CN107293118B - Short-time prediction method for traffic speed dynamic interval - Google Patents

Short-time prediction method for traffic speed dynamic interval Download PDF

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CN107293118B
CN107293118B CN201710584159.6A CN201710584159A CN107293118B CN 107293118 B CN107293118 B CN 107293118B CN 201710584159 A CN201710584159 A CN 201710584159A CN 107293118 B CN107293118 B CN 107293118B
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聂庆慧
邓社军
周扬
肖枭
于世军
刘路
张鹏鹏
谈圣
黄佳宇
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Abstract

The invention discloses a high-reliability short-term prediction method for a traffic speed dynamic interval, which comprises the following steps: (10) acquiring a traffic speed time sequence: acquiring a target section traffic speed time sequence observed value on a road; (20) stationary time series acquisition: converting the traffic speed time sequence into a stable time sequence through first-order difference operation; (30) first order difference prediction value calculation: calculating a first-order difference predicted value of the traffic speed in each current time interval according to the first-order difference time sequence prediction model of the traffic speed; (40) and (3) calculating a predicted value of a standard deviation of a residual item: calculating a predicted value of a standard deviation of the residual term in each current time interval according to a differential prediction model of the comprehensive generalized autoregressive condition of the residual term; (50) determining a traffic speed prediction interval of a target section: and determining a traffic speed prediction interval of the target section in each time interval according to the traffic speed observation value, the traffic speed first-order difference prediction value and the residual error item standard difference prediction value.

Description

Short-time prediction method for traffic speed dynamic interval
Technical Field
The invention belongs to the technical field of short-time prediction of traffic flow, and particularly relates to a short-time prediction method for a high-reliability traffic speed dynamic interval.
Background
The traffic flow running speed is one of the important technical indexes of road traffic operation, management and control. Accurate and reliable short-term traffic speed prediction becomes important research content of urban intelligent traffic systems such as route guidance and active traffic control.
A great deal of research is carried out on the short-term traffic speed prediction technology of road sections at home and abroad. Prediction methods based on techniques such as statistical models and artificial intelligence are continuously proposed, and the accuracy of prediction is also continuously improved.
However, most of researches only carry out modeling and evaluation of a prediction method aiming at the first moment horizontal sequence value of the traffic speed, neglect the fluctuation characteristic of the second moment of the traffic speed, and are difficult to effectively quantify the reliability of the traffic speed prediction. Although a small amount of research also provides a modeling for the volatility of the second moment of the traffic speed, the existing method mostly adopts a model for establishing parameters, and the description of the dynamic structure of the second moment of the traffic speed is greatly limited.
In summary, the prior art has the following problems: the reliability of the short-term prediction of traffic speed is low.
Disclosure of Invention
The invention aims to provide a short-time prediction method for a traffic speed dynamic interval, which has high reliability.
The technical solution for realizing the purpose of the invention is as follows:
a short-time traffic speed dynamic interval prediction method comprises the following steps:
(10) acquiring a traffic speed time sequence: acquiring a target section traffic speed time sequence observed value on a road;
(20) stationary time series acquisition: converting the traffic speed time sequence into a stable time sequence through first-order difference operation;
(30) first order difference prediction value calculation: calculating a first-order difference predicted value of the traffic speed within each current time interval t according to the first-order difference time sequence prediction model of the traffic speed;
(40) and (3) calculating a predicted value of a standard deviation of a residual item: according to the differential prediction model of the comprehensive generalized autoregressive condition of the residual terms, calculating the predicted value of the standard deviation of the residual terms in each current time interval t;
(50) determining a traffic speed prediction interval of a target section: and determining a traffic speed prediction interval of the target section in each time interval t according to the traffic speed observed value in each previous time interval (t-1), the traffic speed first-order difference prediction value in each current time interval t and the standard difference prediction value of the residual error term in each current time interval.
Compared with the prior art, the invention has the following remarkable advantages:
the reliability is high. On the basis of the construction of a short-term prediction model of the road target section traffic speed first-order moment horizontal sequence, the invention further extracts and quantifies the fluctuation characteristic of the traffic speed second-order moment, namely, a conditional variance prediction model is constructed for the second-order moment of the residual sequence, and the short-term prediction of a traffic speed dynamic interval is realized by predicting the dynamic standard deviation of the second-order moment, thereby further improving the reliability of the short-term prediction of the traffic speed of the target section.
The invention is described in further detail below with reference to the figures and the detailed description.
Drawings
Fig. 1 is a main flow chart of the short-term traffic speed dynamic interval prediction method of the invention.
FIG. 2 is a comparison graph of standard deviation prediction results of the first-order difference sequence residual terms of the traffic speed based on the standard GARCH (1, 1), GJR-GARCH (1, 1) and fGARCH (1, 1) models in section No. 1012016.
FIG. 3 is a comparison graph of standard deviation prediction results of the first-order difference sequence residual terms of the traffic speed based on the standard GARCH (1, 1), GJR-GARCH (1, 1) and fGARCH (1, 1) models in section No. 1004030.
FIG. 4 is a comparison graph of standard deviation prediction results of the first-order difference sequence residual terms of traffic speed based on the standard GARCH (1, 1), GJR-GARCH (1, 1) and fGARCH (1, 1) models of section 1001010 in example.
FIG. 5 is a comparison graph of standard deviation prediction results of the first-order difference sequence residual terms of the traffic speed based on the standard GARCH (1, 1), GJR-GARCH (1, 1) and fGARCH (1, 1) models in section No. 1003006.
Detailed Description
As shown in fig. 1, the short-term traffic speed dynamic interval prediction method of the present invention includes the following steps:
(10) acquiring a traffic speed time sequence: acquiring a target section traffic speed time sequence observed value on a road;
the traffic speed data collected from the target section is continuous time series data at equal time intervals of 5 minutes, and the original time series is not stable.
(20) Stationary time series acquisition: converting the traffic speed time sequence into a stable time sequence through first-order difference operation;
(30) first order difference prediction value calculation: calculating a first-order difference predicted value of the traffic speed within each current time interval t according to the first-order difference time sequence prediction model of the traffic speed;
the step of (30) calculating the first-order difference prediction value specifically comprises the following steps:
according to the traffic speed first-order difference time series prediction model, making m equal to max (p, q), acquiring the first-order difference values of the traffic speed time series of the target section of the historical time interval (t-1), (t-2) and (t-m), calculating the traffic speed first-order difference predicted value in the current time interval t as,
Figure BDA0001353068590000041
in the formula,
Figure BDA0001353068590000042
is a first-order difference predicted value, delta y, of the target section traffic speed in the current time interval tt-iA first-order difference observed value of the target section traffic speed in a previous time interval (t-i) is obtained, and c is a constant term; p is the hysteresis order of the autoregressive process, q is the hysteresis order of the moving average process, phiiAnd thetajIs the autoregressive moving average ARMA (p, q) model coefficient,tresidual terms of the traffic speed first order difference sequence in the current time interval t,t-jresidual terms in the previous time interval (t-j) for a traffic speed first order difference sequence and assuming a seriestIt is a white noise process that follows a 0-mean normal distribution.
The autoregressive order p and the moving average order q of the ARMA (p, q) model are determined by a Bayesian information criterion; constant term c and model coefficient phii、θjAnd obtaining the target by least square estimation.
(40) And (3) calculating a predicted value of a standard deviation of a residual item: according to the differential prediction model of the comprehensive generalized autoregressive condition of the residual terms, calculating the predicted value of the standard deviation of the residual terms in each current time interval t;
the (40) residual error item standard deviation prediction value calculating step specifically comprises: according to the different variance prediction model of the comprehensive generalized autoregressive condition of the residual terms, the predicted value of the standard deviation of the residual terms in the time interval t is calculated as
Figure BDA0001353068590000051
Namely, it is
Figure BDA0001353068590000052
In the formula,
f(t-1)＝|t-1-b|-c(t-1-b)，
the differential variance prediction model of the comprehensive generalized autoregressive condition of the residual error term is according to the sequence of the residual error termtThe resulting, comprehensive generalized autoregressive conditional variance fGARCH (1, 1) model with first-order autoregressive terms and first-order moving average terms,
Figure BDA0001353068590000053
wherein,tis the residual value of the first order difference time series of the traffic speed in the current time interval t,t-1is the residual value of the first order difference time series of the traffic speed in the previous time interval (t-1),
Figure BDA0001353068590000054
is the predicted value of the standard deviation of the residual error term in the current time interval t,
Figure BDA0001353068590000055
a sequence of residual terms being a predicted value of the standard deviation of the residual terms in the preceding time interval (t-1)tThe mean obedience is 0 and the standard deviation is sigmatNormal distribution of (2); z is a radical oftA white noise process that follows an independent standard normal distribution with a mean of 0 and a variance of 1; omega, beta and gamma are regression parameters; lambda is Box-Cox transfer coefficient; b is an offset factor used for quantifying smaller traffic speed fluctuations; c is a rotation factor used for quantifying larger traffic speed fluctuation; omega, beta, gamma, lambda, b and c are all parameters to be estimated of the fGARCH (1, 1) model.
Parameters omega, beta, gamma, lambda, b and c to be estimated of the fGARCH (1, 1) model are obtained by maximum likelihood estimation.
(50) Determining a traffic speed prediction interval of a target section: and determining a traffic speed prediction interval of the target section in each time interval t according to the traffic speed observed value in each previous time interval (t-1), the traffic speed first-order difference prediction value in each current time interval t and the standard difference prediction value of the residual error term in each current time interval.
The step (50) of determining the target section traffic speed prediction interval specifically comprises the following steps:
the section prediction value of the traffic speed in the previous time interval t is
Figure BDA0001353068590000061
Wherein the traffic speed prediction upper limit value in the current time interval t is
Figure BDA0001353068590000062
The lower limit value of the traffic speed prediction in the current time interval t is
Figure BDA0001353068590000063
In the formula, yt-1Is the observed value of the traffic speed in the previous time interval (t-1),
Figure BDA0001353068590000064
is a traffic speed first-order difference predicted value in the current time interval t,
Figure BDA0001353068590000065
within the current time interval t
Residual term standard deviation prediction, zα/2Is the upper alpha quantile of the standard normal distribution.
The following examples illustrate the use of the present invention.
In this embodiment, the data used is actually acquired traffic speed time series of 2 sections on the main road and the secondary road of the urban central city of the kunshan city. The main trunk detection sections are respectively 1012016 (cottage road) and 1004030 (forward road), and the secondary trunk detection sections are respectively 1001010 (forest road) and 1003006 (Tongfeng road). The acquisition time of the raw data ranged from 21 days 7/2014 to 22 days 7/2014, with a 5 minute data acquisition time interval. Of the collected data, data on day 7/month 21 in 2014 was used for model construction and parameter estimation, and data on day 7/month 22 in 2014 was used for predictive performance assessment.
The embodiment marks the original (horizontal) time series of the traffic speed of the target section as yt}. Performing first-order difference operation on the horizontal time sequence of the traffic speed of the target section, and performing original unstable time sequence { ytThe conversion into a stationary time series [ Delta y ]t}. An autoregressive moving average ARMA (p, q) model is constructed for a first-order difference time series of section traffic flow velocities obtained in 7, 21 days 2014, and the expression is as follows:
Figure BDA0001353068590000071
in the formula (1)
Figure BDA0001353068590000072
The first-order difference prediction value of the traffic flow speed of the target section in the time interval t is obtained; Δ yt-iA first-order difference observed value of the traffic flow speed of the target section in a time interval (t-i);tresidual terms for the traffic speed first order difference sequence in the time interval t,t-jresidual terms c, phi in time interval (t-j) for traffic speed first order difference sequencei、θjParameters to be estimated of the ARMA (p, q) model; p and q are the autoregressive order and the moving average order of the ARMA (p, q) model, respectively, byBayesian information criterion was determined and the results are given in table 1.
TABLE 1 autoregressive and moving average order of the target section ARMA (p, q) model
Figure BDA0001353068590000073
Figure BDA0001353068590000081
On the basis of determining the autoregressive and moving average orders of the ARMA (p, q) models of the target sections, the parameters of the ARMA (p, q) models of the first-order difference sequence mean value prediction of the traffic speed of the target sections are further estimated by adopting a least square method, and the results are shown in Table 2.
TABLE 2 target section ARMA (p, q) model parameter estimation
Figure BDA0001353068590000082
According to the result of the formula (1) and the ARMA (p, q) model parameter estimation result shown in the table 2, the average prediction results of the first-order difference sequence of the traffic speed of each target section in the time interval t can be calculated and obtained as follows:
section 1012016
Figure BDA0001353068590000091
Section 1004030
Figure BDA0001353068590000092
Section 1001010
Figure BDA0001353068590000093
Section 1003006
Figure BDA0001353068590000094
On the basis of completing the construction of ARMA (p, q) models and parameter estimation of all target sections, extracting residual sequences of the ARMA (p, q) models and constructing fGARCH (1, 1) models of the residual sequences, wherein the expression is as follows
Figure BDA0001353068590000095
The coefficients of the fganch (1, 1) model were estimated using maximum likelihood estimation, and the results are shown in table 3.
TABLE 3 target section fGARCH (1, 1) model parameter estimation
Figure BDA0001353068590000096
Figure BDA0001353068590000101
According to the formula (6) and the estimation result of the fgearch (1, 1) model parameters shown in table 3, the prediction results of the standard deviation of the residual error terms of the first-order difference sequence of the traffic speed of each target section in the time interval t can be calculated and obtained as follows:
section 1012016
Figure BDA0001353068590000102
Wherein f is: (t-1)＝|t-1-0.93|+0.44(t-1-0.93)
Section 1004030
Figure BDA0001353068590000103
Wherein f is: (t-1)＝|t-1-1.24|+0.82(t-1-1.24)
Section 1001010
Figure BDA0001353068590000111
Wherein f is: (t-1)＝|t-1-1.32|+0.77(t-1-1.32)
Section 1003006
Figure BDA0001353068590000112
Wherein f is: (t-1)＝|t-1-0.61|+0.64(t-1-0.61)
Obtaining the average value prediction result of the first-order difference of the traffic speed
Figure BDA0001353068590000116
And residual sequence standard deviation prediction value thereof
Figure BDA0001353068590000117
Given a significance level α of 0.05, that is, a confidence level of 95%, the present embodiment may calculate the prediction upper limit value of the first-order difference sequence of the traffic speeds within the time interval t to be 0.05
Figure BDA0001353068590000113
Lower limit value of
Figure BDA0001353068590000114
On the basis, the traffic speed prediction upper limit value of the target section in the time interval t is further calculated to be
Figure BDA0001353068590000115
Lower limit value of
Figure BDA0001353068590000121
Finally, the predicted average value of the traffic speed of the target section in the time interval t can be obtainedIs composed of
Figure BDA0001353068590000122
The prediction interval is
Figure BDA0001353068590000123
In the embodiment, the average confidence interval width ACL is used to evaluate the interval prediction performance of the traffic speed, and the expression is shown in formula (15).
Figure BDA0001353068590000124
In the formula (15), n is the number of samples; CLtPredicting a section width for the traffic speed within the time interval t, and
Figure BDA0001353068590000126
。
in order to compare with the traditional prediction method, the example simultaneously shows the interval prediction performance based on the standard GARCH (1, 1) model and the GJR-GARCH (1, 1) model. For the standard GARCH (1, 1) model, the model coefficient λ is 2, b is 0, and the other coefficients are estimated by the same method as the fgearch (1, 1) model; for the GJR-GARCH (1, 1) model, the model coefficient λ is 2, b is 0, and the other coefficients are estimated by the same method as in the fgearch (1, 1) model. In addition, in order to compare the prediction performances of different models in the busy traffic period and the non-busy traffic period, the case divides 6:30 AM-9: 30PM. in the evaluation period into the busy traffic period, and divides the other rest periods into the non-busy period. Table 4 gives the interval prediction performance of the standard GARCH (1, 1) model, GJR-GARCH (1, 1) model and fGARCH (1, 1) model.
TABLE 4 comparison of Interval predicted Performance for Standard GARCH (1, 1), GJR-GARCH (1, 1), fGARCH (1, 1) models
Figure BDA0001353068590000125
Figure BDA0001353068590000131
As can be seen from the results given in table 4, given the same confidence level, the width of the average prediction interval of the fganch (1, 1) model is smaller than the other two types of models, especially in the less busy traffic periods where volatility is more difficult to quantify. It can be seen that the dynamic interval short-time prediction of the traffic speed by adopting the fganch (1, 1) model can obtain better prediction reliability. In addition, the present example shows the predicted standard deviation of the traffic speed first-order difference sequence residual terms of the 4 target section standard GARCH (1, 1) models, GJR-GARCH (1, 1) models and fgearch (1, 1) models, which are shown in fig. 2 to 5. It can be intuitively seen from the figure that the predicted value of the standard deviation of the target section traffic speed first-order difference sequence residual error item based on the fganch (1, 1) model has small volatility on the whole, and is particularly reflected in the night time when the traffic is not busy.

Claims (2)

1. A short-time traffic speed dynamic interval prediction method comprises the following steps:
(10) acquiring a traffic speed time sequence: acquiring a target section traffic speed time sequence observed value on a road;
(20) stationary time series acquisition: converting the traffic speed time sequence into a stable time sequence through first-order difference operation;
(30) first order difference prediction value calculation: calculating a first-order difference predicted value of the traffic speed within each current time interval t according to the first-order difference time sequence prediction model of the traffic speed;
(40) and (3) calculating a predicted value of a standard deviation of a residual item: calculating a predicted value of a standard deviation of the residual term in each current time interval according to a differential prediction model of the comprehensive generalized autoregressive condition of the residual term;
(50) determining a traffic speed prediction interval of a target section: determining a traffic speed prediction interval of the target section in each time interval according to the traffic speed observed value in each previous time interval, the traffic speed first-order difference prediction value in each current time interval and the standard difference prediction value of the residual error item in each current time interval;
the step of (30) calculating the first-order difference prediction value specifically comprises the following steps:
according to the traffic speed first-order difference time series prediction model, making m equal to max (p, q), acquiring the first-order difference values of the traffic speed time series of the target section of the historical time interval (t-1), (t-2) and (t-m), calculating the traffic speed first-order difference predicted value in the current time interval t as,
Figure FDA0002606761800000011
in the formula,
Figure FDA0002606761800000012
is a first-order difference predicted value, delta y, of the target section traffic speed in the current time interval tt-iA first-order difference observed value of the target section traffic speed in a previous time interval (t-i) is obtained, and c is a constant term; p is the hysteresis order of the autoregressive process, q is the hysteresis order of the moving average process, phiiAnd thetajIs the autoregressive moving average ARMA (p, q) model coefficient,tresidual terms of the traffic speed first order difference sequence in the current time interval t,t-jresidual terms in the previous time interval (t-j) for a traffic speed first order difference sequence and assuming a seriestThe white noise process obeys 0-mean normal distribution;
the method is characterized in that the step (40) of calculating the standard deviation predicted value of the residual error item specifically comprises the following steps:
according to the different variance prediction model of the comprehensive generalized autoregressive condition of the residual terms, the predicted value of the standard deviation of the residual terms in the time interval t is calculated as
Figure FDA0002606761800000021
Namely, it is
Figure FDA0002606761800000022
In the formula,
f(t-1)＝|t-1-b|-c(t-1-b)，
the differential variance prediction model of the comprehensive generalized autoregressive condition of the residual error term is according to the sequence of the residual error termtThe resulting, comprehensive generalized autoregressive conditional variance fGARCH (1, 1) model with first-order autoregressive terms and first-order moving average terms,
Figure FDA0002606761800000023
wherein,tis the residual value of the first order difference time series of the traffic speed in the current time interval t,t-1is the residual value of the first order difference time series of the traffic speed in the previous time interval (t-1),
Figure FDA0002606761800000024
is the predicted value of the standard deviation of the residual error term in the current time interval t,
Figure FDA0002606761800000025
a sequence of residual terms being a predicted value of the standard deviation of the residual terms in the preceding time interval (t-1)tThe mean obedience is 0 and the standard deviation is sigmatNormal distribution of (2); z is a radical oftA white noise process that follows an independent standard normal distribution with a mean of 0 and a variance of 1; omega, beta and gamma are regression parameters; lambda is a Box-Cox transfer coefficient; b is an offset factor used for quantifying smaller traffic speed fluctuations; c is a rotation factor used for quantifying larger traffic speed fluctuation; omega, beta, gamma, lambda, b and c are all parameters to be estimated of the fGARCH (1, 1) model.
2. The prediction method according to claim 1, characterized in that the step of (50) determining the target section traffic speed prediction interval is specifically:
the section prediction value of the traffic speed in the current time interval t is
Figure FDA0002606761800000026
Wherein the traffic speed prediction upper limit value in the current time interval t is
Figure FDA0002606761800000031
The lower limit value of the traffic speed prediction in the current time interval t is
Figure FDA0002606761800000032
In the formula, yt-1Is the observed value of the traffic speed in the previous time interval (t-1),
Figure FDA0002606761800000033
is a traffic speed first-order difference predicted value in the current time interval t,
Figure FDA0002606761800000034
residual term standard deviation predicted value, z, within current time interval tα/2Is the upper alpha quantile of the standard normal distribution.
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