Multi-station air quality prediction method based on adaptive hierarchical graph convolution

Abstract

The invention provides a multi-site air quality prediction method based on adaptive hierarchical graph convolution, and belongs to the technical field of air quality prediction. The invention discloses a multi-site air quality prediction method based on self-adaptive hierarchical graph convolution, which is used for solving the problem that the real relationship between sites cannot be accurately represented by the current PM2.5 prediction method. According to the method, a hierarchical mapping graph convolution architecture is introduced, and different self-learning adjacency matrixes are used on different hierarchies, so that unique space-time dependence among different sites is effectively mined. And then connecting upper and lower adjacent matrixes based on an attention aggregation mechanism, and accelerating a convergence process. And finally, combining the hidden space state with a gating circulation unit to form a unified prediction architecture, capturing a multi-level space dependency relationship and a multi-level time dependency relationship, and providing a final prediction result. The invention provides a new thought and method for air quality prediction, and is helpful for better monitoring and controlling air pollution.

Description

Technical Field

[0001] This invention belongs to the field of air quality prediction technology, specifically a multi-site air quality prediction method based on adaptive hierarchical graph convolution. Background Technology

[0002] Against the backdrop of industrialization and urbanization, air pollution has become a major concern. PM2.5 (particulate matter with an aerodynamic diameter of 2.5 mm or less) is a particularly dangerous factor, as it can directly enter the human body and harm health. However, controlling smog requires more real-time air quality monitoring data. Accurate and efficient prediction of near-term PM2.5 concentrations is essential for effectively preventing and controlling air pollution and for urban management planning.

[0003] Due to the importance of PM2.5 concentration prediction, significant progress has been made in this field in recent years. The main developments can be divided into three distinct phases:

[0004] (1) Early studies combined data mining methods with statistical analysis. Zhang et al. studied the performance of weather research and forecasting (WRF) / community multiscale air quality (CMAQ) models in the eastern United States (Zhang H, Chen G, Hu J, et al. Evaluation of a seven-year air quality simulation using the Weather Research and Forecasting (WRF) / Community Multiscale Air Quality (CMAQ) models in the eastern United States[J]. Science of the Total Environment, 2014, 473:275-285.). However, due to the limitations of the research area and data, these methods are difficult to fit nonlinear characteristics, resulting in reduced prediction accuracy.

[0005] (2) In recent years, the rapid development of deep learning has provided a new solution for learning spatiotemporal dependencies from input data. Researchers treat the entire city as an image and divide it into grids, using convolutional neural networks to extract spatial correlations within sequences. In addition, Guo et al. used a combination of recurrent neural networks and convolutional neural networks to capture temporal dependencies within sequences, achieving good results. However, the efficient aggregation of spatial neighbors by convolutional neural network-based methods makes them insensitive to long-distance dependencies and only applicable to Euclidean spatial structures. Lin et al. designed a multivariate linear regression gated recurrent unit method based on gated recurrent units and its variants to predict multi-site data (Lin CY, ChangY S, Abimannan S. Ensemble multifeatured deep learning models for air quality forecasting[J]. Atmospheric Pollution Research,2021,12(5):101045.). However, recurrent neural networks and their variants ignore the spatial dependencies of data, which can easily affect the prediction accuracy.

[0006] Convolutional Neural Network (CNN): A deep learning model that primarily uses convolutional operations, suitable for image recognition and processing tasks. Its structure includes convolutional layers, activation layers, pooling layers, etc., and it learns the features of input data to perform tasks such as classification or regression.

[0007] Recurrent Neural Network (RNN): A type of neural network with short-term memory capabilities, capable of capturing time-series information when processing sequential data, such as in tasks like natural language processing, speech recognition, and time series prediction.

[0008] Gated Recurrent Unit (GRU): This is an improved RNN structure that uses a gating mechanism to control the flow of information in the network, effectively solving the problems of vanishing and exploding gradients, and improving the performance of the model when processing long sequence data.

[0009] (3) Graph convolutional networks are a generalization of CNNs to graph structures and are suitable for processing non-Euclidean spatial data. Due to the topology of air quality monitoring stations, graph convolutional networks have been successfully and widely used in the field of PM2.5 concentration prediction. Some researchers have used graph convolutional networks to extract spatial dependencies in PM2.5 concentration prediction. In addition, they have tried to combine graph convolutional networks with bidirectional long short-term memory networks to capture spatiotemporal dependencies. Wang et al. combined multi-graph attention graph convolution with GRU to aggregate the spatiotemporal features of related stations between different graphs, which effectively improved the prediction accuracy (Wang C, Zhu Y, Zang T, et al. Modeling inter-station relationships with attentive temporalgraph convolutional network for air quality prediction[C] / / Proceedings of the 14th ACM international conference on web search and datamining.2021:616-634.).

[0010] Graph Convolutional Networks (GCNs) are deep learning models used to process graph data. Their main function is to capture spatial features in graph-structured data, enabling tasks such as node classification, edge classification, and graph classification. By extracting features from graphs through graph convolution operations, GCNs offer new approaches to solving various graph analysis problems.

[0011] Long Short-Term Memory (LSTM) is an improved RNN structure that effectively solves the gradient vanishing and gradient explosion problems by introducing gating mechanisms, forget gates, input gates, output gates, and memory systems, thereby achieving efficient modeling and processing of long sequence data.

[0012] Bidirectional Long Short-Term Memory (Bi-LSTM) network: This is a special RNN architecture that simultaneously considers historical and future information in a sequence by including a forward LSTM layer and a backward LSTM layer, thereby improving the performance of tasks that process sequence data.

[0013] Although the effectiveness of GCN in PM2.5 prediction has been validated, four important issues remain unresolved: (1) The adjacency matrix determines the aggregation method in graph convolutional networks, but it is often fixed and generated through heuristics based on spatial distance or graph connectivity. These methods fail to capture the true spatiotemporal dependencies. (2) Existing methods neglect the hierarchical dependencies in air quality prediction. Air quality is influenced by a variety of factors at global, regional, and local scales. These factors interact hierarchically, meaning that a prediction or input at one level depends on a prediction at a higher level. For example, the environmental conditions in a surrounding area may be affected by unexpected events (such as factory pollution leaks), but such disturbances may not necessarily affect the air quality of the entire city. (3) Current graph convolutional methods mainly follow the perspective of graph signal processing, tending to smooth the input signals of nodes. In this case, it is difficult to effectively obtain high-level representations of multi-level data using only an adjacency matrix stackable graph convolutional layer. (4) The contribution of different hierarchical representations to the final air quality should not be static but dynamically changing. For example, specific weather anomalies (such as haze) may increase the influence of low-level features. These issues can be used to improve current air quality prediction research. Summary of the Invention

[0014] To address the shortcomings of existing technologies and research, this invention proposes a novel deep learning framework, namely an adaptive hierarchical graph convolutional neural network, for PM2.5 prediction. To achieve the above objective, this invention provides the following technical solution: a multi-site air quality prediction method based on adaptive hierarchical graph convolution.

[0015] Graph Convolutional Neural Network (GCNN) is a deep learning model that learns based on graph structures. It performs convolution operations and extracts node features on graph data to analyze and process graph data, and is widely used in tasks such as node classification, graph classification, and graph edge prediction.

[0016] Adaptive Hierarchical Graph Convolutional Neural Network (AHGCNN) is a deep learning model based on graph convolutional neural networks. It adaptively learns hierarchical features in graph structures to achieve efficient analysis and processing of graph data. This network structure exhibits good performance in tasks such as node classification, edge classification, and graph classification.

[0017] Specifically, to address the inefficiency and inaccuracy of mainstream graph convolutional networks in capturing multi-level spatial dependencies, an adaptive hierarchical graph convolution is introduced. By self-learning the adjacency matrix, this network can dynamically extract spatial dependencies at each level.

[0018] Hierarchical Mapping Graph Convolution (HMGC) is an extension of graph convolutional neural networks that adaptively learns hierarchical features in graph structures. It analyzes and processes graph data in a hierarchical manner to improve performance in tasks such as node classification, edge classification, and graph classification.

[0019] Furthermore, a hierarchical topological correlation model is constructed, providing an attention-based hierarchical aggregation mechanism that implements a graph convolutional structure with low computational cost. Then, the linear units in the GRU are replaced with HMGCs to form adaptive hierarchical graph convolutional gated recurrent units, which are stacked in multiple layers to build the main network structure and output the prediction results.

[0020] The Adaptive Hierarchical Graph Convolution-Gated Recurrent Unit (AHGC-GRU) is a deep learning model that combines graph convolutional neural networks and gated recurrent units. It adaptively learns hierarchical features in graph structures and captures dynamic changes through the gated recurrent units, making it suitable for analyzing and predicting dynamic network data. This model demonstrates good performance in tasks such as node classification, edge classification, and graph classification.

[0021] The basic components of the AHGCNN model of this invention include adjacency matrix generation, hierarchical mapping graph convolution, adaptive dynamic graph construction, hierarchical information fusion based on attention mechanism, and time-dependent modeling. The specific implementation of each module of the AHGCNN model is described in detail below.

[0022] (1) Adjacency matrix generation

[0023] The adjacency matrix determines how nodes and their neighbors are aggregated in graph convolution. Existing research relies on prior knowledge to construct the graph structure in advance, while the method of this invention is entirely data-driven and therefore able to capture the temporal dependencies between data.

[0024] An adjacency matrix is ​​a matrix used to represent the connectivity between nodes in a graph, where the matrix elements are 0 or 1, indicating whether there is an edge connecting the nodes.

[0025] For a given set of graph signals Transform it into a two-dimensional matrix X with dimensions (τ×d)×N.l To effectively capture the internal similarities between different sites and filter out redundant information, this invention uses Singular Value Decomposition (SVD) to transform X... l It can be broken down into two parts. That is:

[0026] SVD(X l )→(X s ,X t (Equation 1)

[0027] Among them, X s and X t These represent matrices divided by time dimension and site dimension, respectively.

[0028] Singular Value Decomposition (SVD) is a matrix factorization method that decomposes a matrix into the product of three matrices, including an orthogonal matrix, a diagonal matrix, and an orthogonal matrix. It is widely used in fields such as machine learning.

[0029] Matrix X l It contains a large amount of redundant information. Dimensionality reduction using SVD can filter out this redundant information, thereby revealing the hidden pattern. Matrix X s ∈R N×γ This invention includes a high-level representation of each site's features, where γ represents the dimension of the feature and N is the number of sites. The invention employs a Gaussian kernel-based method to compute matrix X. s The similarity between the x-th row and the y-th column is used as the edge weight in the generated adjacency matrix. The formula is defined as follows:

[0030]

[0031] Where A xy It refers to the element in the x-th row and y-th column of the adjacency matrix A, where β is the standard deviation.

[0032] Gaussian kernel: Based on the Gaussian function, it is represented by calculating the Euclidean distance from a point to its center point and its exponential decay. The Gaussian kernel plays an important role in image processing, feature extraction, and pattern recognition.

[0033] (2) Hierarchical mapping graph convolution

[0034] To efficiently and accurately capture multi-layer spatial dependencies, this invention introduces a novel graph convolutional network: Hierarchical Graph Convolutional Networks (HGCN). HMGC is an extension of GCN that captures multi-scale information in the graph by introducing a hierarchical structure, thereby extracting features and performing classification and prediction in complex graph structures. A key feature of HMGC is that each layer contains a unique adjacency matrix, allowing for more flexible modeling of the underlying graph structure. This structure can be recursively defined as follows:

[0035]

[0036] Z (m) Z represents the input of layer m+1, while Z (m+1) It is not only the output of the (m+1)th layer, but also the input of the (m+2)th layer. Parameters and θ (m) This represents the parameters of the graph convolution filter in the m-th layer. This represents a graph convolution operation. The hierarchical relationship between nodes is represented by A. (m) Modeling, A (m) The value depends on the hierarchy. This is achieved using a hierarchical mapping function. Construct the upper-level adjacency matrix of the (m+1)th layer:

[0037]

[0038] The initial graph structure generated by equation (3) is normalized and used to initialize the adjacency matrix, and then optimized using stochastic gradient descent. The initial layer of HMGC is defined as follows:

[0039] A (0) =D -1 A xy (Equation 5)

[0040] Z (1) =A (0) Z (0) θ (0) (Equation 6)

[0041] D represents the diagonal matrix of node degrees. Z (0) =X, where at each time step, the feature matrix X∈R N×d As input to the initial layer of HMGC.

[0042] (3) Adaptive dynamic graph construction

[0043] In reality, graph structures are not always available, and the relationships between nodes often change over time. Furthermore, PM2.5 concentrations are closely related to weather conditions. Under similar weather conditions, air quality tends to be more uniform than under different weather conditions. Therefore, this invention follows the model training process to construct a dynamic adjacency matrix between different layers.

[0044] First, the number of nodes leads to the need to update the N×N adjacency matrix and the mapping function. The computational cost is high, leading to overparameterization during training. To address this issue, this invention employs SVD to transform A... (0) ∈R N×N Decomposed into two smaller matrices:

[0045]

[0046] This indicates that the source node of the first layer is embedded, while This represents the target node embedding. L represents the dimension. It is worth noting that the number of trainable parameters has decreased from N×N to N×L.

[0047] function This is implemented using fully connected layers to simulate inter-layer dependencies. The parameters of the fully connected layers are shared between E1 and E2.

[0048]

[0049] in this case, and These represent the source node embedding and the target node embedding in the m-th layer, respectively. The symbol W (m-1) and b (m-1) Let represent the weight matrix and the bias vector, respectively. To simplify the model, the feature dimensions of E1 and E2 at different levels are set to L, thereby reducing the number of parameters for each mapping to L×(L+1).

[0050] Based on equations (3) and (8), the mathematical expression for HMGC can be redefined as:

[0051]

[0052] (4) Hierarchical information fusion based on attention mechanism

[0053] In order to aggregate information from all graph convolutional layers, rather than extracting information from just one fixed layer, this invention implements a multi-layer aggregation strategy through an attention mechanism to selectively select information that has a greater impact on the accuracy of the current prediction task.

[0054] Attention mechanism: A strategy in deep learning models that simulates human attention behavior by assigning different weights to different parts of the input sequence in order to focus on more relevant content when processing sequential data.

[0055] The multi-layer output of the graph signal obtained through HMGC is represented as Z = {Z} (1) Z (2) ,...,Z (M)}, Z∈R (M×N×τ) Where M represents the total number of graph convolutional layers, N is the number of historical data records, and τ represents the feature dimension. This invention uses multi-head attention to adjust the weight ratio between layers to obtain the final feature vector h:

[0056]

[0057] Here, F represents a linear transformation. The flattened output representing Z, W i Q W i K W i V These represent the weights of the three linear layers used for mapping Q, K, and V, respectively, with W0 representing the weights of the last linear layer in the attention module. `Concat` represents the connection between head1,...,head1. i .

[0058] (5) Time-dependent modeling

[0059] GRU is simpler yet more powerful than RNN, and it can solve the gradient vanishing and gradient exploding problems in RNN. Based on previous research, this invention replaces the linear transformation in GRU with HMGC to achieve better performance. Therefore, an Adaptive Hierarchical Graph Convolutional Gated Recurrent Unit (AHGC-GRU) is proposed, as shown below.

[0060]

[0061] h (t) and H (t) Let represent the attention score and the GRU output at time step t, respectively, and perform the Hadamard product operation on them. σ represents the sigmoid activation function, tanh represents the tanh activation function, and the reset gate r... (t) Help the network forget irrelevant information. At the same time, update the portal. (t) The GRU output is controlled at a given time step. (Symbol) This represents the convolution operation, while Θ r ,Θ u ,Θc Then, b represents the parameters of the corresponding filter. r ,b u ,b c It is a parameter.

[0062] Hadamard product is a special matrix operation that multiplies matrix elements and is applicable to two matrices with the same number of rows and columns.

[0063] The sigmoid activation function is a non-linear function that transforms an input value into an output value between 0 and 1. It is commonly used in artificial neural networks as an activation function and in the gradient descent algorithm.

[0064] The tanh activation function is a hyperbolic function that transforms an input value into an output value between -1 and 1. Attached Figure Description

[0065] Figure 1 This is the model architecture of the present invention.

[0066] Figure 2 This invention compares the air quality and meteorological data collected from 39 meteorological monitoring stations in Beijing and surrounding areas with the prediction effects of other different models.

[0067] Figure 3 This is a comparison of the predicted values ​​and actual values ​​of the model of the present invention and the baseline model on site 1 within one month. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.

[0069] Please see Figure 1 This invention provides a technical solution: a multi-site air quality prediction method based on adaptive hierarchical graph convolution (AHGCNN), whose basic components include adjacency matrix generation, hierarchical mapping graph convolution, adaptive dynamic graph construction, hierarchical information fusion based on attention mechanism, and time-dependent modeling. An example of this method is based on three years of data collected from 39 meteorological observation stations in Beijing (from January 1, 2018 to December 31, 2020). After preprocessing (e.g., imputing missing values), the initial data was divided into training, validation, and test sets in a 7:1:2 ratio. The AHGCNN model was trained based on the training and validation sets, as detailed below:

[0070] (1) Adjacency matrix generation

[0071] For a given set of graph signals Transform it into a two-dimensional matrix X with dimensions (τ×d)×N. l To effectively capture the internal similarities between different sites and filter redundant information between sites, this invention uses SVD to... l It can be broken down into two parts. That is:

[0072] SVD(X l )→(X s ,X t (Equation 12)

[0073] Among them, X s and X t These represent matrices divided by time dimension and site dimension, respectively.

[0074] Matrix X l It contains a large amount of redundant information. Dimensionality reduction using SVD can filter out this redundant information, thereby revealing the hidden pattern. Matrix X s ∈R N×γ It contains a high-level representation of the features of each site, where γ represents the dimension of the feature. This invention employs a Gaussian kernel-based method to compute matrix X. s The similarity between the x-th row and the y-th column is used as the edge weight in the generated adjacency matrix. The formula is defined as follows:

[0075]

[0076] Where A xy It refers to the element in the x-th row and y-th column of the adjacency matrix A, where β is the standard deviation.

[0077] (2) Hierarchical mapping graph convolution

[0078] To efficiently and accurately capture multi-layer spatial dependencies, this invention introduces a novel graph convolutional network: Hierarchical Graph Convolutional Networks (HGCN). HMGC is an extension of Graph Convolutional Networks (GCNs) that captures multi-scale information in graphs by introducing a hierarchical structure, thereby extracting features and performing classification and prediction in complex graph structures. A key feature of HMGC is that each layer contains a unique adjacency matrix, allowing for more flexible modeling of the underlying graph structure. This structure can be recursively defined as follows:

[0079]

[0080] Z(m) Z represents the input of layer m+1, while Z (m+1) It is not only the output of the (m+1)th layer, but also the input of the (m+2)th layer. Parameters and θ (m) This represents the parameters of the graph convolution filter in the m-th layer. This represents a graph convolution operation. The hierarchical relationship between nodes is represented by A. (m) Modeling, A (m) The value depends on the hierarchy. This is achieved using a hierarchical mapping function. Construct the upper-level adjacency matrix of the (m+1)th layer:

[0081]

[0082] The initial graph structure generated by equation (3) is normalized and used to initialize the adjacency matrix, and then optimized using stochastic gradient descent. The initial layer of HMGC is defined as follows:

[0083] A (0) =D -1 A xy (Equation 16)

[0084] Z (1) =A (0) Z (0) θ (0) (Equation 17)

[0085] D represents the diagonal matrix of node degrees. Z (0) =X, where at each time step, the feature matrix X∈R N×d As input to the initial layer of HMGC.

[0086] (3) Adaptive dynamic graph construction

[0087] In reality, graph structures are not always available, and the relationships between nodes often change over time. Furthermore, PM2.5 concentrations are closely related to weather conditions. Under similar weather conditions, air quality tends to be more uniform than under different weather conditions. Therefore, this invention follows the model training process to construct a dynamic adjacency matrix between different layers.

[0088] First, the number of nodes leads to the need to update the N×N adjacency matrix and the mapping function. The computational cost is high, leading to overparameterization during training. To address this issue, this invention employs SVD to transform A... (0) ∈R N×N Decomposed into two smaller matrices:

[0089]

[0090] This indicates that the source node of the first layer is embedded, while This represents the target node embedding. L represents the dimension. It is worth noting that the number of trainable parameters has decreased from N×N to N×L.

[0091] function This is implemented using fully connected layers to simulate inter-layer dependencies. The parameters of the fully connected layers are shared between E1 and E2.

[0092]

[0093] in this case, and These represent the source node embedding and the target node embedding in the m-th layer, respectively. The symbol W (m-1) and b (m-1) Let represent the weight matrix and the bias vector, respectively. To simplify the model, the feature dimensions of E1 and E2 at different levels are set to L, thereby reducing the number of parameters for each mapping to L×(L+1).

[0094] Based on equations (3) and (8), the mathematical expression for HMGC can be redefined as:

[0095]

[0096] (4) Hierarchical information fusion based on attention mechanism

[0097] In order to aggregate information from all graph convolutional layers, rather than extracting information from just one fixed layer, this invention implements a multi-layer aggregation strategy through an attention mechanism to selectively select information that has a greater impact on the accuracy of the current prediction task.

[0098] The multi-layer output of the graph signal obtained through HMGC is represented as Z = {Z} (1) Z (2) ,...,Z (M)}, Z∈R (M×N×τ) Where M represents the total number of graph convolutional layers, N is the number of historical data records, and τ represents the feature dimension. This invention uses multi-head attention to adjust the weight ratio between layers to obtain the final feature vector h:

[0099]

[0100] Here, F represents a linear transformation. The flattened output representing Z, W i Q W i K W i VThese represent the weights of the three linear layers used for mapping Q, K, and V, respectively, with W0 representing the weights of the last linear layer in the attention module. `Concat` represents the connection between head1,...,head1. i .

[0101] (5) Time-dependent modeling

[0102] GRU is simpler yet more powerful than RNN, and it can solve the gradient vanishing and gradient exploding problems in RNN. Based on previous research, this invention replaces the linear transformation in GRU with HMGC to achieve better performance. Therefore, an Adaptive Hierarchical Graph Convolutional Gated Recurrent Unit (AHGC-GRU) is proposed, as shown below.

[0103]

[0104] h (t) and H (t) Let represent the attention score and the GRU output at time step t, respectively, and perform the Hadamard product operation on them. σ represents the sigmoid activation function, tanh represents the tanh activation function, and the reset gate r... (t) Help the network forget irrelevant information. At the same time, update the portal. (t) The GRU output is controlled at a given time step. (Symbol) This represents the convolution operation, while Θ r ,Θ u ,Θ c Then, b represents the parameters of the corresponding filter. r ,b u ,b c It is a parameter.

[0105] To test the predictive performance of the AHGCNN model, this invention compared it with common deep learning network models, including LSTM, GRU, RNN, Informer, and FFTransformer, based on air quality and meteorological data collected from observation stations. Simultaneously, to illustrate the importance of graph structures in capturing the spatiotemporal dependence of air data, experiments were conducted to compare it with models such as Diffusion Convolutional Recurrent Neural Network (DCRNN) and Graph WaveNet.

[0106] Informer is a long-sequence time-series forecasting model that employs an efficient global causal attention mechanism, enabling high-quality prediction of long-sequence data while maintaining efficient computation. (Zhou H, Zhang S, Peng J, et al. Informer: Beyond efficient transformer for long sequence time-series forecasting[C] / / Proceedings of the AAAI conference on artificialintelligence.2021,35(12):11106-11115.).

[0107] FFTransformer: FFTransformer is a spatiotemporal wind speed prediction model that combines graph networks and Transformer architecture. By introducing a novel Transformer structure and effectively modeling the spatiotemporal characteristics of wind speed data, it achieves high prediction accuracy and robustness, providing a powerful and efficient prediction tool for the wind power energy field. (BentsenL) Warakagoda ND,Stenbro R,et al.Spatio-temporal wind speed forecastingusing graph networks and novel Transformer architectures[J].Applied Energy,2023,333:120565.).

[0108] This invention uses root mean square error (RMSE) and mean absolute error (MAE) to evaluate the performance of the proposed model in terms of prediction results. Their definitions are as follows:

[0109]

[0110]

[0111] Among them, variables y and denoted by and , respectively, the actual and predicted PM2.5 values, while 'n' represents the total number of test data points. Smaller MAE and RMSE values ​​indicate better final predictions. It's important to note that each error in the RMSE is squared, meaning that each error quadratically increases and has a different impact on the final RMSE value. Therefore, MAE and RMSE are often used together to comprehensively evaluate the performance of the employed method.

[0112] Combination Figure 2RNN, LSTM, and GRU models performed the worst. This is because these models can only access node representations and cannot obtain neighbor information. This illustrates the necessity of capturing neighbor information in PM2.5 prediction.

[0113] The AHGCNN model outperforms existing prediction models. Its improvements are more significant in short-term predictions. Compared to DCRNN, AHGCNN reduces MAE by 5.56%, 6.12%, 5.91%, 13.5%, and 3.18% at 1-hour, 3-hour, 6-hour, 12-hour, and 24-hour time points, respectively, and reduces RMSE by 9.08%, 5.38%, 3.96%, 8.49%, and 0.47%, respectively. Compared to Graph-WaveNet, AHGCNN reduces MAE by 1.9%, 0.91%, 1.59%, 0.87%, and 0.52% at 1-hour, 3-hour, 6-hour, 12-hour, and 24-hour time points, respectively, and reduces RMSE by 1.13%, 4.31%, 4.09%, 3.87%, and 3.35%, respectively. This demonstrates that dynamic adjacency matrices can effectively capture time-varying spatiotemporal dependencies, even when the underlying graph structure is unknown.

[0114] Compared to the long-sequence prediction model Informer, AHGCNN reduced the MAE by 10.95%, 12.11%, 9.76%, 7.97%, and 3.73% at the predicted time points of 1 hour, 3 hours, 6 hours, 12 hours, and 24 hours, respectively, and reduced the RMSE by 17.65%, 9.46%, 6.26%, 3.25%, and 0.47%, respectively. Compared to FFTransformer, AHGCNN reduced the MAE by 11.51%, 9.77%, 13.24%, 8.07%, and 3.16% at the predicted time points of 1 hour, 3 hours, 6 hours, 12 hours, and 24 hours, respectively, and reduced the RMSE by 4.9%, 15.70%, 10.43%, 5.86%, and 2.39%, respectively. These results confirm the advantages of AHGCNN in utilizing spatiotemporal dependent knowledge and demonstrate its reliable predictive ability.

[0115] Figure 3This study demonstrates the discrepancies between predicted and actual values ​​across multiple monitoring stations using various models, including AHGCNN, RNN, LSTM, GRU, DCRNN, Graph-Wavenet, Informer, and FFTranformer. During testing, RNN, LSTM, and GRU models showed significant discrepancies between predicted and actual values, particularly during periods of significant air quality data fluctuation. While DCRNN, Graph-Wavenet, Informer, and FFTranformer models showed improved performance during stable periods, they still exhibited variability and large deviations from actual values ​​during abrupt changes. Conversely, the AHGCNN model demonstrated superior predictive power, performing well across all periods. These findings suggest that other models fail to fully leverage the nonlinear spatial characteristics between monitoring stations, resulting in insufficient adaptability when data changes drastically. However, by aggregating information across multiple layers, the AHGCNN model can more effectively extract information, capturing heterogeneous spatial and temporal features between stations, thus avoiding the significant prediction errors observed in other models when air quality data changes abruptly.

[0116] The above embodiments merely illustrate the implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make several improvements without departing from the concept of this application, and these improvements all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0117] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. To address the shortcomings of existing technologies and research, this invention proposes a novel deep learning framework, namely an adaptive hierarchical graph convolutional neural network, for PM2.5 prediction. To achieve the above objective, this invention provides the following technical solution: a multi-site air quality prediction method based on adaptive hierarchical graph convolution. Specifically, to solve the inefficiency and inaccuracy of mainstream graph convolutional networks in capturing multi-level spatial dependencies, an adaptive hierarchical graph convolution is introduced. Through self-learning the adjacency matrix, this network can dynamically extract spatial dependencies at each level. Furthermore, by modeling the correlation of the hierarchical topology, an attention-based hierarchical aggregation mechanism is provided, realizing the graph convolutional structure with relatively low computational cost. Then, the linear units in the GRU are replaced with HMGCs to form adaptive hierarchical graph convolutional gated recurrent units, and multiple layers are stacked to build the main network structure, outputting the prediction results.

2. The basic components of the AHGCNN model of this invention include adjacency matrix generation, hierarchical mapping graph convolution, adaptive dynamic graph construction, hierarchical information fusion based on attention mechanism, and time-dependent modeling. The specific implementation of each module of the AHGCNN model is described in detail below: Adjacency matrix generation The adjacency matrix determines how nodes and their neighbors are aggregated in graph convolution. Existing research relies on prior knowledge to construct the graph structure beforehand; the method of this invention is entirely data-driven, thus capturing the temporal dependencies between data. For a given set of graph signals... Transform it into a two-dimensional matrix X with dimensions (τ×d)×N. l To effectively capture the internal similarities between different sites and filter out redundant information, this invention uses Singular Value Decomposition (SVD) to transform X... l It can be broken down into two parts. That is: SVD(X l )→(X s ,X t (Equation 1) in, X s and X t These represent matrices divided by time and site dimensions, respectively. Matrix X l It contains a large amount of redundant information. Dimensionality reduction using SVD can filter out this redundant information, thereby revealing the hidden pattern. Matrix X s ∈R N ×γ This invention includes a high-level representation of each site's features, where γ represents the dimension of the feature and N is the number of sites. The invention employs a Gaussian kernel-based method to compute matrix X. s The similarity between the x-th row and the y-th column is used as the edge weight in the generated adjacency matrix. The formula is defined as follows: Where A xy It refers to the element in the x-th row and y-th column of the adjacency matrix A, where β is the standard deviation. Hierarchical mapping graph convolution To efficiently and accurately capture multi-layer spatial dependencies, this invention introduces a novel graph convolutional network: Hierarchical Graph Convolutional Networks (HGCN). HMGC is an extension of GCN that captures multi-scale information in the graph by introducing a hierarchical structure, thereby extracting features and performing classification and prediction in complex graph structures. A key feature of HMGC is that each layer contains a unique adjacency matrix, allowing for more flexible modeling of the underlying graph structure. This structure can be recursively defined as follows: Z (m) Z represents the input of layer m+1, while Z (m+1) It is not only the output of the (m+1)th layer, but also the input of the (m+2)th layer. Parameters and θ (m) This represents the parameters of the graph convolution filter in the m-th layer. This represents a graph convolution operation. The hierarchical relationship between nodes is represented by A. (m) Modeling, A (m) The value depends on the hierarchy. This is achieved using a hierarchical mapping function. Construct the upper-level adjacency matrix of the (m+1)th layer: The initial graph structure generated by equation (3) is normalized and used to initialize the adjacency matrix, and then optimized using stochastic gradient descent. The initial layer of HMGC is defined as follows: A (0) =D -1 A xy (Formula 5) Z (1) = A (0) Z (0) θ (0) (Equation 6) Where D represents the diagonal matrix of node degree. Z (0) =X, where at each time step, the feature matrix X∈R N×d As input to the initial layer of HMGC. Adaptive dynamic graph construction In reality, graph structures are not always available, and the relationships between nodes often change over time. Furthermore, PM2.5 concentration is closely related to weather conditions. Under similar weather conditions, air quality tends to be more uniform than under different weather conditions. Therefore, this invention follows the model training process to construct a dynamic adjacency matrix between different layers. First, the number of nodes leads to the updating of the N×N adjacency matrix and mapping function. The computational cost is high, leading to overparameterization during training. To address this issue, this invention employs SVD to transform A... (0) ∈R N×N Decomposed into two smaller matrices: in, This indicates that the source node of the first layer is embedded, while This represents the target node embedding. L represents the dimension. It's worth noting that the number of trainable parameters has decreased from N×N to N×L. Function This is implemented using fully connected layers to simulate inter-layer dependencies. The parameters of the fully connected layers are shared between E1 and E2, as shown in Equation 8: in this case, and These represent the source node embedding and the target node embedding in the m-th layer, respectively. The symbol W (m-1) and b (m-1) Let represent the weight matrix and the bias vector, respectively. To simplify the model, the feature dimensions of E1 and E2 at different levels are set to L, thereby reducing the number of parameters for each mapping to L×(L+1). Based on equations (3) and (8), the mathematical expression for HMGC is defined as shown in (Equation 9). Hierarchical information fusion based on attention mechanism To aggregate information from all graph convolutional layers, rather than extracting information from a single fixed layer, this invention employs an attention mechanism to implement a multi-layer aggregation strategy, selectively choosing information that has a greater impact on the accuracy of the current prediction task. The multi-layer output of the graph signal obtained through HMGC is represented as Z = {Z...} (1) Z (2) ,...,Z (M) }, Z∈R (M×N×τ) Where M represents the total number of graph convolutional layers, N is the number of historical data records, and τ represents the feature dimension. This invention uses multi-head attention to adjust the weight ratio between layers to obtain the final feature vector h: Here, F represents a linear transformation. The flattened output representing Z, W i Q W i K W i V These represent the weights of the three linear layers used for mapping Q, K, and V, respectively, with W0 representing the weights of the last linear layer in the attention module. `Concat` represents the connection between head1,...,head1. i . Time-dependent modeling GRU is simpler yet more powerful than RNN, and it can solve the gradient vanishing and gradient exploding problems in RNN. Based on previous research, this invention replaces the linear transformation in GRU with HMGC to achieve better performance. Therefore, an Adaptive Hierarchical Graph Convolution Gated Recurrent Unit (AHGC-GRU) is proposed, as shown below: in, h (t) and H (t) Let represent the attention score and the GRU output at time step t, respectively, and perform the Hadamard product operation on them. σ represents the sigmoid activation function, tanh represents the tanh activation function, and the reset gate r... (t) Help the network forget irrelevant information. At the same time, update the portal. (t) The GRU output is controlled at a given time step. (Symbol) This represents the convolution operation, while Θ r ,Θ u ,Θ c Then, b represents the parameters of the corresponding filter. r ,b u ,b c It is a parameter.

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