CN107170233B - A method for obtaining OD matrix of typical daily traffic demand based on matrix decomposition - Google Patents

Abstract

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

A method for obtaining OD matrix of typical daily traffic demand based on matrix decomposition

technical field

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.

Background technique

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.

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.

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.

SUMMARY OF THE INVENTION

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. .

The object of the present invention can be realized through the following technical solutions:

A typical daily traffic demand OD matrix acquisition method based on matrix decomposition, comprising the following steps:

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) Using singular value decomposition method to decompose matrix M into the product of three sub-matrices;

3) Classify the OD distribution according to regularity and explosiveness indicators;

4) Reorganize the OD distribution of each category to obtain the OD matrix of typical daily traffic demand.

In described step 2), matrix M is decomposed into the expression of the product of three sub-matrices:

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.

Described step 3) specifically comprises the following steps:

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) 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.

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.

Compared with the prior art, the present invention has the following advantages:

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.

Description of drawings

Figure 1 shows the singular value distribution of the OD matrix of Shanghai subway stations in September 2011.

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.

Figure 3 shows the typical OD distribution type judgment results in Shanghai in September 2011.

Figure 4 is a typical OD matrix expected line diagram of Shanghai Metro on September 28, 2011.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Example:

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 .

Specifically include the following steps:

1) Construct a "time × OD pair" matrix M

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.

Table 1 Time × OD pair matrix example

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.

By the SVD method, the m×n “time×OD pair” matrix M is decomposed into the product of three matrices:

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.

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) Typical OD distribution analysis

Typical OD distributions were classified using regularity, burstiness indicators. The specific judgment process is as follows:

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. 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. The remaining OD distributions are labeled as the third category.

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) The OD distribution is reorganized into a typical OD matrix

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 Line 10 that has not been suspended. Second, the transfer station OD in the city center has grown substantially, including the transfer station on Line 10 and the Shanghai Railway Station, which was then used as an off-station transfer station.

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.

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 D_iSpread out as a row vector d_iAnd 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 i_iCorresponding 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:

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 S_iIs the ith column, v, of the matrix U_iIs 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 V_iFor the ith traffic demand distribution pattern, the ith column U of the matrix U_iThe 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.

Images