2016年美国大学生数学建模大赛A题获奖论文A Hot Bath
合集下载
华工第十六届数理大赛赛题发布会
2014全国数学建模竞赛题目 2015美国数学建模竞赛题目
2014全国数学建模竞赛题目 A题 嫦娥三号软着陆轨道设计与控制策略 B题 创意平板折叠桌 C题 生猪养殖场的经营管理 D题 储药柜的设计
2015 MCM&ICM Problems • Problem A:Eradicating Ebola • Problem B:Searching for a lost plane • Problem C:Managing Human Capital in Organizations • Problem D:Is it sustainable?
• Convex Optimization • Duality-Theory • Lagrange Multipliers • Kernels function
Deep Learning Neural Network
• • • • AlphaGo Zero强化学习战胜AlphaGo 人工智能推动数学建模 数学建模制造新的信息机器 丘成桐：工程上取得很大发展 但理论基础仍非常 薄弱 • 人工智能需要一个可以被证明的理论作为基础。 • 人工智能需要新数学理论
SVHN – real world image dataset
Image classification
Convolutiona Neural Network
全 连 接 卷 积
池 化
CNN- 图像分类和场景特色
数学建模生产的图形处理机器
LSTM- 翻译语言和语音识别机器
RNN - 语音识别和自然语言分析
2017A题
CT系统参数标定及成像
• 请建立相应的数学模型和算法，解决以下问题： • (1) 在正方形托盘上放置两个均匀固体介质组成的标定模板，模板的 几何信息如图2所示，相应的数据文件见附件1，其中每一点的数值反 映了该点的吸收强度，这里称为“吸收率”。对应于该模板的接收信 息见附件2。请根据这一模板及其接收信息，确定CT系统旋转中心在 正方形托盘中的位置、探测器单元之间的距离以及该CT系统使用的X 射线的180个方向。 • (2) 附件3是利用上述CT系统得到的某未知介质的接收信息。利用(1) 中得到的标定参数，确定该未知介质在正方形托盘中的位置、几何形 状和吸收率等信息。另外，请具体给出图3所给的10个位置处的吸收 率，相应的数据文件见附件4。 • (3) 附件5是利用上述CT系统得到的另一个未知介质的接收信息。利 用(1)中得到的标定参数，给出该未知介质的相关信息。另外，请具 体给出图3所给的10个位置处的吸收率。 • (4) 分析(1)中参数标定的精度和稳定性。在此基础上自行设计新模 板、建立对应的标定模型，以改进标定精度和稳定性，并说明理由。
2016年全国大学生数学建模竞赛获奖论文
5
图 3 第一小问求解思路图
5.1.1.1 多项式函数与高斯函数拟合对比 运用 MATLAB 工具箱对在电流强度为 20A 的数据进行多项式函数和高斯函数的拟 合，得到两个拟合图像如图 4 所示：
多项式函数拟合的图像
高斯函数拟合的图像
图 4 两种函数的拟合图像
根据观察 20A 电流情况下两种拟合函数的放电图像， 发现两种函数的放电图像无明 显差别，无法看出哪种函数的拟合效果好，所以本文用两种函数拟合的拟合精度进行比 较，见表 2：
3
第二小问首先利用 EXCEL 筛选出 231 个电压样本点，采取相对误差是绝对误差与 实际数据的比值的方法，求出 231 个相对误差，取平均即为 MRE . 第三小问是建立在第一小问的基础上， 将数值 9.8V 带入初等函数模型， 求出在 30A， 40A，50A，60A，70A 的电流强度下电池的剩余放电时间. 2.2.2 问题二的分析 问题二要建立适用于任一电流强度在任一时刻的的放电时间，但题中所给数据只有 几个特殊的电流强度，因此利用这些数据来建立任意时刻的模型，就是要建立起任意时 刻都能找到与已有数据的关系，文中引进比例分电压点来建立起这个联系，较好的解决 了不能实现任意时刻的放电时间的计算， 并且与现有数据始终相关， 拟合数据偏差较小. 2.2.3 问题三的分析 对于问题三直接使用衰减状态 3 的数据会导致拟合效果不达要求， 由于新电池状态、 衰减 1 状态和衰减 2 状态使用二次函数拟合效果较好，题目所给是同一电池，因此衰减 状态三应也是与前三个状态变化相似，所以利用前三个状态的与衰减状态 3 现有数据来 作差，进行拟合，补全缺失数据的差值，将补全的差值进行还原，得到衰减状态 3 的缺 失数据，并用 MATLAB 进行四种状态的拟合，结果发现效果较好,
2016美国数模竞赛题目中文翻译
A: 一个人充满热水的浴缸从一个单一的水龙头，并落户到浴缸里清洁和放松。
不幸的是，浴缸不是温泉式浴盆与辅助加热系统和循环飞机，而是一个简单的水安全壳。
一段时间后，在浴变得明显冷却器，所以该人增加的热水恒定涓流从龙头再加热洗澡水。
所述浴缸的设计以这样的方式，当所述桶达到其容量，过量的水逸出通过溢流漏极。
开发浴缸水的空间和时间，以确定该人在浴缸可以采用，以保持温度甚至整个浴缸和尽可能接近到初始温度，而不会浪费过多的水的最佳策略的温度的模型。
使用模型确定哪个你的策略取决于形状和桶，该人在浴缸的形状/体积/温度的体积，并且由该人在浴缸所作的运动的程度。
如果对方使用了泡泡浴的添加剂，而最初填补了浴缸，以协助清洁，怎么会变成这样影响模型的结果吗？除了必需的单页摘要您的MCM提交，你的报告必须包括一份一页纸的非技术性解释浴缸的用户描述你的策略，同时解释了为什么它是如此难以得到整个均匀保持温度浴缸里的水。
B: 小碎片在轨道上绕地球金额已日益受到关注。
据估计，超过50万件的空间碎片，也被称为轨道碎片，目前都被跟踪的潜在危害航天器。
这个问题本身变得更广泛的讨论，在新闻媒体时，俄罗斯卫星的Kosmos-2251和美国铱卫星-33相撞2009年2月10日。
有许多方法以除去碎片已被提出。
这些方法包括小的，基于空间的水射流和用于针对特定的碎片高能激光器和设计，以清扫杂物，其中包括大型卫星。
从漆片的废弃卫星的大小和质量的碎片范围。
碎片“高速轨道进行采集困难。
开发时间依赖模型来确定的替代品，私人公司可以采取作为一个商业机会，以解决空间碎片问题的最佳替代品或组合。
您的模型应该包括成本，风险，效益的定量和/或定性的估计，以及其他重要的因素。
您的模型应该能够评估独立的替代品的替代品，以及组合和能够探索各种重要的“如果？”的情景。
使用模型，确定了经济上有吸引力的机会是否存在，或没有这样的机会是可能的。
如果一个可行的商业机会的存在作为一种替代解决方案，提供了不同的选择去除杂物进行比较，并包括具体建议，以碎片应该如何去除。
2016年美国大学生数学建模大赛A题获奖论文A Hot Bath
Part II Finding the best strategy ...................................................................12 VI. Results ........................................................................................................ 12
The first part has five sections: air’s heat radiation, bathtub wall’s heat radiation, person in, hot water in, bubble existed. We discuss some factors that affect water temperature, such as the shape and the volume of the bathtub and person, especially the motions made by the person in the bathtub because the temperature in the bathtub has a great connection with person. Finally, we get the water temperature variation and distribution model.
In this article, we establish two models. One is water temperature variation and distr one is finding best strategy model. We put forward some acceptable hypothesis to simplify the model. What’s more, we clear the meaning of the word “noticeably”.
The first part has five sections: air’s heat radiation, bathtub wall’s heat radiation, person in, hot water in, bubble existed. We discuss some factors that affect water temperature, such as the shape and the volume of the bathtub and person, especially the motions made by the person in the bathtub because the temperature in the bathtub has a great connection with person. Finally, we get the water temperature variation and distribution model.
In this article, we establish two models. One is water temperature variation and distr one is finding best strategy model. We put forward some acceptable hypothesis to simplify the model. What’s more, we clear the meaning of the word “noticeably”.
2021年美国大学生数学建模竞赛题目A--真菌范文六篇(含Matlab源代码)
with the rate of decomposition, several questions may arise to include: Using these two traits, how
do the different fungi interact and decompose ground litter in a fixed patch of land in different
?12122?1142?1???1???11112206?12?2242?2???1???2222110102025wheremoisturetoleranceiswelldeterminedby
2021年美国大学生数学建模竞赛题目A--真菌范文六
篇（含Matlab源代码）
问题A：真菌……………………………………………………………………2
Include predictions about the relative advantages and disadvantages for each species and
combinations of species likely to persist, and do so for different environments including arid,
(difference of each isolate’s competitive ranking and their
moisture niche width, both scaled to [0,1]) of various fungi
and the resulting wood decomposition rate (% mass loss
Your complete solution.
do the different fungi interact and decompose ground litter in a fixed patch of land in different
?12122?1142?1???1???11112206?12?2242?2???1???2222110102025wheremoisturetoleranceiswelldeterminedby
2021年美国大学生数学建模竞赛题目A--真菌范文六
篇（含Matlab源代码）
问题A：真菌……………………………………………………………………2
Include predictions about the relative advantages and disadvantages for each species and
combinations of species likely to persist, and do so for different environments including arid,
(difference of each isolate’s competitive ranking and their
moisture niche width, both scaled to [0,1]) of various fungi
and the resulting wood decomposition rate (% mass loss
Your complete solution.
2016年美国大学生数学建模竞赛题目
2016年美国大学生数学建模竞赛题目第５卷第２期２０１６年６月、・．．．．・‘．¨．．．‘－．．．．．’．．．Ⅲ’¨．．．．‘．．．．．．‘．．．¨．！数学建模及其应用ＭａｔｈｅｍａｔｉｃａＩＭＯｄｅ¨ｎｇａｎｄｌｔｓＡｐｐＩｉＣａｔｉＯｎｓＶＯＩ．５Ｎｏ．２Ｊｕｎ．２０１６｛竞赛论坛｝＾¨Ｉ・。
・－．．哪・．．．岫・．．．嘶・．．－‘・‘・．．．Ⅵ・‘‘“・・Ｉ２０１６年美国大学生数学建模竞赛题目韩中庚译（解放军信息工程大学四院，河南郑州４５０００１）问题Ａ：热水澡人们经常会通过用一个水龙头将浴缸注满热水，然后坐在浴缸里清洗和放松。
这个浴缸不是带有二次加热系统和循环喷流的温泉式浴缸，而是一个简单的水容器。
过一会儿，洗澡水就会明显变凉，所以洗澡的人需要不停地从水龙头注入热水，以加热洗浴的水。
该浴缸的设计是这样一种方式，即当浴缸里的水达到容量极限时，多余的水就会通过溢水口流出。
考虑空间和时间等因素，建立一个浴缸的水温控制模型，以确定最佳策略，使浴缸里的人可以利用这个策略让整个浴缸中的水保持或尽可能接近初始的温度，而且不浪费太多的水。
利用你们的模型来确定这个策略对浴缸的形状和体积，以及对浴缸中人的形状、体积、温度和活动等因素的依赖程度。
如果这个人一开始用了一种泡泡浴剂加入浴缸中以助清洗，这会对你们的模型结果有怎样的影响？除了要求提交１页的ＭＣＭ摘要之外，你们的报告必须包括１页为浴缸用户准备的非技术性的说明书，来阐述你们的策略，同时解释为什么保持洗澡水的恒温如此之难。
问题Ｂ：太空垃圾地球轨道上的小碎片数量已引起人们越来越多的关注。
据估计，目前有超过５０００００块的空间碎片，也被称为轨道碎片，由于被认为对空间飞行器是潜在的威胁而正在被跟踪。
２００９年２月１０日，俄罗斯卫星Ｋｏｓｍｏｓ一２２５１和美国卫星Ｉｒｉｄｉｕｍ一３３相撞之后，该问题受到了新闻媒体更广泛的讨论。
2016年MathorCup大学生数学建模挑战赛A题评分要点(参考)
问题一，针对四个池塘的所有数据，即整体水体、底泥、间隙水中主要理化因子进行相关系数来度量。
发现池水与间隙水、池水与底泥之间理化因子无直接关联，而间隙水与底泥中的理化因子总体上具有较强相关性。
探究其原因，底泥释放的物质直接作用于间隙水，而对体积庞大的池水影响甚微，池水中理化因子池水中理化因子含量主要受到水生生物吸收与排放、人为调控等因素的影响。
问题二，水体质量可以直接从水体的理化因子指标上体现。
结合我国地表水环境质量标准，选取多个主要理化指标作为评价因子对池塘水质进行评价。
考虑到评价因子的高维性，本文使用了可以探究高维数据特征的投影寻踪法来进行评价系统的构建，并将国家标准中不同等级的水体理化指标代入模型，得到在该模型下的水质评级标准。
根据该模型可知各池水质处于动态变化，总体而言2号和3号池的水质较好，1号池次之，4号池最差。
引起的原因可能是鱼量很多，同时投入的饲料就愈多，这样就会引起池水水质变差。
综合上述，在水池养殖的鱼虾数量会影响饲料的投入，再而引起水质的差异。
问题三，由于藻类植物的生长与池水直接相关，可以选择池水的主要理化指标来运用支持向量回归机模型，小波分析，神经网络等模型，以刻画池水中理化因子与总藻类密度的关系，可以运用多种模型预测未来5周1号池和3号池将会发生水华，其余两池水质较为良好。
通过某种方法确定水华发生时主要理化因子的波动范围，如网格搜索的方法。
注意比较相对误差。
问题四，先对附件6的数据进行分析，剔除了部分异常值后，分别建立了两种鱼类体重与身长的指数回归方程，来描述身长与体重的关系。
对于鱼类净化效果的研究，可以鲢鱼为例，可以考虑水循环的净化效果的基础上建立了池水种群的差分阻滞增长模型，求解该模型得到投入鲢鱼时，在20周的演化后总藻类密度稳定在，该方案可以较好地净化池中藻类。
接着，本文对该模型的参数进行了敏感性分析，结果表明引入水循环，加之投入鲢鱼的生态模式对一号池中藻类的净化效果是较为稳定可靠的。
大学生数学建模竞赛介绍
ICM Problem D (operations research/network science) ICM Problem E (environmental science) ICM Problem F (policy) • Mark your calendars the 2016 MCM/ICM dates are set for January 28 – February 1, 2016
2015 OUTSTANDING WINNERS
• THE FIVE OUTSTANDING WINNERS OF THE CONTINUOUS MCM (A) PROBLEM ARE: • Northwestern Polytechnical University, China • State University of New York, University at Buffalo, NY — MAA Prize Recipient • Chongqing University, China — SIAM Prize RecipientCentral South University, China — Ben Fusaro Award • University of Adelaide, Australia — INFORMS Prize Recipient • THE FIVE OUTSTANDING WINNERS OF THE DISCRETE MCM (B) PROBLEM ARE: • University of Colorado Boulder, CO — SIAM Prize Recipient & Two Sigma Scholarship Award • Bethel University, MN — MAA Prize Recipient & Frank Giordano Award • University of Colorado Boulder, CO • Colorado College, CO — INFORMS Prize Recipient • Tsinghua University, China • THE FIVE OUTSTANDING WINNERS OF THE INTERDISCIPLINARY ICM (C) PROBLEM ARE: • Xidian University, China • Shanghai Jiao Tong University, China • Xi'an Jiaotong University, China — Leonhard Euler Award • Tsinghua University, China • National University of Defense Technology, China • Also winning as a FINALIST is: • University of Colorado Denver, CO — INFORMS Prize Recipient • THE FOUR OUTSTANDING WINNERS OF THE INTERDISCIPLINARY ICM (D) PROBLEM ARE: • NC School of Science and Mathematics, NC — INFORMS Prize Recipient • Xi'an Jiaotong University, China • Humboldt State University, CA — Rachel Carson Award & Two Sigma Scholarship Award • Zhejiang University, China
2015 OUTSTANDING WINNERS
• THE FIVE OUTSTANDING WINNERS OF THE CONTINUOUS MCM (A) PROBLEM ARE: • Northwestern Polytechnical University, China • State University of New York, University at Buffalo, NY — MAA Prize Recipient • Chongqing University, China — SIAM Prize RecipientCentral South University, China — Ben Fusaro Award • University of Adelaide, Australia — INFORMS Prize Recipient • THE FIVE OUTSTANDING WINNERS OF THE DISCRETE MCM (B) PROBLEM ARE: • University of Colorado Boulder, CO — SIAM Prize Recipient & Two Sigma Scholarship Award • Bethel University, MN — MAA Prize Recipient & Frank Giordano Award • University of Colorado Boulder, CO • Colorado College, CO — INFORMS Prize Recipient • Tsinghua University, China • THE FIVE OUTSTANDING WINNERS OF THE INTERDISCIPLINARY ICM (C) PROBLEM ARE: • Xidian University, China • Shanghai Jiao Tong University, China • Xi'an Jiaotong University, China — Leonhard Euler Award • Tsinghua University, China • National University of Defense Technology, China • Also winning as a FINALIST is: • University of Colorado Denver, CO — INFORMS Prize Recipient • THE FOUR OUTSTANDING WINNERS OF THE INTERDISCIPLINARY ICM (D) PROBLEM ARE: • NC School of Science and Mathematics, NC — INFORMS Prize Recipient • Xi'an Jiaotong University, China • Humboldt State University, CA — Rachel Carson Award & Two Sigma Scholarship Award • Zhejiang University, China
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Part II ........................................................................................................... 16 VII. Strengths and Weaknesses....................................................................... 17 VIII. Explanation for users .............................................................................. 18 IX. References......................................................................................................19
For office use only T1 ________________ T2 ________________ T3 _______________ T4 ________________
Team Control Number
46731
Problem Chosen
A
For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________
this page.
Summary
Our experience of everyday life tells us that, bathing quality is relevant to the temperature of the water. Hence the optimality of the water-adding strategy in bathing process has become an issue.
Part II Finding the best strategy ...................................................................12 VI. Results ........................................................................................................ 12
Key words: bathtub; heat-conduction; temperature variation and distribution;
water strategy; finite volume method;
Team # 46731
Page 3 of 19
Contents
Summary ................................................................................................................ 1 I. Introduction......................................................................................................4 II. Analysis ........................................................................................................4 III. Assumptions ................................................................................................. 6 IV. Notation ........................................................................................................ 7 V. Models .......................................................................................................... 8
Part I.............................................................................................................12 Results of Air’s Heat Radiation Model ............................................12 Results of Bathtub Wall’s Heat Radiation........................................13 Results of “Person In”......................................................................13 Results of “Hot Water In” ................................................................ 13 Results of bubble existed model ...................................................... 15 Results of Water Temperature Variation and Distribution Model....15
2016
MCM/ICM Summary Sheet (Your team's summary should be included as the first page of your electronic submission.) Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on
In this article, we establish two models. One is water temperature variation and distribution model and the other one is finding best strategy model. We put forward some acceptable hypothesis to simplify the model. What’s more, we clear the meaning of the word “noticeably”.
The second part aims to finding the best water strategy. Different strategies are considered for adding hot water and the amount of the hot water. The key of strategies is how to choose the moment of opening the faucet and the lasting time. By developing an optimization model of the strategy, we manage to determine a strategy for different users and extend the model with a finite volume method. Under the condition of the same bathing time, we study what’s the ideal time to add the hot water to make it to the initial temperature.
The first part has five sections: air’s heat radiation, bathtub wall’s heat radiation, person in, hot water in, bubble existed. We discuss some factors that affect water temperature, such as the shape and the volume of the bathtub and person, especially the motions made by the person in the bathtub because the temperature in the bathtub has a great connection with person. Finally, we get the water temperature variation and distribution model.
Team # 46731
Page 2 of 19
We transform the weight p. With the restrict condition of the temperature in the bath and the amount of the hot water, the question can be transformed to a nonlinear optimization. We get the conclusion and optimal results through the PDE (Partial Differential Equations) toolbox of MATLAB. And the result shows a clear superiority for choosing a suitable strategy for different users.
For office use only T1 ________________ T2 ________________ T3 _______________ T4 ________________
Team Control Number
46731
Problem Chosen
A
For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________
this page.
Summary
Our experience of everyday life tells us that, bathing quality is relevant to the temperature of the water. Hence the optimality of the water-adding strategy in bathing process has become an issue.
Part II Finding the best strategy ...................................................................12 VI. Results ........................................................................................................ 12
Key words: bathtub; heat-conduction; temperature variation and distribution;
water strategy; finite volume method;
Team # 46731
Page 3 of 19
Contents
Summary ................................................................................................................ 1 I. Introduction......................................................................................................4 II. Analysis ........................................................................................................4 III. Assumptions ................................................................................................. 6 IV. Notation ........................................................................................................ 7 V. Models .......................................................................................................... 8
Part I.............................................................................................................12 Results of Air’s Heat Radiation Model ............................................12 Results of Bathtub Wall’s Heat Radiation........................................13 Results of “Person In”......................................................................13 Results of “Hot Water In” ................................................................ 13 Results of bubble existed model ...................................................... 15 Results of Water Temperature Variation and Distribution Model....15
2016
MCM/ICM Summary Sheet (Your team's summary should be included as the first page of your electronic submission.) Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on
In this article, we establish two models. One is water temperature variation and distribution model and the other one is finding best strategy model. We put forward some acceptable hypothesis to simplify the model. What’s more, we clear the meaning of the word “noticeably”.
The second part aims to finding the best water strategy. Different strategies are considered for adding hot water and the amount of the hot water. The key of strategies is how to choose the moment of opening the faucet and the lasting time. By developing an optimization model of the strategy, we manage to determine a strategy for different users and extend the model with a finite volume method. Under the condition of the same bathing time, we study what’s the ideal time to add the hot water to make it to the initial temperature.
The first part has five sections: air’s heat radiation, bathtub wall’s heat radiation, person in, hot water in, bubble existed. We discuss some factors that affect water temperature, such as the shape and the volume of the bathtub and person, especially the motions made by the person in the bathtub because the temperature in the bathtub has a great connection with person. Finally, we get the water temperature variation and distribution model.
Team # 46731
Page 2 of 19
We transform the weight p. With the restrict condition of the temperature in the bath and the amount of the hot water, the question can be transformed to a nonlinear optimization. We get the conclusion and optimal results through the PDE (Partial Differential Equations) toolbox of MATLAB. And the result shows a clear superiority for choosing a suitable strategy for different users.