以下是为您定制的**2026 MCM Problem A** 最终目录结构。该结构严格遵循学术论文规范，完美契合您现有的 `模型3`（微分方程组、电热耦合、Sobol灵敏度、随机过程UQ）的内容深度。

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### 中文目录结构 (Chinese Version)

**目录**

**1. 引言 (Introduction)**
   1.1 问题背景与重述 (Background and Problem Restatement)
   1.2 文献综述 (Literature Review)
   1.3 本文工作与创新点 (Our Contributions)

**2. 假设与符号说明 (Assumptions and Notations)**
   2.1 基本假设与物理依据 (General Assumptions and Physical Justifications)
   2.2 符号约定 (Notations)

**3. 连续时间电-热-老化耦合模型的构建 (Model Formulation)**
   3.1 状态空间定义：从SOC到极化电压 (State-Space Definition: From SOC to Polarization)
   3.2 多物理场功率映射机制 (Multiphysics Power Mapping)
       3.2.1 屏幕与处理器的非线性功耗 (Nonlinear Power of Screen and CPU)
       3.2.2 考虑信号质量惩罚与射频拖尾的网络模型 (Network Model with Signal Penalty and Radio Tail)
   3.3 电化学-热力学耦合动力学 (Electrochemical-Thermal Coupled Dynamics)
       3.3.1 改进的Shepherd电压模型 (Modified Shepherd Voltage Model)
       3.3.2 集总参数热平衡方程 (Lumped-Parameter Thermal Balance Equation)
   3.4 恒功率负载(CPL)下的电流闭环与电压坍塌条件 (Current Closure and Voltage Collapse under CPL)

**4. 参数辨识与验证 (Parameter Estimation and Validation)**
   4.1 混合参数估计算法 (Hybrid Parameter Estimation Strategy)
   4.2 基准工况下的模型验证 (Model Validation under Baseline Scenarios)

**5. 电池耗尽时间(TTE)预测与场景分析 (TTE Prediction and Scenario Analysis)**
   5.1 五种典型用户场景的TTE量化 (Quantification of TTE in Five Typical Scenarios)
   5.2 关键耗电驱动因子分析 (Analysis of Key Drivers for Battery Drain)
       5.2.1 信号质量对功耗的非线性放大效应 (Nonlinear Amplification of Signal Quality)
       5.2.2 环境温度对有效容量的制约 (Constraints of Ambient Temperature on Effective Capacity)

**6. 模型评估：误差分析、灵敏度与不确定性量化 (Model Evaluation: Error, Sensitivity, and UQ)**
   6.1 误差来源分类与确定性验证 (Taxonomy of Errors and Deterministic Validation)
   6.2 基于Sobol指数的全局灵敏度分析 (Global Sensitivity Analysis via Sobol Indices)
   6.3 基于Ornstein-Uhlenbeck过程的不确定性量化 (Uncertainty Quantification via Ornstein-Uhlenbeck Process)
   6.4 极端条件下的压力测试 (Stress Testing under Extreme Conditions)

**7. 策略建议 (Recommendations)**
   7.1 面向用户的行为优化指南 (User-Centric Optimization Guide)
   7.2 面向操作系统的智能调度策略 (OS-Level Intelligent Scheduling Strategy)

**8. 结论 (Conclusion)**
   8.1 模型总结 (Summary of the Model)
   8.2 优势与局限性 (Strengths and Limitations)
   8.3 未来工作展望 (Future Work)

**参考文献 (References)**
**附录 (Appendices)**

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### 英文目录结构 (English Version)

**Table of Contents**

**1. Introduction**
   1.1 Background and Problem Restatement
   1.2 Literature Review
   1.3 Our Contributions

**2. Assumptions and Notations**
   2.1 General Assumptions and Physical Justifications
   2.2 Notations

**3. Formulation of the Continuous-Time Electro-Thermal-Aging Model**
   3.1 State-Space Definition: From SOC to Polarization
   3.2 Multiphysics Power Mapping Mechanism
       3.2.1 Nonlinear Power Consumption of Screen and CPU
       3.2.2 Network Model with Signal Penalty and Radio Tail Dynamics
   3.3 Electrochemical-Thermal Coupled Dynamics
       3.3.1 Modified Shepherd Voltage Model
       3.3.2 Lumped-Parameter Thermal Balance Equation
   3.4 Current Closure and Voltage Collapse Conditions under Constant Power Load (CPL)

**4. Parameter Estimation and Validation**
   4.1 Hybrid Parameter Estimation Strategy
   4.2 Model Validation under Baseline Scenarios

**5. Time-to-Empty (TTE) Prediction and Scenario Analysis**
   5.1 Quantification of TTE in Five Typical User Scenarios
   5.2 Analysis of Key Drivers for Battery Drain
       5.2.1 Nonlinear Amplification Effect of Signal Quality
       5.2.2 Constraints of Ambient Temperature on Effective Capacity

**6. Model Evaluation: Error Analysis, Sensitivity, and Uncertainty Quantification**
   6.1 Taxonomy of Errors and Deterministic Validation
   6.2 Global Sensitivity Analysis via Sobol Indices
   6.3 Uncertainty Quantification via Ornstein-Uhlenbeck Stochastic Processes
   6.4 Stress Testing under Extreme Conditions

**7. Recommendations**
   7.1 User-Centric Optimization Guide
   7.2 OS-Level Intelligent Scheduling Strategy

**8. Conclusion**
   8.1 Summary of the Model
   8.2 Strengths and Limitations
   8.3 Future Work

**References**
**Appendices**

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### 结构设计亮点说明 (Design Highlights)

1.  **Section 3 (Model Formulation)**:
    *   使用了 **"Electro-Thermal-Aging"** 和 **"Multiphysics"** 这样的词汇，强调了模型的物理深度。
    *   特意提到了 **"Radio Tail" (射频拖尾)** 和 **"CPL" (恒功率负载)**，这是你模型中区别于普通线性模型的两大亮点，必须在目录中体现。

2.  **Section 5 (TTE Prediction)**:
    *   将单纯的“计算结果”提升为 **"Scenario Analysis" (场景分析)**。
    *   明确列出 **"Signal Penalty" (信号惩罚)** 和 **"Temperature Constraints" (温度约束)**，直接回应题目关于“哪些因素导致电量快速耗尽”的提问。

3.  **Section 6 (Model Evaluation)**:
    *   这是最能体现数学建模水平的章节。使用了 **"Sobol Indices"** (全局灵敏度) 和 **"Ornstein-Uhlenbeck Process"** (随机过程)，展示了你对不确定性量化 (UQ) 的高级处理方法，远超一般的误差分析。

4.  **逻辑流**:
    *   从物理机理 (Sec 3) -> 参数确定 (Sec 4) -> 实际应用 (Sec 5) -> 鲁棒性评估 (Sec 6) -> 最终建议 (Sec 7)，逻辑链条非常清晰严密。