CN107170233B - A method for obtaining OD matrix of typical daily traffic demand based on matrix decomposition - Google Patents
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Abstract
本发明涉及一种基于矩阵分解的典型日交通需求OD矩阵获取方法,包括以下步骤:1)将日期为i的OD矩阵为Di展开为行向量di,并将多天的OD矩阵展开得到行向量按时间堆叠成为时间×OD对的矩阵M,日期为i的OD行向量di对应矩阵M的第i行;2)采用奇异值分解方法将矩阵M分解为三个子矩阵的乘积;3)根据规律性和爆发性指标对OD分布进行分类;4)将各类别的OD分布进行重组,得到典型日交通需求OD矩阵。与现有技术相比,本发明具有可以识别交通需求OD矩阵的结构特征和提取典型日OD矩阵、为交通需求分析和预测以及突发事件影响分析提供依据等优点。
The present invention relates to a typical daily traffic demand OD matrix acquisition method based on matrix decomposition, comprising the following steps: 1) expanding the OD matrix with date i as D i into a row vector d i , and expanding the OD matrix of multiple days to obtain The row vectors are stacked by time into a matrix M of time × OD pairs, and the OD row vector d i with date i corresponds to the i-th row of matrix M; 2) The matrix M is decomposed into the product of three sub-matrices by the singular value decomposition method; 3 ) Classify the OD distribution according to the regularity and explosiveness index; 4) Reorganize the OD distribution of each category to obtain the OD matrix of typical daily traffic demand. Compared with the prior art, the invention has the advantages of identifying the structural features of the traffic demand OD matrix, extracting the typical daily OD matrix, and providing a basis for traffic demand analysis and prediction and emergency event impact analysis.
Description
技术领域technical field
本发明涉及交通需求分析领域,尤其是涉及一种基于矩阵分解的典型日交通需求OD矩阵获取方法。The invention relates to the field of traffic demand analysis, in particular to a method for obtaining an OD matrix of typical daily traffic demand based on matrix decomposition.
背景技术Background technique
在交通需求分析中,通常采用出行OD矩阵来表示城市居民的出行需求的空间分布情况。出行OD矩阵的元素dij,表示第i个交通小区(Traffic Analysis Zone,TAZ)到第j个交通小区之间的出行量。In the traffic demand analysis, the travel OD matrix is usually used to represent the spatial distribution of the travel demand of urban residents. The element d ij of the travel OD matrix represents the travel volume between the ith traffic zone (Traffic Analysis Zone, TAZ) and the jth traffic zone.
在传统交通规划和管理中,通常采用居民出行调查方法获取出行OD矩阵,该方法的成本较高,其采样代表性引起了不少学者的质疑,也难以胜任交通需求时变规律分析的要求。一方面,用于交通需求建模的出行OD矩阵通常通过5~10年一次的城市居民出行调查得到,这种城市居民出行调查的成本很高,往往只能获取少部分居民(1~5%)一天的出行信息,这种方法的得到的OD矩阵是否有代表性,是交通需求分析需要回答的问题,在实际工程中,工程师们常用“核查线”来检验OD调查的合理性。另一方面,由于日期类型(节假日)、大型活动、天气(雨雪)等,每天的出行需求在出行总量、空间分布上都可能存在差异,但具体是怎样的差异,受到各种因素的影响程度如何,是否有规律,这些问题受制于数据限制过去都无法被很好地回答。In traditional traffic planning and management, the resident travel survey method is usually used to obtain the travel OD matrix. The cost of this method is high, and its sampling representativeness has aroused the doubts of many scholars, and it is also difficult to meet the requirements of time-varying law analysis of traffic demand. On the one hand, the travel OD matrix used for traffic demand modeling is usually obtained through a survey of urban residents' travel every 5 to 10 years. ) one-day travel information, whether the OD matrix obtained by this method is representative is a question that needs to be answered in traffic demand analysis. In practical engineering, engineers often use "check lines" to test the rationality of OD investigations. On the other hand, due to the type of date (holidays), large-scale events, weather (rain and snow), etc., the daily travel demand may vary in the total amount of travel and spatial distribution, but the specific difference is affected by various factors. The extent of the impact, and whether it is regular, these questions have not been well answered in the past due to data limitations.
近年新兴的数据源如公交卡、浮动车、手机信令等,可以得到各种时间粒度下连续多天、1个月、甚至1年的出行需求信息,为解决上述问题提供了可能。In recent years, emerging data sources, such as bus cards, floating cars, and mobile phone signaling, can obtain travel demand information for multiple consecutive days, one month, or even one year at various time granularities, which provides the possibility to solve the above problems.
发明内容SUMMARY OF THE INVENTION
本发明的目的就是为了克服上述现有技术存在的缺陷而提供一种计算简单、准确、为交通需求分析、预测及突发事件影响分析提供依据的基于矩阵分解的典型日交通需求OD矩阵获取方法。The purpose of the present invention is to provide a method for obtaining a typical daily traffic demand OD matrix based on matrix decomposition, which is simple and accurate in calculation, and provides a basis for traffic demand analysis, prediction and emergency event impact analysis in order to overcome the defects of the above-mentioned prior art. .
本发明的目的可以通过以下技术方案来实现:The object of the present invention can be realized through the following technical solutions:
一种基于矩阵分解的典型日交通需求OD矩阵获取方法,包括以下步骤:A typical daily traffic demand OD matrix acquisition method based on matrix decomposition, comprising the following steps:
1)将日期为i的OD矩阵为Di展开为行向量di,并将多天的OD矩阵展开得到行向量按时间堆叠成为时间×OD对的矩阵M,日期为i的OD行向量di对应矩阵M的第i行;1) Expand the OD matrix with date i as D i into a row vector d i , and expand the OD matrix of multiple days to obtain a row vector stacked by time into a matrix M of time × OD pairs, and the OD row vector d with date i i corresponds to the ith row of matrix M;
2)采用奇异值分解方法将矩阵M分解为三个子矩阵的乘积;2) Using singular value decomposition method to decompose matrix M into the product of three sub-matrices;
3)根据规律性和爆发性指标对OD分布进行分类;3) Classify the OD distribution according to regularity and explosiveness indicators;
4)将各类别的OD分布进行重组,得到典型日交通需求OD矩阵。4) Reorganize the OD distribution of each category to obtain the OD matrix of typical daily traffic demand.
所述的步骤2)中,矩阵M分解为三个子矩阵的乘积的表达式为:In described step 2), matrix M is decomposed into the expression of the product of three sub-matrices:
其中,r为矩阵M的秩,S为对角阵,δi为对角阵S对角线上的第i个元素,ui为矩阵U的第i列,vi为矩阵V的第i列。Among them, r is the rank of the matrix M, S is the diagonal matrix, δ i is the ith element on the diagonal of the diagonal matrix S, ui is the ith column of the matrix U, and vi is the ith of the matrix V. List.
所述的步骤3)具体包括以下步骤:Described step 3) specifically comprises the following steps:
31)定义矩阵V的第i列vi为第i个交通需求分布模式,矩阵U的第i列ui为时间变化模式,且交通需求分布模式的值与时间变化模式的值一一对应;31) Define the i-th row v i of the matrix V to be the i-th traffic demand distribution pattern, and the i-th column u i of the matrix U to be the time change pattern, and the value of the traffic demand distribution pattern corresponds to the value of the time change pattern one-to-one;
32)当采用快速傅里叶变换判断时间变化模式的值具有周期性时,则该OD分布标为第一类,当时间变化模式的值中存在偏离均值超过三倍标准差的值时,则该OD分布标为第二类,其余的标记为第三类。32) When using fast Fourier transform to judge that the value of the time-varying pattern has periodicity, then the OD distribution is marked as the first type, and when there is a value that deviates from the mean and exceeds three times the standard deviation in the value of the time-varying pattern, then This OD distribution is labeled as the second category and the rest as the third category.
所述的步骤32)中,当对于持续时间小于7周的数据,则通过判断周中和周末时间变化模式的值是否存在差异,若存在,则标为第一类。In the step 32), for the data whose duration is less than 7 weeks, it is judged whether there is a difference between the values of the time change patterns during the week and the weekend, and if so, it is marked as the first category.
与现有技术相比,本发明具有以下优点:Compared with the prior art, the present invention has the following advantages:
本发明采用SVD方法识别OD矩阵的结构特征,通过从多天的OD矩阵提取几种典型的OD分布,然后对各种分布进行分类,提取当中特定的部分作为典型的日交通OD需求矩阵,可以为交通需求分析、预测及突发事件影响分析提供依据。The invention adopts the SVD method to identify the structural features of the OD matrix, extracts several typical OD distributions from the OD matrix of multiple days, then classifies the various distributions, and extracts specific parts of them as the typical daily traffic OD demand matrix. It provides the basis for traffic demand analysis, forecast and emergency event impact analysis.
附图说明Description of drawings
图1为上海2011年9月的地铁站点OD矩阵的奇异值分布图。Figure 1 shows the singular value distribution of the OD matrix of Shanghai subway stations in September 2011.
图2为上海2011年9月的典型OD分布实例,其中,图(2a)为第一类的第一种典型OD分布实例,图(2b)为第一类的第二种典型OD分布实例,图(2c)为第二类的第一种典型OD分布实例,图(2d)为第二类的第二种典型OD分布实例,图(2e)为第三类的第一种典型OD分布实例,图(2f)为第三类的第二种典型OD分布实例。Figure 2 is an example of typical OD distribution in Shanghai in September 2011, wherein Figure (2a) is the first typical OD distribution example of the first type, Figure (2b) is the second typical OD distribution example of the first type, Figure (2c) is the first typical OD distribution example of the second type, Figure (2d) is the second typical OD distribution example of the second type, and Figure (2e) is the first typical OD distribution example of the third type , Figure (2f) is the second typical OD distribution example of the third category.
图3为上海2011年9月的典型OD分布类型判断结果。Figure 3 shows the typical OD distribution type judgment results in Shanghai in September 2011.
图4为上海2011年9月28日上海市地铁增加的典型OD矩阵期望线图。Figure 4 is a typical OD matrix expected line diagram of Shanghai Metro on September 28, 2011.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明进行详细说明。The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
实施例:Example:
本方法从连续多天的交通需求OD数据提取了几种典型的OD分布,并分析各种分布的含义,最后根据实际应用的需求将各个成分重组为典型日交通需求OD矩阵。其特征在于:使用矩阵分解方法将多天的OD矩阵分为多个成分;通过分析各个成分随时间的变化,对各个成分进行分类;并根据实际问题将各成分重组为典型日交通需求OD矩阵。This method extracts several typical OD distributions from the traffic demand OD data of several consecutive days, analyzes the meaning of various distributions, and finally reorganizes each component into a typical daily traffic demand OD matrix according to the needs of practical applications. It is characterized by: using the matrix decomposition method to divide the multi-day OD matrix into multiple components; classifying each component by analyzing the change of each component with time; and reorganizing each component into a typical daily traffic demand OD matrix according to actual problems .
具体包括以下步骤:Specifically include the following steps:
1)构建“时间×OD对”矩阵M1) Construct a "time × OD pair" matrix M
设日期i的OD矩阵为Di,将其展开为行向量di,将多天的OD矩阵得到行向量按时间堆叠成为“时间×OD对”矩阵M,形如表1所示。Let the OD matrix of date i be D i , expand it into a row vector d i , and stack the row vectors of the OD matrices of multiple days into a "time × OD pair" matrix M by time, as shown in Table 1.
表1时间×OD对矩阵示例Table 1 Time × OD pair matrix example
2)奇异值分解,分解结果如附图1所示,图1为矩阵M的奇异值分布,图中出现明显的“陡坡”,说明少量维度可以解释多天OD矩阵中的大部分变化。2) Singular value decomposition. The decomposition result is shown in Figure 1. Figure 1 shows the singular value distribution of matrix M. There is an obvious "steep slope" in the figure, indicating that a small number of dimensions can explain most of the changes in the multi-day OD matrix.
通过SVD方法,将m×n的“时间×OD对”矩阵M分解为三个矩阵的乘积:By the SVD method, the m×n “time×OD pair” matrix M is decomposed into the product of three matrices:
其中矩阵下标为矩阵的维度,VT为V的转置,r为矩阵M的秩,S为对角阵,对角线上的第i个元素为δi,ui为矩阵U的第i列,vi为矩阵V的第i列。The subscript of the matrix is the dimension of the matrix, V T is the transpose of V, r is the rank of the matrix M, S is the diagonal matrix, the i-th element on the diagonal is δ i , and u i is the matrix U. i column, vi is the i -th column of matrix V.
定义vi为第i个DemandPattern(交通需求分布模式),定义ui为第i个TemporalFlow(时间变化模式)。其中DemandPattern和TemporalFlow一一对应,Demand Pattern代表了某一种特定的OD分布,Temporal Flow是一个时间序列,表征了某种Demand Pattern在各天OD中的贡献在分析时段内的变化。Define vi as the ith DemandPattern (traffic demand distribution pattern), and define ui as the ith TemporalFlow (time variation pattern). Among them, DemandPattern and TemporalFlow correspond one-to-one, Demand Pattern represents a specific OD distribution, and Temporal Flow is a time series, which represents the change of the contribution of a certain Demand Pattern in OD of each day during the analysis period.
3)典型OD分布分析3) Typical OD distribution analysis
使用规律性、爆发性指标对典型OD分布进行分类。具体判断流程如下:Typical OD distributions were classified using regularity, burstiness indicators. The specific judgment process is as follows:
i.使用快速傅里叶变换(FFT)判断TemporalFlow是否具有周期性,即FFT结果存在峰值,若有,该OD分布标为第一类。(对于持续时间小于7周的数据,该步骤替换为使用ks检验判断周中和周末Temporal Flow的值是否有显著差异,若有,标为第一类);i. Use Fast Fourier Transform (FFT) to determine whether TemporalFlow has periodicity, that is, the FFT result has a peak value, and if so, the OD distribution is marked as the first category. (For data with a duration of less than 7 weeks, this step is replaced by the use of ks test to determine whether there is a significant difference between the values of Temporal Flow during the week and weekends, and if so, mark it as the first category);
ii.判断Temporal Flow中是否有偏离均值超过三倍标准差的值,若有,该OD分布标为第二类;ii. Determine whether there is a value that deviates from the mean by more than three standard deviations in the Temporal Flow, and if so, the OD distribution is marked as the second category;
iii.余下的OD分布标为第三类。iii. The remaining OD distributions are labeled as the third category.
不同类别的OD分布如附图2所示,附图2中第一列(图2a、2c和2e):与日期类型有关(工作日、周末),工作日较大,休息日明显降低,呈现周期性变化;第二列(图2b、2的、和2f):与某些事件有关,在某一天或两天出现爆发性需求,图(2c)和图(2d)对应的事件分别为国庆前一天以及2011年9月27日上海市地铁十号线追尾;第三列:变化无明显规律。所有OD分布的类别判断结果如附图3所示,第一类OD分布主要分布在前几位;第二类和第三类的分布无明显规律。The OD distribution of different categories is shown in Figure 2, the first column in Figure 2 (Figures 2a, 2c and 2e): related to the type of date (weekdays, weekends), working days are larger, and rest days are significantly reduced, showing Periodic changes; the second column (Figures 2b, 2, and 2f): related to certain events, there is an explosive demand on one or two days, and the corresponding events in Figures (2c) and (2d) are National Day, respectively The day before and on September 27, 2011, the Shanghai Metro Line 10 rear-ended; the third column: there is no obvious change. The category judgment results of all OD distributions are shown in Figure 3. The first type of OD distribution is mainly distributed in the top few positions; the second and third types of distribution have no obvious regularity.
4)OD分布重组为典型OD矩阵4) The OD distribution is reorganized into a typical OD matrix
根据实际需求将OD分布重组为典型OD矩阵,例如:将第一类OD分布重组,从而滤除原始OD矩阵中爆发及随机波动的成分,可以作为预测模型的输入;将第二类OD分布重组可以得到特殊事件下OD变化的典型OD矩阵,可用于交通状况变化的建模及分析,为交通需求分析、预测及突发事件影响分析提供依据,如附图4所示,附图4为典型OD矩阵增量的期望线图,从中可以发现在公交接驳的起终点(伊犁路站和海伦路站)增加了大量的OD,OD的另一头主要是位于两端未停运的10号线站点;其次,市中心的换乘站OD大量增长,包括10号线上换乘站及当时作为站外换乘站的上海火车站。Reorganize the OD distribution into a typical OD matrix according to actual needs, for example: reorganize the first type of OD distribution to filter out the burst and random fluctuation components in the original OD matrix, which can be used as the input of the prediction model; reorganize the second type of OD distribution A typical OD matrix of OD changes under special events can be obtained, which can be used for modeling and analysis of changes in traffic conditions, providing a basis for traffic demand analysis, forecasting and analysis of the impact of emergencies, as shown in Figure 4, which is a typical The expected line graph of the OD matrix increment, from which it can be found that a large number of ODs have been added at the starting and ending points of the bus connection (Yili Road Station and Hailun Road Station), and the other end of the OD is mainly located at the two ends of
本发明使用矩阵分解方法(SVD)从多天的OD矩阵分为多个成分,每一个成分代表一种典型的OD分布,通过分析各成分随时间的变化确定其含义,主要分为呈现规律性变化的成分、突然爆发的成分及随机发生的成分,最后根据实际应用的需求将各个成分重组为典型日交通需求OD矩阵,可以为交通需求分析、预测及突发事件影响分析及提供依据,具有良好应有价值。The present invention uses the matrix decomposition method (SVD) to divide the multi-day OD matrix into multiple components, each component represents a typical OD distribution, and its meaning is determined by analyzing the change of each component over time, which is mainly divided into showing regularity. The components of change, the components of sudden outbreaks and the components that occur randomly, and finally, according to the needs of practical applications, each component is reorganized into a typical daily traffic demand OD matrix, which can provide a basis for traffic demand analysis, prediction and emergency impact analysis. Good should have value.
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