2016年数学建模美赛题目原文及翻译-A [个人思路]

PROBLEM A:A Hot Bath    

原题下载：MCM-2016-A

A person fills a bathtub with hot water from a single faucet and settles into the bathtub to cleanse and relax. Unfortunately, the bathtub is not a spa-style tub with a secondary heating system and circulating jets, but rather a simple water containment vessel. After a while, the bath gets noticeably cooler, so the person adds a constant trickle of hot water from the faucet to reheat the bathing water. The bathtub is designed in such a way that when the tub reaches its capacity, excess water escapes through an overflow drain.

Develop a model of the temperature of the bathtub water in space and time to determine the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water.

Use your model to determine the extent to which your strategy depends upon the shape and volume of the tub, the shape/volume/temperature of the person in the bathtub, and the motions made by the person in the bathtub. If the person used a bubble bath additive while initially filling the bathtub to assist in cleansing, how would this affect your model’s results?

In addition to the required one-page summary for your MCM submission, your report must include a one-page non-technical explanation for users of the bathtub that describes your strategy while explaining why it is so difficult to get an evenly maintained temperature throughout the bath water.

A题 一个热水澡

一个人从一个单一的水龙头充满热水浴缸和落户到浴缸清洗和放松。不幸的是，浴缸不是温泉式浴缸与辅助加热系统和循环喷气式飞机，而是一个简单的水安全壳。一会儿之后，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的洗澡水。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出漏极。

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。

使用模型确定哪个您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，和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，而最初填补了浴缸中清洗协助，这将如何影响你的模型的结果吗？

除了为您的MCM提交所要求的一页纸的总结，你的报告必须包括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维持温度的单页非技术性解释浴缸里的水。

个人理解： 

1、连续型模型：

连续值回归模型：  

对于水温与各种影响因素处理，基于连续的实数值，提高模型的泛化性 （在浴缸的形状/体积/温度的体积，和由该人在浴缸所作的运动的程度）

1、对每个 feature赋予一个初始权重

2、训练特征关系

3、循环，权重归一化，选择最优回归器，更新权重，预测，处理.

参考：粒群在上升水流中分层机理的热力学分析

个人理解2:

水温控制的因素可能与热水的流体动力学有关，并且与水的分层原理相关。所以此题可以用热导方程的思路求解。在不考虑很多无关因素时可以用统一的热力学模型求解。