An atmospheric pollution prediction method based on a wavelet transform-based graph convolutional neural network composite model

Abstract

The application provides an atmospheric pollution prediction method based on a wavelet transform-based graph convolutional neural network composite model, adopts a wavelet transform data time-frequency domain decomposition technology to perform time-frequency domain decomposition on the divided data set, solves the entanglement problem of long-time data, constructs time and space information capable of effectively associating pollutants, considers transmission between multiple stations, improves the persuasiveness of the model, and further improves the prediction accuracy of atmospheric pollution. The method is suitable for urban atmospheric pollution prediction, is helpful for simulating and predicting atmospheric environmental changes, and has reference significance for air pollution prevention and control and mining of pollutant transmission rules.

Description

Technical Field

[0001] This invention relates to the fields of big data and artificial intelligence, and in particular to an air pollution prediction method based on a graph convolutional neural network composite model using wavelet transform. Background Technology

[0002] With the advancement of industrialization and urbanization in my country, PM2.5 pollution has become increasingly serious, posing a severe threat to human health. Therefore, PM2.5 monitoring is essential for preventing air pollution. Atmospheric forecasting is influenced by various factors, including meteorological conditions, local characteristics, and environmental topography, and the spread of air pollutants is closely related to spatiotemporal factors. However, most forecasting methods typically lack consideration of spatiotemporal relationships and treat air quality and environmental parameters as individual variables, neglecting long-term characteristics and complex correlations. Therefore, employing a deep learning framework capable of mining correlations in long-term data and integrating spatial geographic information and temporal information is of great significance.

[0003] With the establishment of numerous air quality monitoring stations, the data has become readily available for analysis using deep learning methods, which are widely applied due to their ability to process long-term time-series data. LSTM-FC models have been proposed for pollutant prediction at specific stations; LSTM combined with CNNs has been used to predict PM2.5 concentrations; and ConvNet combined with Dense bidirectional GRUs has also been used to predict PM2.5 concentrations. These models have achieved good prediction results under specific conditions, but time-series data often suffers from noise and a mixture of long-term and short-term information, making it difficult to fully extract temporal characteristics. Furthermore, existing research mainly focuses on air pollution prediction at individual monitoring points, neglecting the spatial correlation between stations, resulting in a lack of understanding and interpretation of pollutant propagation patterns.

[0004] To address spatial relationships, some researchers have embedded spatial feature processing into deep learning methods to uncover patterns in pollutant propagation. However, such embedding has been a challenging task in previous studies. Some researchers have manually rearranged station data into two-dimensional arrays to mine spatial dependencies, achieving relatively good results. However, this lacks analysis of temporal correlations. Other scholars have attempted to simulate spatiotemporal relationships using ConvLSTM; however, this method, based on Convolutional Neural Networks (CNNs), is not suitable for non-Euclidean graphical data structures and performs poorly in atmospheric environment prediction. Summary of the Invention

[0005] To address the technical problems mentioned in the background section, an air pollution prediction method based on a wavelet transform-based graph convolutional neural network composite model is provided, which can improve prediction accuracy.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] An air pollution prediction method based on a graph convolutional neural network composite model using wavelet transform includes the following steps:

[0008] S1, Data preprocessing: Clean the air pollutant data in the area to be predicted and divide it into training set, test set and validation set;

[0009] S2, wavelet transform data time-frequency domain decomposition technique is used to decompose the partitioned dataset in the time-frequency domain;

[0010] S3, construct the decomposed data into a graph structure data;

[0011] S4, construct a graph convolutional neural network composite model, which includes an encoder and a decoder. The encoder is an encoder built based on an attention mechanism, and the decoder is composed of GCN and LSTM.

[0012] S5. Based on the graph structure data and the preset loss function, train the graph convolutional neural network composite model until the loss function converges;

[0013] S6, the pollutant variables obtained in real time from the area to be predicted are input into the graph convolutional neural network composite model in step S5, and after calculation, the prediction results of the target monitoring station in the future preset time period are obtained.

[0014] Furthermore, in step S5, for each iteration of the training process, firstly, the encoder is used to capture the temporal and spatial features in the graph structure data; then, the decoder's GCN is used to extract the encoded spatial features, and LSTM is used to mine the encoded temporal features to obtain the final predicted value. The predicted value is compared with the label value and the loss function value is calculated. The iteration continues until the model reaches its optimal state, that is, the loss function value is minimized, and the training of the model is completed.

[0015] Furthermore, the decoder's workflow is as follows: Original signal X i First, we enter the spatiotemporal block of the GCN, and then use the GCN to extract the original signal X input to the GCN through graph convolution. i Extracting spatial features H from spatial weight matrix A t Then the original signal X i Spatial features H t By performing a connection, we obtain the integrated attention-weighted GCN output. 'l' represents the index of the neural network layer. The output of this GCN forms the input of the LSTM, denoted as Input. lstm =[X i H (l+1)As shown in Equation (1), sequence modeling is shown in Equation (2). The GCN with integrated attention weights is output to LSTM for processing, as shown in Equation (3). Finally, the prediction result is obtained by combining the processing results of the fully connected layer and LSTM.

[0016]

[0017]

[0018]

[0019] In the formula, The output of the LSTM at time t; This represents the hidden state of the LSTM at time t. The hidden state of the LSTM at time t-1 is represented by ; The input represents the output weights of the GCN at time t; t The input represents the original input data. t =X i = [x1,x2,…x t ].

[0020] Furthermore, during the cleaning of air pollutant data in the area to be predicted in step S1, missing and outlier values ​​caused by aging or malfunction of monitoring equipment are processed using linear interpolation to preserve data characteristics and improve computational efficiency.

[0021] Furthermore, in step S2, the partitioned dataset is decomposed into low-frequency components and high-frequency components, as defined by the following formula:

[0022]

[0023]

[0024] In the formula, x[n] represents the original pollutant data, CA1[k] and CD1[k] are the low-frequency and high-frequency parts after the first decomposition, respectively, and CA2[k] and CD2[k] are the low-frequency and high-frequency parts after the second decomposition of CA1[k]; h[kn] and g[kn] represent the low-pass and high-pass filter coefficients, respectively, k is the time index, and n is each point in the data; CA1[n] represents the low-frequency part.

[0025] Furthermore, in step S3, the monitoring stations in the area to be predicted are regarded as graph nodes, the adjacency relationship between the stations is regarded as the edge of the graph, the pollutant parameters constitute the node features, and the distance information between adjacent monitoring stations is used to construct the graph structure.

[0026] Furthermore, the specific method for constructing the graph structure is as follows:

[0027] Given a graph G = (V, A, X, W), where V is the set of nodes, A is the adjacency matrix, X is the feature matrix, and W is the weight matrix, where V = {v1, v2, ..., v...} N}, X∈R N×D N is the number of nodes, D is the feature dimension, and the number of nodes v i The eigenvectors are represented as X i A = {A} 11 A 12 ,…,A ij If A ij =1 indicates that node v i and v j There are edges between them, and nodes are connected according to wind direction, with nodes in the same wind direction connected; the weight matrix W is defined according to the distance between the stations, and the closer the distance d, the greater the weight, that is, the weight of the station edge is defined as the correlation coefficient of the distance, see formula (6):

[0028]

[0029] In the formula, W i,j Let be the weights of node i and node j, and d. i,j The actual distance between node i and node j.

[0030] By adopting the above technical solution, the present invention has the following beneficial effects:

[0031] This invention presents an air pollution prediction method based on a graph convolutional neural network composite model using wavelet transform. The method employs wavelet transform time-frequency domain decomposition technology to decompose the partitioned dataset in the time-frequency domain, resolving the entanglement problem of long-term data. The constructed graph convolutional neural network composite model effectively correlates the temporal and spatial information of pollutants and considers transmission between multiple sites, enhancing the model's persuasiveness and thus improving the accuracy of air pollution prediction. This method is applicable to urban air pollution prediction, aiding in the simulation and prediction of atmospheric environmental changes, and provides valuable insights for air pollution prevention and control and the understanding of pollutant propagation patterns. Attached Figure Description

[0032] Figure 1 The flowchart shows a preferred embodiment of the air pollution prediction method based on a graph convolutional neural network composite model using wavelet transform according to the present invention.

[0033] Figure 2 This is a structural diagram of the encoder in a preferred embodiment of the present invention;

[0034] Figure 3 (a) is a structural diagram of the attention mechanism in the prior art. Figure 3(b) is a structural diagram of the time-space attention mechanism of a preferred embodiment of the present invention;

[0035] Figure 4 This is a flowchart of a method for enhancing the ability to capture the spatiotemporal characteristics of atmospheric pollutant propagation processes in a preferred embodiment of the present invention;

[0036] Figure 5 This is a structural diagram of the decoder in a preferred embodiment of the present invention;

[0037] Figure 6 This is a structural diagram of GCN in a preferred embodiment of the present invention;

[0038] Figure 7 This is a structural diagram of the LSTM in a preferred embodiment of the present invention;

[0039] Figure 8 This is a schematic diagram of the decomposition result of performing time-frequency domain decomposition on the partitioned dataset using the wavelet transform data time-frequency domain decomposition technique of this invention.

[0040] Figure 9 The graph structure constructed using the atmospheric pollution prediction method of this invention for 10 fixed monitoring stations in the Guilin area;

[0041] Figure 10 This is a comparison chart of the predicted results and actual results of the air pollution prediction method of the present invention for the No. 8 Middle School monitoring station.

[0042] Figure 11 This is a comparison chart of the predicted results and actual results for the air pollution prediction method of this invention at the Lingui station.

[0043] Figure 12 A comparison chart of ablation procedures at the No. 8 Middle School site;

[0044] Figure 13 This is a comparison chart of ablation at the Lingui site. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0047] Please see also Figures 1 to 7 A preferred embodiment of the present invention provides an air pollution prediction method based on a graph convolutional neural network composite model using wavelet transform, comprising the following steps:

[0048] S1, Data Preprocessing: Clean the air pollutant data in the area to be predicted and divide it into training set, test set and validation set.

[0049] In this embodiment, the air pollutant data specifically includes PM2.5, PM10, CO, NO2, SO2, O3, and meteorological variable data obtained from various monitoring stations within the area to be predicted. During the data cleaning process in step S1, missing and outlier values ​​caused by aging or malfunctioning monitoring equipment are processed using linear interpolation to preserve data characteristics and improve computational efficiency.

[0050] S2 uses wavelet transform data time-frequency domain decomposition technology to perform time-frequency domain decomposition on the partitioned dataset.

[0051] The temporal correlation of data is often masked. Wavelet transform, as a time-frequency domain decomposition technique, has good performance in frequency division of time-series data, overcoming the limitation of fixed window size and extracting all and local information in the time-frequency domain. Specifically, in step S2, the partitioned dataset is decomposed into low-frequency components and high-frequency components, as defined by the following formula:

[0052]

[0053]

[0054] In the formula, x[n] represents the original pollutant data, CA1[k] and CD1[k] are the low-frequency and high-frequency parts after the first decomposition, respectively, and CA2[k] and CD2[k] are the low-frequency and high-frequency parts after the second decomposition of CA1[k]; h[kn] and g[kn] represent the low-pass and high-pass filter coefficients, respectively, k is the time index, and n is each point in the data; CA1[n] represents the low-frequency part.

[0055] The original data was decomposed using wavelet transform time-frequency domain decomposition (scale 3) to obtain a series of high- and low-frequency variables: CA1, CD1, CA2, CD2, CA3, and CD3. Among them, the low-frequency variable CA1, obtained from the decomposition of the original data, represents the overall trend of pollutant concentration, such as seasonal variations and long-term pollution levels; the high-frequency variable CD1 reflects rapid changes in pollutants, such as diurnal differences and weather influences. CA2, obtained from further decomposition of CA1, represents a more refined medium-term trend, such as monthly variations; CD2 reflects medium-term fluctuations. Finally, CA3, obtained from the decomposition of CA2, represents longer-term trends and influencing factors over longer time scales; CD3 reflects short-term fluctuations and captures more subtle changes. The decomposed variables make it easier for the model to extract spatial dependencies and long-term time-series relationships.

[0056] S3, constructs the decomposed data into a graph structure.

[0057] In this embodiment, in step S3, the monitoring stations within the area to be predicted are considered as graph nodes, the adjacency relationships between stations are considered as edges of the graph, and pollutant parameters constitute node features. Simultaneously, the distance information between adjacent monitoring stations is used to construct the graph structure. Specifically, the method for constructing the graph structure data is as follows:

[0058] Given a graph G = (V, A, X, W), where V is the set of nodes, A is the adjacency matrix, X is the feature matrix, and W is the weight matrix, where V = {v1, v2, ..., v...} N}, X∈R N×D N is the number of nodes, D is the feature dimension, and the number of nodes v i The eigenvectors are represented as X i A = {A} 11 A 12 ,…,A ij If A ij =1 indicates that node v i and v j There are edges between them, and nodes are connected according to wind direction. Nodes with the same wind direction are connected. The weight matrix W is defined according to the distance between the stations. The closer the distance d, the greater the weight. That is, the weight of the station edge is defined as the correlation coefficient of the distance, as shown in formula (3):

[0059]

[0060] In the formula, W i,j Let be the weights of node i and node j, and d. i,j The actual distance between node i and node j.

[0061] S4. Construct a graph convolutional neural network composite model, which includes an encoder and a decoder. The encoder is an encoder built based on an attention mechanism, and the decoder consists of GCN and LSTM.

[0062] An encoder is a deep learning module that transforms input data into a more concise representation that includes key features. The encoder in this embodiment relies on a temporal-spatial attention mechanism, enabling the extraction of spatiotemporal relation weights from the input data. Spatiotemporal relation weights are numerical values ​​used to measure the mutual influence between time and space dimensions; they represent the degree of influence of data at a certain point in time or spatial location on another point in time or spatial location.

[0063] The decoder is a deep learning module that converts the abstract representation generated by the encoder into the original data form or generates new data. For atmospheric data, the decoder can transform complex spatiotemporal features into accurate predictions. In this embodiment, the decoder consists of GCN and LSTM. In the simulation of atmospheric pollution transport, GCN is used to capture the interactions between nodes on the pollution transport surface, while LSTM focuses on the impact of pollutant concentration at a specific moment on future prediction moments.

[0064] GCN improves the accuracy and adaptability of model predictions by performing convolution operations on the nodes of the graph, integrating the feature information of neighboring nodes, and processing complex spatial relationships and dynamic data related to pollutant diffusion. The structure diagram of GCN is shown below. Figure 6 As shown, the workflow is as shown in equations (4)-(6).

[0065] g θ *x=U gθ U T x#(4)

[0066]

[0067]

[0068] Among them, the spectral convolution formula (4) is passed through the Chebyshev polynomial T k (x)=2xT k-1 (x)-T k-2 (x) and a multi-layer graph convolutional network are used to obtain a new expression formula (5), and finally the expression formula (5) is used. Transform into To solve the gradient explosion problem in spatial propagation, the final graph convolution formula (6) is obtained. The input of the l-th layer network is H. (l) , For adjacency matrices with added self-connections, Let w be the degree matrix. (l)Let H be the parameters to be trained, σ be the corresponding activation function, and H be the parameter to be trained. (l+1) For output features. The spectral convolution formula (4) is the existing technology, where g θ is the convolution kernel function, and x is the input.

[0069] LSTM is a special type of recurrent neural network that avoids the vanishing or exploding gradient problem and retains information over a long period of time. It consists of an input layer, hidden layers, and an output layer, with the following structure: Figure 7 As shown, the specific propagation process is as follows:

[0070] f t =σ(w f [h t-1 ,x t ]+b f )# (7)

[0071] i t =σ(w i [h t-1 ,x t ]+b i )#(8)

[0072] o t =σ(w o [h t-1 ,x t ]+b o )#(9)

[0073]

[0074]

[0075] h t =o t *tanh(C t )#(12)

[0076] Where f t i t o t , These are the outputs of the forget gate, input gate, output gate, and candidate memory unit, respectively. f w i w o These are the weight matrices for the three gates, w c Let b be the weight matrix of the candidate memory units. f b i b o b c As a bias term, C t and h t These represent updates to the memory cell state and updates to the hidden state, respectively.

[0077] S5. Based on the graph structure data and the preset loss function, train the graph convolutional neural network composite model until the loss function converges.

[0078] For each iteration of training, firstly, an encoder is used to capture the temporal and spatial features in the graph structure data. In existing technologies, some researchers have used encoders built based on attention mechanisms to capture the spatiotemporal features of atmospheric pollutant propagation processes. However, traditional attention mechanisms suffer from high computational complexity, lack of geospatial structural information, and inability to fully capture multi-scale features. To address this problem, this invention provides a method that enhances the ability to capture the spatiotemporal features of atmospheric pollutant propagation processes, specifically including the following steps:

[0079] S100 maps temporal and spatial features through the linear layer of the encoder, obtaining the query matrix and key matrix of spatial features and the query matrix and key matrix of temporal features, respectively.

[0080] S200, multiply the query matrix of spatial features by the transpose of the key matrix to obtain the spatial relevance matrix, and multiply the query matrix of temporal features by the transpose of the key matrix to obtain the temporal relevance matrix. Specifically, the query matrix and the transpose of the key matrix can be multiplied using the following formula:

[0081] A = QK T

[0082] In the formula, Q is the query matrix, K is the key matrix, and A is the time correlation matrix or spatial correlation matrix obtained by multiplication.

[0083] S300, normalize the obtained spatial correlation matrix and temporal correlation matrix respectively, and use the Tanh activation function to further adjust the normalized spatial correlation matrix and temporal correlation matrix, so that the correlation weights can more accurately capture key features and spatiotemporal relationships.

[0084] Specifically, the obtained time correlation matrix or spatial correlation matrix is ​​normalized using the following formula:

[0085]

[0086] In the formula, S represents the original temporal correlation matrix or spatial correlation matrix. ij Represents the elements of the original temporal correlation matrix or spatial correlation matrix. Represents the elements of the normalized time correlation matrix or spatial correlation matrix.

[0087] The normalized spatial correlation matrix and temporal correlation matrix are further adjusted using the following formula:

[0088]

[0089] In the formula, α is an adjustable scaling factor used to control the sensitivity of the activation function; These are the elements of the adjusted spatiotemporal correlation matrix.

[0090] S400, the adjusted spatial correlation matrix is ​​multiplied by the original data matrix to obtain the spatial feature representation matrix, and the adjusted temporal correlation matrix is ​​multiplied by the original data matrix to obtain the temporal feature representation matrix, so as to strengthen the influence of variables with high spatiotemporal correlation in the final feature representation.

[0091] Specifically, the adjusted spatial correlation matrix or temporal correlation matrix is ​​multiplied by the original data matrix using the following formula:

[0092] H = S adj X

[0093] In the formula, S adj It is the adjusted time correlation matrix or spatial correlation matrix, where X is the original data matrix and H is the adjusted spatial feature representation matrix or time feature representation matrix obtained by multiplication.

[0094] S500 calculates spatial attention weights through spatial feature representation matrices and temporal attention weights through temporal feature representation matrices. It then weights and sums the obtained spatial and temporal attention weights to enhance the temporal and spatial features in atmospheric data.

[0095] Specifically, the spatial attention weight or temporal attention weight α is calculated using the following formula. ij :

[0096] α ij =softmax(A ij )

[0097] In the formula, A ij These are elements of the time correlation matrix or the spatial correlation matrix; for ease of distinction in subsequent calculations, they will be denoted as H′. t Indicates time attention weights. This represents the spatial attention weights; softmax(.) is the exponential normalization function.

[0098] The spatial attention weights and temporal attention weights are weighted and summed according to the following formula to enhance the temporal and spatial characteristics of atmospheric data:

[0099]

[0100] In the formula, H′ t It is time weighting. Here, T is the spatial weight, T is the number of time steps, and H′ is the comprehensive representation of the spatiotemporal feature weights after weighted summation.

[0101] Secondly, the spatial features of the encoded data are extracted using the GCN of the decoder, and the temporal features of the encoded data are mined using LSTM to obtain the final predicted value. Specifically, this includes the following steps:

[0102] Original signal X i First, we enter the spatiotemporal block of the GCN, and then use the GCN to extract the original signal X input to the GCN through graph convolution. i Extracting spatial features H from spatial weight matrix A t Then the original signal X i Spatial features H t By performing a connection, we obtain the integrated attention-weighted GCN output. l is the index of the neural network layer. The output of this GCN forms the input of the LSTM, denoted as Input. lstm =[X i H (l+1) As shown in Equation (14), sequence modeling is shown in Equation (15). The GCN with integrated attention weights is output to LSTM for processing, as shown in Equation (16). Finally, the prediction result is obtained by combining the processing results of the fully connected layer and LSTM.

[0103]

[0104]

[0105]

[0106] In the formula, The output of the LSTM at time t; This represents the hidden state of the LSTM at time t. The hidden state of the LSTM at time t-1 is represented by ; The input represents the output weights of the GCN at time t; t The input represents the original input data. t =X i = [x1,x2,…x t ].

[0107] Finally, the predicted values ​​are compared with the label values, and the loss function value is calculated. This process continues iteratively until the model reaches its optimal state, i.e., the loss function value is minimized, thus completing model training. This embodiment uses a loss function from existing technology to train the model; for brevity, the loss function will not be described in detail here.

[0108] S6, the pollutant variables obtained in real time from the area to be predicted are input into the graph convolutional neural network composite model in step S5, and after calculation, the prediction results of the target monitoring station in the future preset time period are obtained.

[0109] The effectiveness of the air pollution prediction method based on the wavelet transform-based graph convolutional neural network composite model of the present invention will be illustrated below with a specific embodiment.

[0110] The dataset comes from 61 monitoring stations in Guilin area between 2020 and 2023, including 51 micro-monitoring stations and 10 fixed stations, covering PM2.5, PM10, CO, NO2, SO2, O3 and meteorological variables (see Table 1). The dataset is characterized by significant atmospheric turbulence, complex climate, and diverse pollution propagation.

[0111] Table 1

[0112]

[0113] To address missing and outlier values ​​caused by aging or malfunctioning monitoring equipment, this paper employs linear interpolation to preserve data characteristics and improve computational efficiency. The dataset is divided into a 60% training set, a 20% validation set, and a 20% test set.

[0114] Wavelet transform time-frequency domain decomposition (SWT) was used to decompose the partitioned dataset into high-frequency and low-frequency variables to represent the changes in the input data's influence on pollutant propagation at different frequency scales. The decomposition results of the input data are as follows: Figure 8 As shown.

[0115] The graph structure constructed for 10 fixed monitoring stations in the Guilin area is as follows: Figure 9 As shown.

[0116] In atmospheric prediction, the selection of hyperparameters affects the performance and accuracy of the model, making the choice of appropriate hyperparameters particularly important. In this embodiment, the main parameters set are batch size, dropout, learning rate, epoch number, and decomposition scale, as shown in Table 2.

[0117] In terms of evaluation metrics, this paper uses three metrics: root mean square error (RMSE), mean absolute error (MAE), and symmetric mean absolute percentage error (SMAPE). The smaller the value of the above three evaluation metrics, the more accurate the result.

[0118] Table 2. Hyperparameter Definitions

[0119]

[0120] This invention uses atmospheric monitoring data from April 2020 to March 2023 to train the SWT-GCN-LSTM model and evaluates its performance using data from August 1 to 15, 2023. Figure 10 and Figure 11 The comparison between the predicted and actual results for the No. 8 Middle School and Lingui stations is shown separately, with maximum relative errors of 0.10 and 0.15 for PM2.5, respectively. The No. 8 Middle School station performed better than the Lingui station. Although the latter had more missing data and outliers, its overall performance was good, accurately capturing local abrupt changes and long-term time series characteristics of the data.

[0121] The ablation experiments aimed to verify the effectiveness of each module in predicting accuracy. This embodiment constructed three ablation models: SWT-GCN (removing the temporal information extraction module), SWT-LSTM (removing the spatial information extraction module), and GCN-LSTM (removing the frequency separator). Performance was demonstrated using PM2.5 data with the same training parameters. Figure 12 and Figure 13 The observed and predicted values ​​for the No. 8 Middle School and Lingui sites are presented separately. Table 3 shows the quantitative evaluation results of each ablation model. At the No. 8 Middle School site, box 1 shows that although SWT-LSTM has temporal characteristics, its ability to capture local mutations is insufficient; box 2 indicates that GCN-LSTM performs best among the latter three, but due to the lack of time-domain frequency division, it is difficult to accurately capture mutations and temporal relationships; box 3 points out that SWT-GCN can capture some mutations, but it is not sensitive to temporal changes. Similar problems were found at the Lingui site, but due to the insertion of blank data and the processing of more bad values, the performance of GCN-LSTM without frequency division was significantly worse, further proving the necessity and effectiveness of the time-frequency domain decomposition in this paper.

[0122] Ablation experiments demonstrate that each module of the SWT-GCN-LSTM model is effective. Frequency separation improves the model's sensitivity to mutations, GCN extracts spatial features, and LSTM extracts temporal features.

[0123] Table 3. Quantitative results of ablation experiments

[0124]

[0125]

[0126] This invention also compares the existing Random Forest, SVR, RNN, LSTM, and Transformer models with the SWT-GCN-LSTM proposed in this embodiment to verify its superiority. Tables 4 and 5 show the prediction accuracy of the six models for PM2.5 at two sites and different time steps (1, 4, 8, 24h). The results show that SWT-GCN-LSTM has the best prediction performance. Models like RNN and LSTM can capture the temporal nature of data, thus outperforming the non-temporal models Random Forest and SVR in prediction at short to medium time steps (1, 4, 8h). However, they suffer from the "catastrophic forgetting" problem at longer time steps (24h), resulting in poor prediction performance. Although the Transform model is not as good as RNN and LSTM in prediction at short time steps (1, 4h), it performs well in other long time steps. This is because Transform introduces an attention mechanism, which has better prediction stability and avoids the "catastrophic forgetting" problem. The SWT-GCN-LSTM model achieved the best prediction accuracy across all time steps. This is because by separating entangled signals in the data, extracting correlations from complex time-series data, and combining spatial and temporal information, it exhibits better prediction performance and applicability.

[0127] Table 4. Quantitative Results of the Comparative Experiment at the No. 8 Middle School Site

[0128]

[0129]

[0130] Table 5. Quantitative results of the comparative experiment at the Lingui site.

[0131]

[0132] By comparing with a series of deep learning models, it can be concluded that the SWT-GCN-LSTM model constructed in this invention has better predictive performance, which may be attributed to three reasons: First, it separates the mixed signals in the original data, making the temporal variation patterns of variables clearer and thus making it easier to identify the correlations between them; second, it obtains the spatial information of pollutant data and meteorological data through the GCN module, taking into account the spatial location relationship; and third, the model better integrates GCN and LSTM through a space-time attention mechanism, improving the flexibility of the model.

[0133] Using GCN and LSTM models individually each has its advantages and disadvantages: GCN excels at extracting spatial relationships but has limitations in handling temporal dependencies; LSTM can capture time-series features but ignores spatial correlations. Therefore, combining the advantages of both has become a research focus. This invention designs an attention mechanism to extract temporal and spatial weights from atmospheric data and pass these weights to the model, thereby effectively enhancing the model's ability to extract spatiotemporal relationships during the propagation of atmospheric pollutants.

[0134] This attention mechanism enhances the model's ability to capture spatiotemporal relationships by assigning different temporal and spatial weights to the input data, achieving more accurate extraction of spatiotemporal features of atmospheric pollutant propagation processes. Table 6 shows the quantitative results of GCN-LSTM compared to the standalone GCN and LSTM models in terms of prediction. Although GCN and LSTM performed well, GCN-LSTM, utilizing the spatiotemporal attention mechanism, significantly improved its ability to extract spatiotemporal relationships from atmospheric data, achieving the best performance across all evaluation metrics for each station, indicating that the model possesses excellent generalization ability and stability. Although ablation experiments showed that GCN-LSTM performed worse than SWT-GCN-LSTM, GCN-LSTM outperformed both GCN and LSTM standalone models, validating the effectiveness of the improved attention mechanism. This mechanism helps the model capture spatial relationships between stations and the dependencies of temporal data.

[0135] Table 6. Quantitative Results

[0136]

[0137] GCN can automatically learn the spatial relationships between sites through adjacency matrices and graph structures, extract feature similarities between adjacent nodes through convolution operations, capture local changes in pollutant concentration, and aggregate the feature vectors of each node and its neighbors. After multi-layer feature aggregation, the overall diffusion trend of pollutants is extracted. The number of sites affects the ability of GCN to extract spatial features. Table 7 shows the performance of the GCN model under different numbers of sites.

[0138] Table 7. Quantitative Results of the Number of Sites

[0139]

[0140] As can be seen from the table, the predictive performance of the GCN model significantly improves with the increase in the number of sites. Specifically, the RMSE, MAE, and SMAPE values ​​gradually decrease, indicating that more sites provide richer spatial information, enabling the model to more accurately capture the complex relationships between sites and extract the spatial characteristics of pollutants. Therefore, GCN is particularly suitable for multi-site research environments.

[0141] This paper proposes a wavelet transform-based graph convolutional neural network composite model (SWT-GCN-LSTM), which consists of SWT, GCN, and LSTM. The proposed SWT-GCN-LSTM model exhibits excellent performance. Based on experimental results, the following conclusions can be drawn:

[0142] (1) The wavelet transform data time-frequency domain decomposition technique is used to decompose the divided dataset in the time-frequency domain, which can effectively decompose pollutant data in multiple scales, reduce the nonlinearity of the time series, and enhance the model's ability to extract the correlation between pollutant data.

[0143] (2) The proposed SWT-GCN-LSTM model effectively integrates temporal and spatial information on pollutant propagation, achieving prediction errors of only 0.10 and 0.15 for PM2.5 at the No. 8 Middle School and Lingui stations, respectively. Comparative analysis shows that its prediction performance surpasses commonly used prediction models such as Random Forest, SVR, RNN, GRU, and Transformer. Furthermore, ablation experiments demonstrate that each module of the proposed architecture is essential.

[0144] (3) The improved self-attention network mechanism optimizes the processing capability of complex data by extracting time and space weights simultaneously, significantly improves the model's ability to extract the spatiotemporal relationship of atmospheric data, and enhances the ability to capture global and local features.

[0145] This invention proposes a deep learning hybrid model for atmospheric pollution forecasting. By separating signals of different frequencies, it solves the entanglement problem of long-term data, effectively correlating the temporal and spatial information of pollutants, and considering transmission between multiple stations, thus enhancing the model's persuasiveness. This method is applicable to urban air pollution forecasting, helps simulate and predict atmospheric environmental changes, and has reference value for air pollution prevention and control and for understanding the patterns of pollutant propagation.

[0146] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. An atmospheric pollution prediction method based on a wavelet transform-based graph convolutional neural network composite model, characterized in that, Comprising the following steps: S1, data preprocessing: cleaning the atmospheric pollutant data in the to-be-predicted region, and dividing into a training set, a test set and a validation set; S2, using wavelet transform data time-frequency domain decomposition technology to decompose the divided data set in time-frequency domain; S3, constructing the decomposed data into graph structure data; S4, constructing a graph convolutional neural network composite model, the graph convolutional neural network composite model comprising an encoder and a decoder, the encoder being an encoder constructed based on an attention mechanism, and the decoder being composed of GCN and LSTM; S5, training the graph convolutional neural network composite model according to the graph structure data and a preset loss function until the loss function converges; In step S5, for each iteration process of training, first, the encoder is used to capture the time and space features in the graph structure data, comprising the following steps: S100, constructing an encoder based on a time-space attention mechanism, mapping the time features and the space features through the linear layer of the encoder to obtain the query matrix and the key matrix of the space features and the query matrix and the key matrix of the time features, respectively; S200, multiplying the transpose matrix of the query matrix and the key matrix of the space features to obtain a space correlation matrix, and multiplying the transpose matrix of the query matrix and the key matrix of the time features to obtain a time correlation matrix; S300, normalizing the obtained space correlation matrix and time correlation matrix, respectively, and further adjusting the normalized space correlation matrix and time correlation matrix using a Tanh activation function to make the correlation weight more accurately capture the key features and the space-time relationship; S400, multiplying the adjusted space correlation matrix with the original data matrix to obtain a space feature representation matrix, and multiplying the adjusted time correlation matrix with the original data matrix to obtain a time feature representation matrix, to enhance the influence of variables with high correlation in space-time on the final feature representation; S500, calculating the space attention weight through the space feature representation matrix, calculating the time attention weight through the time feature representation matrix, and weighting and summing the obtained space attention weight and time attention weight to enhance the time and space features in the atmospheric data; Then, using the GCN of the decoder to extract the encoded space features, using the LSTM to mine the encoded time features, obtaining the final prediction value, comparing the prediction value with the label value and calculating the loss function value, and continuing iteration until the model reaches the optimum, i.e. the loss function value is minimum, completing the training of the model; The workflow of the decoder is: the original signal X i First, the spatio-temporal block enters the GCN, and the GCN extracts the spatial features H i of the original signal X t through graph convolution. i Then, the original signal X t is connected with the spatial features H lstm to obtain the GCN output integrated with attention weighting. , l is the index of the neural network layer, the GCN output forms the input of the LSTM, denoted as Input i . (l+1) As shown in formula (1), the sequence modeling is as shown in formula (2), and the GCN output integrated with attention weighting is processed by the LSTM as shown in formula (3); finally, the prediction result is obtained by combining the processing result of the LSTM through the full connection layer. wherein, the output of the LSTM representing the t-th time step; the hidden layer state of the LSTM representing the t-th time step, the hidden layer state of the LSTM representing the t-1-th time step; the output weight of the GCN representing the t-th time step; input t representing the original input data, input t = X i = [x1, x2,... x t ]; S6, inputting the pollutant variables obtained in real time from the to-be-predicted region into the graph convolutional neural network composite model of step S5 to obtain the atmospheric pollution prediction result of the target monitoring station in the future preset time period after operation.

2. The wavelet transform-based atmospheric pollution prediction method of claim 1, wherein, In the process of cleaning the atmospheric pollutant data in the to-be-predicted region in step S1, the missing values and abnormal values caused by aging and failure of the monitoring equipment are processed by using linear interpolation method to retain the data characteristics and improve the calculation efficiency. 3.The wavelet transform-based atmospheric pollution prediction method of claim 1, wherein, In step S2, the divided data set is decomposed into low-frequency components and high-frequency components, which are defined by the following formulas: In the formula, x[n] represents the original pollutant data, CA1[k] and CD1[k] are the low-frequency and high-frequency parts after the first decomposition, respectively, CA2[k] and CD2[k] are the low-frequency and high-frequency parts after the second decomposition of CA1[k], h[k-n] and g[k-n] represent the low-pass and high-pass filter coefficients, respectively, k is a time index, n is each point in the data, and CA1[n] represents the low-frequency part. 4.The wavelet transform-based atmospheric pollution prediction method of claim 1, wherein, In step S3, the monitoring stations in the region to be predicted are regarded as graph nodes, the adjacency relationship between the stations is regarded as the edge of the graph, the pollutant parameters constitute the node features, and the distance information between adjacent monitoring stations is utilized to construct the graph structure.

5. The wavelet transform-based atmospheric pollution prediction method of claim 4, wherein the wavelet transform-based graph convolutional neural network composite model is trained by using a dataset including a plurality of atmospheric pollution data and a plurality of atmospheric pollution prediction data. The method for constructing the graph structure is specifically as follows: Given a graph G = (V, A, X, W), V is the node set, A is the adjacency matrix, X is the feature matrix, and W is the weight matrix, where V = {v 1, v2,…,v N}, X ∈ R N×D , N is the number of nodes, D is the feature dimension, and the feature vector of node v i is represented as X i , A = {A 11 , A 12 ,…,A ij}, if A ij = 1, it means that there is an edge between nodes v i and v j , and the nodes are connected according to the wind direction, and the same wind direction nodes are connected; the weight matrix W is defined according to the distance between the stations, the closer the distance d, the greater the weight, that is, the weight of the station edge is defined as the correlation coefficient of the distance, see formula (6): where W i,j is the weight of node i and node j, and d i,j is the actual distance of node i and node j.

Images