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研究生： 邱姿綺
Chiu, Tzu-Chi
論文名稱： 基於分段隨機係數模型預測鋰離子電池的剩餘壽命
Remaining Useful Life Prediction of Lithium-Ion Batteries Based on Piecewise Random Coefficient Models
指導教授： 鄭順林
Jeng, Shuen-Lin
學位類別： 碩士
Master
系所名稱： 管理學院 - 統計學系
Department of Statistics
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 95
中文關鍵詞： 信賴區間 、鋰離子電池 、剩餘可使用壽命 、電容再生現象 、隨機係數模型
外文關鍵詞： Confidence Interval, Lithium-Ion Batteries, Remaining Useful Life, Capacity Regeneration Phenomena, Random Coefficient Model
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    • 預測鋰離子電池的剩餘可使用壽命(Remaining Useful Life, RUL)在預後與健康管理(Prognostics and Health Management, PHM)中非常重要。電容再生現象是指鋰離子電池經歷休息時間後電容量的增加，這會對鋰離子電池的電容退化計算產生很大的影響。因此本研究考慮了電容再生現象，討論了從一般隨機係數退化模型延伸的五個隨機係數模型，當中的分段隨機係數模型可以在經歷休息時間之後捕捉到電容退化的趨勢。最後，根據美國航空暨太空總署(National Aeronautics and Space Administration, NASA)提供的鋰離子電池數據集進行案例應用，結果顯示本文提出的分段隨機係數模型可以比沒有考慮電容再生現象的模型更有效地提高鋰離子電池剩餘可使用壽命預測的準確性。藉此，我們也可以從中獲得剩餘可使用的壽命分配，從該壽命分配去推估鋰離子電池的剩餘可使用平均壽命、剩餘可使用壽命分配的第q個分位數以及相對應的信賴區間。此外，如果我們給定未來可能發生的一些使用狀況的假設去做剩餘可使用壽命的預測，結果顯示考慮電容再生現象的統計模型可以較佳地預估剩餘可使用壽命。利用此資訊可以協助判斷電池適當的置換時間，從而使鋰離子電池的效用最大化。

    Remaining Useful Life (RUL) prediction of lithium-ion batteries are very important in Prognostics and Health Management (PHM). Capacity regeneration phenomena refer to the capacity increment of lithium-ion batteries after a rest time, which leads to a great influence on the calculation of capacity degradation of lithium-ion batteries. Therefore, our research takes the capacity regeneration phenomena into consideration and proposes five random coefficient models based on the general random coefficient degradation model. The piecewise random coefficient models can catch the capacity degradation trend after multiple rest times. Finally, the case applications are carried out according to the lithium-ion battery dataset published by National Aeronautics and Space Administration (NASA). The results show that the piecewise random coefficient models proposed in this research can effectively improve the accuracy of RUL prediction than other models in the literature. Thereby, we also can obtain the estimates of mean RUL, qth quantile of RUL and the corresponding confidence intervals of the tested batteries. We give some usage scenarios may occur in the future to do prediction. The results show that considering capacity regeneration phenomena which gives accurate estimate of RUL can help to build a better statistical model. By using this information, the engineers can set a proper time point for battery replacement to maximize the effectiveness of lithium-ion batteries.

    摘要 i Abstract ii 誌謝 iii Table of Contents iv List of Tables vi List of Figures viii Chapter 1. Introduction 1 1.1 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Research Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Research Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Research Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chapter 2. Literature Review 7 2.1 Degradation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Models for Remaining Useful Life Prediction . . . . . . . . . . . . . . . . 8 2.3 Models with Considering Capacity Regeneration Phenomena for Remaining Useful Life Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Chapter 3. Methodology 14 3.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1. Model1LFDLFR(M1) . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2. Model2LRDLFR(MA2) . . . . . . . . . . . . . . . . . . . . . . 15 3.1.3. Model3LRDLRR(MA3) . . . . . . . . . . . . . . . . . . . . . . 16 3.1.4. Model4PLFDPLFR(M4) . . . . . . . . . . . . . . . . . . . . . 17 3.1.5. Model5PLRDPLFR(M5,MA5,M5,S,andMA5,S) . . . . . . . . . 18 3.1.6. Wiener Stochastic Process Model (MW and MAW) . . . . . . . . . 19 3.2 Likelihood Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.1. Model2LRDLFR . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2. Model3LRDLRR . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.3. Model5PLRDPLFR(M5) . . . . . . . . . . . . . . . . . . . . . 24 3.2.4. Model5PLRDPLFR(MA5) . . . . . . . . . . . . . . . . . . . . 25 3.2.5. Model5PLRDPLFR(M5,S) . . . . . . . . . . . . . . . . . . . . 26 3.2.6. Model5PLRDPLFR(MA5,S) . . . . . . . . . . . . . . . . . . . . 27 3.2.7. Wiener Stochastic Process Model (MW) . . . . . . . . . . . . . . 29 3.2.8. Wiener Stochastic Process Model (MAW) . . . . . . . . . . . . . . 30 3.3 Two-Stage Parameter Estimation Method . . . . . . . . . . . . . . . . . . 30 3.4 Lifetime Distribution Conditioned on Observed Time . . . . . . . . . . . . 32 Chapter 4. Case Application 35 4.1 Estimate of the MLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 Analysis of the Degradation Slope . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Model Fitting Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.1. Models for Individual Battery . . . . . . . . . . . . . . . . . . . . 44 4.3.2. Models for Collective Batteries . . . . . . . . . . . . . . . . . . . 49 4.4 Simulation Paths of Models . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5 Lifetime Distribution and Prediction Interval Conditioned on Observed Time 57 4.6 Prediction Performance Comparison of Models without Considering Capacity Regeneration Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.7 Prediction Performance Comparison of Models with Considering Capacity Regeneration Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.8 Prediction When Some Usage Scenarios are Given . . . . . . . . . . . . . 69 4.8.1. Prediction if There is No Rest Period in the Future . . . . . . . . . 69 4.8.2. Prediction if There are Some Rest Periods in the Future . . . . . . 71 4.8.3. Comparison of Different Usage Scenarios for MBE,MEP ,M5,m and M5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Chapter 5. Summary and Future Work 74 5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 References 78 Appendix A. Likelihood Function of θMA2 after Calculating the Integrals 82 Appendix B. Likelihood Function of θMA3 after Calculating the Integrals 86 Appendix C. MLEs of M1 and M4 91 Appendix D. Simulation Paths of Models 93 Appendix E. Prediction Performance Comparison of Models 94

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