CN114822025B - Traffic flow combined prediction method - Google Patents

Traffic flow combined prediction method Download PDF

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CN114822025B
CN114822025B CN202210417752.2A CN202210417752A CN114822025B CN 114822025 B CN114822025 B CN 114822025B CN 202210417752 A CN202210417752 A CN 202210417752A CN 114822025 B CN114822025 B CN 114822025B
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CN114822025A (en
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殷礼胜
吴洋洋
刘攀
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Hefei University of Technology
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Abstract

The invention discloses a traffic flow combined prediction method, which comprises the following steps: 1. decomposing the traffic flow time sequence of the prediction node and the first-order neighborhood node thereof into a series of relatively stable high-low frequency component sequences by using a traffic flow variation modal decomposition algorithm improved based on mutual information entropy; 2. using a traffic flow spatial correlation model based on the graph attention network, taking each decomposed component sequence as characteristic input of the graph attention network, and weighting each component sequence by using an attention coefficient and then outputting the weighted component sequence; 3. and (3) using a gated cycle unit network-based traffic flow time dependency model, using the weighted component sequence of each node as the characteristic input of the gated cycle unit network, iteratively training each parameter of the model to be optimal by an improved RMSProp traffic flow optimization algorithm, predicting each component by using the model, and superposing and summing the predicted values to obtain a final prediction result. The invention can effectively predict the traffic flow and improve the prediction precision.

Description

Traffic flow combined prediction method
Technical Field
The invention relates to a traffic flow combination prediction method, in particular to a traffic flow combination prediction method based on improved variation modal decomposition, a graph attention network and a gated circulation unit network. Belonging to the intelligent traffic prediction field.
Background
With the development of urbanization and digitization, an intelligent traffic system is constructed, travel services with cooperation of automatic driving and vehicle roads are developed, and the popularization of road intelligent management and traffic signal linkage becomes a key field. And accurate and timely traffic flow prediction is one of the bases for realizing the management and control of the intelligent traffic system.
The current traffic flow prediction methods are mainly summarized into two types: the method is characterized in that the method comprises the following steps that firstly, traditional statistical learning methods such as moving average autoregression, support vector regression, kalman filtering, hidden Markov models and the like are mostly based on the assumption of stability of a time sequence and need to rely on complex manual feature processing, and a traffic flow time sequence belongs to a nonlinear non-stable sequence; and the other is a feedforward neural network method, such as a multilayer perceptron, a radial basis function neural network and the like, which can only simply simulate the nonlinear change in traffic data, cannot accurately and effectively capture the short-term and long-term time dependence of the traffic data, has low prediction precision, and has slow training iteration speed when processing a large amount of traffic flow data. However, the above two types of prediction methods do not consider the influence of the spatial correlation of the traffic flow in the real complex traffic network on the prediction precision, and the model method has limited expression capability.
Based on the analysis, the traffic flow has the characteristics of complex non-stationarity, spatial correlation, time dependence and the like, and the single prediction model and the single prediction method have the limitations in the aspects of specific application conditions, prediction accuracy and the like.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a traffic flow combination prediction method, so that the characteristics of the complex non-stationarity, the spatial correlation and the time dependence of the traffic flow are considered, and the prediction precision and the speed of the traffic flow can be effectively improved.
In order to solve the technical problems, the invention adopts the following technical scheme:
the invention relates to a traffic flow combination prediction method which is characterized by comprising the following steps:
step 1: the traffic flow variation modal decomposition is improved based on mutual information entropy:
step 1.1: the mutual information entropy I (Y; Z) is defined by formula (1):
I(Y；Z)＝H(Y)+H(Z)-H(Y,Z) (1)
in formula (1): y represents a set of traffic flow time series, and Y = (Y) 1 ,y 2 ,···,y i ,···,y N )，y i Represents the ith traffic flow data, Z represents another group of traffic flow time series, and Z = (Z) 1 ,z 2 ,···,z i ,···,z N )，z i Represents the ithTraffic flow data, N is the time series length; h (-) represents the entropy of the edge information, and H (-) represents the entropy of the joint information; p (-) represents an edge probability density function, p (-) represents a joint probability density function, and has:
Figure GDA0003700576320000021
in formula (2): p (y) i ) And p (z) i ) Respectively represent the ith traffic flow data y i And z i The edge probability density function of (a); p (y) i ,z i ) Indicating the ith traffic flow data y i And z i A joint probability density function of (a);
step 1.2: an augmented Lagrangian objective function L (u) is defined using equation (3) k ,ω k ,λ)：
Figure GDA0003700576320000022
In formula (3): u. of k (t) represents the k-th modal component of the traffic flow time series in the time domain t, and u k (t)＝A k (t)cos(φ k (t)), wherein A k (t) denotes the k-th modal component u k (t) amplitude in the time domain t, [ phi ] k (t) denotes the k-th modal component u k (t) instantaneous phase in the time domain t; omega k (t) denotes the k-th modal component u k (t) instantaneous frequency in the time domain t, and ω k (t)＝φ k ' (t); λ (t) represents the lagrange multiplier in the time domain t; alpha represents a secondary penalty term;
Figure GDA0003700576320000028
represents a partial differential over the time domain t; δ (t) represents a unit impulse function in the time domain t; j represents an imaginary number; omega k Representing the k-th modal component u in the time domain t k (t) transforming to a center frequency in the frequency domain ω; * Representing a convolution operator; f (t) represents a traffic flow time sequence Y or Z in a time domain t;
step 1.3: defining n as the number of search iterations and initializing to n =0;
step 1.4: initializing the kth modal component of the n +1 th iteration of the traffic flow time sequence Y or Z in the time domain t
Figure GDA0003700576320000023
Is greater than or equal to>
Figure GDA0003700576320000024
Non-negative phase/phase->
Figure GDA0003700576320000025
Non-decreasing, instantaneous frequency->
Figure GDA0003700576320000026
Is phase->
Figure GDA0003700576320000027
A derivative of (a); lagrange multiplier lambda of n +1 th iteration n+1 (t); defining the number of the modes as K;
step 1.5: respectively obtaining the kth modal component of the n +1 th iteration of the traffic flow time sequence Y or Z under the frequency domain omega by using the formula (4) and the formula (5)
Figure GDA0003700576320000031
And a central frequency->
Figure GDA0003700576320000032
Figure GDA0003700576320000033
Figure GDA0003700576320000034
In the formulae (4) and (5),
Figure GDA0003700576320000035
and &>
Figure GDA0003700576320000036
Respectively in the time domain t
Figure GDA0003700576320000037
f(t)、/>
Figure GDA0003700576320000038
And λ n (t) is transformed by Fourier transform into the frequency domain ω, wherein>
Figure GDA0003700576320000039
Represents the kth 'modal component of the (n + 1) th iteration in the time domain t, <' > is selected>
Figure GDA00037005763200000310
Represents the kth "modal component of the (n + 1) th iteration in the time domain t; k 'denotes a k' th modal component index before the k-th modal component, and k "denotes a k" th modal component index after the k-th modal component; />
Figure GDA00037005763200000311
Representing the center frequency of the k modal component in the frequency domain ω at the nth iteration;
step 1.6: updating Lagrange multiplier for n +1 th iteration using equation (6)
Figure GDA00037005763200000312
Figure GDA00037005763200000313
In the formula (6), τ is a noise margin;
step 1.7: judging whether the formula (7) is established, if so, executing a step 1.8; otherwise, assigning n +1 to n, and returning to the step 1.5;
Figure GDA00037005763200000314
in the formula (7), ε has a predetermined accuracy.
Step 1.8: to pair
Figure GDA00037005763200000315
Performing inverse Fourier transform to obtain a real part which is the kth traffic flow component sequence vimf of the traffic flow time sequence Y or Z k ；
Step 1.9: calculating the kth traffic flow component sequence vimf using equation (8) k Entropy of edge information of H (vimf) k )：
Figure GDA00037005763200000316
In the formula (8), the reaction mixture is,
Figure GDA00037005763200000317
indicating the k-th traffic flow component sequence vimf k The ith traffic flow data->
Figure GDA00037005763200000318
The edge probability density function of (a);
step 1.10: calculating adjacent traffic flow component sequence vimf using equation (9) k And vimf k+1 Mutual information entropy of I (vimf) k ,vimf k+1 )：
I(vimf k ,vimf k+1 )＝H(vimf k )+H(vimf k+1 )-H(vimf k ,vimf k+1 ) (9)
In the formula (9), vimf k+1 A k +1 th traffic flow component sequence representing a traffic flow time sequence Y or Z; h (vimf) k ) Indicating the k-th traffic flow component sequence vimf k The edge information entropy of (1); h (vimf) k+1 ) Represents the k +1 th traffic flow component sequence vimf k+1 The edge information entropy of (1); h (vimf) k ,vimf k+1 ) Denotes vimf k And vimf k+1 The joint information entropy of (1);
step 1.11: by using(10) Determining and dividing traffic flow low-frequency component sequence set { vimf 1 ,vimf 2 ,···,vimf k* } and a set of high-frequency component sequences { vimf' k*+1 ,vimf′ k*+2 ,···,vimf′ K Subscript k of }:
Figure GDA0003700576320000041
in the formula (10), vimf k* Representing a corresponding first traffic flow component sequence when the mutual information entropy I (·,) obtains a minimum value; vimf 'of' k*+1 A second traffic flow component sequence corresponding to the mutual information entropy I (·,) when the minimum value point is obtained; i (vimf) k* ,vimf′ k*+1 ) A minimum value representing the entropy of the mutual information;
step 1.12: calculating k +1 th traffic flow component sequence vimf 'by using formula (11)' k*+1 Is above a threshold value TV k+1 ：
Figure GDA0003700576320000042
In the formula (11), median represents a median operation; Δ represents a scaling factor constant;
step 1.13: TV according to threshold value k*+1 To the k +1 high frequency component sequence vimf' k*+1 Carrying out threshold noise reduction: prepared from vimf' k*+1 The absolute value of the medium amplitude is less than the threshold value TV k*+1 Is set to zero, the absolute value of the amplitude is greater than a threshold value TV k*+1 So as to obtain the kth +1 traffic flow high-frequency component sequence vimf after threshold value noise reduction k*+1 ；
Step 1.14: according to the steps 1.12 to 1.13, K +2 to K high-frequency component sequences { vimf' k*+2 ,···,vimf′ K Carrying out threshold value noise reduction to obtain K-K-number traffic flow high-frequency component sequences { vimf }after noise reduction k*+1 ,vimf k*+2 ,···,vimf K }; meanwhile, the traffic flow low-frequency component sequence { vimf divided in the step 1.11 is reserved 1 ,vimf 2 ,···,vimf k* }; finally obtaining K component sequences { vimf of the traffic flow time sequence Y or Z 1 ,···,vimf k* ,vimf k*+1 ,···,vimf K }；
And 2, step: traffic flow spatial correlation capture based on graph attention network:
step 2.1: selecting a certain traffic flow node in a traffic network, using the selected traffic flow node as a central prediction node and marking the node as a p point, decomposing the traffic flow time sequence of the p point through the process of the step 1, and reducing noise by a threshold value to obtain a traffic flow time sequence x containing K component sequences as shown in a formula (12) p ：
Figure GDA0003700576320000051
In the formula (12), the reaction mixture is,
Figure GDA0003700576320000052
1 st and kth low-frequency component sequences respectively representing p points; />
Figure GDA0003700576320000053
K +1 and K high-frequency component sequences respectively representing p points;
step 2.2: selecting a plurality of traffic flow nodes in a traffic network, taking the nodes as first-order neighborhood nodes of p points, marking the nodes as a set q, wherein m first-order neighborhood nodes are shared in the set q, and marking the nodes as q = { q = 1 ,q 2 ,···,q n ,···,q m In which q is n The point represents the nth first-order neighborhood node of the p point, and the nth first-order neighborhood node q n The traffic flow time series is decomposed and subjected to threshold noise reduction through the process of the step 1 to obtain the traffic flow time series containing K component series shown in the formula (13)
Figure GDA0003700576320000054
Figure GDA0003700576320000055
In the formula (13), the reaction mixture is,
Figure GDA0003700576320000056
respectively represent q n The 1 st, kth low frequency component sequence of a point;
Figure GDA0003700576320000057
respectively represent q n The kth +1, kth high frequency component sequence of points;
step 2.3: the graph attention network calculates the traffic flow time series x of the central prediction node p by using the formula (14) p For the nth first-order neighborhood node q n Time series of traffic flow
Figure GDA0003700576320000058
In a manner known in the art->
Figure GDA0003700576320000059
Figure GDA00037005763200000510
In the formula (14), exp represents a natural base number;
Figure GDA00037005763200000511
representing a learnable weight vector; w represents a learnable weight matrix; | represents a splicing operation; σ (-) denotes the LeakyReLU activation function;
step 2.4: calculating the traffic flow time series x of the central prediction node p using equation (14) p Obtaining the attention coefficient vector alpha shown in the formula (15) for the attention coefficients of the traffic flow time sequence of all the first-order neighborhood nodes in the set q pq ：
Figure GDA00037005763200000512
In the formula (15), the reaction mixture is,
Figure GDA00037005763200000611
and &>
Figure GDA00037005763200000612
Time series x of traffic flows respectively representing central prediction nodes p p Attention coefficients for traffic flow time series for 1 st, 2 nd, nth and mth first order neighborhood nodes;
step 2.5: calculating the traffic flow time series x of the central prediction node p using equation (14) p Self-attention coefficient of (a) pp And is combined with x p Multiplying the component sequences to obtain a p-point weighted traffic flow time sequence x shown in formula (16) p ：
Figure GDA0003700576320000061
Step 2.6: the nth first-order neighborhood node q n Time series of traffic flow
Figure GDA0003700576320000062
Is compared with the attention coefficient->
Figure GDA0003700576320000063
Multiplying to obtain the nth first-order neighborhood node q shown in the formula (17) n Weighted traffic flow time series->
Figure GDA0003700576320000064
Figure GDA0003700576320000065
Step 2.7: obtaining the traffic flow time sequence and the attention coefficient vector alpha of all first-order neighborhood nodes q according to the process of the step 2.6 pq The multiplied weighted traffic flow time series is shown as equation (18):
Figure GDA0003700576320000066
in the formula (18), the reaction mixture,
Figure GDA0003700576320000067
representing the mth first-order neighborhood node q m The traffic flow time series containing K component series; />
Figure GDA0003700576320000068
Representing the mth first-order neighborhood node q m Time series x of traffic flow qm And attention factor->
Figure GDA0003700576320000069
The multiplied weighted traffic flow time series;
and step 3: traffic flow time-dependent capture based on gated cycle cell networks:
step 3.1: weighted traffic flow time series of each node
Figure GDA00037005763200000610
The respective component sequences are respectively used as characteristic input of a gated circulation unit network, and an improved RMSProp traffic flow optimization algorithm is utilized to carry out optimization solution on a gated circulation unit network model to obtain each parameter value in the model;
step 3.1.1: defining e as iteration number, initializing e =0, and setting maximum iteration number e max ；
Step 3.1.2: defining a learning rate hyperparameter as eta, a state variable hyperparameter as gamma, a regularization punishment parameter as rho and a real constant as epsilon, and randomly initializing; define the state variable of the e-th iteration as s e And initializing s e ＝0；
Step 3.1.3: defining a loss function f (u) for the e-th iteration e )，u e Representing a traffic flow argument at the e-th iteration;
step 3.1.4: updating the weighted traffic flow of the p-point using equation (19)Time series x p K component sequence of (1)
Figure GDA0003700576320000071
Small batch sample b at e +1 th iteration e+1 Corresponding small batch random gradient g e+1 ：
Figure GDA0003700576320000072
In the formula (19), b e+1 Representing weighted traffic flow time series x p K component sequence of (1)
Figure GDA0003700576320000073
A small batch of samples at iteration e +1, and->
Figure GDA0003700576320000074
Wherein +>
Figure GDA0003700576320000075
Small batch sample b representing the e +1 th iteration e+1 The ith sample in (1), b | represents the small batch sample b e+1 The number of (2); />
Figure GDA0003700576320000076
Represents the ith sample @, using the e +1 th iteration>
Figure GDA0003700576320000077
Calculated loss function f (u) e ) A random gradient of (a);
step 3.1.5: updating the state variable s of the e +1 th iteration using equation (20) e+1 ：
s e+1 ＝γs e +(1-γ)g e+1 ⊙g e+1 (20)
In equation (20), an indicates an element-by-element product operator;
step 3.1.6: state variable s for the e +1 th iteration using equation (21) e+1 Performing deviation correction to obtain corrected e +1 th iterationState variable
Figure GDA0003700576320000078
Figure GDA0003700576320000079
Step 3.1.7: the loss function argument u for updating the e +1 th iteration is calculated from equation (22) e+1 ：
Figure GDA00037005763200000710
In the formula (22), division, evolution and multiplication are element-by-element operations; epsilon is a real constant added to maintain numerical stability;
step 3.1.8: judging whether e reaches the maximum iteration number e max If yes, the trained gated cycle unit network model and the optimal parameter values thereof are obtained, and step 3.2 is executed; otherwise, assigning e +1 to e, and executing the step 3.1.4 to execute in sequence;
step 3.2: obtaining a weighted traffic flow time sequence x of a point p by applying a trained gated cyclic unit network model p Set of prediction outputs of the K component sequences
Figure GDA00037005763200000711
Wherein it is present>
Figure GDA00037005763200000712
And
Figure GDA00037005763200000713
predicted values of K-th, K-th +1, K' -th and K-th weighted traffic flow component sequences respectively representing p points;
q is to be 1 ～q m Weighted traffic flow time series of points
Figure GDA0003700576320000081
Respective component ofThe sequence is used as the characteristic input of the gated cyclic unit network, and the step 3.1.1 to the step 3.1.8 are executed, so that the trained gated cyclic unit network model is respectively applied to obtain q 1 ～q m Weighted traffic flow time series in each of the nodes +>
Figure GDA0003700576320000082
The prediction output set of K component sequences: />
Figure GDA0003700576320000083
Wherein it is present>
Figure GDA0003700576320000084
And &>
Figure GDA0003700576320000085
Respectively represent q n Predicted values of kth, kth +1, kth and kth weighted traffic flow component sequences of points; />
Figure GDA0003700576320000086
And &>
Figure GDA0003700576320000087
Respectively represent q m Predicted values of kth, kth +1, kth and kth weighted traffic flow component sequences of points;
step 3.3: the weighted traffic flow time sequence x p 、
Figure GDA0003700576320000088
The predicted values in the respective prediction output sets are superposed and summed, so that the final prediction output h of the point p of the central prediction node is obtained by using the formula (23) p ：
Figure GDA0003700576320000089
In the formula (23), the reaction mixture is,
Figure GDA00037005763200000810
set of prediction outputs representing p points->
Figure GDA00037005763200000811
The kth' predicted value of (1); />
Figure GDA00037005763200000812
Representing the nth first order neighborhood node q n Predictive output set of points +>
Figure GDA00037005763200000813
The k-th predicted value of (1).
Compared with the prior art, the technical scheme adopted by the invention has the following technical effects:
based on the characteristics of three aspects of complex non-stationarity, spatial correlation and time dependence of a traffic flow time sequence, compared with the traditional prediction method only considering one or two aspects of characteristics, the method can obtain better prediction precision and speed, and particularly comprises the following steps:
1. in the invention, the complex non-stationarity of the traffic flow time sequence is considered, the optimal central frequency and the limited bandwidth of each mode can be adaptively matched by using a variational mode decomposition algorithm improved by mutual information entropy in the searching and solving processes, the effective separation of mode components and the high-frequency threshold noise reduction are realized, the traffic flow time sequence is decomposed into a series of relatively stable high-low frequency component sequences, the non-stationarity of the time sequence is reduced, and the prediction precision of the traffic flow is improved;
2. according to the method, the spatial correlation of the traffic flow time sequence is considered, the attention mechanism of the graph attention network is utilized, the attention coefficient is used for weighting each component sequence, the traffic flow of the adjacent nodes of the traffic network can be captured to influence of the traffic flow of the central prediction node in different degrees, and the prediction precision is improved;
3. according to the method, the time dependency of the traffic flow time sequence is considered, the time-controlled circulation unit network is utilized to effectively capture the short-term and long-term time dependency of the time sequence data, the weighted traffic flow component sequence is used as the characteristic input of the time-controlled circulation unit network, the improved RMSProp traffic flow optimization algorithm is utilized for iterative training, and the iterative speed is improved and the traffic flow prediction precision is further improved through the deviation correction and regularization strategy.
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FIG. 1 is a view illustrating a construction of a traffic flow combination prediction method according to the present invention;
FIG. 2 is a model diagram of spatial correlation of traffic flow;
FIG. 3 is a traffic flow time-dependent model diagram;
FIG. 4 is a flow chart of a traffic flow combination prediction method according to the present invention;
FIG. 5 is a result graph of traffic flow after improved variational modal decomposition;
fig. 6 is a graph of actual traffic flow and prediction results from 2021, 5, month, 30, day 8.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention improves the prediction precision and speed of a traffic flow prediction model based on the characteristics of three aspects of complexity, non-stationarity, spatial correlation and time dependence of a traffic flow time sequence, and provides a traffic flow combination prediction method based on the combination of improved variation modal decomposition, a graph attention network and a gated cycle unit network. As shown in fig. 1, in this embodiment, a traffic flow combination method includes the following steps:
step 1: the traffic flow variation modal decomposition based on mutual information entropy improvement is as follows:
step 1.1: the mutual information entropy I (Y; Z) is defined by formula (1):
I(Y；Z)＝H(Y)+H(Z)-H(Y,Z) (1)
in formula (1): y represents a set of traffic flow time series, and Y = (Y) 1 ,y 2 ,···,y i ,···,y N )，y i Represents the ith traffic flow data, Z represents another group of traffic flow time series, and Z = (Z) 1 ,z 2 ,···,z i ,···,z N )，z i Representing the ith traffic flow data, wherein N is the length of the time series; h (-) represents the entropy of the edge information, and H (-) represents the entropy of the joint information; p (-) represents an edge probability density function, p (-) represents a joint probability density function, and has:
Figure GDA0003700576320000101
in formula (2): p (y) i ) And p (z) i ) Respectively represent the ith traffic flow data y i And z i An edge probability density function of (a); p (y) i ,z i ) Indicating the ith traffic flow data y i And z i A joint probability density function of (a); when the mutual information entropy value between two traffic flow modal component sequences is larger, the relevance is stronger, otherwise, the relevance is weaker. When the mutual information is zero, the two sequences are completely independent of each other;
step 1.2: the augmented Lagrangian objective function L (u) is defined by equation (3) k ,ω k ,λ)：
Figure GDA0003700576320000102
In formula (3): u. of k (t) represents the k-th modal component of the traffic flow time series in the time domain t, and u k (t)＝A k (t)cos(φ k (t)), wherein A k (t) denotes the kth modal component u k (t) amplitude in the time domain t, [ phi ] k (t) denotes the k-th modal component u k (t) instantaneous phase in the time domain t; omega k (t) denotes the k-th modal component u k (t) instantaneous frequency in the time domain t, and ω k (t)＝φ k ' (t); λ (t) represents the lagrange multiplier in the time domain t for strict enforcement of the constraint; alpha represents a secondary penalty term and is used for reducing Gaussian noise interference in the time sequence, and the weight of the secondary penalty term is deduced by Bayesian prior and is inversely proportional to the noise level;
Figure GDA0003700576320000108
represents a partial differential over the time domain t; δ (t) represents a unit impulse function in the time domain t; j represents an imaginary number; omega k Representing the k-th modal component u in the time domain t k (t) transforming to a center frequency in the frequency domain ω; * Representing a convolution operator; f (t) represents a traffic flow time sequence Y or Z in a time domain t;
step 1.3: defining n as the number of search iterations and initializing to n =0;
step 1.4: initializing the kth modal component of the n +1 th iteration of the traffic flow time sequence Y or Z in the time domain t
Figure GDA0003700576320000103
Is greater than or equal to>
Figure GDA0003700576320000104
Non-negative phase/phase->
Figure GDA0003700576320000105
Non-decreasing, instantaneous frequency->
Figure GDA0003700576320000106
Is phase->
Figure GDA0003700576320000107
A derivative of (a); lagrange multiplier lambda of n +1 th iteration n+1 (t); defining the number of modes as K =5;
step 1.5: respectively obtaining the kth modal component of the n +1 th iteration of the traffic flow time sequence Y or Z under the frequency domain omega by using the formula (4) and the formula (5)
Figure GDA0003700576320000111
And a central frequency->
Figure GDA0003700576320000112
Namely, searching for a saddle point when the eigenvalue of the hessian matrix of the augmented lagrange target function formula (3) at the position where the gradient is zero is positive or negative:
Figure GDA0003700576320000113
Figure GDA0003700576320000114
in the formulae (4) and (5),
Figure GDA0003700576320000115
and &>
Figure GDA0003700576320000116
Respectively denotes ^ under the time domain t>
Figure GDA0003700576320000117
f(t)、/>
Figure GDA0003700576320000118
And λ n (t) transforming the traffic flow time series in the time domain t into the frequency domain ω for iteration by means of a fourier transformation, wherein £ v @>
Figure GDA0003700576320000119
Representing the kth' modal component of the (n + 1) th iteration in the time domain t,
Figure GDA00037005763200001110
represents the kth "modal component of the (n + 1) th iteration in the time domain t; k 'denotes the k' th modal component index preceding the k-th modal component, k "denotes the k" th modal component index following the k-th modal component; />
Figure GDA00037005763200001111
Representing the center frequency of the kth modal component in the frequency domain ω at the nth iteration;
step 1.6: updating Lagrange multiplier for n +1 th iteration using equation (6)
Figure GDA00037005763200001112
Figure GDA00037005763200001113
In the formula (6), τ is a noise margin, and an empirical value τ =0.005 is taken without strict requirement;
step 1.7: judging whether the formula (7) is established, if so, executing a step 1.8; otherwise, assigning n +1 to n, and returning to the step 1.5;
Figure GDA00037005763200001114
in the formula (7), epsilon is a constant with given precision and error control, precision and iteration times are determined, strict requirements are not required, and an empirical value epsilon =1e-6 can be taken;
step 1.8: to pair
Figure GDA00037005763200001115
Performing inverse Fourier transform, converting the frequency domain signal into a time domain signal, and obtaining a real part which is the k-th traffic flow component sequence vimf of the traffic flow time sequence Y or Z without considering the imaginary part value k ；
Step 1.9: calculating the kth traffic flow component sequence vimf using equation (8) k Entropy of edge information of H (vimf) k )：
Figure GDA0003700576320000121
In the formula (8), the reaction mixture is,
Figure GDA0003700576320000122
indicating the kth traffic flow component sequence vimf k The ith traffic flow data->
Figure GDA0003700576320000123
The edge probability density function of (a);
step 1.10: adjacent intersection calculation Using equation (9)Flux component sequence vimf k And vimf k+1 Mutual information entropy of I (vimf) k ,vimf k+1 )：
I(vimf k ,vimf k+1 )＝H(vimf k )+H(vimf k+1 )-H(vimf k ,vimf k+1 ) (9)
In the formula (9), vimf k+1 A k +1 th traffic flow component sequence representing a traffic flow time sequence Y or Z; h (vimf) k ) Indicating the k-th traffic flow component sequence vimf k The edge information entropy of (1); h (vimf) k+1 ) Represents the k +1 th traffic flow component sequence vimf k+1 The edge information entropy of (1); h (vimf) k ,vimf k+1 ) Denotes vimf k And vimf k+1 The joint information entropy of (1);
step 1.11: determining a set of low-frequency component sequences { vimf) for dividing traffic flow by using equation (10) 1 ,vimf 2 ,···,vimf k* } and a set of high-frequency component sequences { vimf' k*+1 ,vimf′ k*+2 ,···,vimf′ K Subscript k of }:
Figure GDA0003700576320000124
in the formula (10), vimf k* Representing a corresponding first traffic flow component sequence when the mutual information entropy I (·,) obtains a minimum value; vimf 'of' k*+1 Representing a corresponding second traffic flow component sequence when the mutual information entropy I (·,) is obtained to a minimum value point; i (vimf) k* ,vimf′ k*+1 ) A minimum value representing the mutual information entropy;
step 1.12: calculating k +1 th traffic flow component sequence vimf 'by using formula (11)' k*+1 Is measured by a threshold value TV k+1 ：
Figure GDA0003700576320000125
In the formula (11), median represents a median operation; Δ represents a scaling factor constant, and may take an empirical value of Δ =0.6745; threshold value TV k+1 Left side part of
Figure GDA0003700576320000126
For calculating the zoom factor, the right part->
Figure GDA0003700576320000127
For calculating a base threshold;
step 1.13: TV according to threshold value k*+1 To k +1 high-frequency component sequences vimf' k*+1 Carrying out threshold noise reduction: prepared from vimf' k*+1 The absolute value of the medium amplitude is less than the threshold value TV k*+1 Is set to zero, the absolute value of the amplitude is greater than a threshold value TV k*+1 So as to obtain the k +1 high-frequency component sequence vimf of the traffic flow after threshold value noise reduction k*+1 ；
Step 1.14: according to the steps 1.12 to 1.13, K +2 to K high-frequency component sequences { vimf' k*+2 ,···,vimf′ K Carrying out threshold value noise reduction to obtain K-K-number traffic flow high-frequency component sequences { vimf }after noise reduction k*+1 ,vimf k*+2 ,···,vimf K }; meanwhile, the traffic flow low-frequency component sequence { vimf divided in the step 1.11 is reserved 1 ,vimf 2 ,···,vimf k* }; finally obtaining K component sequences { vimf) of the traffic flow time sequence Y or Z 1 ,···,vimf k* ,vimf k*+1 ,···,vimf K }；
And 2, step: traffic flow spatial correlation capture based on graph attention network:
step 2.1: selecting a certain traffic flow node in a traffic network, using the selected traffic flow node as a central prediction node and marking the node as a p point, decomposing the traffic flow time sequence of the p point through the process of the step 1, and reducing noise by a threshold value to obtain a traffic flow time sequence x containing K component sequences as shown in a formula (12) p ：
Figure GDA0003700576320000131
In the formula (12), the reaction mixture is,
Figure GDA0003700576320000132
1 st and kth low-frequency component sequences respectively representing p points; />
Figure GDA0003700576320000133
K +1 and K high-frequency component sequences respectively representing p points;
step 2.2: selecting a plurality of traffic flow nodes in a traffic network, taking the nodes as first-order neighborhood nodes of p points, marking the nodes as a set q, wherein m first-order neighborhood nodes are shared in the set q, and marking the nodes as q = { q = 1 ,q 2 ,···,q n ,···,q m Wherein q is n The point represents the nth first-order neighborhood node of the p point, and the nth first-order neighborhood node q n The traffic flow time series is decomposed and subjected to threshold noise reduction through the process of the step 1 to obtain the traffic flow time series containing K component series shown in the formula (13)
Figure GDA0003700576320000134
Figure GDA0003700576320000135
In the formula (13), the reaction mixture is,
Figure GDA0003700576320000136
respectively represent q n The 1 st, k × low frequency component sequence of points;
Figure GDA0003700576320000137
respectively represent q n The kth +1, kth high frequency component sequence of points;
step 2.3: the graph attention network calculates the traffic flow time series x of the central prediction node p by using the formula (14) p For the nth first-order neighborhood node q n Time series of traffic flow
Figure GDA0003700576320000138
Is greater than or equal to>
Figure GDA0003700576320000139
Figure GDA00037005763200001310
In the formula (14), exp represents a natural base number;
Figure GDA0003700576320000141
representing a learnable weight vector; w represents a learnable weight matrix; | | represents the splicing operation; σ (-) denotes the LeakyReLU activation function;
step 2.4: calculation of traffic flow time series x of central prediction node p using equation (14) p Obtaining the attention coefficient vector alpha shown in the formula (15) for the attention coefficients of the traffic flow time sequence of all the first-order neighborhood nodes in the set q pq ：
Figure GDA0003700576320000142
In the formula (15), the reaction mixture is,
Figure GDA0003700576320000143
and &>
Figure GDA0003700576320000144
Time series x of traffic flows respectively representing central prediction nodes p p Attention coefficients for traffic flow time series for 1 st, 2 nd, nth and mth first order neighborhood nodes;
step 2.5: calculation of traffic flow time series x of central prediction node p using equation (14) p Self-attention coefficient of (a) pp And is combined with x p Multiplying the component sequences to obtain a p-point weighted traffic flow time sequence x shown in formula (16) p ：
Figure GDA0003700576320000145
Step 2.6: the nth first-order neighborhood node q n Time series of traffic flow
Figure GDA0003700576320000146
In each component sequence and attention coefficient->
Figure GDA0003700576320000147
Multiplying to obtain the nth first-order neighborhood node q shown in the formula (17) n Weighted traffic flow time series->
Figure GDA0003700576320000148
Figure GDA0003700576320000149
Step 2.7: obtaining the traffic flow time sequence and the attention coefficient vector alpha of all the first-order neighborhood nodes q according to the process of the step 2.6 pq The multiplied weighted traffic flow time series is shown as equation (18):
Figure GDA00037005763200001410
in the formula (18), the reaction mixture,
Figure GDA00037005763200001411
representing the mth first-order neighborhood node q m The traffic flow time series containing K component series; />
Figure GDA00037005763200001412
Representing the mth first-order neighborhood node q m Is based on the traffic flow time series->
Figure GDA00037005763200001413
And attention factor->
Figure GDA00037005763200001414
The multiplied weighted traffic flow time series;
and step 3: traffic flow time-dependent capture based on gated cycle cell networks:
step 3.1: weighted traffic flow time series x of each node p 、x q1 ～x qm The respective component sequences are respectively used as characteristic input of a gated circulation unit network, and an improved RMSProp traffic flow optimization algorithm is utilized to carry out optimization solution on a gated circulation unit network model to obtain each parameter value in the model; step 3.1.1-3.1.8 inputting p point weighted traffic flow time sequence x p K component sequence of (1)
Figure GDA0003700576320000151
For example;
step 3.1.1: defining e as iteration number, initializing e =0, and setting maximum iteration number e max ＝50；
Step 3.1.2: defining a learning rate over-parameter as eta, a state variable over-parameter as gamma, a regularization penalty parameter as rho and a real constant as epsilon, and randomly initializing the learning rate over-parameter eta =0.01, the state variable over-parameter gamma e (0.9,1), the penalty parameter rho e (0,1) and the real constant epsilon e (0,1); define the state variable of the e-th iteration as s e And initializing s e ＝0；
Step 3.1.3: defining a loss function f (u) for the e-th iteration e )，u e Representing a traffic flow argument at the e-th iteration;
step 3.1.4: updating the weighted traffic flow time series x of p points using equation (19) p K component sequence of (1)
Figure GDA0003700576320000152
Small batch sample b at e +1 th iteration e+1 Corresponding small batch random gradient g e+1 ：
Figure GDA0003700576320000153
In formula (19), b e+1 Representing weighted traffic flow time series x p K component sequence of (1)
Figure GDA0003700576320000154
A small batch of samples at iteration e +1, and->
Figure GDA0003700576320000155
Wherein it is present>
Figure GDA0003700576320000156
Small batch sample b representing the e +1 th iteration e+1 The ith sample in (1), b | represents the small batch sample b e+1 Is a hyper-parameter independent of the iteration number e; />
Figure GDA0003700576320000157
Represents the ith sample @, using the e +1 th iteration>
Figure GDA0003700576320000158
Calculated loss function f (u) e ) A random gradient of (a);
step 3.1.5: updating the state variable s of the e +1 th iteration using equation (20) e+1 ：
s e+1 ＝γs e +(1-γ)g e+1 ⊙g e+1 (20)
In equation (20), an indicates the element-by-element product operator;
step 3.1.6: state variable s for the e +1 th iteration using equation (21) e+1 Performing deviation correction to obtain corrected state variable of e +1 th iteration
Figure GDA0003700576320000159
Figure GDA00037005763200001510
Step 3.1.7: the loss of updating the e +1 st iteration is calculated from equation (22)Argument u of loss function e+1 ：
Figure GDA0003700576320000161
In the formula (22), division, evolution and multiplication are element-by-element operations; epsilon is a real constant added to maintain numerical stability;
step 3.1.8: judging whether e reaches the maximum iteration number e max If yes, the trained gating cycle unit network model and the optimal parameter values thereof are obtained, and step 3.2 is executed; otherwise, assigning e +1 to e, and executing the step 3.1.4 to execute in sequence;
step 3.2: obtaining a weighted traffic flow time sequence x of a point p by applying a trained gated cyclic unit network model p Set of prediction outputs of the K component sequences of
Figure GDA0003700576320000162
Wherein it is present>
Figure GDA0003700576320000163
And
Figure GDA0003700576320000164
predicted values of K-th, K-th +1, K' -th and K-th weighted traffic flow component sequences respectively representing p points;
q is to be 1 ～q m Weighted traffic flow time series of points
Figure GDA0003700576320000165
The respective component sequences are used as the characteristic input of the gated cyclic unit network, and the step 3.1.1 to the step 3.1.8 are executed, so that the trained gated cyclic unit network model is respectively applied to obtain q 1 ～q m Respective weighted traffic flow time series->
Figure GDA0003700576320000166
The predicted output set of K component sequences of (a): />
Figure GDA0003700576320000167
Wherein +>
Figure GDA0003700576320000168
And &>
Figure GDA0003700576320000169
Respectively represent q n Predicted values of kth, kth +1, kth' and kth weighted traffic flow component sequences of points; />
Figure GDA00037005763200001610
And &>
Figure GDA00037005763200001611
Respectively represent q m Predicted values of kth, kth +1, kth' and kth weighted traffic flow component sequences of points;
step 3.3: the weighted traffic flow time sequence x p 、x q1 ～x qm The predicted values in the respective prediction output sets are superposed and summed, so that the final prediction output h of the point p of the central prediction node is obtained by using the formula (23) p ：
Figure GDA00037005763200001612
In the formula (23), the compound represented by the formula,
Figure GDA00037005763200001613
set of prediction outputs representing p points->
Figure GDA00037005763200001614
The kth' predicted value of (1); />
Figure GDA00037005763200001615
Representing the nth first order neighborhood node q n Predictive output set of points +>
Figure GDA00037005763200001616
The kth "predicted value in (1); fig. 4 is a flow chart of a traffic flow combination prediction method of the present invention.
Examples of the applications
1) RTMC traffic data set and pre-processing
The data set used in the embodiments of the present invention is collected by a Regional Traffic Management Center (RTMC) under the state of minnesota traffic department (MnDOT), which includes flow data every 30 seconds, hour, and day.
The selected traffic node region I-35W and TH 62 comprises a central prediction node and four neighborhood nodes. The S50 monitoring point is a central prediction node, and the S49, S329 and the two Exit monitoring points are first-order neighborhood nodes.
The sampling time is 8-00-20 from 1/4/2021 to 30/5/2021, and the sampling interval of the traffic flow time series is re-aggregated into 5mins of data, and 8640 data are contained in each node after aggregation. And dividing the data of the first 45 days into training set samples, and dividing the data of the last 15 days into test set samples. A sliding window of width T +1 is used in the training set to generate training samples, where T is the historical timestamp data length and the T +1 th timestamp data is the tag value, and the sliding window is shifted one time unit (5 mins) at a time.
2) Performance index
To evaluate the prediction performance of the combined prediction method of the present invention, mean Absolute Error (MAE), mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE) were used as performance indicators. The definitions are as follows:
(1) Mean absolute Error (MeanAbsolute Error, MAE): average of absolute errors.
Figure GDA0003700576320000171
(2) Mean absolute percent Error (MeanAbsolute Percentage Error, MAPE): the prediction error is a percentage of the true value.
Figure GDA0003700576320000172
(3) Root Mean square Error (Root Mean Squared Error, RMSE): root mean square difference of predicted value and true value.
Figure GDA0003700576320000173
In equations (24), (25) and (26), | b | is the number of small-lot samples of the traffic flow training set, x i And
Figure GDA0003700576320000174
and respectively a real value and a predicted value of the ith traffic flow sample in the test set. The smaller the values of the MAE, MAPE and RMSE indexes are, the better the prediction result is.
3) Model training and experimental analysis
Fig. 2 and 3 show a traffic flow spatial correlation capture model and a traffic flow time-dependent capture model, respectively.
In the main super-parameter setting, the penalty factor alpha of the improved traffic flow variation modal decomposition algorithm is 2000, the noise tolerance parameter tau is 0.005, the step length of a historical timestamp in a training set T =7, the number of neurons in a hidden layer of a GAT network is 128, the number of neurons in a hidden layer of a GRU network is 64, the size of batchSize in batch processing in the network is 32, and the maximum training iteration number Epoch of the improved RMSProp traffic flow optimization algorithm is 50.
The traffic flow time sequence is decomposed into 5 stable component subsequences with different frequencies and amplitudes by using an improved traffic flow variation modal decomposition algorithm, and each modal component sequence vimf normalized from low frequency to high frequency is shown in fig. 5.
Table 1 shows the entropy of mutual information between each vimf component, which is known from the table 2 And vimf 3 Inter-component mutual information entropy value I (vimf) 2 ,vimf 3 ) Decrease, and vimf 3 And vimf 4 Mutual information entropy of components I (vimf) 3 ,vimf 4 ) Opening deviceAt the beginning of the increase, a minimum point occurs, so vimf will be 3 The subscript of the component is taken as the subscript k of the boundary point of the low frequency component and the high frequency component. Preserving low frequency components vimf 1 And vimf 2 And for high frequency component vimf 3 To vimf 5 And (4) carrying out threshold value noise reduction, and reserving the information of the original traffic flow time sequence to the maximum extent.
TABLE 1 mutual information entropy between VIMF components
Figure GDA0003700576320000181
FIG. 6 shows the original traffic flow and the final predicted results from 20 to 00 in 5 months and 30 days in 2021 in test set. It can be seen that the traffic flows in the prediction periods of 8.

Claims (1)

1. A traffic flow combination prediction method is characterized by comprising the following steps:
step 1: the traffic flow variation modal decomposition is improved based on mutual information entropy:
step 1.1: mutual information entropy I (Y; Z) is defined by formula (1):
I(Y；Z)＝H(Y)+H(Z)-H(Y,Z) (1)
in formula (1): y represents a set of traffic flow time series, and Y = (Y) 1 ,y 2 ,···,y i ,···,y N )，y i Represents the ith traffic flow data, Z represents another group of traffic flow time series, and Z = (Z) 1 ,z 2 ,···,z i ,···,z N )，z i Representing the ith traffic flow data, wherein N is the length of the time series; h (-) represents the edge information entropy, and H (-) represents the joint information entropy; p (-) represents an edge probability density function, p (-) represents a joint probability density function, and has:
Figure FDA0004077370970000011
in formula (2): p (y) i ) And p (z) i ) Respectively represent the ith traffic flow data y i And z i The edge probability density function of (a); p (y) i ,z i ) Represents the ith traffic flow data y i And z i A joint probability density function of (a);
step 1.2: the augmented Lagrangian objective function L (u) is defined by equation (3) k ,ω k ,λ)：
Figure FDA0004077370970000012
In formula (3): u. of k (t) represents the k-th modal component of the traffic flow time series in the time domain t, and u k (t)＝A k (t)cos(φ k (t)), wherein A k (t) denotes the k-th modal component u k (t) amplitude in the time domain t, [ phi ] k (t) denotes the k-th modal component u k (t) instantaneous phase in the time domain t; omega k (t) denotes the kth modal component u k (t) instantaneous frequency in the time domain t, and ω k (t)＝φ k ' (t); λ (t) represents the lagrange multiplier in the time domain t; alpha represents a secondary penalty term;
Figure FDA0004077370970000013
represents a partial differential over the time domain t; δ (t) represents a unit impulse function in the time domain t; j represents an imaginary number; omega k Representing the k-th modal component u in the time domain t k (t) transforming to a center frequency in the frequency domain ω; * Representing a convolution operator; f (t) represents a traffic flow time sequence Y or Z in a time domain t;
step 1.3: defining n as the number of search iterations and initializing to n =0;
step 1.4: initializing the kth modal component of the n +1 th iteration of the traffic flow time sequence Y or Z in the time domain t
Figure FDA0004077370970000021
Is greater than or equal to>
Figure FDA0004077370970000022
Non-negative phase/phase->
Figure FDA0004077370970000023
Non-decreasing, instantaneous frequency->
Figure FDA0004077370970000024
Is phase->
Figure FDA0004077370970000025
A derivative of (a); lagrange multiplier lambda of n +1 th iteration n+1 (t); defining the number of modes as K;
step 1.5: respectively obtaining the kth modal component of the n +1 th iteration of the traffic flow time sequence Y or Z under the frequency domain omega by using the formula (4) and the formula (5)
Figure FDA0004077370970000026
And center frequency +>
Figure FDA0004077370970000027
Figure FDA0004077370970000028
/>
Figure FDA0004077370970000029
In the formulae (4) and (5),
Figure FDA00040773709700000210
and &>
Figure FDA00040773709700000211
Respectively denotes ^ under the time domain t>
Figure FDA00040773709700000212
f(t)、/>
Figure FDA00040773709700000213
And λ n (t) is transformed by a Fourier transform into the frequency domain ω, wherein>
Figure FDA00040773709700000214
A kth 'modal component representing an n +1 th iteration in the time domain t, <' >>
Figure FDA00040773709700000215
Represents the kth "modal component of the (n + 1) th iteration in the time domain t; k 'denotes a k' th modal component index before the k-th modal component, and k "denotes a k" th modal component index after the k-th modal component; />
Figure FDA00040773709700000216
Representing the center frequency of the kth modal component in the frequency domain ω at the nth iteration; />
Figure FDA00040773709700000217
Representing the kth modal component of the traffic flow time sequence of the (n + 1) th iteration in the time domain t; lambda [ alpha ] n (t) represents the lagrangian multiplier for the nth iteration in the time domain t;
step 1.6: updating Lagrange multiplier for n +1 th iteration using equation (6)
Figure FDA00040773709700000218
Figure FDA00040773709700000219
In the formula (6), τ is a noise margin;
step 1.7: judging whether the formula (7) is established, if so, executing a step 1.8; otherwise, assigning n +1 to n, and returning to the step 1.5;
Figure FDA00040773709700000220
in the formula (7), epsilon is a given precision;
step 1.8: to pair
Figure FDA0004077370970000031
Performing inverse Fourier transform to obtain a real part which is the kth traffic flow component sequence vimf of the traffic flow time sequence Y or Z k ；
Step 1.9: calculating the kth traffic flow component sequence vimf using equation (8) k Entropy of edge information of H (vimf) k )：
Figure FDA0004077370970000032
In the formula (8), the reaction mixture is,
Figure FDA0004077370970000033
indicating the k-th traffic flow component sequence vimf k The ith traffic flow data->
Figure FDA0004077370970000034
The edge probability density function of (a);
step 1.10: calculating adjacent traffic flow component sequence vimf using equation (9) k And vimf k+1 Mutual information entropy of I (vimf) k ,vimf k+1 )：
I(vimf k ,vimf k+1 )＝H(vimf k )+H(vimf k+1 )-H(vimf k ,vimf k+1 ) (9)
In the formula (9), vimf k+1 Representing traffic flowThe (k + 1) th traffic flow component sequence of the traffic time sequence Y or Z; h (vimf) k ) Indicating the k-th traffic flow component sequence vimf k Entropy of edge information of (a); h (vimf) k+1 ) Represents the k +1 th traffic flow component sequence vimf k+1 The edge information entropy of (1); h (vimf) k ,vimf k+1 ) Denotes vimf k And vimf k+1 The joint information entropy of (2);
step 1.11: determining and dividing traffic flow low-frequency component sequence set { vimf) by using equation (10) 1 ,vimf 2 ,···,vimf k* H and a set of high-frequency component sequences { vimf' k*+1 ,vimf′ k*+2 ,···,vimf′ K Subscript k of }:
Figure FDA0004077370970000035
/>
in the formula (10), vimf k* Representing a corresponding first traffic flow component sequence when the mutual information entropy I (·,) obtains a minimum value; vimf 'of' k*+1 Representing a corresponding second traffic flow component sequence when the mutual information entropy I (·,) is obtained to a minimum value point; i (vimf) k* ,vimf′ k*+1 ) A minimum value representing the mutual information entropy;
step 1.12: calculating k +1 th traffic flow component sequence vimf 'by using formula (11)' k*+1 Is measured by a threshold value TV k*+1 ：
Figure FDA0004077370970000036
In the formula (11), median represents a median operation; Δ represents a scaling factor constant;
step 1.13: TV according to threshold value k*+1 To the k +1 high frequency component sequence vimf' k*+1 Carrying out threshold noise reduction: prepared from vimf' k*+1 The absolute value of the medium amplitude is less than the threshold value TV k*+1 Is set to zero, the absolute value of the amplitude is greater than a threshold value TV k*+1 So as to obtain the k +1 high-frequency component sequence vimf of the traffic flow after threshold value noise reduction k*+1 ；
Step 1.14: according to the steps 1.12 to 1.13, K +2 to K high-frequency component sequences { vimf' k*+2 ,···,vimf′ K Carrying out threshold value noise reduction to obtain K-K-number traffic flow high-frequency component sequences { vimf }after noise reduction k*+1 ,vimf k*+2 ,···,vimf K }; meanwhile, the traffic flow low-frequency component sequence { vimf divided in the step 1.11 is reserved 1 ,vimf 2 ,···,vimf k* }; finally obtaining K component sequences { vimf of the traffic flow time sequence Y or Z 1 ,···,vimf k* ,vimf k*+1 ,···,vimf K }；
Step 2: traffic flow spatial correlation capture based on graph attention network:
step 2.1: selecting a certain traffic flow node in a traffic network, using the selected traffic flow node as a central prediction node and marking the node as a p point, decomposing the traffic flow time sequence of the p point through the process of the step 1, and reducing noise by a threshold value to obtain a traffic flow time sequence x containing K component sequences as shown in a formula (12) p ：
Figure FDA0004077370970000041
In the formula (12), the reaction mixture is,
Figure FDA0004077370970000042
1 st and k-th low-frequency component sequences respectively representing p points; />
Figure FDA0004077370970000043
K +1 and K high-frequency component sequences respectively representing p points;
step 2.2: selecting a plurality of traffic flow nodes in a traffic network, taking the nodes as first-order neighborhood nodes of p points, marking the nodes as a set q, wherein m first-order neighborhood nodes are shared in the set q, and marking the nodes as q = { q = 1 ,q 2 ,···,q n ,···,q m Wherein q is n The point represents the nth first-order neighborhood node of the p point, the nth first-order neighborhoodDomain node q n The traffic flow time series is decomposed and subjected to threshold noise reduction through the process of the step 1 to obtain the traffic flow time series containing K component series shown in the formula (13)
Figure FDA0004077370970000044
Figure FDA0004077370970000045
In the formula (13), the reaction mixture is,
Figure FDA0004077370970000046
respectively represent q n The 1 st, k × low frequency component sequence of points; />
Figure FDA0004077370970000047
Respectively represent q n The kth +1, kth high frequency component sequence of points;
step 2.3: the graph attention network calculates the traffic flow time series x of the central prediction node p by using the formula (14) p For the nth first-order neighborhood node q n Time series of traffic flow
Figure FDA0004077370970000048
In a manner known in the art->
Figure FDA0004077370970000049
Figure FDA0004077370970000051
In the formula (14), exp represents a natural base number;
Figure FDA0004077370970000052
representing a learnable weight vector; w represents a learnable weight matrix; i denotes a splicing operation(ii) a σ (-) denotes the LeakyReLU activation function; />
Step 2.4: calculating the traffic flow time series x of the central prediction node p using equation (14) p For the attention coefficients of the traffic flow time sequence of all the first-order neighborhood nodes in the set q, the attention coefficient vector alpha shown in the formula (15) is obtained pq ：
Figure FDA0004077370970000053
In the formula (15), the reaction mixture is,
Figure FDA0004077370970000054
and &>
Figure FDA0004077370970000055
Time series x of traffic flows respectively representing central prediction nodes p p Attention coefficients for traffic flow time series for 1 st, 2 nd, nth and mth first order neighborhood nodes;
step 2.5: calculating the traffic flow time series x of the central prediction node p using equation (14) p Self-attention coefficient of (a) pp And is combined with x p Multiplying the component sequences to obtain a p-point weighted traffic flow time sequence x shown in formula (16) p ：
Figure FDA0004077370970000056
Step 2.6: the nth first-order neighborhood node q n Time series of traffic flow
Figure FDA0004077370970000057
The sequence of the components and the attention coefficient of
Figure FDA0004077370970000058
Multiplying to obtain the nth first-order neighborhood node q shown in the formula (17) n Weighted traffic flow time series->
Figure FDA0004077370970000059
Figure FDA00040773709700000510
Step 2.7: obtaining the traffic flow time sequence and the attention coefficient vector alpha of all the first-order neighborhood nodes q according to the process of the step 2.6 pq The multiplied weighted traffic flow time series is shown in equation (18):
Figure FDA00040773709700000511
in the formula (18), the reaction mixture,
Figure FDA00040773709700000512
representing the mth first-order neighborhood node q m The traffic flow time series containing K component series; />
Figure FDA00040773709700000513
Representing the mth first-order neighborhood node q m Is based on the traffic flow time series->
Figure FDA00040773709700000514
And attention factor->
Figure FDA00040773709700000515
The multiplied weighted traffic flow time series;
and step 3: traffic flow time-dependent capture based on gated cycle cell networks:
step 3.1: weighted traffic flow time series x of each node p 、
Figure FDA0004077370970000061
The respective component sequences are respectively used as characteristic input of a gated circulation unit network, and an improved RMSProp traffic flow optimization algorithm is utilized to carry out optimization solution on a gated circulation unit network model to obtain each parameter value in the model;
step 3.1.1: defining e as iteration number, initializing e =0, and setting maximum iteration number e max ；
Step 3.1.2: defining a learning rate hyperparameter as eta, a state variable hyperparameter as gamma, a regularization punishment parameter as rho and a real constant as epsilon, and randomly initializing; defining the state variable of the e-th iteration as s e And initializing s e ＝0；
Step 3.1.3: defining a loss function f (u) for the e-th iteration e )，u e Representing a traffic flow argument at the e-th iteration;
step 3.1.4: updating the weighted traffic flow time series x of point p using equation (19) p K component sequence of (1)
Figure FDA0004077370970000062
Small batch sample b at e +1 th iteration e+1 Corresponding small batch random gradient g e+1 ：/>
Figure FDA0004077370970000063
In the formula (19), b e+1 Representing a weighted traffic flow time series x p K component sequence of (1)
Figure FDA0004077370970000064
A small batch of samples at iteration e +1, and->
Figure FDA0004077370970000065
Wherein it is present>
Figure FDA0004077370970000066
To representSmall batch of samples b for the e +1 th iteration e+1 The ith sample in (1), b | represents the small batch sample b e+1 The number of (2); />
Figure FDA0004077370970000067
Represents the ith sample @, using the e +1 th iteration>
Figure FDA0004077370970000068
Calculated loss function f (u) e ) A random gradient of (a);
step 3.1.5: updating the state variable s of the e +1 th iteration using equation (20) e+1 ：
s e+1 ＝γs e +(1-γ)g e+1 ⊙g e+1 (20)
In equation (20), an indicates an element-by-element product operator;
step 3.1.6: state variable s for the e +1 th iteration using equation (21) e+1 Performing deviation correction to obtain corrected state variable of e +1 th iteration
Figure FDA0004077370970000069
Figure FDA00040773709700000610
Step 3.1.7: the loss function argument u for updating the e +1 th iteration is calculated from equation (22) e+1 ：
Figure FDA0004077370970000071
In the formula (22), division, evolution and multiplication are element-by-element operations; epsilon is a real constant added to maintain numerical stability;
step 3.1.8: judging whether e reaches the maximum iteration number e max If yes, the trained gated cycle unit network model and the optimal parameter values thereof are obtained, and the steps are executed3.2; otherwise, assigning e +1 to e, and executing the step 3.1.4 to execute in sequence;
step 3.2: obtaining a weighted traffic flow time sequence x of a point p by applying a trained gated cyclic unit network model p Set of prediction outputs of the K component sequences
Figure FDA0004077370970000072
Wherein it is present>
Figure FDA0004077370970000073
And &>
Figure FDA0004077370970000074
Predicted values of K-th, K-th +1, K' -th and K-th weighted traffic flow component sequences respectively representing p points;
q is to be 1 ～q m Weighted traffic flow time series of points
Figure FDA0004077370970000075
The respective component sequences are used as the characteristic input of the gated cyclic unit network, and the step 3.1.1 to the step 3.1.8 are executed, so that the trained gated cyclic unit network model is respectively applied to obtain q 1 ～q m Weighted traffic flow time series in each of the nodes +>
Figure FDA0004077370970000076
The predicted output set of K component sequences of (a):
Figure FDA0004077370970000077
wherein it is present>
Figure FDA0004077370970000078
And &>
Figure FDA0004077370970000079
Respectively represent q n The kth, kth +1, kth' and kth weighted intersections of dotsA predicted value of the flux component sequence; />
Figure FDA00040773709700000710
And &>
Figure FDA00040773709700000711
Respectively represent q m Predicted values of kth, kth +1, kth' and kth weighted traffic flow component sequences of points;
step 3.3: the weighted traffic flow time sequence x p 、
Figure FDA00040773709700000712
The predicted values in the respective prediction output sets are superposed and summed, so that the final prediction output h of the point p of the central prediction node is obtained by using the formula (23) p ：
Figure FDA00040773709700000713
In the formula (23), the compound represented by the formula,
Figure FDA00040773709700000714
prediction output set representing p points>
Figure FDA00040773709700000715
The kth' predicted value of (1);
Figure FDA00040773709700000716
representing the nth first order neighborhood node q n The predicted output set of points ≥ is>
Figure FDA00040773709700000717
The k-th predicted value of (1). />
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