CN114550454A - Traffic flow prediction method based on traffic flow matrix combination model - Google Patents

Traffic flow prediction method based on traffic flow matrix combination model Download PDF

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CN114550454A
CN114550454A CN202210171664.9A CN202210171664A CN114550454A CN 114550454 A CN114550454 A CN 114550454A CN 202210171664 A CN202210171664 A CN 202210171664A CN 114550454 A CN114550454 A CN 114550454A
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CN114550454B (en
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卞加佳
郭琦
朱磊
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Nanjing Microvideo Technology Co ltd
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    • 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
    • G08G1/0129—Traffic data processing for creating historical data or processing based on historical data
    • 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
    • G08G1/0137—Measuring and analyzing of parameters relative to traffic conditions for specific applications
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
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Abstract

The invention relates to the technical field of traffic big data correlation, in particular to a traffic flow prediction method based on an ARIMA-GM (1,1) fusion prediction model, which comprises the steps of firstly extracting the data of predicted road traffic flow, dividing the data into transverse data and longitudinal data for preprocessing, and constructing a traffic flow data matrix; extracting high-dimensional features of the constructed traffic flow data matrix; then constructing an ARIMA-GM (1,1) fusion prediction model, and fitting the parameters of the ARIMA-GM; the traffic flow data is predicted by using the model, and the final result is checked. The invention provides a new fusion prediction model for traffic flow prediction based on an ARIMA time sequence prediction model and a GM (1,1) gray prediction model, which solves the inaccuracy problem of the ARIMA model caused by traffic flow mutation caused by factors such as holidays and the like and solves the problems of rare traffic samples and the like by using the gray model; the model fully excavates the space-time characteristics of the road traffic flow and improves the accuracy of long-term traffic flow prediction.

Description

Traffic flow prediction method based on traffic flow matrix combination model
Technical Field
The invention belongs to the technical field of traffic information, and particularly relates to a traffic flow prediction method based on a traffic flow matrix combination model.
Background
With the development of science and technology, automobile transportation is more convenient, the occupied amount and the traffic volume of all automobiles of people are gradually increased along with the continuous improvement of the living standard of people, and finally, the problems of dense traffic flow on roads, even traffic jam and the like are caused; therefore, in order to solve the problem of traffic resource allocation caused by overload of road traffic and fully play the positive role of the intelligent traffic system in road regulation, the prediction method of road traffic flow is an important research direction in the traffic field.
The road traffic prediction method at the present stage mainly comprises the following steps: although the traditional time sequence prediction method, the support vector machine, the BP neural network and the like can obtain prediction data in road traffic flow, in the road traffic flow prediction, the models do not fully dig out the space-time correlation characteristics in the road traffic flow data, and the problems of low time and space correlation degree, inaccurate traffic flow prediction caused by traffic data loss, error of long-term traffic flow prediction and the like exist.
Disclosure of Invention
The invention aims to provide a traffic flow prediction method based on a traffic flow matrix combination model, which constructs a model for predicting future short-term and long-term traffic data by statistically analyzing the past traffic data collected from monitoring so as to realize more accurate prediction data calculation.
In order to achieve the purpose, the invention provides the following technical scheme: a traffic flow prediction method based on a traffic flow matrix combination model specifically comprises the following steps:
step S1: firstly, extracting traffic flow data in n continuous time periods before a time point of a traffic flow to be predicted, preprocessing the traffic flow data to construct a traffic flow data matrix, and marking the traffic flow data matrix as a transverse data matrix;
step S2: extracting traffic flow data in a time period with the same date characteristics as the predicted time point, preprocessing the traffic flow data in the same time period, and constructing a traffic flow data matrix marked as a longitudinal data matrix;
step S3: constructing a two-dimensional prediction matrix according to the transverse and longitudinal two-dimensional traffic flow data matrixes obtained in the step S1 and the step S2 respectively to extract high-dimensional features, wherein the construction of the prediction value matrix comprises
Figure BDA0003518390670000021
And constructing a predictor matrix
Figure BDA0003518390670000022
Step S4: prediction value matrix based on difference autoregressive moving average model ARIMA
Figure BDA0003518390670000023
And a predictor matrix based on the grey system prediction model GM (1,1)
Figure BDA0003518390670000024
The predicted traffic flow matrix value is used for constructing an ARIMA-GM (1,1) fusion prediction model, and parameter fitting is carried out on the proportionality coefficient of the ARIMA model and the proportionality coefficient of the GM (1,1) model in the model;
step S5: performing KS test by using the previously known data and the data finally predicted by the model in the step S4; finally, calculating the feasibility of the model according to the KS test formula (1); wherein, in order to verify whether the function distribution of the predicted data is the actual data distribution, a critical value is found by using the sample capacity n and the significance level a, wherein, Fn(x) To predict the functional distribution of data, F0(X) finding the threshold D for the actual data distribution using the sample volume n and significance level anaIf D is<DnaThen the fit is considered satisfactory and the feasibility is defined as D and calculated as follows:
D＝max|Fn(x)-F0(X)| (1)
step S6: and predicting the road traffic flow based on the constructed ARIMA-GM (1,1) fusion prediction model, wherein road two-dimensional real-time traffic flow data is acquired as input data of the ARIMA-GM (1,1) fusion prediction model constructed in the step S4, and the road real-time traffic flow is predicted to obtain a prediction value.
As a further improvement of the present invention, the traffic flow data in the steps S1 and S2 are preprocessed, including deleting the repeated data, filling the missing data, and modifying the error data.
As a further improvement of the present invention, the traffic flow data in step S1 and step S2 are preprocessed, and further include averaging and supplementing the missing value of the individual time point by using two adjacent time spans; selecting the range data which should be discarded for the data loss in the long time span, not processing, and re-selecting the value of the time period n until no data loss in the long time span exists in the value of n; and carrying out adjacent point mean value correction on the error data.
As a further improvement of the invention, the construction of the predictor matrix
Figure BDA0003518390670000031
The traffic flow prediction method specifically comprises the steps of conducting traffic flow prediction on n traffic flow data matrixes A which are in front of a prediction point and take unit time as intervals by using a differential autoregressive moving average model ARIMA (p, d, q), namely, the model regards a data sequence formed by a prediction object along with the time lapse as a random sequence, differentiates the sequence to be stable, then describes the sequence by using a mathematical model, and predicts the future value of the model according to the past and present values of the time sequence after the model is identified, wherein AR is autoregressive, and p is the number of autoregressive terms; i is the difference, d is the number of differences (order) made to make it a plateau sequence; MA is the moving average, q is the number of terms of the moving average, and finally a prediction value matrix model is constructed
Figure BDA0003518390670000032
As a further improvement of the invention, the construction of the predictor matrix
Figure BDA0003518390670000033
Specifically, a gray system prediction model GM (1,1) is used for traffic flow prediction on a traffic flow data matrix B in the extracted time period with the same date characteristics as the prediction time point, namely the model aims at the defect that the elements of a longitudinal matrix are limited, and a system with small samples and poor information uncertainty of 'part of information is known and part of information is unknown' is used as an object, and the analysis of the part of known information is carried outAnd effective information is utilized to realize effective monitoring and correct description of system operation behaviors and change rules, wherein GM (1,1) is a 1-order variable gray model, and a prediction value matrix is finally constructed
Figure BDA0003518390670000034
Compared with the prior art, the invention has the beneficial effects that: according to the technical scheme, the road traffic flow data is subjected to high-dimensional feature extraction through a fusion prediction model of a difference autoregressive moving average model ARIMA and a grey system prediction model GM (1,1), so that long-term and short-term prediction of road traffic is realized; the invention also utilizes ARIMA and GM (1,1) to extract the high-dimensional characteristics of the transverse and longitudinal traffic flow data before the prediction time point, and finally provides the prediction value in the specified time period; the technical scheme fully excavates two-dimensional time and space characteristics of road traffic, solves the problem of overlarge error of a predicted value due to lack of longitudinal data amount, also solves the problem of sudden change of transverse data prediction due to the particularity of a prediction date, and further improves the accuracy of road traffic flow prediction; the traffic flow prediction of the technical scheme is an important component of an intelligent traffic system, and the method can effectively improve the accuracy of the traffic flow prediction to a certain extent and improve the accuracy of traffic flow induction in the intelligent traffic system.
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FIG. 1 is a block diagram of the overall process of the fusion prediction model construction and data prediction according to the present invention.
Fig. 2 is a comparison diagram of the predicted value and the actual value of the traffic flow by using the ARIMA model in the embodiment.
Fig. 3 is a comparison graph of the predicted value and the actual value of the traffic flow using the gray prediction model GM (1,1) in the present embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to fig. 1 to 3 in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
1.1 in this embodiment, a traffic flow prediction method based on a traffic flow matrix combination model is disclosed, which includes the following steps:
taking a time period needing to be predicted as a starting point, dividing past values and present values counted before the time period into time sequences with two dimensions of horizontal and vertical. That is, the horizontal time series is a random time series adjacent to the prediction time period, and the time series is recorded as a matrix a:
Figure BDA0003518390670000041
wherein the n value is the counted number of the random sequences.
1.2 the vertical time series is the past time series with the same characteristics as the predicted time period (if the traffic flow during the spring festival of 2022 is to be predicted, the vertical time series can be selected from the spring festival time period of 2021, the spring festival time period of 2020, the spring festival time period of 2019, etc.), and is marked as a matrix B:
Figure BDA0003518390670000042
wherein the p value is the number of time points in the predicted time period, and the q value is the counted number of the past time periods.
1.3, performing normalization processing on the matrix A and the matrix B to map a value [0,1] interval, namely performing maximum and minimum normalized data preprocessing on traffic flow data in each matrix, wherein a maximum and minimum normalized calculation expression is as follows:
Figure BDA0003518390670000051
finally, a standardized matrix A is constructed*And B*：
Figure BDA0003518390670000052
Figure BDA0003518390670000053
2.1 matrix A after processing*Substituting the ARIMA (q, d, p) model, namely the formula:
Figure BDA0003518390670000054
where L is a lag operator, p is the lag number of the time series data, d is the differencing order of the time series data, q is the lag number of the prediction error, εtIs a white noise sequence; phi and theta are constant coefficients, wherein i is 1,2,3 ….
Will matrix A*Drawing according to the time sequence matrix A*The scatter diagram, the autocorrelation function and the partial autocorrelation function diagram are subjected to ADF (auto-ADF) inspection, the variance, the trend and the change rule of the scatter diagram, the autocorrelation function and the partial autocorrelation function diagram are judged, and whether the sequence is stable or not is observed. The inspection principle is as follows:
(Ⅰ)yt＝ρyt-1+εt (8)
(Ⅱ)yt＝c+ρyt-1+εt (9)
(Ⅲ)yt＝c+γt+ρyt-1+εt (10)
ytfor time series of traffic flow, yt-1Time series of the previous time, t is 1,2,3 …; ρ, γ, c are coefficients where | ρ |. is zero<1，εtIs a white noise sequence, and E [ epsilon ]t]＝0,V(εt)＝σ<∞,Cov(εt，εt)＝μ<∞。
If the original hypothesis is not rejected, ytIs a non-stationary time sequence containing a unit root; if the original hypothesis is rejected, y is in cases (I), (II)tIs a stationary time series; y in case (III)tIs a trend stationary time series.
And (3) carrying out stabilization treatment on the obtained non-stationary sequence: if the data sequence is non-stable and has a certain increasing or decreasing trend, the data needs to be differentially processed; if the data has variance, the data needs to be processed technically until the autocorrelation function value (ACF) and the partial correlation function value (PACF) of the processed data have no significant difference.
And obtaining the optimal parameters p and q by analyzing the autocorrelation graphs and the partial autocorrelation graphs. Constructing an ARIMA model according to the d, p and q obtained in the above step; and carrying out model inspection on the obtained model.
Passing the time sequence matrix A after inspection*Substituting into ARIMA model, predicting traffic flow data of required time period, and constructing into matrix C*. Namely:
Figure BDA0003518390670000061
where the p-value is the number of time points in the predicted time period.
2.2 longitudinal time series matrix B obtained after processing*The values are respectively substituted into the gray prediction model G (1,1) by column units, namely:
x(0)(k)+az(1)(k)＝b (12)
Figure BDA0003518390670000063
Figure BDA0003518390670000071
Figure BDA0003518390670000072
wherein a and b are undetermined parameters required to be solved through modeling, and the corresponding predicted values are as follows:
Figure BDA0003518390670000073
the results obtained were examined, and the residual was examined as follows:
Figure BDA0003518390670000074
if all | ε (k) | <0.1, then the higher requirement is considered to be reached; otherwise, if all | epsilon (k) | <0.2, the general requirement is considered to be met; if all | epsilon (k) | >0.2, the number q of longitudinal time sequence points needs to be increased until the requirement is met.
Finally, the matrix B*Substituting the time sequence of each column into the grey prediction model GM (1,1) to obtain a new prediction matrix D*：
Figure BDA0003518390670000075
Constructing an ARIMA-GM (1,1) fusion prediction model, namely:
ModelARIMA-GM＝f1(x)×(ModelARIMA+f2(x)×ModelGM) (19)；
wherein f is1(x) And f2(x) Fitting coefficient function, the expression form of which is:
Figure BDA0003518390670000076
wherein a and c are fitting coefficients, namely the ARIMA-GM (1,1) fusion prediction model function is expressed as:
ModelARIMA-GM＝ax×(ModelARIMA+cex×ModelGM) (21)；
traffic flow data matrix C to be predicted*And D*Substituting into the fusion prediction model, and finallyDeriving a predicted time series matrix E*Namely:
Figure BDA0003518390670000081
performing anti-standardization operation on the prediction result, and converting the prediction result into real traffic flow data, wherein the anti-standardization calculation expression is as follows:
Figure BDA0003518390670000082
3. finally, a predicted value result is obtained, and KS test is carried out on the predicted value result.
Example (c): the traffic flow prediction method based on the traffic flow matrix combination model, which obtains traffic flow prediction data in practical experiments, comprises the following steps:
3.1 selecting experimental data:
experimental data predicts traffic flow of the Nanjing Quqiao river-crossing channel during the mid-autumn vacation in 2021, namely predicting time is 2021.9.19, namely mid-autumn festival. The data collected by the experiment and the training data are divided into transverse data and longitudinal data, wherein the time period selected by the transverse collected data is 2021.6.1-2021.9.25, and the total time period is 25-day Nanjing four-bridge traffic flow data. The longitudinal collected data is selected as ([2021.5.22,2021.5.23], [2021.5.29,2021.5.30], [2021.6.5,2021.6.6], [2021.6.12,2021.6.13], [2021.6.19,2021.6.20]), namely the time period of the longitudinal data is selected as 7 days. The obtained transverse and longitudinal traffic flow matrixes A and B are as follows, and are subjected to normalization processing to obtain:
Figure BDA0003518390670000083
Figure BDA0003518390670000084
in the experiment, the transverse data takes traffic flow data from 6 months 1 to 25 days as a training set, and takes 6 months 26 to 27 days as a testing set to adjust the parameters of the fusion prediction model. And 9, 19 days are prediction sets and are used for evaluating the accuracy of the model. In the longitudinal data, the test set is from 5 months 22 days to 6 months 20 days to adjust the parameters of the fusion prediction model. And 9, 19 days are prediction sets and are used for evaluating the accuracy of the model.
3.2 parameter determination:
will matrix A*Substituting into ARIMA model, repeating the process of step 2.1 to obtain predicted value matrix C of 26-27 days in 6 months*Namely:
Figure BDA0003518390670000091
will matrix B*Substituting the grey prediction model, and repeating the process of step 2.2 to obtain a prediction value matrix D from 26 days to 27 days in 6 months in 2021*Namely:
Figure BDA0003518390670000092
repeating the processing procedure of step 2.2 to obtain matrix C*、D*And normalized actual value matrix E of 26-27 days in 6 months*Substituting into ARIMA-GM (1,1) fusion prediction model, namely:
Figure BDA0003518390670000093
3.3 Experimental results and tests:
the fitting results of the final ARIMA-GM (1,1) combinatorial model are shown below. And calculating the prediction time sequence matrixes of 9 months and 19 days in the transverse direction and the longitudinal direction, and substituting the prediction time sequence matrixes into the model to calculate a final prediction value matrix. KS test is carried out on the test result and the true value, the test result is shown in the following table 1, the feasibility of the model is proved, and the KS test result of the model is shown in the following table:
Figure BDA0003518390670000094
although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A traffic flow prediction method based on a traffic flow matrix combination model is characterized by comprising the following steps:
step S1: firstly, extracting traffic flow data in n continuous time periods before a time point of a traffic flow to be predicted, preprocessing the traffic flow data to construct a traffic flow data matrix, and marking the traffic flow data matrix as a transverse data matrix;
step S2: extracting traffic flow data in a time period with the same date characteristics as the predicted time point, preprocessing the traffic flow data in the same time period, and constructing a traffic flow data matrix marked as a longitudinal data matrix;
step S3: constructing a two-dimensional prediction matrix according to the transverse and longitudinal two-dimensional traffic flow data matrixes obtained in the step S1 and the step S2 respectively to extract high-dimensional features, wherein the construction of the prediction value matrix comprises
Figure FDA0003518390660000011
And constructing a predictor matrix
Figure FDA0003518390660000012
Step S4: prediction value matrix based on difference autoregressive moving average model ARIMA
Figure FDA0003518390660000013
And a predictor matrix based on the grey system prediction model GM (1,1)
Figure FDA0003518390660000014
The predicted traffic flow matrix value is used for constructing an ARIMA-GM (1,1) fusion prediction model, and parameter fitting is carried out on the proportionality coefficient of the ARIMA model and the proportionality coefficient of the GM (1,1) model in the model;
step S5: performing KS test by using the previously known data and the data finally predicted by the model in the step S4; finally, calculating the feasibility of the model according to the KS test formula (1) below; wherein, in order to verify whether the function distribution of the prediction data is the actual data distribution, the critical value is found by using the sample capacity and the significance level, wherein, Fn(x) To predict the functional distribution of data, F0(X) finding the threshold D for the actual data distribution using the sample volume n and significance level anaIf D is<DnaThen the fit is considered satisfactory and the feasibility is defined as D and calculated as follows:
D＝max|Fn(x)-F0(X)| (1)
step S6: and predicting the road traffic flow based on the constructed ARIMA-GM (1,1) fusion prediction model, wherein road two-dimensional real-time traffic flow data is acquired as input data of the ARIMA-GM (1,1) fusion prediction model constructed in the step S4, and the road real-time traffic flow is predicted to obtain a prediction value.
2. The traffic flow prediction method based on the traffic flow matrix combination model according to claim 1, characterized in that: and preprocessing the traffic flow data in the steps S1 and S2, including deleting the repeated data, filling the missing data and modifying the error data.
3. The traffic flow prediction method based on the traffic flow matrix combination model according to claim 1, characterized in that: the step S1 and the step S2 are performed on the traffic flow data, and further include the step of averaging and supplementing the missing values at the individual time points by using two adjacent time spans; selecting the range data which should be discarded for the data loss in the long time span, not processing, and re-selecting the value of the time period n until no data loss in the long time span exists in the value of n; and carrying out adjacent point mean value correction on the error data.
4. The traffic flow prediction method based on the traffic flow matrix combination model according to claim 1, characterized in that: the constructing a predictor matrix
Figure FDA0003518390660000021
The traffic flow prediction method specifically comprises the steps of conducting traffic flow prediction by using a differential autoregressive moving average model ARIMA (p, d, q) on n traffic flow data matrixes A which take unit time as intervals and are positioned in front of a prediction point, wherein AR is autoregressive, and p is the number of autoregressive terms; i is the difference, d is the number of differences (order) made to make it a plateau sequence; MA is the moving average, q is the number of terms of the moving average, and finally a prediction value matrix model is constructed
Figure FDA0003518390660000022
5. The traffic flow prediction method based on the traffic flow matrix combination model according to claim 1, characterized in that: the constructing a predictor matrix
Figure FDA0003518390660000023
Specifically, traffic flow prediction is carried out by applying a gray system prediction model GM (1,1) to an extracted traffic flow data matrix B in a time period with the same date characteristics as the prediction time point, wherein GM (1,1) is a 1-order variable gray model, and finally a prediction value matrix is constructed
Figure FDA0003518390660000024
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覃劭峰: "基于GM(1,1)-ARIMA最优组合的大坝预测模型", 测绘通报 *
谈苗苗等: "基于ARIMA和灰色模型加权组合的短期交通流预测", 计算机技术与发展 *

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