CN115496257A - Short-term vehicle speed prediction based on space-time fusion - Google Patents
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Abstract
The invention discloses a short-time vehicle speed prediction based on space-time fusion, which comprises the following steps: preprocessing vehicle speed data; inputting a vehicle speed data set into a pre-constructed VMD-GCN-BilSTM model to predict the short-time vehicle speed; the VMD-GCN-BilSTM model construction process comprises the following steps: mathematical modeling of BiLSTM: adding a forgetting gate, an input gate and an output gate which are connected in sequence into an LSTM network on the basis of an RNN network; constructing a BiLSTM network model through a forward LSTM network and a backward LSTM network; carrying out bidirectional training on the BilSTM network model; the method can overcome the defects of a single model, and meanwhile, compared with the existing combined model, the prediction precision is further improved. The invention can accurately predict the short-time vehicle speed and provides a favorable reference value for traffic departments.
Description
Technical Field
The invention relates to the field of short-time vehicle speed prediction, in particular to short-time vehicle speed prediction based on space-time fusion.
Background
In recent years, as the automobile keeping quantity increases year by year, the traffic jam phenomenon becomes more serious. The accurate and real-time short-time vehicle speed prediction is beneficial to route planning and time arrangement of travelers, effectively reduces congestion in peak periods, and provides powerful support for a traffic management part to make a prospective traffic management strategy. If the future speed of the road can be accurately predicted, certain measures can be taken before the congestion occurs to avoid the congestion. Therefore, the development of the vehicle speed prediction algorithm through the behavior information of the vehicle has important practical significance on the advanced control of the highway vehicle.
In order to improve the accuracy of short-term vehicle speed prediction, a large number of studies have been conducted by researchers. The short-time vehicle speed prediction model can be divided into a statistical model and machine learning. A typical example of the statistical model is a differential autoregressive moving average (ARIMA) model, which is predicted based on a regression function after determining parameters through time series data. However, the ARIMA model is suitable for linear data prediction and has certain limitation on traffic flow prediction with high nonlinear strength. The method is characterized in that a rule of vehicle speed change is found from historical data, nonlinearity of vehicle speed can be well reflected, and the change rule of the vehicle speed of a road section travel cannot be fully learned due to the fact that long-time sequence features are difficult to mine in machine learning, and the prediction effect is poor.
With the rise of deep learning, the neural network is widely applied to the field of traffic prediction, and is concerned by many scholars at home and abroad with the strong learning ability and self-adaptive ability. The single deep learning models such as a long-time memory network (LSTM) and a gated cycle unit (GRU) have certain advantages in the prediction field, but the problem of low precision still exists. In recent years, the LSTM and Convolutional Neural Network (CNN) combined model is applied in a large amount, and according to the existing research, the hybrid model tends to have higher prediction accuracy than the single model. However, the non-linearity and uncertainty of the vehicle speed data, and the change of the vehicle speed data are not only influenced by the time factor, but also influenced by the vehicle speeds of the upstream and the downstream, so that the noise of the data and the spatial structure of a road network are also factors to be considered, and a high-precision short-time vehicle speed prediction model is lacked at present.
Disclosure of Invention
In order to solve the defects in the background art, the invention aims to provide a short-time vehicle speed prediction based on space-time fusion, which can help a city to relieve the urban traffic jam problem, and the problems of economic loss, environmental pollution, energy waste and the like caused by traffic jam are increasingly aggravated. In order to solve the problems in the background art, it is noted that a bidirectional long-and-short term memory network is widely applied to vehicle speed prediction, but the change of the vehicle speed is influenced not only by time but also by space, so that prediction only from a time dimension influences the prediction accuracy. Given that the graph convolutional neural network (GCN) is capable of handling data of non-euclidean structure, GCN is herein combined with BiLSTM to mine the spatiotemporal behavior of short term vehicle speeds. Furthermore, in order to reduce the interference of noise on the vehicle speed data, variational Modal Decomposition (VMD) is introduced for noise reduction, and a VMD-GCN-BilSTM short-time vehicle speed prediction model is provided, so that a more scientific means is achieved, and the purpose of improving the short-time vehicle speed prediction accuracy is achieved.
The purpose of the invention can be realized by the following technical scheme:
a short-time vehicle speed prediction method based on space-time fusion comprises the following steps:
step 1: mathematical modeling of GCN
The GCN is capable of handling arbitrary graph structure data, which can be divided into spectral-based methods and spatial-based methods, with spectral-based methods being chosen,
in the convolution layer of the spectrogram, the graph convolution Laplace matrix L which can most reflect the structural property of the graph is shown as the formula (1),
where D is a degree matrix, A is an adjacency matrix, I N Is a matrix of the units,
the convolution operation is distinguished from the convolution operation of the classical convolution operator, the graph convolution is realized by using a linear operator which defines the diagonal in the Fourier domain, the formula of which is shown in formula (2),
g θ *x=Ug θ U T x (2)
wherein, g θ For convolution kernels, U is composed of L eigenvectors, and for larger graph structures, the tangent-ratio schloff polynomial can be used for approximate solution, so that the graph convolution interlayer propagation formula is as (3),
wherein, the first and the second end of the pipe are connected with each other,is the sum of the adjacency matrix and the identity matrix,is composed ofDegree matrix of (H) (l) Is a feature matrix of the l-th layer, W (l) Is the weight matrix of the l-th layer, σ is the activation function,
step 2: mathematical modeling of GCN-BilSTM
The invention captures the vehicle speed space characteristics through GCN network, obtains the space characteristic vector of the vehicle speed sequence, inputs the space characteristic vector into the BilSTM network, excavates the time characteristics, the BilSTM is further improved on the basis of the LSTM, and consists of forward LSTM and backward LSTM, the BilSTM not only can memorize the past state, but also has the dependency on the future state, the BilSTM structure chart is shown in figure 2,
the sequence data enters a hidden layer through an input layer to be respectively subjected to forward and reverse calculation, the final output result is obtained by fusing a forward LSTM output result and a reverse LSTM output result by an output layer according to a certain weight, a BiLSTM hidden output calculation formula is shown in formulas (4) to (6),
wherein the content of the first and second substances,andforward and backward hidden layer states at time q, LSTM is the hidden operation process, y q Representing the spatio-temporal correlation vector of the input at time q, h q For the BiLSTM hidden layer state vector at the moment q, alpha and beta represent the output weights of the forward and reverse hidden layers respectively,
and step 3: mathematical modeling of VMD-GCN-BilSTM
The variational modal decomposition solves the problems of endpoint effect and modal component aliasing existing in Empirical Modal Decomposition (EMD), has the advantage of determining the number of modal decompositions, and has the adaptivity of determining the number of modal decompositions of a given sequence according to the actual situation, compared with the EMD, a non-recursive decomposition mode is adopted, the decomposition result is stable by constructing the variational problem,
and 4, step 4: setting hyper-parameters
The main body of the VMD-GCN-BilTM model is that the VMD processes and decomposes signals, the decomposed signals are input into 2 spliced GCN layers, 2 BilTM layers and 1 full-connection layer, the 2-layer GCN channel is mainly used for extracting the spatial characteristics of the vehicle speed, the added BilTM layer is used for extracting the time characteristics of the vehicle speed,
firstly, because the peak period of going to work and going to work can occur every day, the original vehicle speed data has singular values, in order to avoid adverse effect caused by singular sample data and speed up gradient descent to solve the optimal solution, before signal decomposition, data is limited in a certain range, namely normalization processing is adopted, and a normalization formula is shown as a formula (7)
Wherein X is the original data, X min Is the minimum value, X, in the raw data max Is the maximum value in the original data that,
secondly, the normalized vehicle speed data is input into a decomposition module, the data is decomposed into a plurality of IMF components through a VMD algorithm to obtain time sequences under different frequencies, the influence of noise on the predictive performance of a subsequent model is reduced,
the next training part adopts two layers of GCN to capture the space characteristic learning of the vehicle speed, utilizes two layers of BilSTM to dig the time characteristic,
finally, the prediction value of each subsequence is obtained through the full connection layer, the prediction components are summed to output the prediction result,
and 5: comparison with the present invention by other time series prediction methods
The method is trained to obtain various indexes such as the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), the decision coefficient (R2-score) and the like of the three performance indexes, and other time series prediction methods are compared under the same data set and the same computer.
As a preferred scheme of the invention, the VMD decomposition specifically comprises the following steps:
(1): firstly, constructing variation constraint problem by the formulas (8) - (9)
Where K is the number of modes of decomposition, { u k }、{ω k The components and the center frequency of the k-th mode after decomposition are respectively, delta (t) is a Dirac function,
(2): the variation problem is restrained by transforming through the equation (10),
where alpha is a secondary penalty factor, lambda is a Lagrangian multiplier,
(3): search for saddle points of augmented Lagrange function, alternate optimization iteration { u } k }、{ω k And λ, the expressions are formulas (11) to (13),
wherein gamma in the formula represents the noise tolerance,respectively correspond tou i (t), f (t), and λ (t).
The invention has the beneficial effects that:
aiming at the non-linearity and instability of the vehicle speed data, the VMD is used for decomposition, so that the decomposed data is more stable; the speed is influenced by a road network in space, and the spatial characteristics are excavated by using a GCN network; the speed of the vehicle is influenced by the speed of the vehicle in the first few periods in time, and the time characteristics of the speed of the vehicle are captured by using a BilSTM network. Based on the above, the invention provides a VGBLSTM prediction model to improve the prediction accuracy. Through experimental verification, the defects of a single model can be overcome, and meanwhile, compared with the existing combined model, the prediction precision is further improved. The invention can accurately predict the short-time vehicle speed and provides a favorable reference value for traffic departments.
Drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a block diagram of the GCN of the present invention;
FIG. 2 is a diagram of the structure of the BilSTM according to the present invention;
fig. 3 is an overall flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A short-time vehicle speed prediction method based on space-time fusion comprises the following steps:
step 1: mathematical modeling of GCN
The GCN is capable of handling arbitrary graph structure data, which can be divided into spectral-based methods and spatial-based methods, with spectral-based methods being chosen,
in the convolution layer of the spectrogram, the graph convolution Laplace matrix L which can most reflect the structural property of the graph is shown as the formula (1),
where D is a degree matrix, A is an adjacency matrix, I N Is a matrix of the units,
the convolution operation is distinguished from the convolution operation of the classical convolution operator, the graph convolution is realized by using a linear operator which defines the diagonal in the Fourier domain, the formula of which is shown in formula (2),
g θ *x=Ug θ U T x (2)
wherein, g θ For convolution kernels, U is composed of L eigenvectors, and for larger graph structures, the tangent-ratio schloff polynomial can be used for approximate solution, so that the graph convolution interlayer propagation formula is as (3),
wherein, the first and the second end of the pipe are connected with each other,is the sum of the adjacency matrix and the identity matrix,is composed ofDegree matrix of (H) (l) Is a feature matrix of the l-th layer, W (l) Is the weight matrix of the l-th layer, σ is the activation function,
step 2: mathematical modeling of GCN-BilSTM
The invention captures the vehicle speed space characteristics through the GCN network to obtain the space characteristic vector of the vehicle speed sequence, then inputs the space characteristic vector into the BilSTM network, excavates the time characteristics, the BilSTM is further improved on the basis of the LSTM and consists of a forward LSTM and a backward LSTM, the BilSTM not only can memorize the past state, but also has the dependency on the future state, the structure diagram of the BilSTM is shown in figure 2,
the sequence data enters a hidden layer through an input layer to be respectively subjected to forward and reverse calculation, the final output result is obtained by fusing a forward LSTM output result and a reverse LSTM output result by an output layer according to a certain weight, a BiLSTM hidden output calculation formula is shown in formulas (4) to (6),
wherein the content of the first and second substances,andforward and backward hidden layer states at time q, LSTM is the hidden operation process, y q Space-time association vector, h, representing the input at time q q For the state vector of the BilSTM hidden layer at the moment q, alpha and beta represent the output weights of the forward hidden layer and the reverse hidden layer respectively,
and 3, step 3: mathematical modeling of VMD-GCN-BilSTM
The variational modal decomposition solves the problems of endpoint effect and modal component aliasing existing in Empirical Modal Decomposition (EMD), has the advantage of determining the number of modal decompositions, and has the adaptivity of determining the number of modal decompositions of a given sequence according to the actual situation, compared with the EMD, a non-recursive decomposition mode is adopted, the decomposition result is stable by constructing the variational problem,
and 4, step 4: setting hyper-parameters
The main body of the VMD-GCN-BilTM model is that a VMD processes and decomposes signals, the decomposed signals are input into 2 spliced GCN layers, 2 BilTM layers and 1 full-connection layer, 2 layers of GCN channels are mainly used for extracting the spatial characteristics of the vehicle speed, an added BilTM layer is used for extracting the temporal characteristics of the vehicle speed,
firstly, because the peak period of going to work and going to work can occur every day, the original vehicle speed data has singular values, in order to avoid adverse effect caused by singular sample data and speed up gradient descent to solve the optimal solution, before signal decomposition, data is limited in a certain range, namely normalization processing is adopted, and a normalization formula is shown as a formula (7)
Wherein X is the original data, X min Is the minimum value, X, in the raw data max Is the maximum value in the original data that is,
secondly, the normalized vehicle speed data is input into a decomposition module, the data is decomposed into a plurality of IMF components through a VMD algorithm to obtain time sequences under different frequencies, the influence of noise on the predictive performance of a subsequent model is reduced,
the next training part adopts two layers of GCN to capture the space characteristic learning of the vehicle speed, utilizes two layers of BilSTM to dig the time characteristic,
finally, the prediction value of each subsequence is obtained through the full connection layer, the prediction components are summed to output the prediction result,
and 5: comparison with the present invention by other time series prediction methods
The method is trained to obtain various indexes such as the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), the decision coefficient (R2-score) and the like of the three performance indexes, and other time series prediction methods are compared under the same data set and the same computer.
As a preferred scheme of the invention, the VMD decomposition specifically comprises the following steps:
(1): firstly, constructing variation constraint problem by formulas (8) - (9)
Where K is the number of modes of decomposition, { u k }、{ω k The components and the center frequency of the k-th mode after decomposition are respectively, delta (t) is a Dirac function,
(2): the variation problem is restrained by transforming through the equation (10),
where alpha is a secondary penalty factor, lambda is a Lagrangian multiplier,
(3): search for saddle points of augmented Lagrange function, alternate optimization iteration { u } k }、{ω k And λ, the expressions are formulas (11) to (13),
wherein gamma in the formula represents the noise tolerance,respectively correspond tou i (t), f (t), and λ (t).
And selecting a public vehicle speed data set collected on the los Angeles expressway. The model of the invention is written by adopting Python language, and the flow chart is shown in 3. The specific implementation steps are as follows:
s1: the model inputs vehicle speed data of different time periods of each road section and an adjacency matrix of the relation among the road sections.
S2: because peak periods occur every day, singular values exist in the original vehicle speed data, in order to reduce unnecessary influence of the singular values on the original vehicle speed data and accelerate gradient descent, the original vehicle speed data are subjected to normalization processing, and then the original vehicle speed data are decomposed into a plurality of subsequences with different frequencies by using the VMD module, so that data fluctuation is eliminated, and prediction accuracy is improved.
S3: and modeling the GCN and the GCN-BilSTM according to the methods of the step 1 and the step 2.
S4: firstly, VMD modal components of all sequences are input into a GCN layer, and spatial features of vehicle speed data are captured through GCN network learning to obtain spatial feature vectors of the vehicle speed sequences. Secondly, inputting the feature vectors into a BilSTM layer, and mining the time features of the feature vectors to obtain space-time feature vectors. And finally, transmitting the feature vector to a full-connection layer, and outputting a prediction result of each component.
S5: and performing weighted summation on the prediction of each component, then performing normalization, and finally outputting a prediction result.
S6: and setting parameters. The experiment was carried out in a Python 3.7 environment using a tensiflow framework to complete the construction and training of the model. The method selects a road with the number of 773869 as a prediction point, and the other roads are detection points; selecting the first 6 days as a training set, and selecting the last 1 day as a test set; the model sets a sliding window as 6, and predicts the next 1 time scale; the vehicle speed data is decomposed into 5 components. In GCN-BilSTM, the batch number is set to 64, the training number is 100, the hidden unit layer is 64, and an Adam optimizer is selected. In the training of the model, the learning rate is too small, so that the convergence speed is too low, and the learning rate is too large, so that the convergence is not caused, and therefore, the dynamically-changing learning rate is adopted in the text.
To avoid overfitting during training, the loss function is set to equation (14).
Wherein L is r To regularize the term, λ is the hyperparameter of the loss function in order to prevent overfitting. By tuning the parameters, the lambda of the present invention is set to 0.002.
S7: other time series prediction methods were compared to the present invention. In order to verify the validity of the model proposed by the present invention, mean square error (RMSE), mean Absolute Error (MAE), and decision coefficient R were chosen 2 Sclore was used as an evaluation index in the present invention. The evaluation index is defined by the following formulae (15) to (17).
Wherein, y t Representing the real value of the speed of the road section at the time t,representing the predicted vehicle speed of the road section at the time t,representing the average vehicle speed over the road segment at time t, and n representing the number of samples. RMSE and MAE represent the error condition of the prediction result, and the smaller the value is, the better the prediction result is; r 2 Sclore represents the degree of fit of the regression equation, with larger values indicating better prediction performance.
The model of the invention was compared experimentally on the public data set with 6 other models on 3 indices to obtain the predicted point comparison results shown in table 1.
Table 1: index comparison
As can be seen from the table 1, when the VMD-GCN-BilSTM is compared with other models to run the same group of vehicle speed data, the model of the invention shows good performance on three performance indexes, and the prediction precision of the time sequence is further improved. The method can accurately predict the condition of the short-time vehicle speed, and provides a certain reference value for travelers.
In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and simplifications made in the spirit of the present invention are intended to be included in the scope of the present invention.
Claims (2)
1. A short-time vehicle speed prediction method based on space-time fusion is characterized by comprising the following steps:
step 1: mathematical modeling of GCN
The GCN is capable of handling arbitrary graph structure data, which can be divided into spectral-based methods and spatial-based methods, with spectral-based methods being chosen,
in the convolution layer of the spectrogram, the graph convolution Laplace matrix L which can most reflect the structural property of the graph is shown as the formula (1),
where D is a degree matrix, A is an adjacency matrix, I N Is a matrix of the units,
the convolution operation is distinguished from the convolution operation of the classical convolution operator, the graph convolution is realized by using a linear operator which defines the diagonal in the Fourier domain, the formula of which is shown in formula (2),
g θ *x=Ug θ U T x (2)
wherein, g θ For convolution kernels, U is composed of L eigenvectors, and for larger graph structures, the tangent-ratio schloff polynomial can be used for approximate solution, so that the graph convolution interlayer propagation formula is as (3),
wherein the content of the first and second substances,is the sum of the adjacency matrix and the identity matrix,is composed ofDegree matrix of (H) (l) Is a feature matrix of the l-th layer, W (l) Is the weight matrix of the l-th layer, σ is the activation function,
step 2: mathematical modeling of GCN-BilSTM
The invention captures the vehicle speed space characteristics through the GCN network to obtain the space characteristic vector of the vehicle speed sequence, then inputs the space characteristic vector into the BilSTM network, excavates the time characteristics, the BilSTM is further improved on the basis of the LSTM and consists of a forward LSTM and a backward LSTM, the BilSTM not only can memorize the past state, but also has the dependency on the future state, the structure diagram of the BilSTM is shown in figure 2,
the sequence data enters a hidden layer through an input layer to be respectively subjected to forward and reverse calculation, the final output result is obtained by fusing a forward LSTM output result and a reverse LSTM output result by an output layer according to a certain weight, a BiLSTM hidden output calculation formula is shown in formulas (4) to (6),
wherein the content of the first and second substances,andforward and backward hidden layer states at time q, LSTM is the hidden operation process, y q Representing the spatio-temporal correlation vector of the input at time q, h q For the state vector of the BilSTM hidden layer at the moment q, alpha and beta represent the output weights of the forward hidden layer and the reverse hidden layer respectively,
and step 3: mathematical modeling of VMD-GCN-BilSTM
The variational modal decomposition solves the problems of endpoint effect and modal component aliasing existing in Empirical Modal Decomposition (EMD), has the advantage of determining the number of modal decompositions, and has the adaptivity of determining the number of modal decompositions of a given sequence according to the actual situation, compared with the EMD, a non-recursive decomposition mode is adopted, the decomposition result is stable by constructing the variational problem,
and 4, step 4: setting hyper-parameters
The main body of the VMD-GCN-BilTM model is that the VMD processes and decomposes signals, the decomposed signals are input into 2 spliced GCN layers, 2 BilTM layers and 1 full-connection layer, the 2-layer GCN channel is mainly used for extracting the spatial characteristics of the vehicle speed, the added BilTM layer is used for extracting the time characteristics of the vehicle speed,
firstly, because the peak period of going to work and going to work can occur every day, the original vehicle speed data has singular values, in order to avoid adverse effect caused by singular sample data and speed up gradient descent to solve the optimal solution, before signal decomposition, data is limited in a certain range, namely normalization processing is adopted, and a normalization formula is shown as a formula (7)
Wherein X is the original data, X min Is the minimum value, X, in the raw data max Is the maximum value in the original data that is,
secondly, the normalized vehicle speed data is input into a decomposition module, the data is decomposed into a plurality of IMF components through a VMD algorithm to obtain time sequences under different frequencies, the influence of noise on the predictive performance of a subsequent model is reduced,
the next training part adopts two layers of GCN to capture the space characteristic learning of the vehicle speed, utilizes two layers of BilSTM to dig the time characteristic,
finally, the prediction value of each subsequence is obtained through the full connection layer, the prediction components are summed to output the prediction result,
and 5: comparison with the present invention by other time series prediction methods
The method is trained to obtain various indexes such as the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), the decision coefficient (R2-score) and the like of the three performance indexes, and other time series prediction methods are compared under the same data set and the same computer.
2. The spatiotemporal fusion-based short-term vehicle speed prediction as claimed in claim 1, wherein the VMD decomposition specifically comprises the steps of:
(1): firstly, constructing variation constraint problem by the formulas (8) - (9)
Where K is the number of modes of decomposition, { u k }、{ω k The component and the center frequency of the k-th mode after decomposition are respectively, delta (t) is a Dirac function,
(2): the variation problem is constrained by the transformation of equation (10),
where alpha is a secondary penalty factor, lambda is a Lagrangian multiplier,
(3): search for saddle points of augmented Lagrange function, alternate optimization iteration { u } k }、{ω k And λ, the expressions are formulas (11) to (13),
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