CN107170233B - Typical daily traffic demand OD matrix acquisition method based on matrix decomposition - Google Patents

Typical daily traffic demand OD matrix acquisition method based on matrix decomposition Download PDF

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CN107170233B
CN107170233B CN201710262143.3A CN201710262143A CN107170233B CN 107170233 B CN107170233 B CN 107170233B CN 201710262143 A CN201710262143 A CN 201710262143A CN 107170233 B CN107170233 B CN 107170233B
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段征宇
雷曾翔
杨东援
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Tongji University
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
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    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
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Abstract

The invention relates to a typical daily traffic demand OD matrix obtaining method based on matrix decomposition, which comprises the following steps: 1) let OD matrix with date i be DiSpread out as a row vector diAnd expanding the OD matrix of multiple days to obtain a matrix M with row vectors stacked in time into time × OD pairsOD row vector d of period iiCorresponding to the ith row of matrix M; 2) decomposing the matrix M into products of three sub-matrixes by adopting a singular value decomposition method; 3) classifying the OD distribution according to regularity and explosiveness indexes; 4) and recombining the OD distribution of each category to obtain a typical daily traffic demand OD matrix. Compared with the prior art, the method has the advantages of being capable of identifying the structural characteristics of the traffic demand OD matrix, extracting the typical day OD matrix, providing basis for traffic demand analysis and prediction and emergency influence analysis and the like.

Description

Typical daily traffic demand OD matrix acquisition method based on matrix decomposition
Technical Field
The invention relates to the field of traffic demand analysis, in particular to a typical daily traffic demand OD matrix obtaining method based on matrix decomposition.
Background
In traffic demand analysis, a travel OD matrix is generally used to represent the spatial distribution of travel demands of urban residents. Element d of travel OD matrixijThe travel amount from the ith Traffic Zone (TAZ) to the jth Traffic Zone is shown.
In traditional traffic planning and management, a travel OD matrix is usually obtained by adopting a resident travel investigation method, the cost of the method is high, the sampling representativeness of the method causes the questions of a plurality of students, and the method is difficult to meet the requirement of time-varying rule analysis of traffic demands. On the one hand, a travel OD matrix for traffic demand modeling is usually obtained through once-every-5-10-year urban resident travel investigation, the cost of the urban resident travel investigation is very high, only travel information of a small number of residents (1-5%) in one day can be obtained frequently, whether the obtained OD matrix is representative or not is a problem needing to be answered in traffic demand analysis, and in actual engineering, engineers often use a check line to check the rationality of the OD investigation. On the other hand, the daily travel demands may vary in the total amount of travel and spatial distribution due to the type of date (holiday), heavy event, weather (rain and snow), etc., but what is the difference is how affected by various factors, whether it is regular, and these questions cannot be answered well in the past due to data limitation.
In recent years, emerging data sources such as bus cards, floating cars, mobile phone signaling and the like can obtain travel demand information of continuous multiple days, 1 month and even 1 year under various time granularities, and the possibility is provided for solving the problems.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a typical daily traffic demand OD matrix acquisition method based on matrix decomposition, which is simple and accurate in calculation and provides a basis for traffic demand analysis, prediction and emergency influence analysis.
The purpose of the invention can be realized by the following technical scheme:
a typical daily traffic demand OD matrix obtaining method based on matrix decomposition comprises the following steps:
1) let OD matrix with date i be DiSpread out as a row vector diAnd expanding the OD matrixes of multiple days to obtain a matrix M with row vectors stacked into time × OD pairs in time and an OD row vector d with the date iiCorresponding to the ith row of matrix M;
2) decomposing the matrix M into products of three sub-matrixes by adopting a singular value decomposition method;
3) classifying the OD distribution according to regularity and explosiveness indexes;
4) and recombining the OD distribution of each category to obtain a typical daily traffic demand OD matrix.
In step 2), the expression of the matrix M decomposed into the product of three sub-matrices is:
Figure BDA0001275050400000021
wherein r is the rank of the matrix M, S is the diagonal matrix,ifor the i-th element, u, on the diagonal of the diagonal matrix SiIs the ith column, v, of the matrix UiIs the ith column of matrix V.
The step 3) specifically comprises the following steps:
31) defining the ith column V of the matrix ViFor the ith traffic demand distribution pattern, the ith column U of the matrix UiThe traffic demand distribution mode is a time change mode, and the values of the traffic demand distribution mode correspond to the values of the time change mode one by one;
32) when the value of the time variation pattern is judged to have periodicity by adopting fast Fourier transform, the OD distribution is marked as a first class, when a value deviating from the mean value by more than three times of standard deviation exists in the value of the time variation pattern, the OD distribution is marked as a second class, and the rest are marked as a third class.
In the step 32), when the duration is less than 7 weeks, the data is marked as the first category by judging whether the values of the time variation patterns in the middle of the week and the time variation patterns in the weekend are different, if so.
Compared with the prior art, the invention has the following advantages:
the invention adopts the SVD method to identify the structural characteristics of the OD matrix, extracts several typical OD distributions from the OD matrix of a plurality of days, then classifies the various distributions, extracts specific parts as typical day traffic OD demand matrixes, and can provide basis for traffic demand analysis, prediction and emergency influence analysis.
Drawings
Fig. 1 is a singular value distribution diagram of an OD matrix of a subway station in shanghai 2011 and 9 months.
Fig. 2 shows an example of typical OD distributions in 9 months 2011 in shanghai, where fig. 2a shows a first example of a typical OD distribution in a first class, fig. 2b shows a second example of a typical OD distribution in a first class, fig. 2c shows a first example of a typical OD distribution in a second class, fig. 2d shows a second example of a typical OD distribution in a second class, fig. 2e shows a first example of a typical OD distribution in a third class, and fig. 2f shows a second example of a typical OD distribution in a third class.
Fig. 3 shows typical OD distribution type determination results in the last 2011 month in shanghai.
Fig. 4 is a typical OD matrix expectation plot for the increase in metro in shanghai city of shanghai 2011, 9 and 28.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Example (b):
the method extracts several typical OD distributions from continuous multi-day traffic demand OD data, analyzes the meanings of various distributions, and finally recombines all components into a typical day traffic demand OD matrix according to the actual application demand. The method is characterized in that: dividing the multi-day OD matrix into a plurality of components by using a matrix decomposition method; classifying each component by analyzing the change of each component with time; and recombining the components into a typical daily traffic demand OD matrix according to practical problems.
The method specifically comprises the following steps:
1) construction of a time OD Pair matrix M
Let OD matrix of date i be DiExpand it into a row vector diThe OD matrices for multiple days are time stacked into a "time × OD vs" matrix M, as shown in table 1.
TABLE 1 time OD vs. matrix example
Figure BDA0001275050400000031
2) Singular value decomposition, the decomposition result is shown in figure 1, figure 1 is the singular value distribution of the matrix M, and a distinct 'steep slope' appears in the figure, which shows that a small number of dimensions can explain most of the changes in the multi-day OD matrix.
By the SVD method, the M × n "time × OD pair" matrix M is decomposed into the product of three matrices:
Figure BDA0001275050400000032
wherein the index of the matrix is the dimension of the matrix, VTIs the transpose of V, r is the rank of the matrix M, S is the diagonal matrix, and the ith element on the diagonal isi，uiIs the ith column, v, of the matrix UiIs the ith column of matrix V.
Definition viFor the ith DemandPattern (traffic demand distribution Pattern), define uiIs the ith TemporalFlow (time varying mode). The DemandPattern corresponds to the TemporalFlow one by one, the DemandPattern represents a specific OD distribution, and the TemporalFlow is a time sequence and characterizes the change of the OD contribution of a certain DemandPattern in each day in an analysis period.
3) Typical OD distribution analysis
Typical OD distributions are classified using regularity, explosiveness indicators. The specific judgment process is as follows:
i. and (3) judging whether the TemporalFlow has periodicity by using Fast Fourier Transform (FFT), namely, the FFT result has a peak value, and if so, the OD distribution is marked as a first type. (for data with a duration of less than 7 weeks, this step is replaced with the use of the ks test to determine if there is a significant difference in the mid-week and weekend Temporal Flow values, if any, labeled as first class);
ii, judging whether a value deviating from the mean value by more than three times of standard deviation exists in the Temporal Flow, and if so, marking the OD distribution as a second type;
the remaining OD distributions are labeled as third class.
The distribution of the different classes of OD is shown in fig. 2, the first column in fig. 2 (fig. 2a, 2c and 2 e): the date type is related to (working day, weekend), the working day is larger, the rest day is obviously reduced, and the date type shows periodic change; second column (fig. 2b, 2, and 2 f): regarding some events, explosive demands appear on a certain day or two days, and the events corresponding to the graph (2c) and the graph (2d) are the ten-line rear-end of the subway in Shanghai city on the day before national day of celebration and on 27 th month in 2011 respectively; third column: the change is not obvious and regular. The results of the category determination of all the OD distributions are shown in FIG. 3, and the first type of OD distributions are mainly distributed in the first few bits; the distribution of the second and third classes is not clearly regular.
4) Recombining OD distribution into typical OD matrix
The OD distribution is recombined into a typical OD matrix according to actual requirements, such as: recombining the first type of OD distribution, thereby filtering the components of outbreak and random fluctuation in the original OD matrix, and taking the components as the input of a prediction model; a typical OD matrix of OD change under a special event can be obtained by recombining the second type of OD distribution, can be used for modeling and analyzing traffic condition change, and provides basis for traffic demand analysis, prediction and accident influence analysis, as shown in FIG. 4, FIG. 4 is an expected line graph of typical OD matrix increment, from which a large number of ODs can be found to be added at the starting and ending points (Ili road station and Helen road station) of bus connection, and the other end of the OD is mainly located at a No. 10 line station with two ends not stopped; second, there is a substantial increase in the downtown transfer stations OD, including the number 10 on-line transfer station and the Shanghai train station that was the off-site transfer station at that time.
The method uses a matrix decomposition method (SVD) to divide an OD matrix from a plurality of days into a plurality of components, each component represents a typical OD distribution, the meaning of each component is determined by analyzing the change of each component along with time, the components are mainly divided into components which show regular change, components which suddenly explode and components which randomly occur, and finally, each component is recombined into the OD matrix of the traffic demand of a typical day according to the requirement of practical application, so that the method can provide a basis for the analysis, prediction and influence analysis and the emergency of the traffic demand, and has good due value.

Claims (1)

1. A typical daily traffic demand OD matrix obtaining method based on matrix decomposition is characterized by comprising the following steps:
1) let OD matrix with date i be DiSpread out as a row vector diAnd expanding the OD matrixes of multiple days to obtain a matrix M with row vectors stacked into time × OD pairs in time and an OD row vector d with the date iiCorresponding to the ith row of matrix M;
2) decomposing the matrix M into products of three sub-matrixes by adopting a singular value decomposition method, wherein the expression of the matrix M into the products of the three sub-matrixes is as follows:
Figure FDA0002381949150000011
wherein r is the rank of the matrix M, S is the diagonal matrix,ifor the i-th element, u, on the diagonal of the diagonal matrix SiIs the ith column, v, of the matrix UiIs the ith column of the matrix V;
3) the OD distribution is classified according to regularity and explosiveness indexes, and the method specifically comprises the following steps:
31) defining the ith column V of the matrix ViFor the ith traffic demand distribution pattern, the ith column U of the matrix UiThe traffic demand distribution mode is a time change mode, and the values of the traffic demand distribution mode correspond to the values of the time change mode one by one;
32) when the time variation mode value is judged to have periodicity by adopting fast Fourier transform, the OD distribution is marked as a first class, when a value deviating from the mean value by more than three times of standard deviation exists in the time variation mode value, the OD distribution is marked as a second class, the rest are marked as a third class, in the step 32), when the data with the duration time less than 7 weeks, the OD distribution is marked as a first class by judging whether the values of the time variation mode in the week and the time variation mode at the weekend exist or not, and if the values exist, the OD distribution is marked as a first class;
4) and recombining the OD distribution of each category to obtain a typical daily traffic demand OD matrix.
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