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研究生： 許弘澤
Hsu, Hung-Tse
論文名稱： 兩種品質特徵下鋰離子電池 Cell-to-Pack 衰退模型的建構與比較
Development and Comparison of Cell-to-Pack Degradation Models for Lithium-Ion Batteries under Two Quality Characteristics
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： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 120
中文關鍵詞： 鋰離子電池組 、失效時間分佈 、品質特徵 、衰退模型 、Cell-to-Pack
外文關鍵詞： Lithium-ion Battery Pack, Failure-Time Distribution, Quality Characteristic, Degradation Model, Cell-to-Pack
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    • 本研究探討兩顆單電池並聯形成之鋰離子電池組的衰退建模與可靠度推論問題。我們分析電容量衰退資料，分別以初始放電容量與額定容量為標準化基準，建立SoH/F 與 SoH/R 兩種健康狀態品質特徵。許多電池衰退研究常以 SoH/F 作為品質特徵，然而此定義會將初始健康狀態標準化至 100%，因而忽略初始容量差異對壽命推論的影響，進而高估電池組壽命。因此，本文比較 SoH/F 與 SoH/R 兩種品質特徵對電池組衰退路徑與失效時間分佈推論結果的影響。為描述單電池與電池組之間的衰退差異，並因應電池組實驗中樣本數有限所造成的估計不穩定問題，本研究提出自適應相關係數巢狀隨機係數衰退模型（Adaptive Correlation Nested Effect Degradation Model, AC-NED），分別建立電池組層級與單電池層級的衰退路徑。接著，進一步提出不一致性修正加權單電池到電池組方法（Inconsistency-Corrected Weighted Cell-to-Pack Method, ICW-C2P），利用單電池層級衰退資訊推估電池組層級衰退行為與失效時間分佈。相較於傳統可靠度方塊圖（Reliability Block Diagram, RBD）方法，ICW-C2P 方法不僅考慮單電池失效時間與系統結構，也進一步納入單電池衰退路徑與組內不一致性對電池組可靠度的影響。實際資料分析結果顯示，SoH/F 與 SoH/R會導致不同的衰退路徑表現與失效時間推論結果，說明品質特徵選擇對電池組壽命評估具有重要影響。此外，ICW-C2P 方法在兩種品質特徵下皆能產生接近電池組層級模型的失效時間分佈，顯示其能有效連結單電池與電池組之間的衰退行為。模擬研究與 parametric bootstrap 結果亦顯示，所提出方法在小樣本情境下具有可行性，並可量化失效時間分佈推論的不確定性。

    This study investigates degradation modeling and reliability inference for lithium-ion battery packs formed by two cells connected in parallel. Capacity degradation data are analyzed, and two state of health quality characteristics, SoH/F and SoH/R, are constructed using the initial discharge capacity and the rated capacity as the normalization bases, respectively. Many battery degradation studies commonly use SoH/F as the quality characteristic. However, this definition normalizes the initial health state to 100%, thereby ignoring the influence of initial capacity differences on lifetime inference and potentially overestimating battery pack lifetime. Therefore, this thesis compares the effects of SoH/F and SoH/R on battery pack degradation paths and failure-time distribution inference results. To describe the degradation differences between cells and battery packs and to address the instability of estimation caused by small sample sizes in battery pack experiments, this study proposes the Adaptive Correlation Nested Effect Degradation (AC-NED) model, which establishes degradation paths at both the battery pack level and the cell level. In addition, this study further proposes the Inconsistency-Corrected Weighted Cell-to-Pack (ICW-C2P) Method, which uses cell-level degradation information to infer pack-level degradation behavior and failure-time distributions. Compared with the traditional Reliability Block Diagram (RBD) method, the ICW-C2P Method considers not only cell failure times and system structure, but also the effects of cell degradation paths and within-set inconsistency on battery pack reliability. The empirical results show that SoH/F and SoH/R lead to different degradation path patterns and failure-time inference results, indicating that the choice of quality characteristic has an important influence on battery pack lifetime assessment. In addition, the ICW-C2P Method can produce failure-time distributions close to those obtained from the pack-level model under both quality characteristics, showing that it can effectively connect the degradation behavior between cells and battery packs. The simulation study and parametric bootstrap results also show that the proposed methods are feasible under small-sample settings and can quantify the uncertainty in failure-time distribution inference.

    摘要 i Abstract ii 誌謝 iii Table of Contents iv List of Tables vii List of Figures viii Chapter 1. Introduction 1 1.1 Research Motivation 1 1.2 Research Purpose 2 1.3 Research Datasets 3 1.3.1. Degradation Test Conditions and Observations 3 1.3.2. Datasets for SoH 5 Chapter 2. Literature Review 8 2.1 Battery Degradation Frameworks 8 2.1.1. Random Coefficient Models 8 2.1.2. Stochastic Process Models 9 2.1.3. Statistical Capacity Fading Model 10 2.2 Failure Time and Remaining Useful Life Prediction 11 2.2.1. Machine Learning Models 11 2.2.2. Deep Learning Models 11 2.2.3. Statistical Models for Failure Time Prediction 12 2.3 SoH/F and SoH/R Quality Characteristics 12 2.4 System Reliability Modeling Methods 13 2.4.1. Reliability Block Diagrams (RBD) 13 2.4.2. Universal Generating Functions (UGF) 14 2.4.3. Semi-Markov Process (SMP) 15 2.5 Comparisons with the Proposed Model 16 Chapter 3. Methodology 19 3.1 Statistical Capacity Fading Model 20 3.2 AC-NED: Adaptive Correlation Nested Effect Degradation Model 21 3.2.1. Model Notation 22 3.2.2. Pack-Level AC-NED Model 23 3.2.3. Cell-Level AC-NED Model 26 3.3 Likelihood Functions for AC-NED Models 29 3.3.1. Likelihood Function for the AC-NED-P Model 29 3.3.2. Likelihood Function for the AC-NED-C Model 30 3.4 Laplace Approximation and REML Estimation 32 3.4.1. Laplace Approximation 32 3.4.2. REML Estimation 34 3.5 Reliability Modeling for Battery Packs 34 3.5.1. Pack Method 34 3.5.2. RBD Method 35 3.5.3. ICW-C2P: Inconsistency-Corrected Weighted Cell-to-Pack Method 36 3.6 Failure-Time Distribution Inference 41 3.6.1. Monte Carlo Estimation of Failure-Time Distribution 42 3.6.2. Parametric Bootstrap for Uncertainty Quantification 46 Chapter 4. Simulation Study 49 4.1 Simulation Study for AC-NED Models under SoH/F 50 4.1.1. Simulation Study for the AC-NED-P Model 50 4.1.2. Simulation Study for the AC-NED-C Model 53 4.2 Simulation Study for ICW-C2P Method 57 4.2.1. Simulation Study for ICW-C2P under SoH/F 57 4.2.2. Simulation Study for ICW-C2P under SoH/R 60 4.3 Parametric Bootstrap Simulation Study for Failure-Time CDF Confidence Bands 62 Chapter 5. Case Application 66 5.1 Case Study Dataset 66 5.1.1. Degradation Data under SoH/F 67 5.1.2. Degradation Data under SoH/R 68 5.2 AC-NED Model Fitting Results 68 5.2.1. AC-NED-P Model Fitting Results 71 5.2.2. AC-NED-C Model Fitting Results 73 5.3 Residual Diagnostics 75 5.3.1. Pack-Level Residual Diagnostics 75 5.3.2. Cell-Level Residual Diagnostics 78 5.4 ICW-C2P Model Fitting Results 81 5.5 Failure-Time Inference and CDF Comparison 86 5.5.1. Pack Method under SoH/F and SoH/R 86 5.5.2. RBD Method under SoH/F and SoH/R 89 5.5.3. ICW-C2P Method under SoH/F and SoH/R 90 5.5.4. Comparative Analysis of Failure-Time Distributions 93 5.6 Parametric Bootstrap Confidence Bands for Failure-Time CDF 95 5.6.1. Parametric Bootstrap Confidence Bands under SoH/F 95 5.6.2. Parametric Bootstrap Confidence Bands under SoH/R 96 Chapter 6. Summary and Future Work 98 6.1 Summary 98 6.2 Limitations and Future Work 99 References 102 Appendix A. Derivation of Laplace Approximation 105 Appendix B. Supplementary Residual Diagnostic Results 108

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