy and Recurrent Neural Networks,” International Journal of Electrical Power & Energy Systems, vol. 42, no. 1, pp. 487–494, Nov. 2012, doi: https://doi.org/10.1016/j.ijepes.2012.04.050.
[16] Y. Zhang, R. Xiong, H. He, and M. G. Pecht, “Long Short-Term Memory Recurrent Neural Network for Remaining Useful Life Prediction of Lithium-Ion Batteries,” IEEE Transactions on Vehicular Technology, vol. 67, no. 7, pp. 5695–5705, Jul. 2018, doi: https://doi.org/10.1109/tvt.2018.2805189.
[17] Y. Song, L. Li, Y. Peng, and D. Liu, “Lithium-Ion Battery Remaining Useful Life Prediction Based on GRU-RNN,” International Conference on Reliability, Maintainability and Safety, pp. 317–322, Oct. 2018, doi: https://doi.org/10.1109/icrms.2018.00067.
[18] Z. Zhang, M. Xu, L. Ma, and B. Yu, “A State-of-Charge Estimation Method Based on Bidirectional LSTM Networks for Lithium-ion Batteries,” 2022 17th International Conference on Control, Automation, Robotics and Vision (ICARCV), pp. 211–216, Dec. 2020, doi: https://doi.org/10.1109/icarcv50220.2020.9305394.
[19] C. Jia, Y. Tian, Y. Shi, J. Jia, J. Wen, and J. Zeng, “State of Health Prediction of lithium-ion Batteries Based on Bidirectional Gated Recurrent Unit and Transformer,” Energy, vol. 285, pp. 129401–129401, Oct. 2023, doi: https://doi.org/10.1016/j.energy.2023.129401.
[20] B. Zraibi, C. Okar, H. Chaoui, and M. Mansouri, “Remaining Useful Life Assessment for Lithium-ion Batteries Using CNN-LSTM-DNN Hybrid Method,” IEEE Transactions on Vehicular Technology, vol. 70, no. 5, pp. 4252–4261, 2021, doi: https://doi.org/10.1109/tvt.2021.3071622.
[21] J. Feng, F. Cai, H. Li, K. Huang, and H. Yin, “A data-driven Prediction Model for the Remaining Useful Life Prediction of lithium-ion Batteries,” Process Safety and Environmental Protection, vol. 180, pp. 601–615, Dec. 2023, doi: https://doi.org/10.1016/j.psep.2023.10.042.
[22] W. Wang et al., “State-of-health Estimation for lithium-ion Batteries Based on Bi-LSTM-AM and LLE Feature Extraction,” Frontiers in Energy Research, vol. 11, Aug. 2023, doi: https://doi.org/10.3389/fenrg.2023.1205165.
[23] Z. Wang, N. Liu, and Y. Guo, “Adaptive Sliding Window LSTM NN Based RUL Prediction for lithium-ion Batteries Integrating LTSA Feature Reconstruction,” Neurocomputing, vol. 466, pp. 178–189, Nov. 2021, doi: https://doi.org/10.1016/j.neucom.2021.09.025.
[24] H. Hotelling, “Simplified Calculation of Principal Components,” Psychometrika, vol. 1, no. 1, pp. 27–35, 1936.
[25] M. Belkin and P. Niyogi, “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation,” Neural Computation, vol. 15, no. 6, pp. 1373–1396, Jun. 2003, doi: https://doi.org/10.1162/089976603321780317.
[26] S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Y. Wu, “An Optimal Algorithm for Approximate Nearest Neighbor Searching Fixed Dimensions,” Journal of the ACM, vol. 45, no. 6, pp. 891–923, Nov. 1998, doi: https://doi.org/10.1145/293347.293348.
[27] S. Hochreiter and J. Schmidhuber, “Long Short-term Memory,” Neural Computation MIT-Press, 1997.
[28] K. Cho, B. Van Merriënboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning Phrase Representations Using RNN Encoder-Decoder for Statistical Machine Translation,” arXiv (Cornell University), Jun. 2014, doi: https://doi.org/10.48550/arxiv.1406.1078.
[29] D. P. Kingma, “Adam: a Method for Stochastic Optimization,” arXiv preprint arXiv:1412.6980, 2014.
[30] J. Duchi, E. Hazan, and Y. Singer, “Adaptive Subgradient Methods for Online Learning and Stochastic Optimization,” Journal of Machine Learning Research, vol. 12, no. 7, 2011.
[31] T. Tieleman and G. Hinton, “Lecture 6.5-rmsprop: Divide the Gradient by a Running Average of Its Recent Magnitude,” COURSERA: Neural Networks for Machine Learning, vol. 4, pp. 26–31, 2012.
[32] G. E. Hinton, “Improving Neural Networks by Preventing co-adaptation of Feature Detectors,” arXiv preprint arXiv:1207.0580, 2012.
[33] N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a Simple Way to Prevent Neural Networks from Overfitting,” The Journal of Machine Learning Research, vol. 15, no. 1, pp. 1929–19558, 2014.
[34] B. Saha and K. Goebel, “Battery Data Set,” NASA Prognostics Data Repository, NASA Ames Research Center, Moffett Field, CA, 2007.