From 808dd52bf08913ff181a1b72b7d15395147b92d9 Mon Sep 17 00:00:00 2001 From: ChuXun <70203584+ChuXunYu@users.noreply.github.com> Date: Fri, 30 Jan 2026 09:52:47 +0800 Subject: [PATCH] Add MCM Problem A resources and related PDFs MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Added a markdown file detailing the modeling approach for MCM Problem A (智能手机电池耗电建模), including recommended algorithms, analysis, and solution strategies. Also added several related PDF documents as supporting resources. --- A题/A题翻译.pdf | Bin 0 -> 616904 bytes A题/赛题分析.md | 65 +++++++++++++++++++++++++++++++++++++++++++ 题目翻译/B题翻译.pdf | Bin 0 -> 171088 bytes 题目翻译/C题翻译.pdf | Bin 0 -> 244506 bytes 题目翻译/D题翻译.pdf | Bin 0 -> 194964 bytes 题目翻译/E题翻译.pdf | Bin 0 -> 245532 bytes 题目翻译/F题翻译.pdf | Bin 0 -> 235465 bytes 7 files changed, 65 insertions(+) create mode 100644 A题/A题翻译.pdf create mode 100644 A题/赛题分析.md create mode 100644 题目翻译/B题翻译.pdf create mode 100644 题目翻译/C题翻译.pdf create mode 100644 题目翻译/D题翻译.pdf create mode 100644 题目翻译/E题翻译.pdf create mode 100644 题目翻译/F题翻译.pdf diff --git a/A题/A题翻译.pdf b/A题/A题翻译.pdf new file mode 100644 index 0000000000000000000000000000000000000000..eeae9785a305bcfb70161ccff3cd15f1c158511a GIT binary patch literal 616904 zcmd3P2Rzm7`#(}fC|bxkDarnveNG`~TG=xh8Hbd;vPV)`nGq36MJ17$T}nby85J@r zMKX$%^}o;QsYg9M&(r_=`@O#ZKQEl|8TWnN*Y&>M*SHUH9WqrGE{Emj6u;MWznPm8 z4TE4V)(5#c6%^#D4vwBQcX@qJD`#6PcUyTQ7)o9b{OqAQ+j|~>!4Wul5)~Y$?`g~U 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?VQvU9=1kduqai^IeG7ph*r{Qv*} literal 0 HcmV?d00001 diff --git a/A题/赛题分析.md b/A题/赛题分析.md new file mode 100644 index 0000000..febeb4d --- /dev/null +++ b/A题/赛题分析.md @@ -0,0 +1,65 @@ +# MCM Problem A:智能手机电池耗电建模 +## 1. 赛题基本信息 +| 分析维度 | 具体内容 | +| --- | --- | +| 赛题编号 | MCM-A | +| 整体类型 | 机理分析类 | +| 小问数量/小问类型 | 4个小问;1.机理分析类;2.预测类;3.敏感性分析类;4.决策建议类 | +| 每小问主要问题 | 1. 构建连续时间模型描述电池剩余电量随时间变化,纳入多影响因素;
2. 预测不同场景下剩余续航时间,分析耗电驱动因素;
3. 分析假设、参数和使用模式波动对预测结果的影响;
4. 提出用户和操作系统层面的省电建议 | + +--- + +## 2. 推荐算法+理由 +1. **机理分析类**:扩展型戴维南等效电路模型+微分方程组 + - 理由:贴合锂离子电池电化学机理,可量化多因素(如温度、负载)对SOC的动态影响,符合连续时间建模要求,美赛中机理模型易获高分。 +2. **预测类**:基于机理模型的蒙特卡洛模拟 + - 理由:可处理使用场景的随机性,量化续航时间不确定性,适配多场景预测需求。 +3. **敏感性分析类**:Morris筛选法+Sobol指数法 + - 理由:Morris法快速识别关键影响因素,Sobol指数法精准量化各因素贡献度,兼顾效率与精度。 +4. **决策建议类**:多目标优化算法(NSGA-Ⅱ) + - 理由:可在多个省电目标(如续航时长、使用体验)间找到最优平衡,为建议提供量化支撑。 + +--- + +## 3. 评分依据 +- 模型复杂度:中等,需结合电化学机理与多因素耦合,连续时间建模有一定技术门槛 +- 数据获取难度:低,可通过公开文献、手机厂商规格参数获取电池特性、各组件耗电数据 +- 创新设计要求:中等,需在经典机理模型基础上扩展多影响因素的耦合关系 +- 建模工作量:中等,需完成模型构建、参数校准、多场景验证 +- 综合分析要求:中等,需结合敏感性分析结果提出切实可行的建议 + +--- + +## 4. 解题难点 +1. 多影响因素(屏幕、处理器、温度等)的量化建模与耦合关系处理 +2. 连续时间方程的构建需贴合电池实际放电机理,避免纯数学拟合 +3. 不同使用场景下的参数校准与模型验证 +4. 不确定性量化需兼顾模型误差与场景随机性 + +--- + +## 5. 核心要点 +1. 坚守连续时间建模核心,避免离散化处理 +2. 明确各耗电组件的功率消耗模型与参数取值依据 +3. 模型需区分不同环境条件(如温度)和使用模式的影响 +4. 建议需基于模型结果,具备可操作性 + +--- + +## 6. 解题思路 +1. **模型构建**:先基于锂离子电池电化学原理,建立基础SOC连续时间微分方程;再逐一纳入屏幕、处理器、网络等组件的耗电模型,考虑温度对电池容量的修正 +2. **参数估计**:收集公开的手机组件耗电数据、电池特性参数,通过最小二乘法校准模型参数 +3. **场景预测**:设计典型使用场景(如重度使用、待机、低温环境等),利用模型计算续航时间,对比分析关键耗电因素 +4. **敏感性分析**:采用Morris法和Sobol指数法,识别对续航时间影响最大的因素 +5. **建议提出**:基于敏感性分析结果,从用户行为和操作系统优化两方面提出针对性建议 + +--- + +## 7. 获奖要点 +1. **模型创新**:在经典机理模型基础上,提出多因素耦合的扩展模型,如温度与处理器负载的交互影响机制 +2. **量化结果**:明确给出不同场景下续航时间预测值及误差范围,关键因素的敏感性指数 +3. **可视化**:绘制SOC随时间变化曲线、各因素敏感性排序图、不同场景续航对比图 +4. **模型检验**:通过实测数据(如自行采集或引用公开数据)验证模型精度,计算R²、RMSE等指标 +5. **逻辑闭环**:从机理建模到预测分析,再到敏感性分析和建议,形成完整逻辑链 + +--- diff --git a/题目翻译/B题翻译.pdf b/题目翻译/B题翻译.pdf new file mode 100644 index 0000000000000000000000000000000000000000..67ff1ee4f6bbabdde43e40be6238097815d1e6bd GIT binary patch literal 171088 zcmcG#1yEhfwlT{ZplFi?zmba*!U<}h4bwERwvrZ)C?WKIr7 z_T+f9f;LuGM%IoFcw~QlvDLG7`|Gp4k)ETOjkS=TqY)mN5C;Pt0}CBJBOM(JBO4PP zB^?_n9UbZKHNWM4D|~(Xp!z}XgW?A~qhL+d_ZdkeHy0aw!@pEZ+Zg_Dn&j+l44n*& z-c`LXR-`6YI>)G1AFQgUGvve@x z;ej!-HvAm{`oD)lToKRs_cR`@fHWShjE%jOp5?no{CM>53fyep$Aw)TMHL-?hk({V z50Cy|dRYDyQ9&DP$3G!teIHZ6qm?!?G}9BXamCZ5dmmtCXQpAqV`HMHVF%#R%IVp^ zi{df-C8=QK@W)LDy!XWXYpeG!qKfZ^{;^eohv(gi_bq~yAp9ah6nf%S$-xmEN?;>WFj_r?;p-P)1p%#)7y$QlMu`PJ;`?G zO_$f6%c{|kzCkqE>R40SJ=U%o7%$Lq((EC{t~7=6R4
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