摘要
鋰離子電池(Lithium-Ion batteries)與質子交換膜燃料電池(Proton Exchange Membrane Fuel Cells, PEMFCs)是現今新能源的兩大主流。鋰離子電池的主要優點在於具備高儲存能量密度、使用壽命長、自放電率低、無記憶效應與低溫環境適應強等特性,被廣泛應用於汽車動力電池、筆電、手機、電子裝置電池以及作為儲能電池使用。質子交換膜燃料電池則具備了高能源轉換效率、低污染、高功率產出特性也廣泛應用於車輛動力、可攜式電力與發電廠場所。本論文主要是針對質子交換膜燃料電池與鋰離子電池的健康狀態(State of Health, SOH)及剩餘使用壽命(Remain Useful Life, RUL)的預測模型與演算法的研究。本研究包含了二個議題，在第三章提出長短期記憶-注意力(Long-Short Term Memory with attention, AT-LSTM)、支持向量回歸( Support Vector Regression)與隨機森林回歸(Random Forest Regression)之集成模型(Ensemble Model)應用於質子交換膜燃料電池容量退化預測的研究;第四章提出長短期記憶-注意力與梯昇回歸(Gradient Boosted Regression, GBR)之集成模型堆疊式長短期記憶(Stacked Long-Short Term Memory, SLSTM)應用於鋰離子電池(Lithium-Ion Batteries)循環壽命(Cycle Life)預測的研究，應用差分進化演算法(Differential Evolution Algorithm)尋求最佳參數及蒙地卡羅(Monte Carlo dropout)求得預測區間條件下，以平均絕對百分比誤差(Mean Absolute Percentage Error, MAPE)、根均方誤差(Root Mean Square Error, RMSE) 、平均絕對誤差(Mean Absolute Error, MAE)、相對誤差(Relative Error, RE)、絕對百分比誤差(Absolute Percentage Error, APE)來驗證集成模型的精準度，所得結果皆優於單一模型。最後提出結論及對後續研究的建議。
關鍵字：鋰離子電池；燃料電池；長短期記憶；梯昇回歸

ABSTRACT
Lithium-ion batteries and proton exchange membrane fuel cells (PEMFCs) are two main streams of new energy. The main advantages of lithium-ion batteries are their high storage energy density, long service life, low self-discharge rate, no memory effect, and strong adaptability to the low-temperature environment. They are widely used in automobile power batteries, laptops, mobile phones, electronic devices batteries, and energy storage batteries. Proton exchange membrane fuel cells have high energy conversion efficiency, low pollution, high power output characteristics, and are widely used in vehicle power, portable electricity, and power plant sites. The study of this dissertation is to propose the prediction model and algorithm of state of health (SOH) for lithium-ion batteries and remain useful life (RUL) for PEMFCs and lithium-ion batteries. In the third chapter, the ensemble model of long-short term memory with attention (AT-LSTM), support vector regression (SVR), and random forest regression (RFR)were proposed to predict the capacity degradation of PEMFCs. In chapter 4, To propose a study of the stacked long-short term memory (SLSTM) ensemble model based on the gradient boosted regression(GBR) and AT-LSTM applied to forecast the lithium-ion batteries cycle life. Apply differential evolution (DE)algorithm to get the best parameter and Monte Carlo dropout to get the prediction confidence interval(CI), accuracy of the ensemble model was verified by mean absolute percentage error (MAPE), root means square error (RMSE), mean absolute error (MAE), relative error (RE) and absolute percentage error (APE). The results are superior to the single model. The last chapter is the conclusions and future study.

Keywords: Lithium-ion battery; Fuel cells; Stacked long-short term memory; Monte
Carlo dropout

References
1.Liu, C., Wang, Y., Chen, Z. Degradation model and cycle life prediction for
lithium-ion battery used in hybrid energy storage system. Energy. 2019; 166:
796–806.
2.Harting, N., Schenkendorf, R., Wolff, N., Krewer, U. State-of-health
identification of lithium-ion batteries based on nonlinear frequency response
analysis: First steps with machine learning. Applied Sciences. 2018; 8(5), 821.
3.Tan, Y., Zhao, G. A novel state-of-health prediction method for lithium-ion
batteries based on transfer learning with long short-term memory networks. IEEE
Transactions on Industrial Electronic 2019.doi:10.1109/TIE.2019.2946551.
4.Zhang, C., Zhu, Y., Dong, G., Wei, J. Data‐driven lithium‐ion battery states
estimation using neural networks and particle filtering. International Journal
Energy Research. 2019; 43:8230–8241.
5.Li H, Ravey A, N’Diaye A, Djerdir A. Online adaptive equivalent consumption
minimization strategy for fuel cell hybrid electric vehicle considering power
sources degradation. Energy Conversion and Management. 2019; 192:133-149.
6.Jouin M, Gouriveau R, Hissel D, Péra MC, Zerhouni N. Prognostics of PEM fuel
cell in a particle filtering framework. International Journal of Hydrogen
Energy. 2014;39(1):481-494.
7.Zhang D, Cadet C, Bérenguer C, Yousfi-Steiner N. Some improvements of particle
filtering based prognosis for PEM fuel cells,” IFAC-PapersOnLine.
2016;49(28):162-167.
8.Robin C, Gerard M, Franco AA, Schott P. Multi-scale coupling between two
dynamical models for PEMFC aging prediction. International Journal of Hydrogen
Energy.2013;38(11): 4675-4688.
9.Polverino P, Pianese. Model-based prognostic algorithm for online RUL
estimation of PEMFCs. In: Proceedings 2016 IEEE 3rd Conference Control and
Fault-Tolerant Systems.Barcelona, Spain, 599-604, 2016.
10.Chen K, Laghrouche S, and A. Djerdir A. Fuel cell health prognosis using
unscented Kalman filter: Postal fuel cell electric vehicles case study.
International Journal of Hydrogen Energy. 2019;44(3):1930-1939.
11.Javed K, Gouriveau R, Zerhouni N, Hissel D. Prognostics of proton exchange
membrane fuelcells stack using an ensemble of constraints based connectionist
networks. Journal of Power Sources.2016; 324:745-757.
12.Silva RE, Gouriveau R, Jemei S, Hissel D, Boulon L, Agbossou K, Steiner NY.
Proton exchange membrane fuel cell degradation prediction based on adaptive
neuro-fuzzy inference systems. International Journal of Hydrogen Energy.
2014;39(21):11128-11244.
13.Morando S, Jemei S, Hissel D, Gouriveau R, Zerhouni N. Proton exchange
membrane fuel Cell ageing forecasting algorithm based on echo state network.
International Journal of Hydrogen Energy.2017;42(2):1472-1480.
14.Wu Y, Breaz E, Gao F, Paire D, Miraoui A. Nonlinear performance degradation
prediction of proton exchange membrane fuel cells using relevance vector
machine. IEEE Transactions on Energy Conversion.2016;31(4):1570-1582.
15.Liu J, Li Q, Chen W, Yan Y, Qiu Y, Cao T. Remaining useful life prediction of
PEMFC based on long short-term memory recurrent neural networks. International
Journal of Hydrogen Energy.2019;44(11):5470-5480.
16.Zhou D, Gao F, Breaz E, Ravey A, Miraoui A. Degradation prediction of PEM fuel
cell using a moving window based hybrid prognostic approach.
Energy.2017;138:1175-1186.
17.Ma R, Li Z, Breaz E, Liu C, Bai H, Briois P, Gao F. Data-fusion prognostics of
proton exchange membrane fuel cell degradation. IEEE Transaction on Industry
Applications.2019;55(4):4321-4331.
18.Cheng Y, Zerhouni N, Lu C. A hybrid remaining useful life prognostic method
for proton exchange membrane fuel cell. International Journal of Hydrogen
Energy. 2018;43(27):12314-12327.
19.Li Z, Wu D, Hu C, Terpenny J. An ensemble learning-based prognostic approach
with degradation-dependent weights for remaining useful life prediction.
Reliability Engineering and System Safety.2019;184:110-122.
20.Shao M, Zhu XJ, Cao HF, Shen HF. An artificial neural network ensemble method
for fault diagnosis of proton exchange membrane fuel cell system.
Energy.2014;67:268-275.
21.Zhang D, Baraldi P, Cadet C, Yousfi-Steiner N, Bérenguer C, Zio E. An ensemble
of models for integrating dependent sources of information for the prognosis
of the remaining useful life of proton exchange membrane fuel cells.
Mechanical systems and Signal Processing.2019; 124:479-501.
22.Zhang Y, Xiong R, He H, Pecht M. Long short-term memory recurrent neural
network for remaining useful life prediction of lithium-ion batteries. IEEE
Transactions on Vehicular Technology.2018;67(7):5695–5705.
23.Chollet F, Allaire JJ. Deep learning with R. Shelter Island, NY, USA: Manning
Publications,2017.
24.Wang Y, Huang M, Zhao L. Attention-based LSTM for aspect-level sentiment
classification. In: Proceedings of the 2016 Conference on Empirical Methods in
Natural Language Processing. Austin, Texas, USA, 606-615, 2016.
25.Ma R, Yang T, Breaz E, Li Z, Briois P, Gao F. Data-driven proton exchange
membrane fuel cell degradation predication through deep learning method.
Applied Energy. 2018; 231:102-115.
26.Kim S, Kang M. Financial series prediction using attention LSTM,”
arXiv:1902.10877.2019.
27.Liu J, Wang G, Duan LY, Abdiyeva K, Kot AC. Skeleton-based human action
recognition with global context-aware attention LSTM networks. IEEE
Transactions on Image Processing.2017;27(4):1586-1599.
28.Ran X, Shan Z, Fang Y, Lin C. An LSTM-based method with attention mechanism
for travel time prediction. Sensors. 2019;19(861):1-22.
29.Jouin M, Gouriveau R, Hissel D, Péra MC, Zerhouni N. Prognostics of proton
exchange membrane fuel cell stack in a particle filtering framework including
characterization disturbances and voltage recovery. In: 2014 International
Conference on Prognostics Health Management. Cheney, WA, USA, 1-6, 2014.
30.Huang J, Bo Y, Wang H. Electromechanical equipment state forecasting based on
genetic algorithm–support vector regression. Expert Systems with Applications.
2011;38(7):8399-8402.
31.García FT, Villalba LJ, Portela J. Intelligent system for time series
classification using support vector machines applied to supply-chain. Expert
Systems with Applications.2012;39(12):10590-10599.
32.Wang FK, Du T. Implementing support vector regression with differential
evolution to forecast motherboard shipments. Expert Systems with Applications.
2014;41(8)3850-3855.
33.Breiman L. Random forests. Machine Learning. 2001;45(1):5-32.
34.Wang LA, Zhou X, Zhu X, Dong Z, Guo W. Estimation of biomass in wheat using
random forest regression algorithm and remote sensing data. The Crop Journal.
2016; 4(3):212-219.
35.Li Y, Zou C, Berecibar M, Nanini-Maury E, Chan JC, van den Bossche P, Van
Mierlo J, Omar N. Random forest regression for online capacity estimation of
lithium-ion batteries.Appl Energy. 2018; 232:197-210.
36.Baudron P, Alonso-Sarría F, García-Aróstegui JL, Cánovas-García F, Martínez-
Vicente D, Moreno-Brotóns J. Identifying the origin of groundwater samples in
a multi-layer Aquifer system with random forest classification. Journal of
Hydrology .2013;499:303-315.
37.Gu F, Guo J, Yao X, Summers P A, Widijatmoko SD, Hall P. An investigation of
the current status of recycling spent lithium-ion batteries from consumer
electronics in China. Journal of Cleaner Production. 2017;161: 765-780.
38.Mansouri SS, Karvelis P, Georgoulas G, Nikolakopoulos G. Remaining useful
battery life prediction for UAVs based on machine learning. IFAC-
PapersOnLine.2017;50:4727-4732.
39.Zhang Y, Xiong R, He H, Pecht MG. Long short-term memory recurrent neural
network for remaining useful life prediction of lithium-ion batteries. IEEE
Transactions on Vehicular Technology. 2018;67(7):5695-5705.
40.Li X, Zhang L, Wang Z, Dong P. Remaining useful life prediction for lithium-
ion batteries based on a hybrid model combining the long short-term memory and
Elman neural networks. Journal of Energy Storage.2019;21:510-518.
41.Li Y, Zou C, Berecibar M, Nanini-Maury E, Chan JCW, van den Bossche P, Van
Mierlo J, Omar N. Random forest regression for online capacity estimation of
lithium-ion batteries. Applied Energy.2018;232:197-210.
42.Mishra M, Martinsson J, Rantatalo M, Goebel K. Bayesian hierarchical model-
based prognostics for lithium-ion batteries. Reliability Engineering and
system Safety. 2018;172: 25-35.
44.Guo, P., Cheng, Z., Yang, L. A data-driven remaining capacity estimation
approach for lithium-ion batteries based on charging health feature
extraction. Journal of Power Sources. 2019; 412:442–450.
45.Cheng, Y., Zerhouni, N., Lu, C. A hybrid remaining useful life prognostic
method for proton exchange membrane fuel cell. International Journal of
Hydrogen Energy. 2018; 43, 12314–21237.
46.Li, Z., Wu, D., Hu, C., Terpenny, J. An ensemble learning-based prognostic
approach with degradation-dependent weights for remaining useful life
prediction. Reliability Engineering and System Safety.2019;184:110–122.
47.Javed, K., Gouriveau, R., Zerhouni, N.; Hissel, D. Prognostics of proton
exchange membrane fuel cells stack using an ensemble of constraints based
connectionist networks.Journal of Power Sources. 2016; 324:45–757.
48.Shao, M., Zhu, X.J., Cao, H.F., Shen, H.F. An artificial neural network
ensemble method for fault diagnosis of proton exchange membrane fuel cell
system. Energy 2014, 67, 268–275.
49.Zhang, D., Baraldi, P., Cadet, C., Yousfi-Steiner, N.; Bérenguer, C.; Zio, E.
An ensemble of models for integrating dependent sources of information for the
prognosis of the remaining useful life of proton exchange membrane fuel cells.
Mechanical systems and Signal Processing.2019; 124: 479–501.
50.Li, Z., Fang, H., Yan, Y. An ensemble hybrid model with outlier detection for
prediction of lithium-ion battery remaining useful life. In Proceedings of the
2019 Chinese Control and Decision Conference (CCDC), Nanchang, China, 2019;
pp. 2630–2635.
51.Zhang, Y., Xiong, R., He, H., Liu, Z. A LSTM-RNN method for the lithuim-ion
battery remaining useful life prediction. In Proceedings of the 2017
Prognostics and System Health Management Conference (PHM-Harbin), Harbin,
China, 2017; pp. 1–4.
52.Breiman, L. Random forests. Machine. Learning. 2001; 45:5–32.
53.Friedman, J.H. Stochastic gradient boosting. Computational Statistics and Data
Analysis.2002; 38:367–378.
54.Ridgeway, G. Generalized boosted models: A guide to the GBM package. Update
2007, 1–15.
55.Storn R, Price K. Differential evolution – a simple and efficient heuristic
for global optimization over continuous spaces. Journal of Global
Optimization.1997;11:341-359. https://doi.org/10.1023/A:1008202821328.
56.Gal, Y., Ghahramani, Z. Dropout as a bayesian approximation: Representing
model uncertainty in deep learning. In Proceedings of the International
Conference on Machine Learning 2016; pp. 1050–1059.
57.https://www.depends-on-the-definition.com/model-uncertainty-in-deep-learning-
with-monte-carlo-dropout/ Accessed on 12 June 2020
58.Bressel M, Hilairet M, Hissel D, Bouamama BO. Extended Kalman filter for
prognostic of proton exchange membrane fuel cell. Applied Energy.2016;164:220-
227.
59.Zhou D, Al-Durra A, Zhang K, Ravey A, Gao F. Online remaining useful lifetime
prediction of proton exchange membrane fuel cells using a novel robust
methodology. Journal of Power Sources.2018; 399:314-328.
60.Liu H, Chen J, Hissel D, Su H. Remaining useful life estimation for proton
exchange membrane fuel cells using a hybrid method. Applied
Energy.2019;237:910-919.
61.Chen K, Laghrouche S, Djerdir A. Degradation prediction of proton exchange
membrane Fuel cell based on grey neural network model and particle swarm
optimization. Energy Conversion and Management. 2019;195: 810-818.
62.Ma R, Yang T, Breaz E, Li Z, Briois P, Gao F. Data-driven proton exchange
membrane fuel cell degradation predication through deep learning method.
Applied Energy. 2018; 231:102-115.
63.Zhu L, Chen J. Prognostics of PEM fuel cells based on Gaussian process state
space models. Energy.2018;149:63-73.
64.Gouriveau R, Hilairet M, Hissel D, Jemeï S, Jouin M, Lechartier E, Morando S,
Pahon E, PéraMC, Zerhouni N. IEEE PHM 2014 Data Challenge-Details for
articipants. 2014.
65.Jouin M, Gouriveau R, Hissel D, Péra MC, Zerhouni N. Prognostics of proton
exchange membrane fuel cell stack in a particle filtering framework including
characterization disturbances and voltage recovery. In: 2014 International
Conference on Prognostics Health Management. Cheney, WA, USA, 1-6, 2014.
66.Storn R, Price K. Differential evolution – a simple and efficient heuristic
for global optimization over continuous spaces. Journal of Global
Optimization.1997;11(4):341-359.
67.Price K, Storn RM, Lampinen JA. Differential evolution: a practical approach
to global optimization. New York: Springer, 2005.
68.Gal Y, Ghahramani Z. Dropout as a Bayesian approximation: representing model
uncertaintyin deep learning. In: Proceedings of The 33rd International
Conference on Machine Learning New York, NY, USA,2016.
69.Smith, K., Saxon, A., Keyser, M., Lundstrom, B., Cao, Z. and Roc, A. Life
prediction model for grid-connected Li-ion battery energy storage system. In
Proceedings of the 2017American Control Conference (ACC), Seattle, WA, 2017;
pp. 4062–4068.
70.Severson, K.A., Attia, P.M., Jin, N., Perkins, N., Jiang, B., Yang, Z., Chen,
M.H., Aykol,M., Herring, P.K., Fraggedakis, D., et al. Data-driven prediction
of battery cycle life before capacity degradation. Nature Energy. 2019; 4: 383
–391.
71.Chen, Z., Sun, M., Shu, X., Xiao, R., Shen, J. Online state of health
estimation for lithium-ion batteries based on support vector machine. Applied
Sciences. 2018, 8, 925.
72.Wang, F.K., Mamo, T. A hybrid model based on support vector regression and
differential evolution for remaining useful lifetime prediction of lithium-ion
batteries. Journal of Sources.2018;401: 49–54.
73.Price, K., Storn, R.M., Lampinen, J.A. Differential Evolution: A Practical
Approach to Global Optimization; Springer Science & Business Media, 2006.
74.Mullen, K., Ardia, D., Gil, D.L., Windover, D., Cline, J. DEoptim: An R
package for global optimization by differential evolution. Journal of
Statistical Software. 2011;40: 1-26.