技术领域technical field
本发明属于道路交通控制系统技术领域，具体的为一种高速公路地点交通状态估计方法。The invention belongs to the technical field of road traffic control systems, in particular to a method for estimating traffic states at expressway locations.
背景技术Background technique
随着高速公路在我国交通运输中占的重要性越来越大，伴随着出现的交通拥堵、交通事故、环境污染等问题也越来越严重。无论是交通管理者还是出行者对交通的信息化管理需求都在逐渐增加，因此，如何利用现有的检测设备，尽可能有效准确地实现高速公路交通状态的估计，实时准确的把握当前道路的交通状况是高效管理与服务的前提，具有重要的理论研究和实际应用意义。With the increasing importance of expressway in my country's transportation, traffic congestion, traffic accidents, environmental pollution and other problems are becoming more and more serious. Whether it is traffic managers or travelers, the demand for traffic information management is gradually increasing. Therefore, how to use existing detection equipment to estimate the traffic status of expressways as effectively and accurately as possible, and grasp the current road conditions in real time and accurately. Traffic conditions are the premise of efficient management and service, and have important theoretical research and practical application significance.
高速公路上安装了各种用于交通数据采集的设备，如固定检测器、视频检测器、浮动车等。但是，由于覆盖面、成本等各种各样的原因，使得目前在对于高速公路交通状态估计的研究中使用较多的是固定型检测器的数据，基于固定检测器数据的地点交通状态估计方法也是多种多样的：Various devices for traffic data acquisition, such as fixed detectors, video detectors, floating cars, etc., are installed on expressways. However, due to various reasons such as coverage and cost, the current research on highway traffic state estimation uses more data from fixed detectors, and the location traffic state estimation method based on fixed detector data is also many different types of:
(1)交通运输系统工程与信息(第5卷第1期，2005年2月)公开了一种基于模糊聚类的快速路交通流状况分类方法，其利用模糊聚类的方法对交通流状况的分类进行了研究，实验结果表明：用模糊聚类进行交通流状况分类是一种可行的方法，不同的交通流参数对于分类的影响不同，在速度很高、速度很低或者占有率很大的情况下可直接判断交通流状况，其他情况下需要根据交通流三个变量来综合判断；(1) Transportation System Engineering and Information (Volume 5, No. 1, February 2005) discloses a fuzzy clustering-based classification method for expressway traffic flow conditions. The classification of traffic flow conditions has been studied, and the experimental results show that it is a feasible method to use fuzzy clustering to classify traffic flow conditions. Different traffic flow parameters have different effects on classification. In some cases, the traffic flow status can be directly judged; in other cases, it needs to be judged comprehensively according to the three variables of traffic flow;
(2)Transportation science(第41卷第2期，2007年5月)公开了一种基于扩展卡尔曼滤波的高速公路交通状态估计方法，其以安装在高速公路特定路段上的检测器检测的数据为输入，通过设计的随机宏观交通流模型，并借助于扩展卡尔曼滤波的方法实现对道路交通状态的判别，实验结果表明该方法能在一定程度上反映实际道路上交通状态的变化；(2) Transportation science (Volume 41, No. 2, May 2007) discloses a highway traffic state estimation method based on extended Kalman filtering, which uses the data detected by the detector installed on a specific section of the highway As input, through the designed stochastic macro-traffic flow model, and with the help of the extended Kalman filter method, the identification of the road traffic state is realized. The experimental results show that the method can reflect the change of the actual road traffic state to a certain extent;
(3)交通运输工程与信息学报(第5卷第3期，2007年9月)公开了一种基于遗传动态模糊聚类的道路交通状态判定方法，其通过遗传算法不断优化交通流参数间的模糊相似性与样本间的欧氏距离的映射，实现了动态的模糊聚类，实验结果表明该方法的有效性与可行性；(3) Journal of Traffic and Transportation Engineering and Information (Volume 5, No. 3, September 2007) discloses a road traffic state determination method based on genetic dynamic fuzzy clustering, which continuously optimizes the relationship between traffic flow parameters through genetic algorithms. The mapping between fuzzy similarity and Euclidean distance between samples realizes dynamic fuzzy clustering, and the experimental results show the effectiveness and feasibility of this method;
(4)公路工程(第33卷第2期，2008年4月)公开了一种基于模糊的城市快速路交通流状态判别方法，其根据交通状态的模糊特征，结合基于知识的模糊系统，提出了用于交通状态划分的模糊集和模糊规则，并将交通状态划分为五种类别，该方法可以动态的显示路网的交通拥挤范围,为实施交通信息发布以及后期交通瓶颈的判别和改善提供依据；(4) Highway Engineering (Vol. 33, No. 2, April 2008) discloses a fuzzy-based method for discriminating traffic flow status on urban expressways. According to the fuzzy characteristics of traffic status, combined with a knowledge-based fuzzy system, a Fuzzy sets and fuzzy rules for the division of traffic states are established, and the traffic states are divided into five categories. This method can dynamically display the range of traffic congestion in the road network, and provides a basis for the implementation of traffic information release and the identification and improvement of traffic bottlenecks in the later period. in accordance with;
(5)系统工程(第28卷第8期，2010年8月)公开了一种基于FCM-粗糙集的城市快速路交通状态判别方法，其针对城市快速路的交通状态的特性，重点研究了对快速路的常发性拥挤的判别，实验结果表明模型在一定条件下可行，能够有效处理海量多源传感器数据，具有较高的判别率和较低的误判率。(5) System Engineering (Volume 28, No. 8, August 2010) discloses a traffic state discrimination method for urban expressways based on FCM-rough sets, which focuses on the characteristics of the traffic state of urban expressways. For the discrimination of frequent congestion on expressways, the experimental results show that the model is feasible under certain conditions, can effectively process massive multi-source sensor data, and has a high discrimination rate and a low misjudgment rate.
纵观以上各种基于固定检测器数据的方法，大多采用速度、流量、占有率三参数进行聚类分析，进而对交通状态进行判断。聚类分析主要是对历史样本数据的分析，使得相同类别属性下的数据之间的相关性大，不同类别之间的数据相关性小，但是通过对历史样本的分析可以发现，样本的空间分布存在着不均衡性，即不同状态类别的样本容量存在差异，而传统的FCM在聚类时对样本数量敏感，这样在对这类数据进行聚类时会产生误判。此外，还可以发现不同的交通流参数对于聚类时的影响不一样，因此，在采用聚类分析估计交通状态时需要考虑不同类别样本数量的差异性和不同交通流参数的差异性，这样才能更为科学、合理的估计交通状态。Looking at the above methods based on fixed detector data, most of them use the three parameters of speed, flow, and occupancy for cluster analysis, and then judge the traffic state. Cluster analysis is mainly the analysis of historical sample data, so that the correlation between data under the same category attribute is large, and the data correlation between different categories is small. However, through the analysis of historical samples, it can be found that the spatial distribution of samples There is an imbalance, that is, there are differences in the sample size of different state categories, and the traditional FCM is sensitive to the number of samples when clustering, so misjudgment will occur when clustering this type of data. In addition, it can also be found that different traffic flow parameters have different effects on clustering. Therefore, when using cluster analysis to estimate the traffic state, it is necessary to consider the differences in the number of samples of different categories and the differences in different traffic flow parameters. A more scientific and reasonable estimation of traffic conditions.
发明内容Contents of the invention
有鉴于此，本发明的目的在于提供一种基于特征参数加权GEFCM算法的高速公路地点交通状态估计方法，能够考虑到历史样本中数据分布不均衡性和不同特征参数权重的差异性特点，通过调整聚类的目标函数，进而优化聚类模型，从而达到交通状态估计的目的，提高状态估计的可靠性。In view of this, the object of the present invention is to provide a method for estimating the traffic state of expressway locations based on the characteristic parameter weighted GEFCM algorithm, which can take into account the unbalanced data distribution and the difference characteristics of different characteristic parameter weights in historical samples, by adjusting The objective function of clustering is used to optimize the clustering model, so as to achieve the purpose of traffic state estimation and improve the reliability of state estimation.
为达到上述目的，本发明提供如下技术方案：To achieve the above object, the present invention provides the following technical solutions:
基于特征参数加权GEFCM算法的高速公路地点交通状态估计方法，包括以下步骤：A method for estimating the traffic state of expressway locations based on the characteristic parameter weighted GEFCM algorithm, including the following steps:
1)获取高速公路微波车检器采集得到的车流量、平均车速和平均占有率这三种特征参数的历史数据，构成样本矩阵；1) Obtain the historical data of the three characteristic parameters of traffic volume, average vehicle speed and average occupancy collected by the microwave vehicle detector on the expressway to form a sample matrix;
2)对步骤1)获取的数据进行预处理，所述预处理包括错误数据的识别与剔除、数据的修复、数据滤波处理；2) Preprocessing the data obtained in step 1), the preprocessing includes identification and elimination of erroneous data, data repair, and data filtering;
3)确定三种特征参数在聚类分析时的权重；3) Determine the weights of the three characteristic parameters during cluster analysis;
4)对历史数据进行聚类分析；4) Perform cluster analysis on historical data;
5)当获取到当前断面的交通流参数时，实时估计交通状态。5) When the traffic flow parameters of the current section are obtained, the traffic state is estimated in real time.
进一步，所述步骤2)中，具体采用如下方法进行错误数据的识别与剔除：Further, in the step 2), the following methods are specifically adopted to identify and eliminate erroneous data:
在一个数据更新周期内，设定总车流量数据的阀值范围为[0,Qmax]，平均车速的阀值范围为[0,Vmax]；若采集到的总车流量数据或平均车速的数据不在对应的阀值范围内时，则表明采集的数据不可靠，并将其剔除；若采集到的总车流量数据和平均车数的数据均落在对应的阀值范围内时，则表明采集的数据可靠，保留采集的数据；其中，Qmax、Vmax分别表示在一个数据更新周期内的流量最大值和速度最大值；In a data update cycle, set the threshold range of the total traffic flow data to [0, Qmax ], and the threshold range of the average vehicle speed to [0, Vmax ]; if the collected total traffic flow data or average vehicle speed If the collected data is not within the corresponding threshold range, it indicates that the collected data is unreliable and will be eliminated; Indicates that the collected data is reliable, and the collected data is retained; among them, Qmax and Vmax respectively represent the maximum flow rate and maximum speed within a data update cycle;
根据交通流理论建立错误数据判断规则，即剔除规则；然后，判断采集的数据序列是否满足剔除规则；当满足剔除规则时，将对应的数据需剔除；当不满足剔除规则时，保留对应的数据。According to the traffic flow theory, the wrong data judgment rule is established, that is, the elimination rule; then, it is judged whether the collected data sequence meets the elimination rule; when the elimination rule is satisfied, the corresponding data needs to be eliminated; when the elimination rule is not satisfied, the corresponding data is retained .
进一步，所述步骤2)中，通过下式对数据进行修复：Further, in said step 2), the data is repaired by the following formula:
其中，为t时段的数据修复值；x(t-1)为(t-1)时段的实际检测值；x′(t)为同一时刻前n天的采集数据的历史均值；α为遗忘因子，α∈[0,1]；in, is the data restoration value of period t; x(t-1) is the actual detection value of period (t-1); x′(t) is the historical mean value of the collected data of n days before the same moment; α is the forgetting factor, α ∈[0,1];
进一步，通过下式对数据进行滤波处理：Further, the data is filtered by the following formula:
St＝αXt+(1-α)St-1St =αXt +(1-α)St-1
式中，St为t时段得到的一次指数平滑值；St-1为t-1时段得到的一次指数平滑值；Xt为t时段得到的观测值；α∈[0,1]为平滑系数。In the formula, St is an exponential smoothing value obtained in period t; St-1 is an exponential smoothing value obtained in period t-1; Xt is an observed value obtained in period t; α∈[0,1] is smoothing coefficient.
进一步，所述步骤3)具体包括如下步骤：Further, said step 3) specifically includes the following steps:
31)将通过步骤2)预处理的车流量、平均车速和平均占有率这三种特征参数构成的样本矩阵X进行Z-score标准化，得到标准化之后的矩阵Z；31) carry out Z-score standardization to the sample matrix X formed by these three characteristic parameters of the traffic volume, average vehicle speed and average occupancy rate of step 2) pretreatment, obtain the matrix Z after standardization;
32)对Z-score标准化后的矩阵Z进行相关系数计算，得到相关系数矩阵R；32) Carry out correlation coefficient calculation to matrix Z after Z-score standardization, obtain correlation coefficient matrix R;
33)对相关系数矩阵R构造其特征方程|R-λI|＝0，得到p个特征根和特征向量，以及bt和ct，t＝1,2,…,p；33) Construct the characteristic equation |R-λI|=0 for the correlation coefficient matrix R, and obtain p characteristic roots and characteristic vectors, as well as bt and ct , t=1,2,...,p;
其中，bt为第t个主成分的方差贡献率，ct为前t个主成分的累计方差贡献率；Among them, bt is the variance contribution rate of the t-th principal component, and ct is the cumulative variance contribution rate of the first t principal components;
34)计算得到车流量、平均车速和平均占有率这三种特征参数的权重系数ωo＝{ωo1,ωo2,…,ωot}。34) Calculate the weight coefficient ωo ={ωo1 ,ωo2 ,…,ωot } of the three characteristic parameters of traffic volume, average vehicle speed and average occupancy rate.
进一步，所述步骤4)中，通过如下方法对历史数据进行聚类分析：Further, in the step 4), the historical data is clustered and analyzed by the following method:
反复迭代计算下面三式子，直至满足算法停止条件，最终确定代表不同交通状态类的聚类中心；Iteratively calculate the following three formulas until the algorithm stop condition is met, and finally determine the cluster centers representing different traffic status classes;
其中，xj为第j个样本点，xjk第j个样本点的第k个特征参数；U＝(uik)c×n为隶属度矩阵，用uij表示第j个样本属于第i类的隶属度，0≤uij≤1，m∈[1,+∞)表示模糊加权指数，表征隶属度矩阵的模糊程度；ci＝(ci1,ci2,…cip)(i＝1,2,…,c)表示不同类别的聚类中心；项表现了第i类的容量属性；ω＝{ω1,ω2,…,ωt},ωk∈[0,1]，为与输入的参数序列相对应的一个特征参数权重，表示第k个特征参数在聚类中的重要性；t为特征参数的个数；n为样本点数量。Among them, xj is the jth sample point, xjk is the kth feature parameter of the jth sample point; U=(uiik )c×n is the membership matrix, and uij means that the jth sample belongs to the i Class membership, 0≤uij ≤1, m∈[1,+∞) represents the fuzzy weighted index, representing the degree of fuzziness of the membership matrix; ci =(ci1 ,ci2 ,…cip )(i=1,2,…,c) means cluster center; Item represents the capacity attribute of the i-th class; ω＝{ω1 ,ω2 ,…,ωt },ωk ∈[0,1] is a feature parameter weight corresponding to the input parameter sequence, representing the The importance of k characteristic parameters in clustering; t is the number of characteristic parameters; n is the number of sample points.
进一步，所述步骤5)中，通过下式的计算，比较实时数据样本与各状态类的聚类中心的距离，基于最短距离的原则确定交通状态；Further, in described step 5), by the calculation of following formula, compare the distance of real-time data sample and the cluster center of each state class, determine the traffic state based on the principle of the shortest distance;
其中，表示第i个聚类中心ci与第j个样本点xj之间的距离；ω＝{ω1,ω2,…,ωt},ωk∈[0,1]，为与输入的参数序列相对应的一个特征参数权重，表示第k个特征参数在聚类中的重要性；t为特征参数的个数，对于本文交通状态估计而言为3。in, Indicates the distance between the i-th cluster center ci and the j-th sample point xj ; ω={ω1 ,ω2 ,…,ωt },ωk ∈[0,1], which is the A characteristic parameter weight corresponding to the parameter sequence indicates the importance of the kth characteristic parameter in clustering; t is the number of characteristic parameters, which is 3 for the traffic state estimation in this paper.
基于最短距离的原则确定当前交通流参数对应的交通状态为：对于样本点xj，根据上式分别计算与三类交通状态中心的距离，得到与畅通、缓行、拥堵三类状态中心的距离分别为比较三者距离的大小，最小的距离对应的状态类别则为当前的交通状态估计值。Based on the principle of the shortest distance, the traffic state corresponding to the current traffic flow parameters is determined as follows: for the sample point xj , the distances to the centers of the three types of traffic states are calculated according to the above formula, and the distances to the centers of the three types of states are obtained: for Comparing the distances among the three, the state category corresponding to the smallest distance is the estimated value of the current traffic state.
本发明相对于现有技术具有如下优点：基于特征参数加权GEFCM算法的高速公路地点交通状态估计方法，算法简单，效率高，从交通数据样本分布不均衡性和不同交通流参数对聚类的影响不同的角度出发，提出了特征参数加权GEFCM算法，弱化了各类样本容量差异对聚类判别的影响，同时采用主成分分析法确定了不同特征参数的权重。本发明在考虑聚类时历史交通数据样本中存在的不均衡性的同时，考虑到不同交通流参数对于聚类的影响的差异性，从而使得提出的特征参数加权GEFCM聚类模型具有更好的聚类效果，进而在对交通状态的估计时也有更好的效果和可靠性。Compared with the prior art, the present invention has the following advantages: the method for estimating the traffic state of the expressway location based on the characteristic parameter weighted GEFCM algorithm has simple algorithm and high efficiency, and the influence of the unbalanced distribution of traffic data samples and the influence of different traffic flow parameters on clustering Starting from different perspectives, a feature parameter weighted GEFCM algorithm is proposed, which weakens the impact of various sample size differences on clustering discrimination, and uses principal component analysis to determine the weight of different feature parameters. The present invention considers the imbalance existing in the historical traffic data samples when clustering, and at the same time considers the differences in the impact of different traffic flow parameters on clustering, so that the proposed feature parameter weighted GEFCM clustering model has better performance. Clustering effect, and then it has better effect and reliability in estimating traffic state.
附图说明Description of drawings
图1示出了基于特征参数加权GEFCM算法的高速公路地点交通状态估计方法的流程示意图。Fig. 1 shows a schematic flowchart of a method for estimating traffic state at expressway locations based on the characteristic parameter weighted GEFCM algorithm.
具体实施方式detailed description
为了使本发明的目的、技术方案和优点更加清楚，下面将对本发明的具体实施方式作进一步的详细描述。In order to make the purpose, technical solution and advantages of the present invention clearer, the specific implementation manners of the present invention will be further described in detail below.
参见图1，本实施例的基于特征参数加权GEFCM算法的高速公路地点交通状态估计方法，包括以下步骤：Referring to Fig. 1, the expressway location traffic state estimation method based on characteristic parameter weighted GEFCM algorithm of the present embodiment, comprises the following steps:
1)获取高速公路微波车检器采集得到的车流量(q1～qn)、平均车速和平均占有率(o1～on)这三种特征参数的历史数据，构成样本矩阵1) Obtain the traffic flow (q1 ~qn ) and average speed collected by the microwave vehicle detector on the expressway The historical data of the three characteristic parameters and the average occupancy rate (o1 ~ on ) form a sample matrix
对于聚类分析，需要历史数据具有一定的丰富度，本实施例的数据序列的样本量n选取当前时刻前一周的数据。For the cluster analysis, the historical data needs to have a certain richness, and the sample size n of the data sequence in this embodiment selects the data of the week before the current moment.
2)实际采集的数据存在着一系列的质量问题，包括数据的缺失、无效、重复、冗余、错误等，对步骤1)获取的历史数据进行预处理，剔除错误数据并进行数据序列的修复，得到处理后的样本矩阵X；2) There are a series of quality problems in the actual collected data, including missing data, invalidity, duplication, redundancy, errors, etc., to preprocess the historical data obtained in step 1), eliminate wrong data and repair the data sequence , get the processed sample matrix X;
具体的，具体采用阈值理论与交通流理论识别和剔除不符合交通实际情况的错误数据：Specifically, threshold theory and traffic flow theory are used to identify and eliminate erroneous data that do not conform to the actual traffic situation:
读取步骤1)获得的历史数据；在一个数据更新周期内，设定总车流量数据的阀值范围为[0,Qmax]，平均车速的阀值范围为[0,Vmax]；若采集到的总车流量数据或平均车速的数据不在对应的阀值范围内时，则表明该组数据不可靠，并将其剔除；若采集到的总车流量数据和平均车数的数据均落在对应的阀值范围内时，则表明该组数据可靠，保留该组数据；其中，Qmax、Vmax分别表示在一个数据更新周期内的流量最大值和速度最大值，本实施例Qmax取值为300辆，Vmax取值为150km/h。Read the historical data obtained in step 1); within a data update cycle, set the threshold range of the total traffic flow data to [0, Qmax ], and the threshold range of the average vehicle speed to [0, Vmax ]; if When the collected total traffic flow data or average vehicle speed data are not within the corresponding threshold range, it indicates that this group of data is unreliable and will be eliminated; if the collected total traffic flow data and average vehicle number data fall below When it is within the corresponding threshold range, it indicates that the set of data is reliable, and the set of data is retained; wherein, Qmax and Vmax respectively represent the maximum flow rate and the maximum speed within a data update cycle. In this embodiment, Qmax The value is 300 vehicles, and the value of Vmax is 150km/h.
根据交通流理论建立错误数据判断规则，即剔除规则；然后，判断采集的数据序列是否满足剔除规则；当满足剔除规则时，将对应的数据需剔除；当不满足剔除规则时，保留对应的数据；本实施例交通流理论错误数据判断规则如表1所示。According to the traffic flow theory, the wrong data judgment rule is established, that is, the elimination rule; then, it is judged whether the collected data sequence meets the elimination rule; when the elimination rule is satisfied, the corresponding data needs to be eliminated; when the elimination rule is not satisfied, the corresponding data is retained ; The error data judgment rules of the traffic flow theory in this embodiment are shown in Table 1.
表1：基于交通流理论的错误数据判别规则Table 1: Discrimination rules for wrong data based on traffic flow theory
本发明采用当前路段的实测数据与历史数据的加权方式得出的值来对故障数据进行修复，该方法既考虑了当期路段前一时段的实际数据，又考虑了历史数据中相同时间的数据的趋势，具体如下式所示：The present invention uses the value obtained by weighting the measured data of the current road section and the historical data to repair the fault data. trend, as shown in the following formula:
其中，为t时段的数据修复值；x(t-1)为(t-1)时段的实际检测值；x′(t)为同一时刻前n天的采集数据的历史均值；α为遗忘因子，α∈[0,1]，α取值的大小决定对于历史的数据依赖程度。in, is the data repair value of period t; x(t-1) is the actual detection value of period (t-1); x′(t) is the historical mean value of the collected data of n days before the same moment; α is the forgetting factor, α ∈[0,1], the value of α determines the degree of dependence on historical data.
本发明采用指数平滑法对数据进行滤波处理，通过消除数据的极大值和极小值，得到数据序列的平滑值，是一种通过修匀历史数据来区别基本数据模式和随机变动的方法，一次指数平滑法的数学模型如下式：The present invention uses the exponential smoothing method to filter the data, and obtains the smooth value of the data sequence by eliminating the maximum value and minimum value of the data, which is a method for distinguishing basic data patterns and random changes by smoothing historical data, The mathematical model of an exponential smoothing method is as follows:
St＝αXt+(1-α)St-1St =αXt +(1-α)St-1
式中，St为t时段得到的一次指数平滑值；St-1为t-1时段得到的一次指数平滑值；Xt为t时段得到的观测值；α∈[0,1]为平滑系数。In the formula, St is an exponential smoothing value obtained in period t; St-1 is an exponential smoothing value obtained in period t-1; Xt is an observed value obtained in period t; α∈[0,1] is smoothing coefficient.
3)针对不同的交通流参数对于聚类的影响不同的特点，本实施例采用主成分分析法对获取的交通流参数的矩阵进行主特征提取，确定三种特征参数在聚类分析时的权重；具体包括如下步骤：3) In view of the fact that different traffic flow parameters have different influences on clustering, this embodiment adopts the principal component analysis method to extract the main features of the obtained traffic flow parameter matrix, and determine the weights of the three characteristic parameters in the cluster analysis ; Concretely include the following steps:
31)将通过步骤2)预处理的车流量、平均车速和平均占有率这三种特征参数构成的样本矩阵X进行Z-score标准化，得到标准化之后的矩阵Z；31) carry out Z-score standardization to the sample matrix X formed by these three characteristic parameters of the traffic volume, average vehicle speed and average occupancy rate of step 2) pretreatment, obtain the matrix Z after standardization;
由于不同的交通流参数其取值的范围不同，所以在进行分析前，需要将其转换到相同的维度下，即对样本数据进行标准化。Since different traffic flow parameters have different value ranges, it is necessary to convert them to the same dimension before analysis, that is, to standardize the sample data.
取n个交通流参数样本序列X＝(X1,X2,...,Xn)T，每个样本由p个向量组成，即Xi＝(xi1,xi2,...,xip),i＝1,2,...,n，构造成矩阵对样本进行Z-score标准化变换：Take n traffic flow parameter sample sequences X=(X1 ,X2 ,...,Xn )T , each sample consists of p vectors, that is, Xi =(xi1 ,xi2 ,..., xip ), i=1,2,...,n, constructed as a matrix Perform Z-score normalization transformation on samples:
其中，表示的是样本数据序列的均值，表示的是样本数据序列的方差。in, Represents the mean value of the sample data sequence, Represents the variance of the sample data sequence.
32)对Z-score标准化后的矩阵Z进行相关系数计算，得到相关系数矩阵R：32) Calculate the correlation coefficient on the Z-score standardized matrix Z to obtain the correlation coefficient matrix R:
33)对相关系数矩阵R构造其特征方程|R-λI|＝0，得到p个特征根λ1,λ2,…,λp和特征向量e1,e2,…,ep，从而得到bt,ct，t＝1,2,…,p：33) Construct the characteristic equation |R-λI|=0 for the correlation coefficient matrix R, and obtain p characteristic roots λ1 ,λ2 ,…,λp and eigenvectors e1 ,e2 ,…,ep , thus obtaining bt ,ct , t=1,2,...,p:
则bt为第t个主成分的方差贡献率，ct为前t个主成分的累计方差贡献率，通常在特征选取问题中当ct≥0.85时，就可以用前t个主成分来表示整个指标，本文中通过分析可得t＝2。Then bt is the variance contribution rate of the t-th principal component, and ct is the cumulative variance contribution rate of the first t principal components. Usually, when ct ≥ 0.85 in the feature selection problem, the first t principal components can be used to Represents the whole index, and t=2 can be obtained through analysis in this paper.
并得到每个主成分对于原来指标的成分矩阵：And get the component matrix of each principal component for the original index:
其中，i,k＝1,2,…,p为载荷数表示每个主成分对于原来指标的重要程度。in, i, k=1, 2,..., p is the number of loads, indicating the importance of each principal component to the original index.
34)用成分矩阵中的载荷数除以主成分相对应的特征根开平方便得到两个主成分中每个指标所对应的系数，得到的两个主成分如下：34) Divide the load number in the component matrix by the characteristic root Kaiping corresponding to the principal component to obtain the coefficient corresponding to each index in the two principal components, and the two principal components obtained are as follows:
其中，F1、F2表示两个主成分；X1、X2、X3表示的为不同的指标，本文中为速度、流量、占有率；α1～α3、β1～β3表示的为各个指标所对应的系数。Among them, F1 and F2 represent two principal components; X1 , X2 , and X3 represent different indicators, in this paper, speed, flow, and occupancy rate; α1 ~ α3 , β1 ~ β3 represent is the coefficient corresponding to each index.
用第一主成分F1中每个指标所对应的系数α1～α3，乘上第一主成分F2所对应的贡献率b1，再除以所提取两个主成分的两个贡献率之和c2，然后加上第二主成分F2中每个指标所对应的系数β1～β3，乘上第二主成分F2所对应的贡献率b2，再除以所提取两个主成分的两个贡献率之和c2，即可得到综合得分模型：Multiply the coefficients α1 ~ α3 corresponding to each indicator in the first principal component F1 by the contribution rate b1 corresponding to the first principal component F2 , and then divide by the two contributions of the extracted two principal components Then add the coefficients β1 ~ β3 corresponding to each indicator in the second principal component F2 , multiply by the contribution rate b2 corresponding to thesecond principal component F2 , and divide by the extracted The sum c2 of the two contribution rates of the two principal components can be used to obtain the comprehensive score model:
Y＝ω1X1+ω2X2+ω3X3；Y＝ω1 X1 +ω2 X2 +ω3 X3 ;
其中，指标X1～X3所对应的系数ω1～ω3表示为每个指标的权重。Wherein, the coefficients ω1 -ω3 corresponding to the indicators X1 -X3 represent the weight of each indicator.
对于综合系数进行归一化，即得到车流量、平均车速和平均占有率这三种特征参数的权重系数ωo＝{ωo1,ωo2,ωo3}。The comprehensive coefficient is normalized to obtain the weight coefficient ωo ={ωo1 ,ωo2 ,ωo3 } of the three characteristic parameters of traffic volume, average vehicle speed and average occupancy rate.
4)对历史数据根据改进的特征参数加权GEFCM算法对历史交通数据进行聚类分析，确定代表不同交通状态类的聚类中心，具体的聚类分析步骤如下：4) Carry out cluster analysis on historical traffic data according to the improved characteristic parameter weighted GEFCM algorithm to determine the cluster centers representing different traffic status classes. The specific cluster analysis steps are as follows:
41)初始化模型的参数类别个数c＝3，模糊指数选择m＝2，阈值ε＝1e-6，最大迭代次数Lmax＝200，在满足下式的前提下采用[0,1]之间的随机数初始化隶属度矩阵U：41) The number of parameter categories of the initialization model is c=3, the choice of fuzzy index m=2, the threshold ε=1e-6, the maximum number of iterations Lmax =200, and the value between [0,1] is used under the premise of satisfying the following formula: Initialize the membership matrix U with random numbers:
42)根据下式计算c＝3个类的聚类中心ci,i＝1,2,3；42) Calculate the cluster centers ci of c=3 classes according to the following formula, i=1,2,3;
43)根据如下公式计算目标函数的值：43) Calculate the value of the objective function according to the following formula:
如果满足：If satisfied:
||J(b+1)-J(b)||<ε或者l≥Lmax；||J(b+1) -J(b) ||<ε or l≥Lmax ;
则算法停止，得到聚类中心ci，否则转44)；Then the algorithm stops, and the clustering center ci is obtained, otherwise go to 44);
44)根据下式计算更新后的隶属度矩阵U：44) Calculate the updated membership degree matrix U according to the following formula:
然后返回步骤42)；Then return to step 42);
步骤41-44)中，xj为第j个样本点，xjk为第j个样本点的第k个特征参数；U＝(uik)c×n为隶属度矩阵，用uij表示第j个样本属于第i类的隶属度，0≤uij≤1，m∈[1,+∞)表示模糊加权指数；ci＝(ci1,ci2,…cip)(i＝1,2,…,c)表示不同类别的聚类中心；项表现了第i类的容量属性；ω＝{ω1,ω2,…,ωt},ωk∈[0,1]，为与输入的参数序列相对应的特征参数权重；t为特征参数的个数；n为样本点数量。In steps 41-44), xj is the jth sample point, xjk is the kth characteristic parameter of the jth sample point; U=(uik )c×n is the membership matrix, and uij represents the The j samples belong to the membership degree of the i-th class, 0≤uij ≤1, m∈[1,+∞) represents the fuzzy weighted index; ci =(ci1 ,ci2 ,…cip )(i=1,2,…,c) represents the cluster centers of different categories; Item represents the capacity attribute of the i-th class; ω={ω1 ,ω2 ,…,ωt },ωk ∈[0,1], is the feature parameter weight corresponding to the input parameter sequence; t is the feature The number of parameters; n is the number of sample points.
5)当获取到当前断面的交通流参数时，根据下面公式，计算得到属于不同聚类中心的距离，按照最短距离原则，判断所述的交通状态类别。5) When the traffic flow parameters of the current section are obtained, the distance belonging to different cluster centers is calculated according to the following formula, and the traffic state category is judged according to the principle of the shortest distance.
其中，表示第i个聚类中心ci与第j个样本点xj之间的距离；ω＝{ω1,ω2,…,ωt},ωk∈[0,1]，为与输入的参数序列相对应的一个特征参数权重，表示第k个特征参数在聚类中的重要性；t为特征参数的个数，对于本文交通状态估计而言为3。in, Indicates the distance between the i-th cluster center ci and the j-th sample point xj ; ω={ω1 ,ω2 ,…,ωt },ωk ∈[0,1], which is the A characteristic parameter weight corresponding to the parameter sequence indicates the importance of the kth characteristic parameter in clustering; t is the number of characteristic parameters, which is 3 for the traffic state estimation in this paper.
基于最短距离的原则确定当前交通流参数对应的交通状态为：对于样本点xj，根据上式分别计算与三类交通状态中心的距离，得到与畅通、缓行、拥堵三类状态中心的距离分别为比较三者距离的大小，最小的距离对应的状态类别则为当前的交通状态估计值。Based on the principle of the shortest distance, the traffic state corresponding to the current traffic flow parameters is determined as follows: for the sample point xj , the distances to the centers of the three types of traffic states are calculated according to the above formula, and the distances to the centers of the three types of states are obtained: for Comparing the distances among the three, the state category corresponding to the smallest distance is the estimated value of the current traffic state.
6)下一次当前断面的交通流参数数据更新时，执行步骤5)。6) When the traffic flow parameter data of the current section is updated next time, step 5) is executed.
最后说明的是，以上实施例仅用以说明本发明的技术方案而非限制，尽管参照较佳实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，可以对本发明的技术方案进行修改或者等同替换，而不脱离本发明技术方案的宗旨和范围，其均应涵盖在本发明的权利要求范围当中。Finally, it is noted that the above embodiments are only used to illustrate the technical solutions of the present invention without limitation. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be carried out Modifications or equivalent replacements without departing from the spirit and scope of the technical solution of the present invention shall be covered by the claims of the present invention.
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