CN107230349B - A kind of online real-time short time traffic flow forecasting method - Google Patents
A kind of online real-time short time traffic flow forecasting method Download PDFInfo
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- G08G1/00—Traffic control systems for road vehicles
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Abstract
The present invention proposes a kind of online real-time Short-time Traffic Flow Forecasting Methods, the solution procedure of Lagrange multipliers vector in LS SVM models is simplified, it proposes and controls the addition of new data sample and the removal of legacy data sample using the movement of sliding time window, in sliding time window after data sample update, it only can be in the hope of Lagrange multiplier vector updated value, so as to complete the online updating of short-term traffic flow forecasting model by the linear operation of vector.This method can effectively shorten the time of prediction model online updating, improve the real-time of online short-time traffic flow forecast.
Description
Technical field
The present invention relates to a kind of Forecasting Methodologies of traffic flow, and in particular to a kind of online real-time based on LS-SVM technologies
Short time traffic flow forecasting method.
Background technology
Forecasting traffic flow is the key components of intelligent transportation system, has important research significance.Forecasting traffic flow
A kind of predictive research mainly carried out to the dynamical system being made of the arithmetic for real-time traffic flow time series of certain statistical interval.
The main study subject of forecasting traffic flow is that statistical interval is short-term traffic flow time series in 2 to 15 minutes, by above-mentioned short
When the traffic flow Force system that forms of Traffic Flow Time Series there is the feature of non-linear and non-stationary.At present, short-term traffic flow
Non-linear mainly includes the methods of gray system theory, neural network and support vector machines, wherein support vector machines
(Support Vector Machine, SVM) is by using structural risk minimization and introduces kernel method, effectively solves small
Sample, high-dimensional problem concerning study, and pass through the optimization problem that learning algorithm is converted into convex quadratic programming, efficiently solve office
Portion's extreme-value problem, due to above-mentioned advantage and complete Statistical Learning Theory basis and good Generalization Capability, SVM has been at present
It is widely used in prediction of short-term traffic volume field.In practical applications, short-term traffic flow time series are over time
It is gradually injected into prediction model, this just needs the arrival with new samples, and former prediction model real-time online is updated.Traditional
SVM prediction algorithms participate in all training samples to solve quadratic programming problem, when adding in new samples, need with all
Data re -training prediction model, the training effectiveness with the increase prediction model of sample size constantly decline.In contrast, exist
The SVM prediction algorithms of wire type can make full use of the learning outcome of back, learn without restarting, so as to subtract
The training time of prediction model when few new samples add in.
At present, common online SVM regression forecastings algorithm mostly will according to Karush Kuhn Tucker (KKT) condition
The sample point that training data is concentrated is divided into boundary supporting vector set, error supporting vector set and retains vector set three
Class, when training dataset updates, the KKT conditions that master mould is met are destroyed, and need iterative point-by-point number after judging update
According to the type for concentrating each sample point, and correct SVM according to migration situation of each sample point between three classes set and return mould
Type relevant parameter so that model meets KKT conditions again.Above-mentioned algorithm needs the increase of new sample point and the deletion of old sample point
To complete in two stages, each stage is required for being iterated model the amendment of formula, algorithm realize complicated and convergence without
Method is effectively ensured, and is difficult to apply in Practical Project, hence it is imperative that proposing a kind of more efficient online SVM predictions
Algorithm.
Invention content
For the above-mentioned prior art the problem of, the object of the present invention is to provide it is a kind of it is online in real time in short-term
Traffic flow forecasting method, prediction model repetition training, prediction model update calculation when overcoming conventional online short-time traffic flow forecast
The defects of computation complexity of method is high, realizes the online updating of short-term traffic flow forecasting model, and simplifies prediction model more
New algorithm under conditions of precision of prediction is not reduced, improves the real-time of online short-time traffic flow forecast.
In order to realize above-mentioned task, the present invention uses following technical scheme：
A kind of online real-time short time traffic flow forecasting method, includes the following steps：
Step 1 selectes the section for needing to carry out forecasting traffic flow, obtains the short-term traffic flow historical data of road section selected,
And build the short-term traffic flow historical data base of road section selected；
Step 2 according to the short-term traffic flow historical data of acquisition, determines the prediction period of short-time traffic flow forecast；
Step 3 according to the prediction period, determines the sample cycle of short-term traffic flow data；
Step 4 according to the sample cycle, determines the newer sliding time window length of on-line prediction time samples,
I.e. each on-line prediction when required traffic flow historical data quantity；
Step 5 carries out the initial predicted of short-term traffic flow
First, according to the length of sliding time window, initial short-term traffic flow sample data is selected, and form least square
The initial training data set of supporting vector machine model, i.e. LS-SVM models, the traffic flow historical data which concentrates are pressed
Time reverses, and is numbered according to the sequence of sampling instant；Then, institute is trained using the initial training data set
The LS-SVM models stated；Finally, initial forecasting traffic flow is carried out using trained most LS-SVM models；
Step 6 carries out the update of traffic flow historical data according to sliding time window
In short-term traffic flow historical data base, a new traffic flow data is obtained, according to adopting for the traffic flow data
The sample moment determines number of the data in sliding time window；Then, according to determining number, former sliding time window is deleted
New data are inserted into the position by the data of middle reference numeral, and such sliding time window just completes a data update；
Step 7 is updated the LS-SVM models, then carries out the short-time traffic flow forecast of a new round.
Further, the section short-term traffic flow historical data refers to section Short-Term Traffic Flow data, the data
By highway operation, administrative department obtains；Section short-term traffic flow historical data stores in chronological order, and data include data
Acquire date, moment and traffic flow magnitude.
Further, the prediction period described in step 2 is 5~15 minutes.
Further, in step 5, sliding time window is expressed as the data acquisition system shown in formula：
{(xi,yi) | i=1,2 ..., M, xi=i } (1)
In formula 1, xiSubscript i represent number of the traffic flow data in sliding time window, value range for 1 to
M, M are the length of sliding time window；xiValue be equal to its subscript i, i.e. xi=i；yiRepresent xth in sliding time windowiNumber hand over
Through-current capacity sampled value.
Further, in step 5, the LS-SVM models of structure are expressed as：
In above formula, M is sliding time window length；Parameter preset λ values are 1；Kernel function k (x, xi) using radial direction base
RBF kernel functions, aiIt is i-th of element of Lagrange multiplier vectors a, x is the number for the traffic flow data for it is expected prediction, and y is
The value of traffic flow that the number of prediction is x, wherein x values are more than M.
Further, in the formula (2), the calculation formula of Lagrange multiplier vectors a is：
A=(K+ λ2E+C-1I)-1Y (4)
In above formula, parameter preset λ values are 1, and regularisation parameter C values are all 1's matrix that 4, E is M × M ranks, and I is M × M
Rank unit matrix, K be M × M rank kernel matrixes, Y=(y1,y2,...,yM)TFor the traffic flow history in sliding time window
Data；
Enable H=K+ λ2E+C-1I, (λ ＞ 0, C ＞ 0), is known as core extended matrix by H.
Further, in step 6, number i' of the new traffic flow data in sliding time window is calculated using following
Formula：
I'=((n-1) mod N) * T+d (6)
In above formula, n represents that new traffic flow historical data is the sampled data of n-th day, and N is structure initial sliding time window
The traffic flow historical data of continuous N days chosen during mouth, T represent the sample cycle of traffic flow data, and the traffic flow that d represents new is gone through
The sampling instant number of history data.
Further, in step 7 to LS-SVM models be updated the specific steps are：
If the inverse matrix of core extended matrix H obtained in step 5 is expressed as R, then when a number occurs for sliding time window
After update, according to the number i' updated the data, after the calculating sliding time window data update of generation of formula 7
Lagrange multiplier vectors anew：
In formula 7, aoldRepresent the Lagrange multipliers obtained before time slip-window oral replacement vector；R(:, i') and it represents
The column vector being made of the i-th ' column element of matrix R；Represent newly to add in the friendship of sliding time window in this data update
Through-flow historical data sampled value；Represent the traffic flow historical data sampled value being replaced in this data update；
Lagrange multiplier vectors a is acquired by formula 7newAfterwards, then the LS-SVM prediction models of online updating can represent
For:
The present invention has following technical characterstic compared with prior art：
The present invention does not need to carry out the repetition training of LS-SVM prediction models when carrying out online short-time traffic flow forecast,
According only to newer traffic flow training dataset, LS-SVM prediction models are directly updated using simplified more new algorithm, are not being dropped
Under conditions of low precision of prediction, the real-time of online short-time traffic flow forecast is improved.It is pre- that the method for the present invention is suitable for traffic flow
It surveys, there is important application value in intelligent transportation system.
Description of the drawings
Fig. 1 is the flow chart of the method for the present invention；
Specific embodiment
Least square method supporting vector machine (Least Square-Support Vector Machine, LS-SVM) will be traditional
ε-loss function of SVM regression models is changed to quadratic loss function, and the inequality constraints of SVM model training samples is become
Formula constrains, and then the solution of SVM is converted into solution system of linear equations problem, while Lagrange multipliers from quadratic programming problem
Quantity also reduces half, therefore LS-SVM models are relatively suitble to line modeling problem.Meanwhile short-term traffic flow data belong to the period
Property non-stationary random series data, by making full use of the periodic feature of short-term traffic flow data, ensure predict prediction essence
Under conditions of degree, the solution procedure of Lagrange multipliers during on-line study can be further simplified, effectively reduces calculating again
Miscellaneous degree shortens the model online updating time, increases substantially the real-time of online short-time traffic flow forecast.
The detailed step of the present invention is described below：
Step 1 selectes the section for needing to carry out forecasting traffic flow, obtains the short-term traffic flow historical data of road section selected,
And build the short-term traffic flow historical data base of road section selected；
The section short-term traffic flow historical data refers to section Short-Term Traffic Flow data, which is transported by highway
Administrative department is sought to obtain；Section short-term traffic flow historical data stores in chronological order, data include data acquisition the date, when
It carves and the contents such as traffic flow magnitude；Build the short-term traffic flow historical data base of road section selected.
Step 2 according to the short-term traffic flow historical data of acquisition, determines the prediction period of short-time traffic flow forecast, that is, needs
Predict it is following how long interior traffic flow.The prediction period of short-time traffic flow forecast is usually 5 minutes to 15 minutes, this reality
It applies example and prediction period is set as 15 minutes.
Step 3 according to the prediction period, determines the sample cycle of short-term traffic flow data；
It is found by sample autocorrelation analysis, the sample cycle T of the short-term traffic flow data may be defined as in one day
Acquire the quantity of traffic flow data.The use of the sampling interval is the short-term traffic flow data of 15 minutes in the present embodiment, in one day
96 datas are acquired, then the sample cycle of short-term traffic flow data is 96.
Step 4 according to the sample cycle, determines the newer sliding time window length of on-line prediction time samples,
I.e. each on-line prediction when required traffic flow historical data quantity；
The sliding time window refers to carry out first time initial predicted and follow-up online single prediction in the present invention
When used short-term traffic flow data sample set；The length of the sliding time window refers to carry out in the present invention initial
The quantity of used short-term traffic flow data sample, sliding time window length quilt when prediction and follow-up online single prediction
The integral multiple of sample cycle T is appointed as, N*T can be expressed as, continuous number of days of the wherein N for used data sample, T is in short-term
The sample cycle of traffic flow data.The sample cycle of short-term traffic flow data is 96 in the present embodiment, selects the traffic of continuous 5 days
Historical data is flowed as sliding time window, then sliding time window length is 5*96=480.
Step 5 carries out the initial predicted of short-term traffic flow
First, according to the length of sliding time window, initial short-term traffic flow sample data is selected, and form least square
The initial training data set (i.e. sliding time window) of supporting vector machine model, i.e. LS-SVM models, what which concentrated
Traffic flow historical data temporally reverses, and is numbered according to the sequence of sampling instant；Then, using described initial
The training dataset training LS-SVM models；Finally, it is pre- using the initial traffic flow of trained most LS-SVM models progress
It surveys；
In the present embodiment, selecting the traffic flow historical data of continuous 5 days, sliding time window is long as sliding time window
Spend is 480.Traffic flow historical data in the sliding time window sorts simultaneously by the sequence of sampling instant and sample cycle
It is numbered, for example, the traffic flow historical data number at the 1st moment of the 1st sample cycle is 1, the of the 1st sample cycle
The traffic flow historical data number at 2 moment is 2 ... ..., the traffic flow historical data number at the 1st moment of the 2nd sample cycle
It is 97 ... ..., the traffic flow historical data number at the 96th moment of the 5th sample cycle is 480 etc..
Sliding time window is expressed as the data acquisition system shown in formula：
{(xi,yi) | i=1,2 ..., M, xi=i } (1)
In formula 1, xiSubscript i represent number of the traffic flow data in sliding time window, value range for 1 to
M, M are the length of sliding time window；In the present embodiment, M 480；xiValue be equal to its subscript i, i.e. xi=i；yiIt represents to slide
Xth in time windowiNumber magnitude of traffic flow sampled value.
The LS-SVM models of structure are expressed as：
In above formula, M is sliding time window length；Preferably, parameter preset λ values are 1；Kernel function k (x, xi) adopt
With radial direction base RBF kernel functions, aiIt is i-th of element of Lagrange multiplier vectors a, x is the traffic flow data for it is expected prediction
Number, y are the value of traffic flow that the number of prediction is x, and wherein x values are more than M, and in the present embodiment, x, can be as the following formula more than 480
Value：
X=480+l (3)
In equation 3, in intraday moment serial number, the present embodiment, l takes the traffic flow data that l represents it is expected prediction
It is worth the positive integer for 1 to 96.
In formula 2, Lagrange multiplier vectors a is the unknown parameter of LS-SVM prediction models, when needing according to sliding
Between traffic flow historical data in window be calculated.The calculating process of Lagrange multiplier vectors a is exactly LS-SVM prediction moulds
The training process of type.Lagrange multiplier vectors a is calculated by following formula：
A=(K+ λ2E+C-1I)-1Y (4)
In formula 4, preferably, parameter preset λ values are 1, regularisation parameter C values are 4；E is complete the 1 of M × M ranks
Matrix, I are M × M rank unit matrixs, and K is M × M rank kernel matrixes, wherein the element of the i-th row, jth row can be expressed as k (xi,
xj), k (xi,xj) it is radial direction base RBF kernel functions；Y=(y1,y2,...,yM)TFor the traffic flow history number in sliding time window
According to a=(a1,a2,...,aM)TFor Lagrange multipliers vector to be asked.
Enable H=K+ λ2E+C-1I, (λ ＞ 0, C ＞ 0), then formula 4 is reduced to 5 formula of formula, wherein H is known as core extended matrix
A=H-1Y (5)
In the present embodiment, calculated according to selected sliding time window and with reference to formula 5, you can acquire
Lagrange multiplier vector a, and then forecasting traffic flow can be proceeded by by formula 2 and formula 3.While it can be found that
If data update has occurred in sliding time window, it is necessary to recalculate core extended matrix H and ask its inverse matrix, Ran Houzai
New Lagrange multipliers vector is calculated by formula 5, wherein the calculating process of matrix inversion is complicated and elapsed time is more,
The present invention simplifies the solution procedure of Lagrange multipliers vector in subsequent step, occurs in sliding time window
In the case of data update, it is no longer necessary to calculate the inverse matrix of core extended matrix H.
Step 6 carries out the update of traffic flow historical data according to sliding time window
In short-term traffic flow historical data base, a new traffic flow data is obtained, according to adopting for the traffic flow data
The sample moment determines number of the data in sliding time window；Then, according to determining number, former sliding time window is deleted
New data are inserted into the position by the data of middle reference numeral, and such sliding time window just completes a data update；
Number i' of the new traffic flow data in sliding time window is calculated using the following formula：
I'=((n-1) mod N) * T+d (6)
In above formula, n represents that new traffic flow historical data is the sampled data of n-th day, and the value of n is just whole more than N
Number；N is to build the traffic flow historical data of continuous N days chosen during initial sliding time window, in the present embodiment N=5, is calculated
Son (n-1) mod N expressions rem to n-1 using N as mould；T represents the sample cycle of traffic flow data, in the present embodiment T=
96；D represents the sampling instant number of new traffic flow historical data, in the present embodiment d=1,2 ..., 96.For example, the 6th day
Number i'=2 of the traffic flow historical data at the 2nd moment in sliding time window, the traffic flow history at the 9th day the 30th moment
Number i'=318 of the data in sliding time window.
Step 7 is updated the LS-SVM models, then carries out the short-time traffic flow forecast of a new round.
Specifically, in the present embodiment, the LS-SVM prediction model online updating methods perform in the steps below：
Step 7.1, if the inverse matrix of core extended matrix H obtained in step 5 is expressed as R, then when sliding time window is sent out
After a raw data update, according to the number i' updated the data, calculate sliding time window by formula 7 and a data update occurs
Lagrange multipliers vector a afterwardsnew：
In formula 7, aoldRepresent the Lagrange multipliers obtained before time slip-window oral replacement vector；R(:, i') and it represents
The column vector being made of the i-th ' column element of matrix R；Represent newly to add in the traffic of sliding time window in this data update
Flow historical data sampled value；Represent the traffic flow historical data sampled value being replaced in this data update.
Step 7.2, Lagrange multiplier vectors a is acquired by formula 7newAfterwards, then LS-SVM prediction models of online updating
It is represented by：
Meaning of parameters in above formula is the same.
Step 7.3, new forecasting traffic flow is carried out according to the LS-SVM prediction models after formula 9 i.e. online updating；
Step 7.4, if necessary to update traffic flow historical data, then return to step 6 continues, and otherwise continues with public affairs
Formula 9 carries out forecasting traffic flow.
Forecasting traffic flow is the key components of intelligent transportation system.Relative to traditional traffic flow forecasting method,
Wire type traffic flow forecasting method mainly has many advantages, for example, prediction mould can be adjusted with the update dynamic of gathered data
Type is to improve precision of prediction；Existing learning outcome can be made full use of to effectively reduce the renewal time of prediction model.However,
In existing online traffic flow forecasting method, it is complete that the increase of new sample point and the deletion of old sample point are divided into two stages
Into each stage is required for being iterated model the amendment of formula, and algorithm realizes that complicated and convergence can not be effectively ensured, in reality
It is difficult to apply in the engineering of border.In view of the above-mentioned problems, the present invention proposes a kind of efficient online Short-time Traffic Flow Forecasting Methods,
The solution procedure of Lagrange multipliers vector in LS-SVM models is simplified, new sample is controlled using sliding time window
This addition and the removal of old sample, it is only necessary to can be acquired by the linear operation of vector and be drawn by the update of training sample set
The Lagrange multipliers vector to change, and then the time of prediction model online updating is shortened, improve line short-term traffic flow
The real-time of prediction.The method of the present invention is when carrying out online short-time traffic flow forecast, with faster training effectiveness and more
The short model training time.
Claims (8)
1. a kind of online real-time short time traffic flow forecasting method, which is characterized in that include the following steps：
Step 1 selectes the section for needing to carry out forecasting traffic flow, obtains the short-term traffic flow historical data of road section selected, and structure
Build the short-term traffic flow historical data base of road section selected；
Step 2 according to the short-term traffic flow historical data of acquisition, determines the prediction period of short-time traffic flow forecast；
Step 3 according to the prediction period, determines the sample cycle of short-term traffic flow data；
Often step 4 according to the sample cycle, determines the newer sliding time window length of on-line prediction time samples, i.e.,
The quantity of required traffic flow historical data during secondary on-line prediction；
Step 5 carries out the initial predicted of short-term traffic flow
First, according to the length of sliding time window, initial short-term traffic flow sample data is selected, and forms least square support
The initial training data set of vector machine model, i.e. LS-SVM models, the traffic flow historical data which concentrates is temporally
It reverses, and is numbered according to the sequence of sampling instant；Then, it is described using described initial training data set training
LS-SVM models；Finally, initial forecasting traffic flow is carried out using trained most LS-SVM models；
Step 6 carries out the update of traffic flow historical data according to sliding time window
In short-term traffic flow historical data base, a new traffic flow data is obtained, during according to the sampling of the traffic flow data
It carves and determines number of the data in sliding time window；Then, according to determining number, it is right in former sliding time window to delete
New data are inserted into the position by the data that should be numbered, and such sliding time window just completes a data update；
Step 7 is updated the LS-SVM models, then carries out the short-time traffic flow forecast of a new round.
2. online real-time short time traffic flow forecasting method as described in claim 1, which is characterized in that the section is short
When traffic flow historical data refer to section Short-Term Traffic Flow data, which is obtained by highway operation administrative department；Section
Short-term traffic flow historical data stores in chronological order, and data include data acquisition date, moment and traffic flow magnitude.
3. online real-time short time traffic flow forecasting method as described in claim 1, which is characterized in that described in step 2
Prediction period be 5~15 minutes.
4. online real-time short time traffic flow forecasting method as described in claim 1, which is characterized in that sliding in step 5
Dynamic time window is expressed as the data acquisition system shown in formula：
{(xi,yi) | i=1,2 ..., M, xi=i } (1)
In formula 1, xiSubscript i represent number of the traffic flow data in sliding time window, value range is 1 to M, and M is
The length of sliding time window；xiValue be equal to its subscript i, i.e. xi=i；yiRepresent xth in sliding time windowiNumber traffic flow
Measure sampled value.
5. online real-time short time traffic flow forecasting method as claimed in claim 2, which is characterized in that in step 5, structure
The LS-SVM models built are expressed as：
In above formula, M is sliding time window length；Parameter preset λ values are 1；Kernel function k (x, xi) using radial direction base RBF core letters
Number, aiIt is i-th of element of Lagrange multiplier vectors a, x is the number for the traffic flow data for it is expected prediction, and y is the volume of prediction
Number for x traffic flow value, wherein x values be more than M.
6. online real-time short time traffic flow forecasting method as claimed in claim 5, which is characterized in that the formula
(2) in, the calculation formula of Lagrange multiplier vectors a is：
A=(K+ λ2E+C-1I)-1Y (4)
In above formula, parameter preset λ values are 1, and regularisation parameter C values are all 1's matrix that 4, E is M × M ranks, and I is single for M × M ranks
Bit matrix, K be M × M rank kernel matrixes, Y=(y1,y2,...,yM)TFor the traffic flow historical data in sliding time window；
Enable H=K+ λ2E+C-1I, (λ ＞ 0, C ＞ 0), is known as core extended matrix by H.
7. online real-time short time traffic flow forecasting method as described in claim 1, which is characterized in that in step 6, meter
Number i' of the new traffic flow data in sliding time window uses the following formula：
I'=((n-1) mod N) * T+d (6)
In above formula, n represents that new traffic flow historical data is the sampled data of n-th day, when N is structure initial sliding time window
The traffic flow historical data of continuous N days chosen, T represent the sample cycle of traffic flow data, and d represents new traffic flow history number
According to sampling instant number.
8. online real-time short time traffic flow forecasting method as claimed in claim 6, which is characterized in that right in step 7
LS-SVM models be updated the specific steps are：
If the inverse matrix of core extended matrix H obtained in step 5 is expressed as R, then when a data occur for sliding time window more
After new, according to the number i' updated the data, calculate Lagrange after a data update occurs for sliding time window by formula 7 and multiply
Subvector anew：
In formula 7, aoldRepresent the Lagrange multipliers obtained before time slip-window oral replacement vector；R(:, i') and it represents by square
The column vector that the i-th ' column element of battle array R is formed；Represent newly to add in the traffic flow of sliding time window in this data update
Historical data sampled value；Represent the traffic flow historical data sampled value being replaced in this data update；
Lagrange multiplier vectors a is acquired by formula 7newAfterwards, then the LS-SVM prediction models of online updating are represented by：
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| CN110517494A (en) * | 2019-09-03 | 2019-11-29 | 中国科学院自动化研究所 | Forecasting traffic flow model, prediction technique, system, device based on integrated study |
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