A traffic prediction method based on multi-graph gated convolution and Conv-LSTM

Abstract

The application belongs to the technical field of transportation, and particularly relates to a traffic prediction method based on multi-graph gated convolution and Conv-LSTM. The DTWN similarity value filling module is used to calculate the similarity between time series, and the average value of K data with high similarity is taken to fill in the missing data, so as to ensure the integrity of the traffic data. The traffic data is decomposed into approximate coefficients and detail coefficients through DWT. The approximate coefficients reflect the long-term trend of traffic flow, and the detail coefficients contain short-term fluctuation information. Different models are combined to process the data obtained through DWT. The detail coefficients are processed through the multi-graph gated dilated convolution MGDCN to capture the short-term fluctuation, and the approximate coefficients are processed through the Conv-LSTM to capture the long-term trend. Compared with the existing traffic prediction model, the application can fully fill in the missing data, capture the short-term fluctuation and long-term trend of traffic, effectively reduce the error in traffic prediction, and improve the accuracy of traffic prediction.

Description

Technical Field

[0001] The present invention belongs to the field of transportation technology, and specifically relates to a traffic prediction method based on multi-graph gated convolution and Conv-LSTM. Background Art

[0002] Traffic forecasting is an indispensable part of intelligent transportation systems (ITS). Its purpose is to predict the future conditions of urban transportation systems (such as traffic flow and speed, passenger demand, etc.), optimize traffic resource allocation and scheduling, better help travelers arrange their daily travel reasonably, and alleviate traffic congestion and environmental problems.

[0003] Traffic forecasting aims to predict future traffic conditions based on historical traffic data and road network structure. Traditional forecasting methods, including statistical and machine learning approaches, treat forecasting as a regression problem. The most representative algorithms are the historical average algorithm (HA) and the autoregressive integrated moving average algorithm (ARIMA). However, these methods typically only consider temporal information and ignore the spatial correlation of traffic data. Later, some traditional machine learning methods, such as vector regression (VAR), were proposed to model more complex data to solve traffic forecasting problems. While these methods can model more complex data, they place high demands on data quality and are still unable to meet the requirements of nonlinear and non-stationary time series data. With the rise of deep learning, such as in speech recognition, natural language processing, and image processing, an increasing number of researchers are applying deep learning to spatiotemporal data forecasting tasks. Various deep learning-based traffic forecasting models have been developed. These models can provide drivers with real-time road flow information, thereby improving road utilization.

[0004] However, this task remains challenging due to the complex interdependencies between time and space. On the one hand, this is limited by incomplete data. In real-world traffic data collection, data is often missing due to external factors such as sensor failures and communication interruptions. If this missing data is not processed, prediction models will make inferences based on incomplete data, thereby reducing prediction accuracy. On the other hand, traffic time series data is highly dynamic, primarily characterized by its variation consisting of both short-term fluctuations (such as traffic peaks and emergencies) and long-term trends (such as daily commuting patterns and seasonal variations). If a model focuses only on one of these characteristics, it may overlook significant factors, such as changes in traffic patterns caused by holidays or special events. Existing models fail to simultaneously consider these two key characteristics. Furthermore, the non-Euclidean structure of traffic networks further complicates analysis and prediction: two roads that are relatively close but travel in opposite directions can exhibit vastly different traffic conditions. Summary of the Invention

[0005] In view of the technical problem of missing data in real-world traffic data collection due to sensor failure, communication interruption and other external factors, if the missing data is not processed, the prediction model will make inferences based on incomplete data, thereby reducing the prediction accuracy, the application provides a traffic prediction method based on multi-graph gated convolution and Conv-LSTM, which calculates the similarity between time series through DTW, and then takes the average value of K data with high similarity to fill in the missing data, ensuring the integrity of the traffic data.

[0006] In order to solve the above technical problems, the technical scheme adopted by the application is:

[0007] A traffic prediction method based on multi-graph gated convolution and Conv-LSTM, comprising the following steps:

[0008] S1, obtaining historical traffic flow data, preprocessing the data, including detecting data integrity, incomplete data interpolation, normalization, obtaining preprocessed data;

[0009] S2, multi-scale decomposition is performed on the preprocessed data in S1, and discrete wavelet transform DWT is used to input the time series into a low-pass filter and a high-pass filter to obtain approximate coefficients and detail coefficients of different components;

[0010] S3, the detail coefficients are processed by a multi-graph gated convolution network MGDCN to capture short-term fluctuation changes, and the MGDCN is composed of a multi-graph convolution network MGCN and a gated dilated convolution network GDCN;

[0011] S4, the approximate coefficients are processed by a Conv-LSTM to capture long-term trend feature changes, and in the long and short convolution memory network Conv-LSTM, all inputs, forgetting, output gates and cell state updates are completed by convolution operation;

[0012] S5, the data set is divided into training set, validation set and test set in time sequence according to 7:2:1, and the past 10 consecutive time steps are used to predict the future 15min, 30min and 60min traffic state;

[0013] S6, using the trained traffic prediction model in S5 to detect the authenticity of the test data

[0014] The method for preprocessing data in S1 is: using the DTW algorithm in the DTWN module to calculate the similarity value of the missing data points with other time series, for each missing value, the DTW algorithm calculates the K most similar time series, selects the most similar sequence to fill in the missing data points; using Min-Max normalization method to standardize the data to ensure that the data is in the same range.

[0015] The method of using discrete wavelet transform DWT in S2 is: inputting the time series into a low-pass filter and a high-pass filter to obtain the approximate coefficients dA and detail coefficients dD of different components; this process is expressed by the following formula:

[0016]

[0017] Where x is the original data sequence, the low-pass filter L(n) is used to capture the overall trend and major changes in the signal, and the output is the approximate coefficient dA; the high-pass filter H(n) is used to capture the fluctuation details or differences in the signal, and obtain the detail coefficient dD.

[0018] The method for processing detail coefficients by the multi-graph gated convolutional network MGDCN in S3 is:

[0019] S3.1, MGCN focuses on capturing the spatial features of different semantics in the traffic network. By fusing the predefined adjacency matrix and the similarity matrix based on different similarity metrics, the weighted parameters α and β are used to adjust Aperson and Aspearson to adapt to the dynamically changing spatial relationships in the traffic flow. The activated output is added to the hidden state H of the previous layer through the addition operation. l Combined to generate the hidden state H of the next layer 1+1 ;

[0020] S3.2. GDCN further captures temporal features through gating mechanisms and dilated convolutions. The expanded receptive field of dilated convolutions allows the network to capture a wider range of node neighborhoods. The activation function σ is applied to the output of the dilated convolution, enabling the model to learn more complex feature representations.

[0021] The method for processing the approximate coefficients by Conv-LSTM in S4 is:

[0022] S4.1. The input gate receives the feature map of the input time series and processes the input feature map through convolution operations to capture spatial information and determine which information will be written into the cell state. The forget gate uses convolution operations to process the hidden state of the previous moment and the current input, generating a weight for the cell state of the previous moment, indicating the degree of retention of each state unit and determining which information will be discarded from the cell state. The forget gate, input gate, and current hidden state are calculated respectively.

[0023] S4.2. Under the control of the input gate and forget gate, Conv-LSTM updates the unit state; the candidate unit state fuses the hidden state at the current moment and the hidden state at the previous moment. After the output gate determines the information of the output unit state, it is multiplied element by element by the activation function to obtain the final result.

[0024] The DTW algorithm is used to calculate the similarity between missing data points and other time series. The DTW algorithm formula is as follows:

[0025] D(i,j)=|x i ―y j |+min(D(i―1,j),D(i,j―1),D(i―1,j―1))

[0026] where X i =(x1,x2,…,x n ) and Y j =(y1,y2,…,y n ) represent the traffic sequence data of node i and node j respectively, DTW(i, j) represents the similarity value between traffic nodes i and j. The higher the similarity, the closer the two time series are in morphology and pattern.

[0027] The DTW algorithm calculates the K time series that are most similar to it. The formula is as follows:

[0028]

[0029] For each missing data point, find the set of K data points that are most similar to it, and then take the average of these K most similar data points as the interpolation value of the missing point.

[0030] The hidden state H of the next layer is generated in S3.1 1+1 The method is as follows: MGCN focuses on capturing the spatial features of different semantics in the traffic network, and by fusing the predefined adjacency matrix and the similarity matrix based on different similarity measures, it uses the weighted parameters α and β to adjust Aperson and Aspearson to adapt to the dynamically changing spatial relationships in the traffic flow; the MGCN module designs two different adjacency matrices: the predefined adjacency matrix A and the dynamic similarity matrix A s , are input into GCN to capture different semantic space features of the traffic network. The formula is as follows:

[0031]

[0032] Among them, X i =(x1,x2,…,x n ) and Y j =(y1,y2,…,y n ) represent the traffic sequence data of node i and node j respectively, Person(X i ,Y j ) and Spearman(X i ,Y i ) represent the sequence X i and Yj The Pearson and Spearman correlation coefficients between them, α and β are the influencing factors controlling these two coefficients, and ε is the standard deviation of the distance; given the adjacency matrix A and the similarity matrix A s Afterwards, we use GCN to capture the spatial features of the traffic network under different semantics. The formula is as follows:

[0033]

[0034] Among them, σ(·) is a nonlinear activation function, W l and W s l Represent the weight matrix of the l-th layer GCN, and They are the predefined adjacency matrix A and similarity matrix A respectively s The symmetric normalized matrix of I represents the identity matrix, They are The degree matrix of the word is then fused with different semantic space features to obtain the output result H gcn , the formula is as follows:

[0035] H gcn =H l+1 +H s l+1 .

[0036] The method of GDCN in S3.2 to further capture temporal features through gating mechanism and dilated convolution is as follows: GDCN further captures temporal features through gating mechanism and dilated convolution. The dilated receptive field of dilated convolution allows the network to capture a wider range of node neighborhoods. The activation function σ is applied to the output of dilated convolution, enabling the model to learn more complex feature representations. The core of GDCN is the dilated convolutional neural network Dilated CNN. The dilation operation increases the receptive field of the convolution kernel, enabling the network to capture a wider range of contextual information without increasing computational complexity, thereby better simulating traffic flow characteristics at different time scales. In this structure, GDCN first receives the output H of the multi-graph convolution. gcn , the dilated convolution can better capture the long time series features, and combine them using the gating mechanism to obtain the spatiotemporal features H final , the formula is as follows:

[0037] H final =Z*H gcn +(1―Z)σ(DilationConv(H gcn )).

[0038] The method for calculating the forget gate, input gate and the hidden state at the current moment in S4.1 is: the forget gate ft Determine the feature information to be retained, input gate i t To control the transmission of characteristic information, the formula for each gate is shown below:

[0039] f t =σ(W f *[h t―1 ,x t ]+b f )

[0040] i t =σ(W i *[h t―1 ,x t ]+b i )

[0041]

[0042] Among them, f t 、i t and Represent the forget gate, input gate and the hidden state at the current moment, W f 、W i 、W C and b f 、b i 、b C are the trainable parameters of each gate, σ(·) represents the Sigmod activation function, and * represents the convolution operation.

[0043] In S4.2, after the output gate determines the information of the output unit state, the activation function is multiplied element by element to obtain the final result as follows:

[0044] After the forget gate and input gate are calculated, the candidate unit state is integrated with the hidden state at the current moment. and the hidden state C at the previous moment t―1 , the formula is as follows:

[0045]

[0046] Among them, Wc and b c are trainable weights, and C t Respectively represent the cell state at time t and its updated value, ⊙ represents the Hadamard product; after the cell state is updated, it passes through the output gate o t Determine which information of the cell state is output and multiply it element-wise with the cell state through the tanh activation function to obtain the final result h t , whose formula is as follows:

[0047] o t =σ(Wo *[h t―1 ,x t ]+b o )

[0048] h t =o t ⊙tanh(C t )

[0049] where h t represents the output state; W o and b o are trainable weights.

[0050] Compared with the prior art, the present application has the beneficial effects that:

[0051] 1、The present application proposes a DTWN similarity value filling module, which ensures the integrity of traffic data through DTW calculation. In real-world traffic data collection, due to sensor failure, communication interruption and other external factors, data is missing, and if these missing data are not processed, the prediction model will make inferences based on incomplete data, thereby reducing the prediction accuracy. Although some studies fill in missing data through mean, hot platform or random interpolation methods, these methods usually cannot take into account the time dependence, such as seasonality and trend changes, and mean interpolation may smooth too many data details, while hot platform interpolation may introduce bias due to the selection of inappropriate "neighbor" data. K-Nearest Neighbor (KNN) and multiple interpolation methods are widely used, among which KNN interpolation fills in missing data by finding the K nearest neighbor values in the data set with the Euclidean distance of the missing data point, and multiple interpolation generates multiple possible complete data sets to estimate the uncertainty of interpolation while filling in, these methods can better maintain the essential features and structure of the data, and provide more accurate interpolation effect than simple methods. However, existing data interpolation methods often ignore a key factor when dealing with missing data problems: the similarity between data points, which will result in the inability to fully utilize the inherent relevance and patterns of data in the interpolation process, and the inability to reflect the essential characteristics of real data. The present application calculates the similarity between time series through DTW, and then takes the average value of K data with high similarity to fill in the missing data, ensuring the integrity of traffic data.

[0052] 2. The present invention uses DWT to decompose traffic flow data, and separately processes the approximate coefficients that reflect the long-term trend of traffic flow and the detailed coefficients that contain short-term fluctuation information. Traffic time series data is highly dynamic, mainly reflected in the fact that its changing pattern is composed of short-term fluctuations (traffic peaks, emergencies, etc.) and long-term trends (daily commuting patterns, seasonal changes, etc.). If the model only focuses on one of the characteristics, some factors with significant influence may be ignored, such as changes in traffic patterns that may be caused by holidays or special events, and the existing models fail to consider these two key characteristics at the same time. The present invention decomposes traffic data through DWT and divides it into approximate coefficients and detailed coefficients. The approximate coefficients reflect the long-term trend of traffic flow, while the detailed coefficients contain short-term fluctuation information. The data obtained by processing DWT is obtained by combining different models.

[0053] 3. This invention designs a multi-graph gated dilated convolution (MGDCN) to process detail coefficients to capture short-term fluctuations; and uses Conv-LSTM to process approximate coefficients to capture long-term trends. A key parameter of traffic flow data is time series. Multi-graphs cannot meet the needs of increasingly complex time-dependent sequence data and real-time changes. Scholars have begun to use codec architectures to develop prediction models. For example, the Multi-Scale Spatiotemporal Aware Transformer (MSSTAT) model, by combining a multi-scale transformer architecture with a data-driven graph convolutional network, can not only capture static features of geographic locations but also dynamically reflect the similarity of traffic patterns, thereby better simulating and predicting traffic flow. However, existing models ignore two major characteristics of traffic data: short-term fluctuations and long-term trends. This can lead to the inability to adjust prediction strategies in time when faced with emergencies, resulting in a slow or inaccurate response to traffic conditions. The decomposition model strategy of this invention not only improves the model's ability to capture short-term and long-term traffic data characteristics, but also enables a more comprehensive understanding and prediction of the complex changing patterns of traffic flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can, without inventive effort, derive other implementation drawings based on the provided drawings.

[0055] The structures, proportions, sizes, etc. illustrated in this specification are intended solely to complement the contents disclosed herein and to facilitate understanding and reading by persons skilled in the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, without affecting the efficacy and objectives of the present invention, shall remain within the scope of the technical contents disclosed herein.

[0056] Figure 1 It is a schematic diagram of the principle of the present invention.

[0057] Figure 2 Schematic diagram of the MGDCN module of the present invention.

[0058] Figure 3 Schematic diagram of the Dilated CNN module of the present invention.

[0059] Figure 4 Schematic diagram of the Conv-LSTM module of the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of this application, not all the embodiments. These descriptions are only to further illustrate the features and advantages of the present invention, rather than to limit the claims of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0061] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following embodiments are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0062] refer to Figures 1-4 , the technical solution of the present invention is introduced in detail below.

[0063] Step 1) Obtain historical traffic flow data and preprocess the data, including checking data integrity, interpolating incomplete data, and normalizing the data to obtain preprocessed data;

[0064] Step 2) Use the DTW algorithm in the DTWN module to calculate the similarity between the missing data points and other time series. For each missing value, the DTW algorithm calculates the K most similar time series and selects the series with the highest similarity to fill the missing data point. Use the Min-Max normalization method to normalize the data to ensure that the data are within the same range.

[0065] Step 3) Perform multi-scale decomposition on the pre-processed data in step 1, use discrete wavelet transform (DWT), input the time series into low-pass filter and high-pass filter, and obtain the approximate coefficients of different components and detail coefficients.

[0066] Step 4) Process the detail coefficients through the Multi-Graph Gated Convolutional Network (MGDCN) to capture changes in short-term fluctuations. MGDCN consists of two parts: the Multi-Graph Convolutional Network (MGCN) and the Gate-Dilated Convolutional Network (GDCN).

[0067] Step 5) MGCN focuses on capturing the spatial features of different semantics in the traffic network. By fusing the predefined adjacency matrix and the similarity matrix based on different similarity metrics, it uses the weighted parameters α and β to adjust Aperson and Aspearson to adapt to the dynamically changing spatial relationships in the traffic flow. The activated output is added to the hidden state H of the previous layer through the addition operation. l Combined to generate the hidden state H of the next layer 1+1 ;

[0068] Step 6) GDCN further captures temporal features through a gating mechanism and dilated convolution. The dilated receptive field of dilated convolution allows the network to capture a wider range of node neighborhoods. The activation function σ is applied to the output of the dilated convolution, enabling the model to learn more complex feature representations.

[0069] Step 7) Process the approximate coefficients through Conv-LSTM to capture long-term trend feature changes. In the long short-term convolutional memory network Conv-LSTM, all input, forget, output gates, and unit state updates are completed by convolution operations;

[0070] Step 8) The input gate receives the feature map of the input time series and processes the input feature map through a convolution operation to capture spatial information and determine which information will be written into the cell state. The forget gate uses a convolution operation to process the hidden state of the previous moment and the current input, generating a weight for the cell state of the previous moment, indicating the degree of retention of each state unit and determining which information will be discarded from the cell state. The forget gate, input gate, and current hidden state are calculated separately;

[0071] Step 9) Under the control of the input gate and forget gate, the Conv-LSTM updates the cell state. The candidate cell state is a fusion of the current hidden state and the previous hidden state. After passing through the output gate to determine the output cell state information, it is multiplied element-by-element by the activation function to obtain the final result.

[0072] Step 10) The dataset is divided into training, validation, and test sets in a temporal ratio of 7:2:1. The traffic status for the next 15 minutes, 30 minutes, and 60 minutes is predicted using the past 10 consecutive time steps. The proposed method is compared with other algorithms, and the impact of parameters is analyzed. Ablation experiments are performed to understand the individual contributions of each module to the traffic prediction task.

[0073] Step 11) Use the traffic prediction model trained in step 5 to perform authenticity check on the test data.

[0074] A series of experiments were conducted on two datasets, PEMSD7(M) and PEMSD7(L), which are collected in real time every 30 seconds by the California Transportation Performance System (PEMS). These two datasets cover traffic information collected on weekdays from May to June 2012. The raw data are aggregated into timestamps every 5 minutes. The PeMSD7(M) dataset contains data monitored by 228 sensors, and the PeMSD7(L) dataset contains data monitored by 1026 sensors. The accuracy (ACC) on these two datasets reached 0.92 and 0.91 respectively, while the mean absolute error (MAE) was reduced to 2.86 and 3.18 respectively, and the root mean square error (RMSE) was reduced to 4.96 and 5.53 respectively. It was verified that the present invention has high accuracy and low error and can be applied to traffic flow prediction.

[0075] The above only describes in detail the preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the purpose of the present invention, and various changes should be included in the scope of protection of the present invention.

Claims

1. A traffic prediction method based on multi-graph gated convolution and Conv-LSTM, characterized in that: The following steps are involved: S1. Obtain historical traffic flow data and preprocess the data, including detecting data integrity, interpolating incomplete data, and normalizing the data to obtain preprocessed data; S2, perform multi-scale decomposition on the pre-processed data in S1, use discrete wavelet transform DWT, input the time series into low-pass filter and high-pass filter, and obtain the approximate coefficients of different components and detail coefficients; S3. Processing detail coefficients through the Multi-graph Gated Convolutional Network (MGDCN) to capture short-term fluctuations. MGDCN consists of two parts: the Multi-graph Convolutional Network (MGCN) and the Gate-controlled Dilated Convolutional Network (GDCN). S3.1, MGCN focuses on capturing the spatial features of different semantics in the traffic network. By fusing the predefined adjacency matrix and the similarity matrix based on different similarity metrics, the weighted parameters α and β are used to adjust Aperson and Aspearson to adapt to the dynamically changing spatial relationships in the traffic flow. The activated output is added to the hidden state H of the previous layer through the addition operation. l Combined to generate the hidden state H of the next layer 1+1 ; The MGCN module designs two different adjacency matrices: a predefined adjacency matrix A and a dynamic similarity matrix A. s , are input into GCN to capture different semantic space features of the traffic network. The formula is as follows: Among them, X i =(x1,x2,…,x n ) and Y j =(y1,y2,…,y n ) represent the traffic sequence data of node i and node j respectively, Person(X i ,Y j ) and Spearman(X i ,Y j ) represent the sequence X i and Y j The Pearson and Spearman correlation coefficients between them, α and β are the influencing factors controlling these two coefficients, and ε is the standard deviation of the distance; given the adjacency matrix A and the similarity matrix A s Afterwards, GCN is used to capture the spatial features of the traffic network under different semantics. The formula is as follows: Among them, σ(·) is a nonlinear activation function, W l and W s l Represent the weight matrix of the l-th layer GCN, and They are the predefined adjacency matrix A and similarity matrix A respectively s The symmetric normalized matrix of I represents the identity matrix, They are The degree matrix of the word is then fused with different semantic space features to obtain the output result H gcn , the formula is as follows: H gcn =H l+1 +H s l+1 ; S3.2, GDCN further captures temporal features through gating mechanisms and dilated convolutions. The dilated receptive field of dilated convolutions allows the network to capture a wider range of node neighborhoods. The activation function σ is applied to the output of the dilated convolution, enabling the model to learn more complex feature representations. The core of GDCN is the Dilated Convolutional Neural Network (CNN). The dilation operation increases the receptive field of the convolution kernel, enabling the network to capture a wider range of contextual information without increasing computational complexity, thereby better simulating traffic flow characteristics at different time scales. In this structure, GDCN first receives the output H of the multi-graph convolution. gcn , through the expansion convolution, we can better capture the long time series features, and use the gating mechanism to combine them to obtain the spatiotemporal features The formula is as follows: H final =Z*H gcn +(1-Z)σ(DilationConv(H gcn )); S4. Use Conv-LSTM to process approximate coefficients and capture long-term trend feature changes. In the long short-term convolutional memory network Conv-LSTM, all input, forgetting, output gates, and unit state updates are completed by convolution operations; S5. Divide the dataset into training set, validation set and test set in chronological order of 7:2:1, and use the past 10 consecutive time steps to predict the traffic status of the next 15 minutes, 30 minutes and 60 minutes; S6. Use the traffic prediction model trained in S5 to perform authenticity check on the test data.

2. A traffic prediction method based on multi-graph gated convolution and Conv-LSTM according to claim 1, characterized in that: The method for preprocessing the data in S1 is: using the DTW algorithm in the DTWN module to calculate the similarity value between the missing data point and other time series. For each missing value, the DTW algorithm calculates the K time series that are most similar to it, and selects the series with the highest similarity to fill the missing data point; The data were normalized using the Min-Max normalization method to ensure that the data were within the same range.

3. The traffic prediction method based on multi-graph gated convolution and Conv-LSTM according to claim 1, characterized in that: The method of using discrete wavelet transform DWT in S2 is: inputting the time series into a low-pass filter and a high-pass filter to obtain the approximate coefficient dA and detail coefficient dD of different components; this process is expressed by the following formula: Where x is the original data sequence, the low-pass filter L(n) is used to capture the overall trend and major changes in the signal, and the output is the approximate coefficient dA; the high-pass filter H(n) is used to capture the fluctuation details or differences in the signal, and obtain the detail coefficient dD.

4. The traffic prediction method based on multi-graph gated convolution and Conv-LSTM according to claim 1, characterized in that: The method for processing the approximate coefficients by Conv-LSTM in S4 is: S4.

1. The input gate receives the feature map of the input time series and processes the input feature map through convolution operations to capture spatial information and determine which information will be written into the cell state. The forget gate uses convolution operations to process the hidden state of the previous moment and the current input, generating a weight for the cell state of the previous moment, indicating the degree of retention of each state unit and determining which information will be discarded from the cell state. The forget gate, input gate, and current hidden state are calculated respectively. S4.

2. Under the control of the input gate and forget gate, Conv-LSTM updates the unit state; The candidate unit state fuses the hidden state of the current moment and the hidden state of the previous moment. After passing through the output gate to determine the information of the output unit state, it is multiplied element by element through the activation function to obtain the final result.

5. The traffic prediction method based on multi-graph gated convolution and Conv-LSTM according to claim 2, characterized in that: The DTW algorithm is used to calculate the similarity between missing data points and other time series. The DTW algorithm formula is as follows: D(i,j)=|x i -y j |+min(D(i-1,j),D(i,j-1),D(i-1,j-1)) where X i =(x1,x2,…,x n ) and Y j =(y1,y2,…,y n ) represent the traffic sequence data of node i and node j respectively, D(i, j) represents the similarity value between traffic nodes i and j. The higher the similarity, the closer the two time series are in morphology and pattern. The DTW algorithm calculates the K most similar time series. The formula is as follows: For each missing data point, find the set of K data points that are most similar to it, and then take the average of these K most similar data points as the interpolation value of the missing point.

6. The traffic prediction method based on multi-graph gated convolution and Conv-LSTM according to claim 4, characterized in that: The method for calculating the forget gate, input gate and the hidden state at the current moment in S4.1 is: the forget gate f t Determine the feature information to be retained, input gate i t To control the transmission of characteristic information, the formula for each gate is shown below: f t =σ(W f *[h t-1 ,x t ]+b f ) i t =σ(W i *[h t-1 ,x t ]+b i ) Among them, f t 、i t and Represent the forget gate, input gate and the hidden state at the current moment, W f 、W i 、W C and b f 、b i 、b C are the trainable parameters of each gate, σ(·) represents the Sigmod activation function, and * represents the convolution operation.

7. The traffic prediction method based on multi-graph gated convolution and Conv-LSTM according to claim 6, characterized in that: In S4.2, after the output gate determines the information of the output unit state, the activation function is multiplied element by element to obtain the final result as follows: After the forget gate and input gate are calculated, the candidate unit state is integrated with the hidden state at the current moment. and the hidden state C at the previous moment t-1 , the formula is as follows: in, and C t Respectively represent the cell state at time t and its updated value, ⊙ represents the Hadamard product; after the cell state is updated, it passes through the output gate o t Determine which information of the cell state is output and multiply it element-wise with the cell state through the tanh activation function to obtain the final result h t , whose formula is as follows: the t =σ(W o *[h t-1 ,x t ]+b o ) h t =o t ⊙tanh(C t ) Among them, h t Indicates output status; W o and b o are trainable weights.

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