数学建模MCM美赛 M 奖

2024美赛数学建模题目
2024年美国大学生数学建模竞赛（MCM/ICM）赛题包括以下六道题目：
MCM A（环境类）题目：遭受旱灾的植物群落。

题目要求建立预测模型，预测植物群落未来随时间的变化。

MCM B（环境类、政策类）题目：重新想象马赛马拉。

题目难度主要在数据不好找，预测动物和人们相互作用的模型。

MCM C（数图、图论优化类知识）题目：预测单词结果。

可以采用神经网络模型，利用隶属度函数进行分类，用聚类模型转换为不同的类，再用神经网络作为输出。

ICM D 题目：联合国可持续发展目标的优先顺序。

关键在数据层面，构建
各个指标之间的关系网络，各个指标之间存在限制。

ICM E（环境类）题目：光污染。

难度系数主要还是在获取光污染的数据上。

ICM F 题目：绿色GDP。

择某个标准来计算绿色GDP，基于水资源安全的模型来构建它对全球气候变化的影响。

以上就是2024年美国大学生数学建模竞赛的六道赛题，每道题目的主题和要求均已给出。

如需更多信息，可以登录美赛官网进行查询。

美国数学建模竞赛的相关信息一．美国数学建模竞赛MCM简介MCM全称：The Mathematical Contest in Modeling（数学建模竞赛，国内称为美国国际数模竞赛）ICM全称：The Interdisciplinary Contest in Modeling（交叉学科建模竞赛，国内称为美国大学生数学建模与交叉学科竞赛）MCM始于1985年，由美国自然基金协会和美国数学应用协会共同主办，美国运筹学学会、工业与应用数学学会、数学学会等多家机构协办。

其宗旨是鼓励大学生对范围并不固定的各种实际问题予以阐明、分析并提出解法，每队在4天内对问题展开设计，要以清楚定义的格式写出解法论文。

该项比赛吸引了中国（含香港）、美国、英国、加拿大、芬兰、爱尔兰、澳大利亚、南非、新加坡等多个国家的著名大学代表队参加。

1999年COMAP推出了交叉学科建模竞赛。

其特等奖论文将刊登于同年UMAP杂志。

近年来，MCM/ICM比赛越来越具有影响力，也得到越来越多的学校和单位认可。

其获奖学生在出国留学、保送研究生、找工作时，在激烈的竞争中胜出的机会要多很多。

MCM将题目公开在网络上这种开放式的竞赛方式，竞赛环境相对而言比较自由，然而参赛选手来世界各地，竞争之激烈可想而知。

MCM/ICM其要求与国内竞赛大致相同，除了要求用英语阅读、写作水平外。

这对于中国的学生来说是一个非常大的挑战，如果成功参赛，将极大程度上提高英语水平。

总而言之，在建模期间，知识将会进一步积累，知识面也会得到提高，而英语写作能力、资料的检索能力、创新能力等都将得到训练，这些能力综合起来其实就是科研能力，将为今后的科研打下坚实的基础。

二．美国数学建模竞赛网站进入方法首先进入中国数学建模网站，点击友情链接页面，找到美国大学生数学建模竞赛，点击即可直接进入网站。

具体过程如下：全国数学建模竞赛/友情链接/html_cn/block/f104f25e0431f7882cb1ddd5be2d8a14.html美国大学生数学建模竞赛(MCM & ICM in USA)/undergraduate/contests/三．2011年美国大学生数学建模竞赛（MCM/ICM）竞赛2011年美国大学生数学建模竞赛（MCM/ICM）竞赛于（美国东部时间）2011年2月10日晚8:01~14日晚8:00举行。

For office use onlyT1________________ T2________________ T3________________ T4________________ Team Control Number70028Problem ChosenBFor office use onlyF1________________F2________________F3________________F4________________2017MCM/ICMSummary 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 this page.SummaryThe performance of highway toll plaza directly affects the capacity of the highway, so the design of road toll plaza is imperative.In this paper, we conduct performance analysis for a specific toll plaza in New Jersey, USA, including accident prevention, throughput and cost. First of all, we usegrey model to predict the future output of the toll plaza, and compared with the realdata, the average value of the residual value is 0.429. Then we can draw a conclusionthat the throughput performance of the toll plaza is secondary. Next, we use queuingtheory to get the service index of the toll plaza in the light and heavy traffic, and thecellular automaton model is used to consider the changing circumstances of servicelevel, uses regression model to establish a function relation between traffic accidentand four factors. Then, we find that the rate of change has the greatest influence onit and the pavement performance has the least influence . In terms of cost, weconsider the toll plaza land and road construction. And the cost of road constructionis divided into the labor cost and material cost.Next, according to the influence of road geometry on the traffic performance of Toll Plaza, we select the transition curve trajectory model to improve the toll plazatransition, which can also have an improvement on the size and shape of the toll plazaand merge mode.Finally, we do a series of performance studies for our improved toll plaza. First of all, the improvement in the square flow and car flow under the condition of servicelevel are determined respectively through simulation .Next, we draw a conclusion thatthe service performance of the toll plaza is not obvious in small car flow, but there is amarked increase in large flow. Then, due to the fact that the unmanned vehicle coulddeal with a variety of road conditions, it undoubtedly expands our improved optionalscheme. Eventually, we obtain the throughput of toll before and after the improvementunder the different proportion of mixed charge mode and find that the improvedthroughput in the toll plaza has been increased on the performance.contents1 Introduction: (1)1.1 Problem background: (1)1.2 Steps: (1)1.3 Our work: (1)2 Assumptions (2)3 Nomenclature (2)4 Throughput analysis of grey forecasting model (3)5 error analysis (4)6 Service level of toll station (5)7 Vehicle lane changing rules based on Cellular Automata (6)8 Security analysis based on multivariate statistical regression mode (8)8.1 Study on the rate of change of Toll Plaza (8)8.2 Study on the longitudinal slope of entrance section of Toll Plaza (9)8.3 Research on service level of toll station (10)8.4 Study on pavement performance of toll station (10)9 Safety performance evaluation model of toll station (11)10 Cost analysis model of toll station (11)11 Analysis of the influence of lane geometry parameters on its capacity (12)11.1 Determination of lane changing rate (12)11.2 Influence of geometric parameters on the flow of the car lane (14)11.3 Energy consumption analysis based on cellular automata model (15)Definition of energy consumption: (16)Numerical simulation and analysis of the results: (17)Influence of curvature radius on energy consumption (17)Influence of arc length on energy consumption (18)12 The effect of traffic flow on service performance based on improved queuing theory 1913 The influence of unmanned vehicles on the improved model of Toll Plaza .. 2114 The influence of charging method on improving model of Toll Plaza (21)15 Strengths and Weaknesses (22)15.1 Strengths: (22)15.2 Weaknesses: (22)15.3 Future Model Development: (22)Comprehensive improvement strategy of tollplaza1Introduction:1.1Problem background:Highway toll and toll plaza is to ensure traffic safety and unimpeded, however because of lack of unified design specification, toll station and its square construction exists many problems. Such as: low value because of the technical indicators to make square construction scale too small and cause the toll plaza opened only few years as the traffic bottleneck, and use the high value on the one hand, because of the technical indicators and make the toll station construction scale is too large, waste a lot of money and resources. Due to incorrect linear indicators, or too short, the gradual square square length is insufficient, square road centerline offset, etc., it is too difficult to use after the completion of the square.so establishing the toll gates and the toll plaza design norms, as soon as possible, has the very vital significance in standardizing the construction of the toll station, ensuring the smooth general characteristic of toll plaza and traffic safety, improving the charging efficiency and management level, reducing the land acquisition and controlling investment and so on .1.2Steps:·A performance analysis of any particular toll plaza design that may already be implemented through the following three factors: accident prevention, throughput and cost .·Determine if there are better solutions (shape, size, and merging pattern) than any in common use.·Consider the performance of your solution in light and heavy traffic.·Consider the situation where more autonomous (self-driving) vehicles are added and how the solution is affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths (such as electronic toll collection via a transponder in the vehicle)1.3Our work:·Based on the available data ,we make a performance analysis of any particulartoll plaza design that may already be implemented .·According to the problem from the performance analysis ,we make out a better solutions (shape, size, and merging pattern) than any in common use.·Determine the performance of the solution in light and heavy traffic ,how the solution change as more autonomous (self-driving) vehicles are added to the traffic mix and how the solution is affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths.2AssumptionsTo simplify the problem and make it convenient for us to simulate real-life conditions, we make the following basic assumptions.1. Each section of roads is one-way traffic2.Vehicles in the retention period of toll station can be neglected3.In any hour of the vehicle arrival rate is proportional to the length of time4.The probability of any vehicle arrival in one hour of time is not affected by the previous history .5. The vehicles arrive in line with the Poisson distribution, namely the headway is negative exponential distribution3Nomenclatureε(0)(t)the residual errorq(t)the relative errorc the variance ratioP the small error probabilityr the curvature of the bend radiusu the static friction coefficientl the gradual change ratiok the number of serving drivewayρ/k traffic intensityw mean time to stay at a toll stationd automotive braking distancef the tire and road surface friction coefficientY the number of traffic accidents in toll stations per year∆W Width of the gradualα1curve angle R 1the radius of convex curve points pdelay probability e(n,t) energy consumption of the first n vehicles from time t to t+14 Throughput analysis of grey forecasting modelFigure 4-0-1Schematic diagram of New Jersey toll plazaFirst of all, we chose a toll plaza on the New Jersey in the United States for a specific performance analysis of toll plaza, and it includes the accident prevention, throughput, and cost.In view of the throughput of the toll plaza, we choose the grey forecasting model GM(1,1) , to predict the throughput of the toll plaza. Due to the problem of uncertainty, so we take the grey prediction model to deal with it.Suppose x (0)(1),x (0)(2)…,x (0)(M )In order to overcome the irregular , we use accumulation processx (1)(t )=∑x (0)(i)M i<1 Such a relatively smooth new series approximation can be described by the following differential equation:dx (1)dt +ax (1)=μ Its an albino form discrete solution of differential equation is: x ̂(1)(i +1)=.x (1)−u a /e ;ai +u aThe type of the parameter a、u be determined by the least squares fitting method is as follows:（1）（2）（3）A ̂=0a u 1=(B T B);1B T Y N Among them the matrix is:B =[ −12,x (1)(1)+x (1)(2)-1−12,x (1)(2)+x (1)(3)-1⋯⋯−12,x (1)(m −1)+x (1)(m )-1] Y N =(x (0)(2),x (0)(3),⋯,x (0)(m ))TSo the original data fitting sequence is:x ̂(0)(1)=x (0)(1)x ̂(0)(i +1)=x (1)(i +1)−x (1)(i )Table 4-0-1 Traffic flow prediction table5 error analysisIn equation (11), and regulations, the original data of reducing value and its residual error and relative error between observed value is as follows{ε(0)(t )=x (0)(t )−x′(0)(t )q (t )=ε(0)(t )x (0)(t )×100%The following inspection of the accuracy: x(0)=1M ∑x (0)(t )M t<0 ε(0)=1M;1∑(ε(0)(t )−ε0M t<2)2Second, calculate the variance ratio c =s 2s 1and small error probability P =2|ε(0)(t )−ε(0)|<0.6745s 13（4）（5）（6） （7） （8） （9） （10） （11）Figure 5-0-2comparison chart of grey prediction modelWe use m、p、v max to represent quality of the vehicle, random delayprobability and maximum speed respectively, g represents the local acceleration of gravity, r represents curvature of the bend radius and u represents the static friction coefficient . With the road statistical analysis carried out on the real value and the error of predicted value, we obtain the following res ults:It shows that the GM(1,1)model prediction results have a better response to .reflect the actual situation.6 Service level of toll stationThe direct feeling of the driver to the traffic environment of the toll station is from the queue length of the toll lane, and the length of the queue depends on the service level of the toll station V/C. In this regard, we use the queuing theory model of multichannel Queuing service, in which the vehicle arrival time is in a Poisson distribution, which is the negative exponential distribution; Suppose m is random arrival rate ,c i is output rate,k is the number of serving driveway, ρ=m c .There is the probability of having no vehicle in the queuing theoryρ(0)=1,∑1n!k−1n=0p n :1k!ρk k k−ρ- Average number of vehicles in queueing theory:n =ρ+p n ρ(0)k!k n−k (1;ρk )2 （12）（13）queue length: q =n −ρ=p n ρ(0)k!k n−k (1;ρk )2 Average number of waiting vehicles per lanea =q kAverage waiting time in queue systems:d =n m =q m +1c Average waiting time in queue:W =q mMean tardinessDeceleration time of vehicle entering toll stationt 1=v 03.6a 1Mean time to stay at a toll stationw =E ,S -+W qVehicle acceleration time of leaving toll stationt 2=v 03.6a 2 In this equation, v 0 is the normal traffic flow (km/h); a 1 、a 2 are deceleration of the vehicle (m/s 2); W q is average queue time (s)； E ,S - is expected service time (s);7 Vehicle lane changing rules based on CellularAutomataWe apply the previous cellular automata model, which is now extended to multi Lane case. The main difference between multi lane and single lane is to consider the model of lane changing. In this paper, we take 4 lanes as an example.In reality, it may be possible to change lanes when the driver is found to be close to the exit and the front of the adjacent lane is empty. If you want to change lanes ,you should consider the vehicle behind the adjacent lane. When the distance （14）（15） （16） （17） （18） （19） （20）to the rear of the adjacent lane reaches to a certain length, you can change the road. Lane change scenarios can be shown in figure (), when the c car on the 1 Lane is blocked by the c 1 car, while the c 2 and c 3 cars on the 2 lanes are relatively large. in order to maintain the speed, c car will change to the road lane 2.Figure 7-0-3Schematic diagram of lane changingWhether or not the driver chooses the lane change is mainly decided by the d 0,d n,otℎer 、d n ,back three indicators, through the previous research, this paper thinks that the lane changing rule is:When d n,back >v maxC n ={1−C n d n <min{v n +1，v max } d n,otℎer >d n ,d n,back >v max c n Otℎer circumstancesWhen d n,back ≤v max ,C n ={1−C n d n <min{v n +1，v max } d n,otℎer >d nv max −θ(−∆x )α>1+min{d n,otℎer +1,v max }−min *V n +1，v max +c n Otℎer circumstancesAmong them, C n is the n car in the lane , C n =0 or 1,d n 、d n,otℎer andd n,back are the distance between the first n vehicle and the front vehicle, the distance from the adjacent lane and the distance from the vehicle in the adjacent lane, respectively. d safe is safety lane change model.d n,back −v max , ∆x <0, v max −θ(−∆x )α is the distance between the vehicle and the vehicle in the adjacent lane after correction by the value function, 1+min{d n,otℎer +1,v max }−min *V n +1，v max + is Limit Lane distance. The parameters α and θchange according to the psychological status of driver. If α>1, the greater α is, the more careful the driver is. If θ>1, the greater θis, the more careful the driver is. When α=1，θ=1,that ’s Lane changing model.（21） （22）In order to discuss the αandθ, we use Cellular automata simulation. In a two lane road with a length of7.5km, adopting the open boundary condition, each lane is composed of 1000cells with a length of7.5km, the maximum speed of vehicle v max=5. The random slowing down rate was 0.2.8Security analysis based on multivariate statistical regression modeAimed at the prevention of the accident, we use multiple linear regression to establish a function between the number of traffic accidents and the following four factors: toll square gradient, service level, Toll plaza entrance section of the longitudinal slope, the Pavement performance of Toll station .Figure 8-1Cause analysis of accident8.1Study on the rate of change of Toll PlazaFan in and fan out area of toll plaza are designed to make the gradual vehicles more natural smoothly in and out of the toll plaza. In order to drive vehicle easily , there has a requirement on its gentle gradient change. Otherwise the driver could produce driving deviation, which may cause improper operation and endangers safety.The relationship is as follow:（23）l=b,LAccording to the experience, the vehicles with straight into another lane deviation than at around 0.9m s⁄, drivers usually have no move feeling and uncomfortable feeling.Figure 8-1 The relationship between Accident number and Toll plaza ramp rateFigure 8-1 shows the relation curve between highway toll plaza ramp rate and traffic accident, the figure demonstrates that as the toll plaza ramp rate increases, the traffic accidents will increase, whereas the security of the toll plaza will decrease.Through the data regression analysis, we get the related models between toll plaza ramp rate and the number of traffic accidentsY =1.423e .0064xIn this equation, Y is the forecasted numbers of traffic accident corresponding to the toll plaza ramp rate , x is the toll plaza ramp rate of toll plaza.The correlation coefficient in the model R 2=0.8621, it shows that description model of correlation is higher, From the model ,we can learn that the occurrence of traffic accident frequency is proportional to the toll plaza ramp rate. Gradient length is insufficient, so it can't meet to slow down and change lanes entering the toll plaza vehicle safety requirements, resulting in the occurrence of traffic accidents .8.2 Study on the longitudinal slope of entrance section ofToll PlazaHighway toll entrance section of the longitudinal slope design without fully considering the characteristics of vehicles entering the toll plaza, a long downhill or turn downhill and so on bad road alignment, those will affect the normal operation of the pilot and make the vehicles entering the toll plaza slowdown not sufficient, longitudinal safe driving distance not enough and driving direction can't adjust to the charge lane ,which will causetraffic accidents. This will lead to serious losses. （24）Figure 8-0-4 entrance section of the longitudinal slope and accident numberThrough regression analysis, we get the relevant model between the toll plaza entrance section of longitudinal wave and traffic accidentsY =2.6254e 0.638xIn this equation, Y is the forecasted numbers of traffic accident corresponding to the toll plaza ramp rate , x is the longitudinal wave of t oll plaza’s entry section .The correlation coefficient in the model R 2=0.9219,it shows the correlation of this model is relatively high. But we can learn that toll station ‘s traffic accident and its entrance section of longitudinal wave have a positive correlation from figure model representation ,.The greater the slope, the lower charge war security.8.3 Research on service level of toll stationBased on the previous research of service performance of toll station, we take V C as the measure of service level and Cite previous results. 8.4 Study on pavement performance of toll stationAccording to the vehicle dynamics, the vehicle's braking distance can be expressed as follows:d =u 257.9(f:I) In this equation, d is automotive braking distance , u is the speed at the beginning of the automobile brake, f is the tire and road surface friction coefficient, Iis road longitudinal slope（25）9 Safety performance evaluation model of toll stationBased on the above analysis, the evaluation model of descriptive can be written as the equation form, using multiple linear regression model .Y is the number of traffic accidents in toll stations every year , x 1=1l ,x 2=V C ,x 3=i,则Y =β0+β1x 1+β2x 2+β3x 3N is sample size , Y i (i =1,2,…,N ) represent the Y value of sample i , x i 1,x i 2,…x i n (i =1,2…，N) represent the value of each variable insample I, respectively.令Y =[Y 1Y 2⋮Y n], X =[11⋮1x 11x 21⋮x n 1⋯⋯⋮⋯x 1n x 2n ⋮x n n ] β=[β0β1⋮βn ] Y =Xβ,making maximum likelihood estimate of each variable coefficient β1，β2，…βn , it can get a normal equations:X T Xβ=X T YSo you can get the following regression equationY =−4.4012−9.947511l +10.098V C +11.25i 10 Cost analysis model of toll stationWe selected the American New Jersey a toll plaza to make cost analysisFirstly, according to relevant data, we learn that New Jersey’s average price is （26） （27）（28）（29）（30）$3500 per mu,And the toll plaza which we analyzed occupies about 5 mu, therefore, the land price of the toll plaza is about $17500;Second, the road construction costs include labor and material cost, and the local construction industry ’s average monthly salary is $3000, we use it to calculate labor, this occupies the largest in the road construction costs; As for material cost, we calculate by the current prices in the United States, is about $40 per cubic meter, then according to the size of the toll plaza, it will cost about $45000.In conclusion, the cost of toll plaza spend mainly on the labor cost of highway construction, the material cost also accordingly account for part of it.11Analysis of the influence of lane geometry parameters on its capacity11.1Determination of lane changing rateAccording to the analysis of vehicle trajectory and running state of vehicle , vehicle trajectory in the middle of the gradual path is similar to vehicle lane changing trajectory, and considering the factors when the driver turns, we select the easement curve trajectory model to design the gradual change section of toll plaza. And in the middle of the two convex type curve , we join a long for L straight section , it is shown in the figure belowFigure 11-0-5Toll plaza improvementsAccording to characteristics of convex curve geometric elements, we can use the following formula to calculate the first period of convex curve of easement curve tangent length T1:T1=(R1+p1)tanα1+q1（31）2In this equation, R 1 is the radius of the first section of convex curve points , ρ1 is Within shift, q 1 is tangent increment, α1 is curve angle, and α1=2β1, β1 is easement curve angleSuppose the first and second convex curve gradient width are ∆W 1 and ∆W 2 respectively, the width of one side with the gradient is ∆W .Depending on the figure with the easement curve in orbit, there are: ∆W 1=T 1∙sin α1∆W 2=T 2∙sin α2∆W =∆W 1+∆W 2+Lsinα1∆W =0(R 1+p 1)(1−cos L S1R 1 )+q 11∙sin L S1R 1 +0(R 2+p 2)(1−cos L S2R 2)+q 21∙sin Ls2R 2 +Lsinα1 L S1 and L S2 are the length of easement curve of two convex curve respectivelyL is radial tangent of two convex curve, so α1=α2,then it Can be introduced as follows:L S1R 1 =L S2R 2 Associate (38) and (39),we can get the length of easement curve of two - Section convex curve L S1 and L S2, then the transition section longitudinal distance L y can use the following formula to calculate:L y =[(R 1+p 1)tan L S12R 1 +q 1+(R 2+p 2)tan L S22R 2 +q 2](1+cos L S1R 1 )+Lcosα1 Suppose the ramp rate of transition period is K ,then we can adopt the following equation:K =∆WL y From this equation , we can learn that the driving radius and the straight line segment L have a great influence on the length and the gradient of the gradient. The greater the radius, the longer the straight line, the longer the length of the gradient, the smaller the rate of change（32） （33） （34） （35） （36）（37）（38）11.2 I nfluence of geometric parameters on the flow of thecar laneAssuming C 0 and C 1=dC dl represent respectively bend and itsgradient , l represents the length of the curve itself , we can get C (l )=C 0+C 1lso ，the bend of the direction Angle isφ(l )=φ0+∫C(τ)l 0dτ=φ0+C 0l +12C 1l 2 The bend of the longitudinal distance x(l) and transverse distance y(l) are{x (l )=x 0+∫cosφ(τ)dτl 0y (l )=y 0+∫sinφ(τ)dτl 0 Assuming sinφ≈φ,cosφ≈1,and when x 0(l )=0,x (l )=l , then the bend of transverse distance y(x) and direction angle φ(x) can be expressed{φ(x )=φ0+C 0x +12C 1x 2y (x )=y 0+φl +12C 0x 2+16C 1l 3 Using the ideas of analytical mechanics, assuming that the longitudinal velocity along the x axis for x ′, along the y axis transverse speed for y ′ , along the z axis of horizontal pendulum angular velocity as the bits of ψ′, then from The Lagrange's equations we can get{ d dt .ðE T ðẋ/−ψðE T ðẏ=F Q 1d dt .ðE T ðẏ/+ψðE T ðẋ=F Q 2d dt .ðE T ðψ/+ẋ ðE T ðẏ−y ðE T ðẋ=F Q 3 Defining the system kinetic energy E T =12m (ẋ+ẏ)+12I z ψ2In the formula, m,I z respectively represent Vehicle quality and Rotary inertia take the derivative of (46),we can get{ d dt .ðE T ðẋ/−ψðE T ðẏ=d dt(mẋ)−ψ (mẏ)d dt .ðE T ðẏ/+ψðE T ðẋ=d dt (mẏ)−ψ (mẋ)d dt .ðE T ðψ/+ẋ ðE T ðẏ−y ðE T ðẋ=d dt (I z ψ)−x (mẏ)−y (mẋ) （39）（40）（41）（42）（43）Delimiting generalized force: {F Q 1=∑F xF Q 2=∑F y F Q 3=∑M zIn summary we can get the Vehicle longitudinal coupling model.We mainly consider the lateral situation∑F y =F yr +F xf +F xf cosδ If the vehicle driving in the bend is only disturbed by small disturbance near the equilibrium state, the front wheel angle is small enough , so cosδ≈1,sinδ≈δ ∑F y =−(C f +C r )y ẋ−(aC f −bC f )ψẋ+(F xf +C f )δ We put the formula () and formula () into ()y =−d 2ẏẋ−.ẋ+kd 3ẋ/ψ−(F xf :C f m )δ In the formula d 2=C f :C r m ,d 3=aC f ;bC rI z ,k =I z mThen, the resultant force ∑M z along the vertical direction is∑M z =aF xf sinδ+aF xf cosδ−bF yrWhen sinφ≈φ,cosφ≈1,then∑F y =−(a 2C f +b 2C r )ψẋ−(aC f −bC f )ẏẋ+a(F xf +C f )δψ=−d 4ψẋ−−d 3y ẋ+a I z (F xf :C f m )δ In the formula, d 4=(a 2C f :b 2C r )I z 11.3 E nergy consumption analysis based on cellularautomata modelConsidering the influence of different shapes on traffic performance is mainly reflected in the curve, we mainly study the influence of the curve on the whole problem. On the road segment, Lane set of sections containing only one plane curve, the curve is provided with the deceleration section of L , the road will be regarded as the length of the L 1D discrete lattice chain, each lattice point at each moment or is empty or occupied for a car.m 、p and v max represent the quality of the vehicle, the （44） （45）（46）（47） （48） （49） （50）（51）stochastic delay probability and maximum speed ,respectively, g is the local acceleration of gravity, r and u represent the static friction coefficient of curvature radius and static coefficient of friction between wheel and road, respectively. The vertical direction of the vehicle is subjected to a pair of balance forces, and the influence of tangential friction on the vehicle is mainly reflected in the change of the speed, Therefore , the centripetal force required for the safety of the vehicle is provided by the normal static friction force,v safe is maximum speed of safetyturning, then mv safe2r =μmg,⁄v safe =√μgr .In each step of t →t +1 , all vehicles are in accordance with the following rules of the evolution of the speed and location of the synchronization update :Determine the vehicle delay probability p ：When the vehicle is in the buffer section , if v >v safe,take the probability of delay p =p 1 (larger), in other cases, take p =p 2 (smaller),Acceleration process: v n (t)→min (v n (t )+1,v max );deterministic deceleration process: v n (t)→min (v n (t ),gap n (t))Stochastic deceleration process with probability p ：v n (t)→max (v n (t )−1,0) deceleration process ：When the vehicle is in the corner of the road, and the speed v (t )>v safe , in order to turn the corner ，it must be slowed down :v n (t)→min (v n (t ),v safe )location update process: x n (t )→x n (t )+v n (t)Among them, v n (t) and x n (t ) are the speed and position of the first n vehicle at time t respectively , x n:1(t ) is the position of the first n +1 vehicle at time t . gap n (t )=x n:1(t )−x n (t )−1is the spacing between the first n car and the foregoing vehicle which is close to it.Definition of energy consumptionSuppose the mass of vehicle is m , when it slows down, its kinetic energy is reduced, we define the kinetic energy reduction for energy consumption, e(n,t) represents that energy consumption of the first n vehicles from time t to t+1 .e (n,t )={m,v 2(n,,t );v 2(n,,t:1)-2v (n,t )>v (n,t +1);0,v (n,t )≤v (n,t +1)The average energy consumption per vehicle per unit time:E d =1T 1N ∑∑e(n,t) N n<1t0:T;1t<t0 N is the total number of vehicles on the driveway, t 0 is relaxation time. For（52） （53）the energy consumption of the vehicle, if it is because the speed of t moment is greater than the Vehicle-to-vehicle distance v(n,t)>gap n(t), the vehicle decelerates, thatis defined as the interaction energy, denoted by E di; If it is because of the random deceleration caused, defined as the random deceleration energy consumption, denotedby E dr;if it is because the car speed In the corner v(n,t)>v safe, there is deceleration for the sake of driving safely, defined as safe energy consumption, denoted by E ds.Then total energy consumption is:E d=E di+E dr+E ds（54）Numerical simulation and analysis of the resultsTo simplify the problem, assuming that the length of actual road is 7.5km, Divided into 1000lattices, equivalent to the actual length of each grid correspondsto 7.5m, Delay probability p1=0.8,p2=0.25,Quality unit is defined 1. Entering probability changes from 0~1.0.The state of each vehicle is represented by its own speed v, v∈,0,v max-We let v max=5cell he actual speed is135km/h.We take8×104time steps every run .Influence of curvature radius on energy consumptionThe arc length s, the friction coefficient μand the radius of curvature of r are carried out numerical simulation. parameters are as follows: s=30m,μ=0.5,r=10、50、100、200、300m.According to v max=5cell/s,the maximum speed of the vehicle v max=37.5m/s. Results show that when r=300m, the safetyspeed v safe=√μgr=38.73m/s,v safe>v max, the bottleneck of the curve disappears and the speed limit is lost. The change of the probability in_p of therandom energy consumption（E di、E dr、E ds、E d）is shown in the figure.。

数学建模美赛获奖证书
数学建模竞赛是一个非常受欢迎的学术竞赛，旨在培养学生的数学建模能力和解决实际问题的能力。

获得数学建模竞赛的奖项和证书是对参赛者优异表现的认可和肯定。

以下是关于数学建模竞赛获奖证书的一些相关信息：
1. 获奖级别和类别，数学建模竞赛通常设有不同的获奖级别，如一等奖、二等奖、三等奖，以及荣誉奖等。

此外，还会根据参赛者的年级和不同的类别，如数学建模、数学实验等进行评奖。

2. 证书内容，数学建模竞赛获奖证书通常包括以下内容，证书的名称，如“数学建模竞赛获奖证书”；获奖者的姓名和学校；获奖级别和类别；颁发单位和日期等。

3. 证书的意义，获得数学建模竞赛的奖项和证书可以在学术和职业发展中起到积极的作用。

这些证书可以作为学生个人能力的证明，有助于提升学生的学术声誉和竞争力。

此外，这些证书还可以为学生申请大学和研究生院的录取提供有力的支持。

4. 证书的使用和展示，获得数学建模竞赛的奖项和证书后，学
生可以将其列入个人简历中，以展示自己的学术成就和能力。

此外，学生还可以在学校、社区或学术会议等场合展示这些证书，与他人
分享自己的学习经历和成果。

总结起来，数学建模竞赛获奖证书是对参赛者在数学建模能力
和解决实际问题方面的优异表现的认可和肯定。

获得这些证书可以
为学生的学术和职业发展提供积极的支持和帮助。

数学建模美赛数学建模美赛是一项由美国数学协会（MAA）、美国数学模型联盟（AMM）、美国数学教师协会（MCTA）和美国数学教育基金会（MEF）联合举办的国际数学建模竞赛。

它自1993年以来一直是一项年度数学建模竞赛，旨在激发学生的探索精神，培养学生的创新能力，促进学生的科学素养和思维能力，以及拓展学生的数学知识。

一、数学建模美赛的竞赛范围数学建模美赛的竞赛范围包括现代数学、应用数学、计算机科学、统计学、物理学、化学、生物学、社会学、经济学、工程学和其他科学领域。

竞赛任务要求参赛者使用数学建模的方法，对实际问题进行分析和把握，并以数学模型的形式提出解决方案。

二、数学建模美赛的参赛资格数学建模美赛的参赛者必须是高中生，可以是学校里的学生，也可以是家庭里的学生，只要他们的年龄在14-18岁之间。

参赛者可以单独参赛，也可以组队参赛，但每个团队最多只能有三名参赛者。

三、数学建模美赛的奖项设置数学建模美赛的奖项设置包括金牌、银牌、铜牌和优秀奖，其中金牌由最高分的参赛者获得，银牌由次高分的参赛者获得，铜牌由第三高分的参赛者获得，优秀奖由最具创新性的参赛者获得。

四、数学建模美赛的评审标准数学建模美赛的评审标准包括：模型的准确性、模型的创新性、模型的可行性、模型的可操作性、模型的可解释性、模型的可扩展性以及模型的可维护性。

五、数学建模美赛的参赛作品数学建模美赛的参赛作品包括：参赛者的模型报告、模型的计算结果、模型的结果分析、模型的可视化图表、模型的实际应用等。

参赛者需要根据竞赛任务，按照规定的格式提交参赛作品。

六、数学建模美赛的实施效果数学建模美赛的实施效果显著，它不仅激发了学生的探索精神，培养了学生的创新能力，促进了学生的科学素养和思维能力，拓展了学生的数学知识，而且还为学生提供了一个实现自我价值的平台，让他们有机会展示自己的才华。

七、数学建模美赛的未来发展数学建模美赛的未来发展前景一片光明。

数学建模美赛不仅将继续为学生提供一个实现自我价值的平台，而且还将不断推出新的数学建模竞赛，以更好地满足学生的学习需求，促进学生的科学素养和创新能力的发展。

关于“美国大学生数学建模竞赛”的组织管理办法一、赛事背景美国大学生数学建模竞赛（MCM/ICM，以下简称美赛），是唯一的国际性数学建模竞赛，也是世界范围内最具影响力的数学建模竞赛。

美赛始于1985年，由COMAP（the Consortium for Mathematics and Its Application，美国数学及其应用联合会）主办，得到了SIAM，NSA，INFORMS 等多个组织的赞助。

MCM/ICM 着重强调研究问题、解决方案的原创性、团队合作、交流以及结果的合理性。

竞赛以三人（本科生）为一组，在四天时间内，就指定的问题完成从建立模型、求解、验证到论文撰写的全部工作。

竞赛每年都吸引大量著名高校参赛。

20XX 年MCM/ICM 有超过7700支队伍参加，遍及五大洲。

MCM/ICM 已经成为最著名的国际大学生竞赛之一。

同济大学于20XX年首次组织学生参加该项赛事。

近年来，在学校领导关心指导下，在数学系数学建模指导教师团队的努力下，我校取得了令人瞩目的成绩，这不仅提高了同济大学的国际知名度，更为学校培养具有创新精神和竞争力的优秀人才、推动数学学科教学改革做出了一定的贡献。

为了更好的组织和管理美国大学生数学建模竞赛，特制定本办法。

二、组织参赛美赛由同济大学教务处主办，数学系承办以及负责具体指导工作，设立组织工作委员会和组委会秘书处，并指导数学建模协会工作。

三、竞赛奖励和学分认定1. 奖项设置美赛奖项设置如下：●Outstanding Winner 美赛特等奖（国内称法）●Finalist 美赛特等奖提名（国内称法）●Meritorious Winner 美赛一等奖（国内称法）●Honorable Mention 美赛二等奖（国内称法）●Successful Participant 成功参赛奖（国内称法）●Unsuccessful 不成功没有奖注：Finalist奖励给进入特等奖角逐未得到特等奖的队伍；Finalist 与Outstanding Winner全球一共约20支队伍。

MCM/ICM竞赛简介享有数学建模“奥林匹克”之称的MCM/ICM竞赛是一项面向世界各国大学生的国际性赛事，包括The Mathematical Contest in Modeling(数学建模竞赛)、The Interdisciplinary Contest in Modeling(交叉学科建模竞赛)和MCM/ICM Media Contest(数学建模媒体竞赛)，由美国自然基金协会和美国数学及其应用联合会共同主办，运筹学与管理科学学会、工业与应用数学学会、数学学会等多家机构协办，目前已成为全世界最具影响力的大学生学科竞赛。

MCM(The Mathematical Contest in Modeling，数学建模竞赛)始于1985年，其宗旨是鼓励大学生通过对实际问题予以阐明、分析、建立数学模型并提出解法，来提高应用数学解决实际问题的能力和写作能力；ICM(The Interdisciplinary Contest in Modeling，交叉学科建模竞赛)始于2000年，其宗旨是发展并提升大学生运用数学方法解决交叉学科问题的能力和写作能力。

比赛每年举办一次。

竞赛形式为三名学生组成一队在四天内任选一题，完成该实际问题的数学建模的全过程，并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解（及软件）、检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出论文。

该项竞赛共设置四个奖项，分别为Outstanding Winner，Finalist，Meritorious Winner，Honorable Mentions。

在国内，约定俗成地将这四个奖项分别对应为特等奖、特等奖提名奖、一等奖、二等奖。

2013年吸引了来自中国、美国、加拿大、德国、印度、芬兰等15个国家和地区的6593支队伍参赛。

学习资料参赛规则【数学中国翻译】2014美国大学生数学建模竞赛（MCM/ICM）参赛规则中英文对照/thread-201325-1-1.html数学中国MCM/ICM参赛指南翻译（2014版）（任何单位转载须注明来源：）MCM:The Mathematical Contest in ModelingMCM：数学建模竞赛ICM:The InterdisciplinaryContest in ModelingICM：交叉学科建模竞赛ContestRules, Registration and Instructions比赛规则，比赛注册方式和参赛指南(All rules and instructions apply to both ICM and MCMcontests, exceptwhere otherwisenoted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）To participate in a contest, each team must be sponsoredby a faculty advisor fromits institution.每个MCM的参赛队需有一名所在单位的指导教师负责。

美国数学建模竞赛成绩揭晓近日，2021美国大先生数学建模竞赛效果揭晓。

西交利物浦大学92个队参赛共获一等奖4个、二等奖21个、三等奖67个，获奖总数再创新高。

值得一提的是，往年西交利物浦大学初次有7个队参与交叉学科建模竞赛〔ICM〕，该赛事要求参赛者具有运用数学模型处置跨学科效果的才干，同时对应用计算机处置大批量信息的才干也有着更高的要求。

最终西交利物浦大学有6支参赛队伍取得ICM类二等奖，该获奖比例在全国各高校中首屈一指。

美国大先生数学建模竞赛〔MCM〕是数学建模范围内的国际性威望赛事，由美国自然基金协会和美国数学运用协会共同主办，美国数学学会、运筹学学会、工业与运用数学学会等多家机构协办。

自1985年以来，美国大先生数学建模竞赛曾经成功举行28届，大赛每年吸引了包括哈佛大学、麻省理工学院、北京大学、清华大学等著名高校的优秀先生参与奖项角逐，2021年吸引了来自全球各高校的3000余支队伍参与。

美国大先生数学建模竞赛分普通类型〔MCM〕和交叉学科〔ICM〕两类，往年的赛事于美国东部时间2月9日早晨8点在全球经过网络准时末尾。

MCM往年共设两个标题：关于树叶分类与重量计算的A题«TheLeavesofaTree»，关于漂流时间布置与河流容量计算的B题«CampingalongtheBigLongRiver»。

ICM的赛题是C题：从网络通讯记载中找出潜在作案同谋«ModelingforCrimeBusting»。

参赛先生3人组成一队，任选其中一题，应用树立数学模型的方法处置实践效果。

大赛不只要求参赛选手具有扎实的数学、计算机和论文写作功底，同时对其学术英文表达水平等也提出了相当高的要求。

西交利物浦大学本着〝自愿参与、自行组队、不选拔、不扫除〞的原那么，积极为先生搭建参与此高水平国际赛事的平台。

〝美国数学建模竞赛为先生们提供了一个培育数学学习与运用才干的时机，相较于竞赛效果，我们更看重的是先生在竞赛进程中失掉的锻炼时机。

美国大学生数学建模竞赛等级评审标准2014.1.4评审要点是否对赛题给出了满意的解读方式，并对赛题中可能出现的概念给予了必要的澄清；是否明确列出了建模用到的所有条件及假设，并对其合理性给出了解释或论证；是否通过对赛题的分析给出了建模的动机或论证了建模的合理性；是否设计出了能有效地解答赛题的模型；是否对模型给出了稳定性测试；是否讨论了模型的优缺点，并给出了清晰的结论；是否给出了圆满的摘要。

没有全部完成解答的论文不但是可接受的，而且如果在某些方面有创新并有独到之处，仍然可能获得较好的评审结果。

等级划分参赛论文如果没有按要求讨论赛题，或违反了竞赛规则，则会被定为不合格论(Unsuccessful Participants) 。

其余参赛论文根据评审标准按质量分为 5 个级别，由低到高分别为合格论文 (Successful Participants)、乙级论文 (Honorable Mention)、甲级论文(Meritorious)、特级提名论文 (Finalist)、特级论文 (Outstanding Winner) (也称为优胜论文)。

任何论文只要对赛题进行了适当的讨论，没有违反竞赛规则，就是合格论文。

只有建模和写作都最优秀的论文才可能评为特级论文。

每个级别的论文所占的百分比如下：合格论文，大约 50% 的论文属于这个级别。

乙级论文，大约 30% 的论文属于这个级别。

甲级论文，大约 10% 到 15% 的论文属于这个级别。

特级提名论文，大约 1% 的论文属于这个级别。

特级论文，大约 1% 的论文属于这个级别。

除了给论文评级外，MCM/ICM 竞赛还设有 INFORMS 奖、SIAM 奖、 MAA 奖及 Ben Fusaro 奖等 4 个奖项，奖励优秀论文。

INFORMS 奖是由美国运筹及管理学协会 (the Institute for Operations Research and the Management Sciences) 设立的。

美赛奖项设置
美赛全称是美国大学生数学建模竞赛，是一项国际性的赛事。

美赛的奖项设置，主要分为以下几类：
·特等奖（Outstanding Winner）简称O奖；
·特等奖提名（Finalist）简称F奖；
·一等奖（优异奖）（Meritorious）简称M奖；
·二等奖（荣誉奖）（Honourable Metion）简称H奖；
·成功参与奖（Successful Participant）简称S奖；
·不成功参赛（Unsuccessful Participant）简称U奖；
·资格取消（Disqualified）
拓展：
美赛的比赛内容：
美国大学生数学建模竞赛目前分为两种类型，MCM（Mathematical Contest In Modeling）和ICM（Interdisciplinary Contest In Modeling)，两种类型竞赛采用统一标准进行，竞赛题目出来之后，参数队伍通过美赛官网进行选题，一共分为 6 种题型。

MCM:对于参赛者的数学模型素养以及建模能力要求较高，一般A题为连续问题，B题为离散问题。

C题，与大数据和数据挖掘有关。

ICM:一般涉及的问题较宏观和复杂。

对于参赛者把握问题主线、权衡宏观与
微观、整体与细节的能力要求较高。

ICM有3道题，D题一般与网络科学或优化有关，E题与环境科学有关，F题与政策、社会科学相关，主要讨论社会科学中的建模问题。

全美数学建模大赛往届证书全文共四篇示例，供读者参考第一篇示例：全美数学建模大赛（MCM）是一项备受关注的国际性的学术竞赛，吸引着来自全美各地以及世界范围内的优秀学生参与。

为了鼓励和表彰参赛者的优秀表现，该比赛设立了丰厚的奖金以及丰富的证书奖励。

获得全美数学建模大赛的届证书不仅能够证明参赛者在学术和科研领域的杰出表现，还可以在学术和职业发展中起到一定的推动作用。

一份全美数学建模大赛往届证书，不仅仅是一张纸质证明，更是一份学生辛勤努力的见证。

这些证书记录着参与者在数学建模领域中所做出的努力和成就，不仅肯定了他们在数学建模方面的能力，也为他们未来的学业和职业发展提供了有力的支持和推荐。

每一份证书都是一份宝贵的证明，鼓励着学生在数学建模领域中不断挑战自我、超越自我，追求卓越。

一份全美数学建模大赛往届证书的内容包括了参赛者的姓名、所在学校、比赛届次、获奖等级等基本信息，具有一定的权威性和认可度。

这些证书的颁发不仅是对学生优秀表现的肯定，也是对学校教育质量的认可和鼓励，更是对数学建模领域成果的认可和奖赏。

在学生获得这样的证书后，不仅能够增强他们的自信心，还会激励他们继续在学术研究和科研领域中精益求精，不断挑战创新，为学术事业做出更多的贡献。

往届证书的丰富多样性也是其吸引人之处。

从证书的设计、材质、图案、字体等各个方面都能够体现出其独特性和特色。

有些证书可能采用了精美的纸张和优雅的印刷图案，有些证书可能融入了数学建模的元素，或者添加了令人眼前一亮的创意设计。

这些设计不仅能够增强证书的美观性和艺术性，更能够激发参赛者的兴趣和热情，促使他们更加珍惜这份属于自己的荣誉。

随着全美数学建模大赛的不断发展和壮大，往届证书的意义也日益凸显。

获得这份证书的学生，无疑是在数学建模领域中的佼佼者，他们的努力和智慧都值得肯定和鼓励。

这份证书的获得，不仅对他们未来学习和职业生涯的发展有着积极的影响，也将成为他们一生中值得骄傲和自豪的成就。

MCM/ICM竞赛简介享有数学建模“奥林匹克”之称的MCM/ICM竞赛是一项面向世界各国大学生的国际性赛事，包括The Mathematical Contest in Modeling(数学建模竞赛)、The Interdisciplinary Contest in Modeling(交叉学科建模竞赛)和MCM/ICM Media Contest(数学建模媒体竞赛)，由美国自然基金协会和美国数学及其应用联合会共同主办，运筹学与管理科学学会、工业与应用数学学会、数学学会等多家机构协办，目前已成为全世界最具影响力的大学生学科竞赛。

MCM(The Mathematical Contest in Modeling，数学建模竞赛)始于1985年，其宗旨是鼓励大学生通过对实际问题予以阐明、分析、建立数学模型并提出解法，来提高应用数学解决实际问题的能力和写作能力；ICM(The Interdisciplinary Contest in Modeling，交叉学科建模竞赛)始于2000年，其宗旨是发展并提升大学生运用数学方法解决交叉学科问题的能力和写作能力。

比赛每年举办一次。

竞赛形式为三名学生组成一队在四天内任选一题，完成该实际问题的数学建模的全过程，并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解（及软件）、检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出论文。

该项竞赛共设置四个奖项，分别为Outstanding Winner，Finalist，Meritorious Winner，Honorable Mentions。

在国内，约定俗成地将这四个奖项分别对应为特等奖、特等奖提名奖、一等奖、二等奖。

2013年吸引了来自中国、美国、加拿大、德国、印度、芬兰等15个国家和地区的6593支队伍参赛。

学习资料参赛规则【数学中国翻译】2014美国大学生数学建模竞赛（MCM/ICM）参赛规则中英文对照/thread-201325-1-1.html数学中国MCM/ICM参赛指南翻译（2014版）（任何单位转载须注明来源：）MCM:The Mathematical Contest in ModelingMCM：数学建模竞赛ICM:The InterdisciplinaryContest in ModelingICM：交叉学科建模竞赛ContestRules, Registration and Instructions比赛规则，比赛注册方式和参赛指南(All rules and instructions apply to both ICM and MCMcontests, exceptwhere otherwisenoted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）To participate in a contest, each team must be sponsoredby a faculty advisor fromits institution.每个MCM的参赛队需有一名所在单位的指导教师负责。

美赛题目参考答案美赛题目参考答案在数学建模竞赛中，美国大学生数学建模竞赛（MCM/ICM）是其中最具代表性和影响力的比赛之一。

每年，数以千计的学生参加这一竞赛，争夺着优胜奖项。

本文将探讨美赛题目的参考答案，并分析其中的解题思路和方法。

首先，我们来看一道典型的美赛题目：假设你是一家电商公司的数据分析师，负责分析用户的购物习惯。

你需要设计一个算法，根据用户的购买历史，预测他们未来的购买行为。

请给出你的解决方案。

针对这个题目，我们可以从以下几个方面进行分析和解答。

第一，我们需要收集用户的购买历史数据。

这些数据可以包括用户的购买时间、购买金额、购买商品的类别等信息。

通过对这些数据的分析，我们可以了解用户的购买习惯和偏好。

第二，我们可以利用机器学习算法来预测用户的未来购买行为。

常用的机器学习算法包括决策树、支持向量机、随机森林等。

我们可以将用户的购买历史作为训练集，利用这些算法进行模型训练，然后利用训练好的模型对未来的购买行为进行预测。

第三，我们可以利用时间序列分析的方法来预测用户的未来购买行为。

时间序列分析是一种专门用于处理时间相关数据的方法。

通过对用户购买历史数据的时间序列进行分析，我们可以发现其中的规律和趋势，并用这些规律和趋势来预测未来的购买行为。

第四，我们可以利用关联规则挖掘的方法来预测用户的未来购买行为。

关联规则挖掘是一种用于发现数据中的频繁项集和关联规则的方法。

通过对用户购买历史数据的分析，我们可以找到一些频繁购买的商品组合，然后根据这些组合来预测用户的未来购买行为。

综上所述，针对这个题目，我们可以采用数据分析、机器学习、时间序列分析和关联规则挖掘等方法来预测用户的未来购买行为。

当然，具体的解决方案还需要根据实际情况进行调整和优化。

除了以上的解题思路，还有很多其他的方法可以用于解决这个问题。

例如，我们可以利用深度学习算法来进行预测，或者利用网络分析的方法来分析用户之间的关系等等。

不同的方法有不同的优缺点，我们可以根据具体情况选择合适的方法。