CN109979195B - Sparse regression-based short-term traffic flow prediction method integrating space-time factors - Google Patents

Sparse regression-based short-term traffic flow prediction method integrating space-time factors Download PDF

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CN109979195B
CN109979195B CN201910222787.9A CN201910222787A CN109979195B CN 109979195 B CN109979195 B CN 109979195B CN 201910222787 A CN201910222787 A CN 201910222787A CN 109979195 B CN109979195 B CN 109979195B
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factor dictionary
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郑增威
杜俊杰
孙霖
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Hongfujin Precision Industry Shenzhen Co Ltd
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    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
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Abstract

The invention relates to a sparse regression-based short-time traffic flow prediction method fusing space-time factors, which comprises the steps of 1) traffic flow data preprocessing, namely using min-max standardization to predict the traffic flow data, standardizing the traffic flow data of each detection point to be in a range of [0,1], 2) constructing a space-time factor dictionary, namely constructing a time factor dictionary according to a formula, and constructing a space factor dictionary according to the formula, and 3) solving and predicting sparse coefficients, namely sparsely coding training data according to the formula, solving the sparse coefficients α, and predicting the traffic flow at the next moment according to the sparse coefficients α and the space-time factor dictionary.

Description

Sparse regression-based short-term traffic flow prediction method integrating space-time factors
Technical Field
The invention relates to a short-time traffic flow prediction method, in particular to a short-time traffic flow prediction method based on sparse regression and integrating space-time factors.
Background
At present, a traditional time series prediction method and a machine learning-based time series prediction method are all applied to traffic flow prediction. A short-term traffic flow prediction model considering space factors is disclosed in a short-term traffic flow prediction model based on SVM and self-adaptive space-time data fusion, Lichaiguan and the like, the journal of Beijing industry university, 2015, 4 months and 3 days, and the main idea of the model is to correct a traffic flow time sequence prediction result by using a space sequence prediction value. A traffic flow prediction method and a system are disclosed in 8.3.2018, and the method comprises the steps of constructing a target sequence according to current observation flow information from A to T acquired from a preset situation database in sequence, constructing a fusion distance matrix according to the target sequence and a matching sequence matrix, and determining a prediction function according to the fusion distance matrix, a preset coefficient and a preset algorithm. An improved gravitation search least square support vector machine traffic flow prediction, Xunzhoushuai and the like is disclosed, a computer is applied and researched, a new improved gravitation search algorithm (TCK-AGSA) is published in 2018, 9, 30 and is used for carrying out parameter optimization on the prediction, and experimental results show that the model effectively improves the prediction accuracy. A traffic flow short-term prediction method based on space-time analysis and CNN, Qianwei and the like, control engineering, and 1, 20 days in 2019, a short-term traffic flow prediction combination model is published, and comprises a gray algorithm and 2 sub-models of ELM (extreme learning machine) neural network. In summary, most of the current research work still relies on historical traffic flow data of the current site to predict the traffic flow at the next moment. Some researches consider space-time factors in traffic flow, but the methods often face the problems of complex modeling, poor model expandability, incapability of carrying out quantitative analysis on the factors and the like. Therefore, how to efficiently fuse the space-time factors and improve the accuracy of traffic flow prediction is still a difficult point of research.
Disclosure of Invention
The invention aims to overcome the defects and provide a short-time traffic flow prediction method based on sparse regression and integrating space-time factors.
The short-time traffic flow prediction method based on the sparse regression and with the fusion of the space-time factors comprises the following steps:
step one, preprocessing traffic flow data
Traffic flow data prediction processing is performed using min-max normalization, normalizing the traffic flow data for each probe point to be within [0,1], as shown in equation (2):
Figure BDA0002004169680000021
wherein y represents the original traffic flow data, min and max represent the minimum and maximum values of y, respectively, and y' represents the normalized result;
step two, constructing a space-time factor dictionary
1) Constructing a time factor dictionary according to equation (3) assuming that the predicted time point is
Figure BDA0002004169680000022
The time factor dictionary T is defined as follows:
Figure BDA0002004169680000023
wherein
Figure BDA0002004169680000024
Representing the traffic flow data of the nth day in the past at the time t, wherein n represents the selected historical days, and k represents the length of the training data;
2) a space factor dictionary is constructed according to the formula (4) assuming that the predicted time point is
Figure BDA0002004169680000025
The space factor dictionary S is defined as follows:
Figure BDA0002004169680000026
wherein
Figure BDA0002004169680000027
Representing the traffic flow data of the nth peripheral information point at the time of t-1, wherein n represents the number of the selected adjacent points, and k represents the length of the training data;
3) completion of space-time factor dictionary DfConstructing;
constructing a traffic flow space-time factor dictionary D according to the orthogonal DCT-II dictionary shown in the formula (5), the Kronecker Delta function shown in the formula (6), the time factor dictionary and the space factor dictionaryfAs shown in formula (7);
Figure BDA0002004169680000028
Kj(n)＝δ(n-j)j＝N,N+1,...,2N-1 (6)
wherein i, j represents the ith and jth columns of the dictionary, N represents the magnitude of the column vectors of the dictionary, and N represents the number of column vectors;
Figure BDA0002004169680000031
wherein, the first 2N columns are dictionaries generated by orthogonal DCT-II and Kronecker Delta functions, and the last 2 columns are respectively time factors and space factors;
step three, solving and predicting sparse coefficient
1) Carrying out sparse coding on the training data according to a formula (8), and solving a sparse coefficient α;
Figure BDA0002004169680000032
wherein
Figure BDA0002004169680000033
Indicating the historical traffic flow and,
Figure BDA0002004169680000034
is a space-time factor dictionary constructed in the second step, the time is from t1To tkα is the sparse coefficient to be solved for
2) Predicting the traffic flow at the next moment according to the sparse coefficient α and the space-time factor dictionary, as shown in formula (9);
Figure BDA0002004169680000035
wherein
Figure BDA0002004169680000036
Indicating the traffic flow at the next moment in time,
Figure BDA0002004169680000037
and (4) constructing a space-time factor dictionary in the step two, wherein α represents the sparse coefficient obtained by solving.
The invention has the beneficial effects that: the sparse regression prediction method (ST-SR) fusing the space-time factors is obviously better than other prediction methods, and the influence of the factors can be quantitatively analyzed. From the view of RMSE, the average prediction precision of the ST-SR model at 4 sites is respectively improved by 2.70%, 1.87% and 2.11% at a prediction interval of 5 minutes, improved by 17.71%, 16.59% and 9.53% at a prediction interval of 15 minutes, and improved by 35.60%, 27.63% and 10.83% at a prediction interval of 30 minutes compared with that of SVR, LSTM and KNN. From MAPE, the mean prediction accuracy of the ST-SR model improved by 1.73%, 2.91%, and 1.69% over the 5-minute prediction interval, respectively, and the prediction intervals at 15 minutes and 30 minutes were also superior to the comparative model.
Drawings
FIG. 1 is a general flow diagram of the present method;
fig. 2 is a graph of the weight distribution for different factors.
Detailed Description
The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
The short-time traffic flow prediction method based on the sparse regression and with the fusion of the space-time factors comprises the following steps:
step one, preprocessing traffic flow data
In the traffic flow data, the traffic flow numerical values of different detection points may have a large difference, but this does not mean that there is no correlation between the detection points, in order to better mine the relationship between the detection stations, facilitate the training of subsequent models, and reduce the influence caused by the numerical value difference, the invention uses min-max standardization to preprocess the traffic flow.
Step two, constructing a space-time factor dictionary
The method firstly constructs a basic dictionary according to a DCT dictionary and a Kronecker Delta function. Then analyzing the correlation between the traffic flows from time and space, respectively constructing a time factor dictionary and a space factor dictionary, and finally completing a traffic flow space-time factor dictionary DfAs shown in formula (1):
Df＝[D,T,S](1)
wherein D is a base dictionary composed of a DCT dictionary and a Kronecker Delta function, T is a time factor dictionary, and S is a space factor dictionary.
Step three, solving and predicting sparse coefficient
And D, performing sparse decomposition on the historical traffic flow data by using the space-time factor dictionary established in the step two, solving a sparse coefficient, and finally predicting the traffic flow at the next moment by using the obtained sparse coefficient and combining the space-time factor dictionary.
The short-term traffic flow prediction method based on sparse regression and integrating space-time factors has the general flow chart shown in fig. 1, and specifically comprises the following steps:
step one, preprocessing traffic flow data
The present invention uses min-max normalization to predict traffic flow data, normalizing the traffic flow data for each probe point to the [0,1] range, as shown in equation (2):
Figure BDA0002004169680000041
where y represents the raw traffic flow data, min and max represent the minimum and maximum values of y, respectively, and y' represents the normalized result.
Step two, constructing a space-time factor dictionary
4) Constructing a time factor dictionary according to equation (3) assuming that the predicted time point is
Figure BDA0002004169680000051
The time factor dictionary T is defined as follows:
Figure BDA0002004169680000052
wherein
Figure BDA0002004169680000053
The data of the traffic flow at the time t on the past nth day are shown, n represents the selected historical days, and k represents the length of the training data.
5) A space factor dictionary is constructed according to the formula (4) assuming that the predicted time point is
Figure BDA0002004169680000054
The space factor dictionary S is defined as follows:
Figure BDA0002004169680000055
wherein
Figure BDA0002004169680000056
And (3) traffic flow data of the nth peripheral information point at the time t-1 is represented, n represents the number of the selected adjacent points, and k represents the length of the training data.
6) Completion of space-time factor dictionary DfAnd (4) constructing.
Constructing a traffic flow space-time factor dictionary D according to the orthogonal DCT-II dictionary shown in the formula (5), the Kronecker Delta function shown in the formula (6), the time factor dictionary and the space factor dictionaryfIs constructed as shown in equation (7).
Figure BDA0002004169680000057
Kj(n)＝δ(n-j)j＝N,N+1,...,2N-1 (6)
Where i, j represents the ith and jth columns of the dictionary, N represents the magnitude of the dictionary column vectors, and N represents the number of column vectors.
Figure BDA0002004169680000058
Where the first 2N columns are dictionaries generated by the orthogonal DCT-II and Kronecker Delta functions, and the last 2 columns are temporal and spatial factors, respectively.
Step three, solving and predicting sparse coefficient
3) Sparse coding is carried out on training data according to a formula (8) to solve sparse coefficients α. the sparse coefficients are solved by using a Method disclosed in An article An interlayer-Point Method for Large-Scale l 1-regulated Least Squares by Kim and other scholars of IEEE journel of selected topics in signal processing.
Figure BDA0002004169680000061
Wherein
Figure BDA0002004169680000062
Indicating the historical traffic flow and,
Figure BDA0002004169680000063
is a space-time factor dictionary constructed in the second step, the time is from t1To tkα is the sparse coefficient to be solved for
4) And predicting the traffic flow at the next moment according to the sparse coefficient α and the space-time factor dictionary, as shown in formula (9).
Figure BDA0002004169680000064
Wherein
Figure BDA0002004169680000065
Indicating the traffic flow at the next moment in time,
Figure BDA0002004169680000066
and (4) constructing a space-time factor dictionary in the step two, wherein α represents the sparse coefficient obtained by solving.
Experiments and results are as follows:
the data set used in the experiment is from the Caltrans Performance Measurement System (PeMS) website, which provides traffic flow data of over 39000 detection sites, and in order to better verify the Performance of the prediction method, the invention selects the traffic flow data of 4 sites located in urban and suburban areas for carrying out the relevant experiment, and the IDs of the 4 sites are 500010021, 1201100, 1017510 and 400665 respectively.
The method aims to provide a short-time traffic flow prediction method capable of fusing space-time factors. To measure the effectiveness of this method, we compared SVR, KNN, LSTM on the data set and the prediction method (ST-SR) of the fusion spatio-temporal factors proposed by the present invention. The experimental data are from 1 month 2017 to 6 months 2017, and holidays therein are removed. The test time is the last 30 days of the valid days, i.e. the average error of 30 days is used to measure the performance of the model. The error index adopted by the invention is the most commonly used RMSE and MAPE used in traffic flow prediction, which are respectively shown in a formula (10) and a formula (11).
Figure BDA0002004169680000067
Figure BDA0002004169680000068
Wherein N represents the length of the prediction, FtAnd AtRespectively representing the predicted value and the true value of the model.
TABLE 1 influence of spatial factors on different traffic environments
Figure BDA0002004169680000069
Figure BDA0002004169680000071
Experiment a comparative experiment was performed on four prediction points, the first group adding only a temporal factor and the second group adding both a temporal and a spatial factor. The results of the experiment are shown in table 1. The surrounding environment of the prediction point 1 and the prediction point 3 is a suburban area, and the prediction point 2 and the prediction point 4 are located in an urban area, as can be seen from table 1, after the spatial factors are added, by combining RMSE and MAPE analysis, the improvement of the prediction accuracy of the prediction points 2 and 4 is more obvious than that of 1 and 3, which indicates that the traffic flow in the city is more easily affected by the surrounding traffic conditions. Fig. 2 shows the distribution of the weights of different factors in the ST-SR model, and in general, the weight of the time factor is significantly higher than that of the space factor, indicating that the time factor has a greater influence on the traffic flow than the space factor.
Experiment two compares the predicted effects of SVR, KNN, LSTM and ST-SR, and to further demonstrate the performance of each model, we performed related experiments at the prediction intervals of 5 minutes, 15 minutes and 30 minutes, and the results are shown in tables 2, 3, 4 and 5, respectively. From the view of RMSE, the average prediction precision of the ST-SR model at 4 sites is respectively improved by 2.70%, 1.87% and 2.11% at a prediction interval of 5 minutes, improved by 17.71%, 16.59% and 9.53% at a prediction interval of 15 minutes, and improved by 35.60%, 27.63% and 10.83% at a prediction interval of 30 minutes compared with that of SVR, LSTM and KNN. From MAPE, the average prediction precision of the ST-SR model is improved by 1.73%, 2.91% and 1.69% respectively in the prediction interval of 5 minutes, and the average prediction precision is superior to that of the comparison model in the other two prediction intervals. The experimental result proves that the prediction accuracy of the ST-SR at four different positions is obviously higher than that of other models, and the ST-SR model can be better adapted to different traffic environments.
TABLE 2 comparison of Performance of different prediction models at prediction Point 1
Figure BDA0002004169680000072
TABLE 3 comparison of Performance of different prediction models at prediction Point 2
Figure BDA0002004169680000081
TABLE 4 comparison of Performance of different prediction models at prediction Point 3
Figure BDA0002004169680000082
TABLE 5 comparison of Performance of different prediction models at prediction Point 4
Figure BDA0002004169680000083

Claims (1)

1. A short-time traffic flow prediction method based on sparse regression and integrating space-time factors is characterized by comprising the following steps:
step one, preprocessing traffic flow data
Traffic flow data prediction processing is performed using min-max normalization, normalizing the traffic flow data for each probe point to be within [0,1], as shown in equation (2):
Figure FDA0002004169670000011
wherein y represents the original traffic flow data, min and max represent the minimum and maximum values of y, respectively, and y' represents the normalized result;
step two, constructing a space-time factor dictionary
1) Constructing a time factor dictionary according to equation (3) assuming that the predicted time point is
Figure FDA0002004169670000012
The time factor dictionary T is defined as follows:
Figure FDA0002004169670000013
wherein
Figure FDA0002004169670000014
Representing the traffic flow data of the nth day in the past at the time t, wherein n represents the selected historical days, and k represents the length of the training data;
2) a space factor dictionary is constructed according to the formula (4) assuming that the predicted time point is
Figure FDA0002004169670000015
The space factor dictionary S is defined as follows:
Figure FDA0002004169670000016
wherein
Figure FDA0002004169670000017
Indicating the nth peripheral letterThe traffic flow data of the information point at the time t-1, n represents the number of the selected adjacent points, and k represents the length of the training data;
3) completion of space-time factor dictionary DfConstructing;
constructing a traffic flow space-time factor dictionary D according to the orthogonal DCT-II dictionary shown in the formula (5), the Kronecker Delta function shown in the formula (6), the time factor dictionary and the space factor dictionaryfAs shown in formula (7);
Figure FDA0002004169670000021
Kj(n)＝δ(n-j) j＝N,N+1,...,2N-1 (6)
wherein i, j represents the ith and jth columns of the dictionary, N represents the magnitude of the column vectors of the dictionary, and N represents the number of column vectors;
Figure FDA0002004169670000022
wherein, the first 2N columns are dictionaries generated by orthogonal DCT-II and Kronecker Delta functions, and the last 2 columns are respectively time factors and space factors;
step three, solving and predicting sparse coefficient
1) Carrying out sparse coding on the training data according to a formula (8), and solving a sparse coefficient α;
Figure FDA0002004169670000023
wherein
Figure FDA0002004169670000024
Indicating the historical traffic flow and,
Figure FDA0002004169670000025
is a space-time factor dictionary constructed in the second step, the time is from t1To tkα is the sparse coefficient to be solved for
2) Predicting the traffic flow at the next moment according to the sparse coefficient α and the space-time factor dictionary, as shown in formula (9);
Figure FDA0002004169670000026
wherein
Figure FDA0002004169670000027
Indicating the traffic flow at the next moment in time,
Figure FDA0002004169670000028
and (4) constructing a space-time factor dictionary in the step two, wherein α represents the sparse coefficient obtained by solving.
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