美赛 数学建模写作模板1 摘要 文档资料
美赛数模论文格式
美赛数模论文格式篇一:2015年数学建模美赛论文格式2015年美国数学建模要求1( 文章标题居中用宋体142( 第一/第二/第三作者宋体143( 第一作者详细地址，包括国家，电子邮件(宋体11)，第二第三作者一样4( 关键词:文章涵盖你论文中的关键词。
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数学建模论文标题与摘要模板
• 无论什么论文中摘要都是十分重要的，尤其是在 全国赛和美国赛中摘要的地位很显赫的，两个组 委会都提出了摘要的重要性，再三明文提醒参赛 者要注重摘要。
• 要知道，无论国赛还是美赛，评阅专家首先要看 的一定是摘要。通过看摘要，判断所建模型是什 么，采用什么算法，结果是否正确，有无创新点。
(2)分问题表述
一般国内的竞赛的题目，分3-4个问题。多 数情况下第一个问题建模与求解基本上是整篇 论文的精髓，因此在摘要中一定要写好对第一 个问题的解决。可以在分问题表述上第一句写 一下解题的思考过程，比如,“通过理论推导 (物理手段),由于什么理由(假设),我们得到XX 模型……云云”。后面的几句话，主要写一下 解题过程、结果及结论即可。
• 明确一点，你必须把一些数值的结果放在摘要里面， 例如：“我们的最终算法执行效率较一个简单的贪 婪算法提高67.5％，较随机选择算法提高123.3％”。
• 摘要字数事先是很难确定的。必须把所有的核心观 点包含在摘要里面，但是简洁是非常重要的。一般 情况下600－900个字，即超过2/3页比较合适。
ቤተ መጻሕፍቲ ባይዱ
• 摘要（甚至是整篇文章），应该由整个团队合作完 成。
• 一种实现方式是，每个队员单独地花一个小时（至 少）时间写一个他们认为最好的摘要。然后，大家 聚到一起，相互阅读这些摘要；反复推敲文字，凝 练语言，最后形成一个最终版本。
5.关键词的凝炼
• 一般3-5个 • 所用方法、所属领域标志性词汇 • 要求用词规范，多用专业词汇 • 检索文献的重要工具，放在摘要后面 • 注意：标题和关键词中一般不能使用缩略词
(3) 最后陈述模型检验、评价与推广
陈述给出模型的检验（稳定性检验、敏感性 分析），模型的特点（优点和不足）是什么 （也可写出论文中提到的改进思路等），可推 广到哪些方面。要求简明扼要，例如: “我们 对此模型在XXX的验证过程中发现了一些不足 之后，提出了N点建议(不要超过4个)。
建模美赛获奖范文
建模美赛获奖范文全文共四篇示例，供读者参考第一篇示例：近日，我校数学建模团队在全国大学生数学建模竞赛中荣获一等奖的喜讯传来，这是我校首次在该比赛中获得如此优异的成绩。
本文将从建模过程、团队合作、参赛经验等方面进行详细介绍，希望能为更多热爱数学建模的同学提供一些借鉴和参考。
让我们来了解一下比赛的背景和要求。
全国大学生数学建模竞赛是由中国工程院主办，旨在促进大学生对数学建模的兴趣和掌握数学建模的基本方法和技巧。
比赛通常会设置一些实际问题，参赛队伍需要在规定时间内通过建立数学模型、分析问题、提出解决方案等步骤来完成任务。
最终评选出的优胜队伍将获得一等奖、二等奖等不同级别的奖项。
在本次比赛中，我们团队选择了一道关于城市交通拥堵研究的题目，并从交通流理论、路网优化等角度进行建模和分析。
通过对城市交通流量、拥堵原因、路段限制等方面的研究，我们提出了一种基于智能交通系统的解决方案，有效缓解了城市交通拥堵问题。
在展示环节，我们通过图表、数据分析等方式清晰地呈现了我们的建模过程和成果，最终赢得了评委的认可。
在整个建模过程中，团队合作起着至关重要的作用。
每个成员都发挥了自己的专长和优势，在分析问题、建模求解、撰写报告等方面各司其职。
团队内部的沟通和协作非常顺畅，大家都能积极提出自己的想法和看法，达成共识后再进行实际操作。
通过团队合作，我们不仅完成了比赛的任务，也培养了团队精神和合作能力，这对我们日后的学习和工作都具有重要意义。
参加数学建模竞赛是一次非常宝贵的经历，不仅能提升自己的数学建模能力，也能锻炼自己的解决问题的能力和团队协作能力。
在比赛的过程中，我们学会了如何快速建立数学模型、如何分析和解决实际问题、如何展示自己的成果等，这些能力对我们未来的学习和工作都将大有裨益。
在未来，我们将继续努力，在数学建模领域不断学习和提升自己的能力，为更多的实际问题提供有效的数学解决方案。
我们也希望通过自己的经验和教训，为更多热爱数学建模的同学提供一些指导和帮助，共同进步，共同成长。
美国大学生数学建模大赛英文写作
写作要求 ： 1. 简短 论文标题一般在10个字内，最多不超 过15个词。
多用复合词
如：self-design, cross-sectional, dust-free, water-proof, input-orientation, piece-wiselinear 利用缩略词 如：e.g., i.e., vs.（与…相对), ibid.(出处相同）， etc., cit.(在上述引文中), et al.(等人), viz.(即,就是), DEA (data envelopment analysis), OLS(Ordinary least-squares)
“Investigation on …”, “Observation on …”, “The Method of …”, “Some thought on…”, “A research on…”等冗余套语 。
4. 少用问题性标题 5. 避免名词与动名词混杂使用 如:标题是 “The Treatment of Heating and Eutechticum of Steel” 宜改为 “Heating and Eutechticuming of Steel” 6. 避免使用非标准化的缩略语 论文标题要 求简洁,但一般不使用缩略语 ,更不能使用 非标准化的缩略语 。
关键词（Keywords)
基本功能：顾名思义；便于检索 语言特点：多用名词；字数有限（4-6）； 出处明确 写作要求 :论文的关键字一般列在作者与单 位之下，论文摘要之上。也有列在论文摘 要之下的。关键词除第一个字母大写外， 一般不要求大写。关键词间用逗号、分号 或大间隔隔开。最末一个关键词一般不加 用逗号、分号或句号。
美赛-数学建模-写作模版(各部分)70339
摘要第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move〞 irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life mon phenomenonwith many plexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例 1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematicallyanalyzing the……problem, our modelinggroupwouldliketo presentourconclusions,strategies,(andremendations )tothe…….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。
美赛数学建模比赛论文实用模板
The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic.As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left.As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow .Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (4)5.1 Building of the Cellular automaton model (4)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (9)5.2.2 Conclusion (9)5.3 Taking the an intelligent vehicle system into a account (9)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (10)6. Improvement of the model (11)6.1 strength and weakness (11)6.1.1 Strength (11)6.1.2 Weakness (11)6.2 Improvement of the model (11)7. Reference (13)1. IntroductionAs is known to all, it’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless theyare passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models,then analyze the performance of this rule in light and heavy traffic. Firstly,we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules,and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions●The highway of double row three lanes that we study can representmulti-lane freeways.●The data that we refer to has certain representativeness and descriptive●Operation condition of the highway not be influenced by blizzard oraccidental factors●Ignore the driver's own abnormal factors, such as drunk driving andfatigue driving●The operation form of highway intelligent system that our analysis canreflect intelligent system●In the intelligent vehicle system, the result of the sampling data hashigh accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years. Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t , p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not takethe initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one) [4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number ofsmall vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed control Fig.5.1.3Fig.5.1.3 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it willbecome difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.● Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate the speed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio of small vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.). It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake.● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control.a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6 Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam situation, applying ))(,2(x P B R results with a tendency of moving to the right lane for this driver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by us to perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table 5.1, 5.2, 5.3. Table.5.1 measured results for the unenforced speed limit scenariodem q case#1 #2 #3 #4 #5 TTS:mean(std ) TPN 4700no shock 494.7452.1435.9414.8428.3445.21(6.9%) 5:4wave 3 5 8 8 0 14700nocontrolled520.42517.48536.13475.98539.58517.92(4.9%)6:364700 controlled 513.45488.43521.35479.75-486.5500.75(4.0%)6:244700 no shockwave493.9472.6492.78521.1489.43493.96(3.5%)6:034700 uncontrolled635.1584.92643.72571.85588.63604.84(5.3%)7:244700 controlled 575.3654.12589.77572.15586.46597.84(6.4%)7:19●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Because of the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance ofthe freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby, with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consideractual traffic conditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantimethe conclusion is more persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensivelyanalysis.●Due to there are many traffic factors, we are only studied some of the factors,thus our model need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, We further put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig .6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the 85V speed of each model as the main reference basis. In recent years, the 85V of some researchers for the typical countries from Table 6.1[ 21]: Table 6.1 Operating speed prediction modeAuthorCountry Model Ottesen andKrammes2000America LC DC L DC V C ⨯---=01.0012.057.144.10285Andueza2000Venezuel a ].[308.9486.7)/894()/2795(25.9885curve horizontal L DC Ra R V T ++--= ].[tan 819.27)/3032(69.10085gent L R V T +-= Jessen2001 America ][00239.0614.0279.080.86185LSD ADT G V V P --+=][00212.0432.010.7285NLSD ADT V V P -+=Donnell2001 America 22)2(8500724.040.10140.04.78T L G R V --+=22)3(85008369.048.10176.01.75T L G R V --+= 22)4(8500810.069.10176.05.74T L G R V --+=22)5(8500934.008.21.83T L G V --=BucchiA.BiasuzziK.And SimoneA.2005Italy DC V 124.0164.6685-= DC E V 4.046.3366.5585--= 2855.035.1119.0745.65DC E DC V ---= Fitzpatrick America KV 98.17507.11185-= Meanwhile, there are other vehicles driving rules such as speed limit in adverseweather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane traffi csimulations using cellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffi c Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
美赛数学建模比赛论文资料材料模板
The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic.As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left.As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow .Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (3)5.1 Building of the Cellular automaton model (3)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (8)5.2.2 Conclusion (8)5.3 Taking the an intelligent vehicle system into a account (8)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (9)6. Improvement of the model (10)6.1 strength and weakness (10)6.1.1 Strength (10)6.1.2 Weakness (10)6.2 Improvement of the model (10)7. Reference (12)1. IntroductionAs is known to all, it ’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless they are passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models, then analyze the performance of this rule in light and heavy traffic. Firstly, we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules, and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions● The highway of double row three lanes that we study can representmulti-lane freeways.● The data that we refer to has certain representativeness and descriptive● Operation condition of the highway not be influenced by blizzard or accidental factors ● Ignore the driver's own abnormal factors, such as drunk driving and fatigue driving ● The operation form of highway intelligent system that our analysis can reflectintelligent system● In the intelligent vehicle system, the result of the sampling data has high accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years.Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t ,p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not take the initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.● Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one)[4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number of small vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed controlFig.5.1.3Fig.5.1.3Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it will become difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate thespeed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio ofsmall vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.).It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake. ● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control. a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.● Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam BP(situation, applying ))results with a tendency of moving to the right lane for this,2(xRdriver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by usto perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table5.1, 5.2, 5.3.●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Becauseof the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance of the freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby, with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consider actual trafficconditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantime the conclusion ismore persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensively analysis.●Due to there are many traffic factors, we are only studied some of the factors, thus ourmodel need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, Wefurther put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig.6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the85V speed of each model as the main reference basis. Inrecent years, the85V of some researchers for the typical countries from Table 6.1[ 21]:Author Country ModelOttesen andKrammes2000America LCDCLDCVC⨯---=01.0012.057.144.10285Andueza2000 Venezuela].[308.9486.7)/894()/2795(25.9885curvehorizontalLDCRaRVT++--=].[tan819.27)/3032(69.10085gentLRVT+-=Jessen2001 America][00239.0614.0279.080.86185LSDADTGVVP--+=][00212.0432.010.7285NLSDADTVVP-+=Donnell2001 America22)2(8500724.040.10140.04.78TLGRV--+=22)3(85008369.048.10176.01.75TLGRV--+=22)4(8500810.069.10176.05.74TLGRV--+=22)5(8500934.008.21.83TLGV--=BucchiA.BiasuzziK.And SimoneA.2005 ItalyDCV124.0164.6685-=DCEV4.046.3366.5585--=Meanwhile, there are other vehicles driving rules such as speed limit in adverse weather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane traffic simulations usingcellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffic Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
【完整解析】美赛-数学建模-写作模版(各部分)
Summary：clearly describe your approach to the problem and,most prominently,your most important conclusions.●Restatement and clarification of the problem:State in your own words what you aregoing to do.●Explain assumptions and rationale（principle）/justification:Emphasize the assumptionsthat bear on the problem.Clearly list all variables used in your model.●Include your model design and justification for type model used or developed.●Describe model testing and sensitivity analysis,including error analysis,etc.●Discuss the strengths and weaknesses of your model or approach摘要第一段：写论文解决什么问题.1．问题的重述a.介绍重点词开头：例1：“Hand move”irrigation,a cheap but labor-intensive system used on small farms,consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An(effective plan)is crucial to………b.直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes:the number of tollbooths that minimizes average delay experienced by cars.我们找到了在给定XX的情况下最佳的……例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.XX需要具有B性能的C例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.我们通过分析参数B确定A，并且检验了现实情况C例4:After mathematically analyzing the……problem,our modeling group would like to present our conclusions,strategies,(and recommendations)to the…….在数学分析B后，我们的模型组将呈现了我们的结论和建议We begin by considering only the rigid recoil effects of the bat–ball col-LisionOur main goal is to understand the sweet spot.A secondary goal is tounderstand the differences between the sweet spots of different bat types.Because the collision happens on such a short time-scale(around1ms),we treat the bat as a free body.That is to say,we are not concerned with the batter’s hands exerting force on the bat that may be transferred to the ball....Our paper is organized as follows....例5：Our goal is...that(minimizes the time)……….2．解决这个问题的伟大意义反面说明。
美赛-数学建模-写作模版(各部分)讲课稿
美赛-数学建模-写作模版(各部分)摘要第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例 1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。
数学建模美赛写作模版(包含摘要、格式、总结、表格、公式、图表、假设)
论文reference 格式中文解说版总体要求1 正文中引用的文献与文后的文献列表要完全一致.ν文中引用的文献可以在正文后的文献列表中找到；文献列表的文献必须在正文中引用。
2 文献列表中的文献著录必须准确和完备。
3 文献列表的顺序文献列表按著者姓氏字母顺序排列；姓相同,按名的字母顺序排列；著者姓和名相同，按出版年排列。
νν相同著者，相同出版年的不同文献，需在出版年后面加a、b、c、d……来区分，按文题的字母顺序排列。
如: Wang, M. Y。
（2008a). Emotional……Wang, M。
Y。
(2008b). Monitor……Wang，M。
Y. (2008c). Weakness……4 缩写chap. chapter 章ed。
edition 版Rev. ed。
revised edition 修订版2nd ed. second edition 第2版Ed. (Eds。
）Editor （Editors）编Trans. Translator（s) 译n.d. No date 无日期p。
(pp。
）page （pages）页Vol. Volume (as in Vol。
4) 卷vols。
volumes （as in 4 vols.）卷No。
Number 第Pt。
Part 部分Tech. Rep. Technical Report 技术报告Suppl. Supplement 增刊5 元分析报告中的文献引用ν元分析中用到的研究报告直接放在文献列表中，但要在文献前面加星号＊。
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（2)也可放在引用句尾的括号中，如:在语言学上，音节是语音结构的基本单位，也是人们自然感到的最小语音片段。
数模美赛论文模板
内容格式：AbstractIntroductionAssumptionsAnalysis of the problemTask 1 : predicting survivorshipTask2 : achieving stability….Sensitivity analysisStrengthsWeaknessesConclusionReferencesTitle(use Arial 14)First author , second author , the other (use Arial 14)Full address of first author . Including country and mail(use Arial 11)Full address of second author . Including country and mailList all distinct addresses in the same wayKeywords(use Arial 11)Abstract1985:模型概述-考虑因素-使用理由We modelled …. Since … – we used …. We included …which were to be chosen in order to …假设条件-数据处理方法We assumed that…We used actual data to estimate realistic ranges on the parameters in the model.评估标准-衡量方法-得到结论-结论的可靠性We defined…We then used …we found …We examined the results for different values of the mortality parameters and found them to be the same . Therefore ,our solution appears to be stable with respect to environmental conditions.2000:背景设置-模型引入…in order to determine …, we develop models using…解决问题-模型解决（层次排比）For the solution of …, we develop… model based … to … . For the solution of … , we employ … What is more , a self-adaptive traffic light is employed to … according to …模型检验-模型修正By comparison of … simulation results , the models are evaluated . …is formulated to judge which solution is effective .2002:The task is to … we begin by constructing a model of … base on … Using this model we can … Using… , we model … through … and obtain … we compare the performance of our model in … simulations show that …2001:We examine the … . Such evacuations been required due to … . in order to … , we begin with an analysis of … . For a more realistic estimate , including the effects of … , we formulate models of … . The model we construct is based on … .This model leads to a … and it further show that … what’ more , it agrees with …2004:（修正递进式模型摘要模板）The purpose of this paper is to propose … . We propose that … . To build a solid foundation , we define and test a simple model for … . We then develop … system , but we find it would be far from optimal in practice . We then propose that the best model is one that adapts to … . We implement … . We simulate the … with … and we find this system quickly converges to a nearly optimal solution subject to our constraints . It is , however , sensitive to some parameters . We discuss the effects of these findings on the expected effectiveness of the system in a real environment . We conclude that … is a good solution .问题分析句式：… is a real-life common phenomenon with many complexities .For a better view of … , we …To give a clear expression, we will introduce the method presented by …模型引入句式：In this paper , we present … model to simulate efficient methods for …We also apply … methods to solve …We address the problem of …. through ….We formulate the problem as …We formulate a … model to account for …Base on … , we establish a model ….We build a model to determine …We modify the model to reflect …To provide a more complete account for … , ... model has been employed .In this paper , in order to … , we design a … model based on …We propose a solution that …We have come up with an … for … andStrong evidence of ... , and powerful models have been created to estimate ...模型推进：… will scale up to an effective model for …模型求解：We employ … , one based on … and the other … , whose results agree closely.To combat this , we impose …结合数据：Using data from … , we determine …To ground this model in reality , we incorporate extensive demographic data ….We use data assembled by …Using a wide scale regression , we found that …We extrapolate from longevity data and explore the long-term behavior of …The base we developed was based off real-life data that gathered by …We estimate these characteristic numbers for a representative sample of …We fit the modified model to data , we conclude that …By statistical processing to results of …By analyzing the … on the basis of historic data in the same way mentioned in …结果给出句式：Results of this computation are presented , and ….We elicit that a conclusion …We conclude with a series of recommendations for …Given a … deviation in the value of the parameter , we calculate the percentage change in the value that the system converges to …As we can find out , in the situation of …. , …. is subject to the logistic regression .We conclude through analyzing that ….it is apparent that …Through comparing the … , we conclude that …According to the laws of … , we draw a conclusion of …From the formula , we know that …Thus we arrive at the conclusion :We elicit that a conclusion …As a consequence , we can get …模型可行性：Our suggested solution , which is easy to ….Since our model is based on … it can be applied to …Importantly , we use some practical data to test our model and analysis its stability , we simulate this model and receive a well effect .Therefore , we trust this model as an accurate testing ground for …Our algorithm is broad enough to accommodate various …定理可靠说明：That is the theoretical basis for … in many application areas .模型简化With further simplification, utilizing … we can reach …承上启下：In addition to the model , we also discuss …Because the movement of … operates by the same laws and equations as the movement of … , we can ….Based on the above discussion, considering …., let’s …误差句式：… does not deviate more than … from the target value .Theoretically , error due to … should not play a tremendous role under our model .Up to this point , we have made many approximations , not all of which are justified theoretically , but the results of algorithm are quite reasonable .This is a naïve approach which may mot ensure the …. , however if we … , the error is negligible .Context:方程给出：We derive the equation expressing the … as a function of… we haveA simple formula determined by the … is given by the equation :… can be written as the following system of equations :In particular , the … is defined in terms of … ,It is convenient to rewrite equations into the vector form:The expression of … can be expanded as …Equation (1) is reduced to ..Substitute the values into equation (1) ,we get …So its expression can be derived from equation (1) with small changes .Our results are summarized in the formula for …Plugging (1) into the equation for (2) , we obtain …Therefore , from (1)(2)(3) , we have the junction that …We use the following initial conditions to determine …When computing , we suppose … ,so this suppose doesn’t … ,then by … , we can get :According to equation (1)(2) , we can eliminate … ,then we can acquire :By connecting equation (6)(7) , we get the conclusion that …Then we can acquire … through the following equation :Its solution is the following …, in which … is …客观条件引入：A commonly accepted fact is that …A lot of research has been done to explain and find …In our model , we prefer to follow the conclusion used by …Here , we cite the model constructed by …There is one paper from … ,which concluded that …We get performance of … by citing the experimental results of …Here, we will introduce some terms used to address the problem, and we …方法给出句式：We construct … intelligent algorithms , a conservative approach , and an enthusiastic system to ..We formulate a simplified differential equation governing …This equation will be based on …The above considerations lead us to formulate the … asGiven this , it is easy to determine …To analyze the accuracy of our model , and determine a reasonable value for …We will evaluate the performance of our … by …We tabulate the … as a function of …Analysis for the … can be carried out exactly in the same fashion as …The main goal in attempting to model … is to determine … and … should be considered .The first requirement that the model reproduce is to determine if the model is reasonable .We begin our analysis of the phenomenon of congestion with the question of …In modeling this behavior , we begin with …In laying down the mathematics of this model , we begin with …When … is not taken into account ,it is …We give the criterion that …We fix A and examine the change of B with respect to CAttention has been draw to determine …To reveal the trend of … in a long horizonTo deal with the problem, we need figure out …图表句式：We can graph … with …,and such a plot is shown in …According to the above data , we can see that … . This phenomenon shows that … . Hence, we can safely arrive the conclusion that …Table 7 reports the general statistics under …文献句式：There is rather substantial literature on models for evaluating regional health condition, and most models fall into one of two categories: microscopic and macroscopic. Nevertheless, to get a more accurate understanding, we need to conduct quantitative modeling in our call for a better evaluation and predictive model.假设句式：In order to present our solution , we have made numerous simplifications to the given problem . we made several assumptions regarding either the problem domain itself , or …For the sake of simplicity , we will generally assume in our discussions that …… are assumed to have …We assume … are …Due to the symmetry of the image we can assume that …We came up with a few different hypotheses that …For simplicity we consider …We will use the following symbols and definitions in the description of the model:To get the general picture of the … , we rely on the assumption that …Hence we are bale to …This assumption makes sense , because we expect …Assumption … is valid , since if it was not the case , the … would …Make the following assumptions to approximate and simplify the problem …As a sweet spot , there is no doubt that … ,if not , …For the purpose of reaching a conclusion conveniently , we assume …We adopt a set of assumptions as follows …模型验证：To test our model , we developed a … simulator based on … , and the simulator was written in … and can be executed on several platforms .To demonstrate how our model works , we apply it to …跨段内容：For a further discussion of this model , please see Appendix A .The underlying idea is fairly simple内容引导：What we are really interested in is …With this consideration in mind , we now …Our goal is to … , one that would …We must restate the problem mathematically by narrowing our focus and defining our goals in order to obtain a good model .Given this idea , it is clear that we cannot compromise the …This immediately leads to useful conclusions . For example , …Given these assumptions , the following results can be quickly derived …We will pursue this goal …We turn our attention to …We restrict our attention to …In addition to the model , we also discuss policies for …In our paper , we take … factors into consideration to …… is not as simple a task as it might seem , because …For the … , we only take … into account .As the next step , we will introduce our advanced method to …Under the premise of this , …On the basis of previous analyses , we find the …效果评价:This is a good indication that our simulations are producing reasonable results .The results of our simulations ,shown in … indicate that the performance of …This is no surprise the distinguishing features of …This would appear very encouraging indeed , were it not …We therefore regard this model as reasonable .Here very little congestion occurs …As we will see when we apply our model to … ,this model works well . It should be noted ,though that this is not the only way to define the location of generator points , but it is a very good firs approach .//数据缺乏的理论化模型Of course , only theoretical explanations are not completely convincing . But mass of data relevant to our calculation can be obtained through experiments . Owing to our limit conditions , we only quote some experimental results from other literatures to assist and analyze our derived theoretical conclusion .变量指定句式：Let … denote … , and … to be …The … is … , where … is , W stands for , and … stands for bucks .For better description we assign …Note for brief description of the model , we will denote …解释句式：In fact , this assumption is reasonable not only because … but also that …In other word , …The key feature of this algorithm is …It is important to note that … can no longer be ignored when considering …If … , we can gain more insight into the nature of …The reason we care about … is that … ,the problem is determining …, if … so we ..Our approach weighs heavily on …To show that … are negligible , we vary …This is likely due to …修正：We modify … according to …We modify the model to reflect … and generalize the model to …影响：Because the effect of … and omit the resistance of …As the effect of …The model also incorporates the …At other impact points , the impact may …... has been implicated as the major component of ...图表用语：However , from this figure it is clear that the …From this figure one can see that …,one also notices that …This graph can be compared to the results of the symbolic model to see how well the model agrees with our simulated …The two plots at above which show … .According to …, there exists the fact that …According to …, it is no doubt that…拟合近似,模拟：Given the above assumptions , we may approximate …In simulations over a suitably long time period , we find …For each run of the simulation we fire enough blobs so that results are …An appropriate estimate for the … can be obtain as follows .In assessing the accuracy of a mathematical model , …We now propose a way to extend our model using a computer simulation of …It is obvious , however , that this is a highly subjective value that must be determined through experiment for each … that our model is applied to .This model leads to a computer simulation of …主要因素:Analyzing what parameters have the greatest effect on the simulation results indicates the things that we should focus on in order to produce a more effective evacuation scheme .Sensitivity analysisWe use the sensitivity analysis to defend our model . The sensitivity of a model is a measure of how sensitive the result changes at small changes of parameters . A good model is corresponding to low sensitiveness .Considering the parameters used in our solutions , here we provide following discussion .The above models we have built is based on … ,which has well solved … . To the final issue , we have take … into account in order to …Strength:On the whole , we have hound our model to be quite natural and easy to apply . Here , we list some of the advantages of our approach to the problem .The most distinct advantage of our model is that …Our methods can incorporate various scenarios : ….This model is simple enough for … to understand .Our method is robust (健壮), so that other variables or situations can be easily introduced .Our model … and is not overly sensitive to small changes in …Additionally , we avoided harsh assumptions that would constrain the possible …Most of the assumptions we did make could be accounted for as well in a more general model .We use random events to simulate the chaos of real world .The key insight to our model is that ….Our model also takes into account the …The model allows … which is more close to reality .The model is able to handle a range of …Besides rigorous theoretical derivation , we also citing the research results of numerous experts and scholars to test the result of our method .Weakness:Of course , there are many ways to attack a problem such as this one , In this section , we discuss some of the drawbacks of our approach to the problem , and some things that could have been done to deal with these issues .Some special data can’t be found , and it makes that we have to do some proper assumption before the solution of our models . A more abundant data resource can guarantee a better result in our model .The model responds slowly to dramatic changes in …The method does not allow … , which might be possible with a more radicalmodel .However , … constraints arise when pursuing this methodology .Additionally , this method would have required … , which would …However , the algorithms do have unique strengths and weaknesses when …Our model does take into account the complicated effects that …Factors considered in our method is relatively unitary , we only take the important factor into consideration .Lacking brief numerical calculation in our method , though we display rigorous theoretical derivation .。
美国大学生数学建模大赛模拟1论文
生猪年末存栏量及猪肉价格 周期性波动研究
摘要
本文是关于时间序列数据的预测探究的，我们利用灰色系统理论和自己建立 的模拟函数对生猪的年末存栏量和 36 个大中城市的猪肉价格进行了模拟和预 测。 在对第一问生猪年末存栏量的预测中，由于 1997 年以前的统计数据不真实， 从而导致可用信息贫乏，据此特点我们采用了灰色系统理论中的 GM(1,1)模型。 通过对已知数据和生猪养殖业的分析我们发现生猪养殖随供求关系的变化呈周 期性的波动， 波动周期为 3 至 4 年，又鉴于我国经济社会和人民生活水平的不断 发展，生猪养殖业总体上呈现上升趋势。GM(1,1)并无对周期性变化数据的预测 能力， 但对单调趋势的小信息量数据有较好的预测能力，据此我们剔除数据中的 波动成分，即选取原始序列时每隔 3 年取一点，得出 2010 的生猪存栏量为 44770.6 （万头） 。 最后对预测结果的检验发现其与原数据的偏差不会超过 3.03%， 从而保证了预测结果的可靠性。 利用生猪年末存栏量随时间增长但呈现周期性波 动的特性， 我们还建立了与之适应的模拟函数模型，模拟函数包括由一次函数表 征的增长部分、由正弦函数表征的波动部分和由正态函数表征的冲击部分（如 03 年和 06 年生猪养殖业遭到了重大变故，反应在存栏量上有很大波动） 。以最 小二乘法确定此模拟函数的各项参数，进而预测出 2010 年末的生猪存栏量为 46813 万头。由于模拟函数是在机理分析的基础上建立的，所以很好的吻合了已 知数据， 从而对未来数据的预测也就有了保证。两种预测模型预测结果还是有较 大差异的，但我们认为机理分析在预测中是更有效的方式，所以更倾向于把 46813 万头作为最终预测结果。 第二问要求对 36 个大中城市的猪肉价格做出预测。通过对猪肉市场和已有 数据的分析研究， 我们发现猪肉价格在总体上仍然呈现 3 到 4 年为一个周期的波 动，而在每一年中，猪肉价格受节假日、经济波动和病疫等诸多因素的影响，呈 现小幅度短周期的波动情况。 鉴于此变化规律，我们构造的模拟函数包括表示初 始价格的常数、 表示总体波动的周期为 4 年的正弦函数和表示众多繁杂因素影响 的傅里叶级数（出于计算考虑取级数前 50 项） 。通过最小二乘法确定各参数，得 出的模拟函数对已知数据完全贴合。在模型检验中，我们只用部分已知数据来确 定模拟函数， 发现模拟结果与未使用的数据也有很好的吻合程度。 为了进一步检 验模型我们查阅了新的猪肉价格信息发现其与预测价格有相近的走势。 这些都验 证了模拟方法的正确性和模拟函数的有效性。
美赛-数学建模-写作模版(各部分)
摘要第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例 1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。