CN107293118B - A short-term prediction method for traffic speed dynamic interval - Google Patents

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

A short-term prediction method for traffic speed dynamic interval

technical field

The invention belongs to the technical field of short-time prediction of traffic flow, in particular to a short-time prediction method for dynamic interval of traffic speed with high reliability.

Background technique

Traffic flow speed is one of the important technical indicators of road traffic operation, management and control. Accurate and reliable short-term prediction of traffic speed has become an important research content in urban intelligent transportation systems such as route guidance and active traffic control.

A large number of researches have been carried out on the short-term prediction technology of road cross-section traffic speed at home and abroad. Prediction methods based on statistical models and artificial intelligence technologies are constantly being proposed, and the accuracy of predictions has also been continuously improved.

However, most of the researches only carry out the modeling and evaluation of prediction methods for the first-order moment level sequence value of traffic speed, ignoring the fluctuation characteristics of the second-order moment of traffic flow speed, and it is difficult to effectively quantify the reliability of traffic speed prediction. Although a few studies have proposed to model the volatility of the second-order moment of traffic speed, most of the existing methods use a model with defined parameters, which greatly limits the description of the dynamic structure of the second-order moment of traffic speed.

In a word, the problem existing in the prior art is that the reliability of short-term prediction of traffic speed is low.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a short-term prediction method of traffic speed dynamic interval with high reliability.

The technical solution that realizes the purpose of the present invention is:

A short-term prediction method for a traffic speed dynamic interval, comprising the following steps:

(10) Acquisition of traffic speed time series: obtain the observation value of traffic speed time series of the target section on the road;

(20) Stationary time series acquisition: The traffic speed time series is transformed into a stationary time series through the first-order difference operation;

(30) Calculation of first-order difference predicted value: According to the first-order difference time series prediction model of traffic speed, calculate the first-order difference predicted value of traffic speed in each current time interval t;

(40) Calculation of the standard deviation prediction value of the residual item: According to the residual item synthesizing the generalized autoregressive conditional heteroskedasticity prediction model, the predicted value of the residual item standard deviation in each current time interval t is calculated;

(50) Determination of the traffic speed prediction interval of the target section: according to the observed traffic speed in each previous time interval (t-1), the first-order difference prediction value of traffic speed in each current time interval t, and the residual item of each current time interval The standard deviation prediction value is used to determine the traffic speed prediction interval of the target section within each time interval t.

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

High reliability. The invention further extracts and quantifies the fluctuation characteristics of the second-order moment of the traffic speed on the basis of the construction of the short-term prediction model of the first-order moment level sequence of the traffic speed of the target section of the road, that is, the conditional heteroscedasticity is constructed for the second-order moment of the residual sequence. The prediction model realizes the short-term prediction of the dynamic range of traffic speed by predicting the dynamic standard deviation of the second-order moment, which further improves the reliability of the short-term prediction of the traffic speed of the target section.

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

Description of drawings

Fig. 1 is the main flow chart of the short-term prediction method of the traffic speed dynamic interval according to the present invention.

FIG. 2 is a comparison chart of the standard deviation prediction results of the residual item of the first-order difference sequence of traffic speed based on the standard GARCH(1,1), GJR-GARCH(1,1), and fGARCH(1,1) models of section No. 1012016 of the embodiment.

Figure 3 is a comparison chart of the standard deviation prediction results of the first-order difference sequence residual items of traffic speed based on the standard GARCH(1,1), GJR-GARCH(1,1), and fGARCH(1,1) models of section No. 1004030 of the embodiment.

Figure 4 is a comparison chart of the standard deviation prediction results of the residual term of the first-order difference sequence of traffic speed based on the standard GARCH(1,1), GJR-GARCH(1,1), and fGARCH(1,1) models of section No. 1001010 of the embodiment.

Figure 5 is a comparison chart of the standard deviation prediction results of the residual term of the first-order difference sequence of traffic speed based on the standard GARCH(1,1), GJR-GARCH(1,1), and fGARCH(1,1) models of section No. 1003006 of the embodiment.

Detailed ways

As shown in Fig. 1, the short-term prediction method of traffic speed dynamic interval of the present invention includes the following steps:

(10) Acquisition of traffic speed time series: obtain the observation value of traffic speed time series of the target section on the road;

The traffic speed data collected from the target section are continuous time series data with equal time intervals of 5 minutes, and the original time series is not stationary.

(20) Stationary time series acquisition: The traffic speed time series is transformed into a stationary time series through the first-order difference operation;

(30) Calculation of first-order difference predicted value: According to the first-order difference time series prediction model of traffic speed, calculate the first-order difference predicted value of traffic speed in each current time interval t;

The step of (30) first-order difference prediction value calculation is specifically:

According to the first-order difference time series prediction model of traffic speed, let m=max(p, q), obtain the historical time interval (t-1), (t-2), ..., until the target section traffic of (t-m) The first-order difference value of the speed time series, the first-order difference prediction value of the traffic speed in the current time interval t is calculated as,

为目标断面交通速度在当前时间间隔t内的一阶差分预测值，Δy_t-i为目标断面交通速度在前一时间间隔(t-i)内的一阶差分观测值，c为常数项；p为自回归过程的滞后阶数，q为移动平均过程的滞后阶数，φ_i和θ_j为自回归移动平均ARMA(p，q)模型系数，ε_t为交通速度一阶差分序列在当前时间间隔t内的残差项，ε_t-j为交通速度一阶差分序列在前一时间间隔(t-j)内的残差项，并且假设系列{ε_t}为服从0均值正态分布的白噪声过程。In the formula,

is the first-order difference prediction value of the target section traffic speed in the current time interval t, Δy _ti is the first-order difference observation value of the target section traffic speed in the previous time interval (ti), c is a constant term; p is the autoregressive The lag order of the process, q is the lag order of the moving average process, φ _i and θ _j are the autoregressive moving average ARMA(p, q) model coefficients, ε _t is the traffic speed first-order difference sequence in the current time interval t The residual term of , ε _tj is the residual term of the first-order difference series of traffic speed in the previous time interval (tj), and the series {ε _t } is assumed to be a white noise process obeying a normal distribution with 0 mean.

The autoregressive order p and moving average order q of the ARMA(p, q) model are determined by the Bayesian information criterion; the constant term c and the model coefficients φ _i and θ _j are estimated by the least squares method.

(40) Calculation of the standard deviation prediction value of the residual item: According to the residual item synthesizing the generalized autoregressive conditional heteroskedasticity prediction model, the predicted value of the residual item standard deviation in each current time interval t is calculated;

The step of (40) calculating the predicted value of the residual item standard deviation is specifically: synthesizing the generalized autoregressive conditional heteroskedasticity prediction model according to the residual item, calculating the predicted value of the residual item standard deviation within the time interval t as:

which is

In the formula,

f(ε _t-1 )=|ε _t-1 -b|-c(ε _t-1 -b),

The residual term comprehensive generalized autoregressive conditional heteroscedasticity prediction model is, according to the residual term sequence {ε _t }, the comprehensive generalized autoregressive conditional heteroscedasticity fGARCH (1 , 1) Model,

为当前时间间隔t内残差项标准差的预测值，

为前一时间间隔(t-1)内残差项标准差的预测值,残差项序列{ε_t}为服从均值为0、标准差为σ_t的正态分布；z_t为服从均值为0、方差为1的独立标准正态分布的白噪声过程；ω、β、γ为回归参数；λ为Box-Cox转移系数；b为偏移因子，用于量化较小的交通速度波动；c为旋转因子，用于量化较大的交通速度波动；ω、β、γ、λ、b、c均为fGARCH(1，1)模型的待估参数。Among them, ε _t is the residual value of the first-order difference time series of traffic speed in the current time interval t, ε _t-1 is the residual value of the first-order difference time series of traffic speed in the previous time interval (t-1),

is the predicted value of the standard deviation of the residual term in the current time interval t,

is the predicted value of the standard deviation of the residual item in the previous time interval (t-1), the residual item sequence {ε _t } is a normal distribution obeying the mean value of 0 and the standard deviation is σ _t ; z _t is obeying the mean value of 0. White noise process of independent standard normal distribution with variance 1; ω, β, γ are regression parameters; λ is Box-Cox transfer coefficient; b is offset factor, used to quantify small traffic speed fluctuations; c is a rotation factor, which is used to quantify large fluctuations in traffic speed; ω, β, γ, λ, b, and c are all parameters to be estimated in the fGARCH(1, 1) model.

The parameters to be estimated ω, β, γ, λ, b, and c of the fGARCH(1, 1) model are estimated by the maximum likelihood method.

(50) Determination of the traffic speed prediction interval of the target section: according to the observed traffic speed in each previous time interval (t-1), the first-order difference prediction value of traffic speed in each current time interval t, and the residual item of each current time interval The standard deviation prediction value is used to determine the traffic speed prediction interval of the target section within each time interval t.

The step of (50) determining the traffic speed prediction interval of the target section is specifically:

The interval prediction of traffic speed in the previous time interval t is

Among them, the upper limit of traffic speed prediction in the current time interval t is

The lower limit of traffic speed prediction in the current time interval t is

为当前时间间隔t内交通速度一阶差分预测值，

当前时间间隔t内where y _t-1 is the observed traffic speed in the previous time interval (t-1),

is the first-order difference prediction value of traffic speed in the current time interval t,

within the current time interval t

Residual term standard deviation predicted value, z _α/2 is the upper α quantile of the standard normal distribution.

The use process of the present invention is described in detail below with specific examples.

In this embodiment, the data used are actually collected time series of traffic speeds of two sections on the main road and the secondary road in the central urban area of Kunshan. The inspection section numbers of the main road are 1012016 (Bolu Road) and 1004030 (Qianjin Road), and the inspection section numbers of the secondary roads are 1001010 (Xiaolin Road) and 1003006 (Tongfeng Road). The collection time range of raw data is from July 21, 2014 to July 22, 2014, and the data collection time interval is 5 minutes. Among the collected data, the data on July 21, 2014 was used for model construction and parameter estimation, and the data on July 22, 2014 was used for prediction performance evaluation.

This embodiment marks the original (horizontal) time series of traffic speeds of the target section as {y _t }. The first-order difference operation is performed on the horizontal time series of the traffic speed of the target section, and the original non-stationary time series {y _t } is transformed into a stationary time series {Δy _t }. An autoregressive moving average ARMA(p, q) model is constructed for the first-order difference time series of cross-section traffic flow velocity obtained on July 21, 2014, and the expression is as follows:

为目标断面交通流速度在时间间隔t内的一阶差分预测值；Δy_t-i为目标断面交通流速度在时间间隔(t-i)内的一阶差分观测值；ε_t为交通速度一阶差分序列在时间间隔t内的残差项，ε_t-j为交通速度一阶差分序列在时间间隔(t-j)内的残差项c、φ_i、θ_j为ARMA(p，q)模型的待估参数；p和q为分别为ARMA(p，q)模型的自回归阶数和移动平均阶数，通过贝叶斯信息准则确定，其结果在表1中给出。In formula (1)

is the first-order difference prediction value of the traffic flow velocity of the target section within the time interval t; Δy _ti is the first-order difference observation value of the traffic flow velocity of the target section within the time interval (ti); ε _t is the first-order difference sequence of the traffic speed at Residual items in the time interval t, ε _tj is the residual items of the traffic speed first-order difference sequence in the time interval (tj) c, φ _i , θ _j are the parameters to be estimated in the ARMA(p, q) model; p and q are the autoregressive order and moving average order of the ARMA(p, q) model, respectively, determined by the Bayesian information criterion, and the results are given in Table 1.

Table 1 Autoregressive and moving average orders of the target section ARMA(p, q) model

On the basis of determining the autoregression and moving average order of the ARMA(p, q) model for each target section, the least squares method is further used to predict the parameters of the ARMA(p, q) model for the mean value of the first-order difference series of traffic speeds at each target section. Estimated and the results are shown in Table 2.

Table 2 Parameter estimation of the ARMA(p, q) model for the target section

According to the results of formula (1) and the parameter estimation results of the ARMA(p, q) model shown in Table 2, the mean prediction results of the first-order difference sequences of traffic speeds of each target section within the time interval t can be calculated as follows:

Section 1012016

Section 1004030

Section 1001010

Section 1003006

After completing the construction of the ARMA(p, q) model and parameter estimation of each target section, the residual sequence of the ARMA(p, q) model is extracted, and the fGARCH(1, 1) model of the residual sequence is constructed, and the expression is as follows

The maximum likelihood estimation method is used to estimate the fGARCH(1,1) model coefficients, and the results are shown in Table 3.

Table 3. Parameter estimation of the fGARCH(1, 1) model of the target section

According to formula (6) and the fGARCH (1, 1) model parameter estimation results shown in Table 3, the standard deviation prediction results of the first-order difference sequence residual items of the traffic speed of each target section within the time interval t can be calculated as follows:

Section 1012016

Among them, f(ε _t-1 )=|ε _t-1 -0.93|+0.44(ε _t-1 -0.93)

Section 1004030

Among them, f(ε _t-1 )=|ε _t-1 -1.24|+0.82(ε _t-1 -1.24)

Section 1001010

Among them, f(ε _t-1 )=|ε _t-1 -1.32|+0.77(ε _t-1 -1.32)

Section 1003006

Among them, f(ε _t-1 )=|ε _t-1 -0.61|+0.64(ε _t-1 -0.61)

及其残差序列标准差预测值

的条件下，本实施例给定显著性水平α＝0.05，即指定95％的置信水平时，可计算获得时间间隔t内交通速度一阶差分序列的预测上限值为After obtaining the mean prediction result of the first-order difference of the traffic speed

and its residual series standard deviation predicted value

Under the conditions of the given significance level α=0.05 in this embodiment, that is, when the confidence level of 95% is specified, the upper limit of the prediction of the first-order difference sequence of traffic speeds in the time interval t can be calculated and obtained as

The lower limit is

On this basis, the upper limit of the traffic speed prediction of the target section within the time interval t is further calculated as

The lower limit is

预测区间为

Finally, the predicted mean traffic speed of the target section within the time interval t can be obtained as

The prediction interval is

In this 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).

。In formula (15), n is the number of samples; CL _t is the width of the traffic speed prediction interval within the time interval t, and

.

In order to compare with traditional forecasting methods, the interval forecasting performance based on standard GARCH(1,1) model and GJR-GARCH(1,1) model is presented in this case. For the standard GARCH(1,1) model, the model coefficients λ=2, b=c=0, and the estimation methods of other coefficients are the same as the fGARCH(1,1) model; for the GJR-GARCH(1,1) model, the In other words, its model coefficient λ=2, b=0, and the estimation method of other coefficients is the same as the fGARCH(1, 1) model. In addition, in order to compare the prediction performance of different models during peak traffic hours and non-peak traffic hours, this case divides the evaluation period from 6:30AM to 9:30PM. Table 4 presents the interval prediction performance of standard GARCH(1,1) model, GJR-GARCH(1,1) model and fGARCH(1,1) model.

Table 4 Standard GARCH(1,1), GJR-GARCH(1,1), fGARCH(1,1) model interval prediction performance comparison

From the results given in Table 4, it can be seen that, given the same confidence level, the width of the average prediction interval of the fGARCH(1, 1) model is smaller than that of the other two models, especially when the volatility is more difficult to quantify. During non-peak traffic hours. It can be seen that using the fGARCH(1, 1) model for the short-term prediction of the dynamic interval of traffic speed can obtain better prediction reliability. In addition, this case gives the prediction of the residuals of the first-order difference sequence of traffic speed for the above four target sections standard GARCH(1,1) model, GJR-GARCH(1,1) model and fGARCH(1,1) model Standard deviation, see Figures 2 to 5. It can be seen intuitively from the figure that the predicted value of the standard deviation of the residual term of the first-order difference sequence of the traffic speed of the target section based on the fGARCH(1, 1) model has small fluctuations in general, especially when the traffic is not busy at night. time period.

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,

in the formula,

is a first-order difference predicted value, delta y, of the target section traffic speed in the current time interval t_t-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, phi_iAnd theta_jIs 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 series_tThe 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

Namely, it is

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 term_tThe resulting, comprehensive generalized autoregressive conditional variance fGARCH (1, 1) model with first-order autoregressive terms and first-order moving average terms,

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),

is the predicted value of the standard deviation of the residual error term in the current time interval t,

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 sigma_tNormal distribution of (2); z is a radical of_tA 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

Wherein the traffic speed prediction upper limit value in the current time interval t is

The lower limit value of the traffic speed prediction in the current time interval t is

In the formula, y_t-1Is the observed value of the traffic speed in the previous time interval (t-1),

is a traffic speed first-order difference predicted value in the current time interval t,

residual term standard deviation predicted value, z, within current time interval t_α/2Is the upper alpha quantile of the standard normal distribution.

Images