Electric power information physical system key node identification method based on GCN-IDDA

Abstract

The invention provides an electric power information physical system key node identification method based on GCN-IDDA, and the method is used for the key node identification of an electric power information physical system (CPPS), achieves the multi-scale feature extraction through introducing an Inception network structure, enhances the space self-adaptive capability through combining with a deformable convolution (DCN), reduces the complexity of a model through employing a depth separable convolution (DSC), and achieves the recognition of the key node of the CPPS. And an attention mechanism is embedded to realize key feature dynamic weighting. The model is trained by adopting a PyTorch framework based on an adjacent matrix and a node feature matrix fusing topology and physical features, and is verified by utilizing a BA scale-free network and four representative CPPS networks (network 1 to network 4). Experimental results show that the Kendall correlation coefficient of the GCN-IDDA is more than 0.93, the superiority and adaptability of the GCN-IDDA in complex network key node identification are proved, and a new thought is provided for CPPS structure optimization and reliability improvement.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power cyber-physical systems, and relates to a GCN-IDDA-based power cyber-physical system key node identification method. BACKGROUND

[0002] Cyber-Physical Power System (CPPS) as the core architecture of modern smart grid, deeply integrates the physical process of power system and information communication technology, realizes the efficient cooperation of power flow, information flow and business flow. Key nodes play a crucial role in CPPS, they are not only the key hub of power transmission and information interaction, but also the key to system stable operation and fault isolation. Accurate identification of key nodes in CPPS is of great significance for optimizing system structure, improving system reliability and attack resistance.

[0003] The traditional key node identification method in Cyber-Physical Power System (CPPS) is mainly based on the local topological structure characteristics of the network, such as degree centrality, betweenness centrality and closeness centrality. These methods evaluate the importance of nodes by analyzing their local connection, but often ignore the position and role of nodes in the global network, as well as the dynamic characteristics of the network. In recent years, with the development of complex network theory, some improved methods have been proposed. A neural diffusion model based on weighted independent cascade model, through deep learning method to extract the weighted features of nodes and construct node embedding representation, so as to more accurately identify the weighted influence nodes in complex network, this model depends on small-scale synthetic network in training process, may be better adapted to specific network structure, but when facing complex network with different topological structure, its performance may be affected. A node importance ranking method based on network structure entropy, considering local and global information, by calculating the local entropy of each connected component and the global entropy of the whole network, more accurately identifies the key nodes in complex network. For large-scale complex network, the calculation amount is large, in the case of low network connectivity, it may not be able to accurately evaluate the importance of nodes. A node importance evaluation method based on time series network information fusion, by establishing time series correlation index and time series feature index, from the perspective of network topology and information fusion, identifies the key nodes in space-time coupled CPPS. This method mainly analyzes based on time series network, depends on time series correlation index and time series feature index.

[0004] Graph Neural Networks (GNNs) are a class of deep learning models specifically designed to handle graph-structured data, and have made significant progress in recent years in complex network analysis, social networks, bioinformatics, and other fields. Based on the Pytorch framework, a multi-layer graph attention network model (GAT) with residual structure is constructed for fast selection of critical paths in digital circuits. By improving the aggregator and encoder of the graph attention network model, efficient critical path selection is achieved. A RumorGFAN model that considers rumor propagation structure, information propagation structure, and user attribute information is proposed. The SEIRS model is used to evaluate node influence and identify key rumor nodes in the rumor propagation process. A complex network key node identification method based on graph attention mechanism is proposed, which considers the node propagation force and structural influence, and learns the importance of nodes through the graph attention network model. A complex network key node identification method based on graph neural network is proposed, which combines graph neural network and attention mechanism, and proposes a graph neural network KAGNN to solve the node importance ranking problem. However, the above models have limited applicability and can only be applied to specific types of networks such as digital circuits or rumor propagation networks, making it difficult to generalize to other types of complex networks. Moreover, the feature fusion capability is limited, and the multi-type features of nodes are not fully integrated, which affects the accuracy of key node identification. Some models have complex structures, resulting in high computational resource consumption and long training time, which limits their practical application in large-scale networks. SUMMARY

[0005] The purpose of the present application is to provide a GCN-IDDA-based critical node identification method for power information physical systems, which aims to solve the above problems.

[0006] To solve the above technical problems, the present application provides a GCN-IDDA-based critical node identification method for power information physical systems, comprising the following steps:

[0007] S1, a node feature matrix integrating topological information and physical features is constructed, and the physical features of the nodes are spliced with the network topological features to form a rich feature representation;

[0008] S2, a graph convolutional neural network model is constructed, which integrates multi-scale feature extraction through the Inception module, enhances spatial adaptive ability through deformable convolution, reduces model complexity through depth separable convolution, and realizes dynamic weighting of key features through attention mechanism;

[0009] S3, the graph convolutional neural network model is trained using the PyTorch framework, wherein the model architecture includes two layers of graph convolutional networks, the first layer has 32 output channels, the second layer has 64 output channels, and a fully connected layer is used to map the fused multi-scale features to the output space.

[0010] S4, applying the trained model to identify key nodes in the power information physical system.

[0011] Further preferably, in step S1, in the power communication network, a graph G=(V, E) is set, where: V={i=1, 2, …, N} is a node set, N is the number of nodes; E is an edge set, based on this graph structure, a corresponding adjacency matrix A and node feature matrix X are generated;

[0012] S1.1, adjacency matrix A

[0013] The adjacency matrix A represents the connection relationship between nodes in the power information physical system, and the nodes can represent power equipment or communication equipment, and the edges represent the physical or communication connection therebetween. The adjacency matrix A is an N×N matrix, where N is the number of nodes, and is defined as:

[0014]

[0015] S1.2, node feature matrix X

[0016] The node feature matrix X is an N×d matrix, where N is the number of nodes and d is the feature dimension of each node. This matrix integrates topological information and physical characteristics to provide comprehensive representation of nodes for the graph convolutional neural network model. The degree, clustering coefficient and physical characteristics of the nodes are introduced to enhance the perception of local structure in the power communication network and improve the comprehensiveness and accuracy of feature expression.

[0017] The physical characteristics Physical(i) of node i can include electrical parameters of the power grid and communication parameters of the information network, aiming to capture the physical nature and functional characteristics of the nodes in the power information physical system, and to give the nodes rich representation dimensions beyond the topological structure, thereby deepening the understanding of the nature of the nodes by the model.

[0018] Physical(i)=[V(i), I(i), P(i), B(i), D(i), R(i), …]

[0019] Wherein, V(i) is the voltage, I(i) is the current, P(i) is the power, B(i) is the bandwidth, D(i) is the time delay, and R(i) is the data transmission rate.

[0020] The node degree k(i): the number of connections of node i, defined as:

[0021]

[0022] Wherein, A ij is the adjacency matrix element;

[0023] Clustering coefficient C(i): reflects the connection tightness between the neighbors of the node, defined as:

[0024]

[0025] Where M(i) is the number of triangles containing node i;

[0026] The physical and topological features are spliced to form the feature vector of each node, and the corresponding node feature matrix X is:

[0027]

[0028] By effectively splicing the physical and topological features, a more rich feature vector is constructed for each node, thereby improving the model's perception of complex structures.

[0029] Further preferably, in step S2, the following steps are specifically included:

[0030] S2.1, introduce Inception module, capture features of different scales by using convolution kernels of different sizes in parallel, represented as:

[0031] H (l+1) =Concat(Conv 3×3 (H (l) ),Conv 5×5 (H (l) ))

[0032] Where Conv 3×3 (H (l) ),Conv 5×5 (H (l) ) respectively represent 3×3 and 5×5 convolution operations, and Concat represents splicing the convolution results in the channel dimension;

[0033] S2.2, introduce deformable convolution, adjust the position of the convolution kernel by introducing an offset, so that the model can adaptively focus on important regions in the input feature map, thereby better capturing the local features of the node. The model uses convolution kernels of different sizes to capture features of different ranges, represented as:

[0034]

[0035] Where σ is a nonlinear activation function, φ(i) is the neighbor node set of node i, w j is the weight corresponding to neighbor node j, H (l) (i+ΔP (l) (i,j)) represents the feature of node i in the lth layer by adding an offset ΔP (l)(i,j) is sampled after the sampling of (i,j), ΔP (l) (i,j) is the offset of node i to neighbor node j in the lth layer, which is obtained by learning, b (l) is the bias term of the lth layer;

[0036] S2.3, introduce a depth separable convolution, divided into two stages of depthwise convolution and pointwise convolution, wherein the depthwise convolution is responsible for performing n x n convolution operation on each input channel independently in the spatial dimension, realizing fine spatial feature capture; the pointwise convolution uses a 1 x 1 convolution kernel to upgrade the dimension on the basis of the depthwise convolution, and obtains a feature map with information fusion between different channels;

[0037] S2.4, introduce an attention mechanism, dynamically allocate weights by calculating the attention coefficients between nodes, realize weighted aggregation of features, and the calculation process of the attention mechanism is as follows:

[0038] H (l+1) =σ(αH (l) W (l) )

[0039] Wherein, sigma is a nonlinear activation function, alpha is an attention coefficient, W (l) is the weight matrix of the attention layer.

[0040] Further preferably, in step S3, the model architecture adopts a multi-scale feature fusion strategy, extracts node features of different scales through 3x3 and 5x5 graph convolution kernels, and combines deformable convolution and depth separable convolution technology to enhance the model's ability to capture the topological relationship of nodes at different spatial scales;

[0041] The model structure is designed as a two-layer graph convolution network, the input channel number is 5, the first layer output channel number is 32, the second layer output channel number is 64, the full connection layer is responsible for mapping the fused multi-scale features to the output space, and finally realizes the prediction of node influence;

[0042] The channel number of the hidden layer of the model is set to 16, the output channel number is 1, the multi-head attention mechanism is adopted, the number of heads is 2, the feature expression ability is enhanced, and the dropout rate is set to 0.1 to prevent overfitting, the mean square error is used as the loss function in the training process, and the Adam optimization algorithm is used for parameter optimization, and the learning rate is set to 0.001;

[0043] In each training period, the model performs forward propagation calculation on the input node feature matrix and edge index, obtains the prediction result, calculates the mean square error loss between the prediction result and the real label, updates the model parameters through the back propagation mechanism, and the training process continues for 2000 periods until the model converges.

[0044] Compared with the prior art, the present application has the following beneficial effects:

[0045] The present application integrates multi-scale feature extraction, deformable convolution (DCN), deep separable convolution (DSC) and attention mechanism. The node feature matrix integrating topological information and physical features is constructed, the multi-type features of nodes are fully mined, the representation ability of the model for node characteristics is improved, the deep separable convolution is introduced, the model complexity is reduced, the computing resource demand is reduced, the training efficiency is improved, and the model can more efficiently process large-scale network data, providing a new solution for key node detection of CPPS and other complex coupled systems, enriching the application of graph neural network in the key node identification task of CPPS, and having important theoretical significance and practical application value for the structure optimization, reliability and attack resistance of CPPS. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a key node identification model framework based on GCN-IDDA;

[0047] Figure 2 is a framework diagram of deep separable convolution;

[0048] Figure 3 is a schematic diagram of the Kendall correlation coefficient of different algorithms under four networks. DETAILED DESCRIPTION

[0049] The present application is further described in detail below in combination with the drawings and specific embodiments. According to the following description, the advantages and features of the present application will be more apparent. It should be noted that the drawings are very simplified and use non-precise proportions, only for the purpose of facilitating and clearly assisting the description of the embodiments of the present application. The same or similar reference numerals in the drawings represent the same or similar parts.

[0050] Embodiment, a key node identification method for power information physical system based on GCN-IDDA.

[0051] 1Model implementation

[0052] To improve the accuracy of network key node identification and enhance the adaptability to complex topological structure, the present application proposes a key node identification model based on GCN-IDDA, and the overall architecture is as follows: Figure 1The model realizes the accurate description of node influence by multi-scale feature extraction and dynamic feature weighting mechanism. In the feature extraction stage, the network is first abstracted into a graph structure to generate the adjacency matrix A and the node feature matrix X. Then, the feature matrix is input into the GCN-IDDA model, which performs multi-scale graph convolution operation in parallel through the Inception module, captures spatial non-uniform features through DCN, and uses DSC to compress the parameter quantity; in the model construction stage, the extracted features are dynamically weighted through the cross-attention mechanism, supplemented by a multi-layer dense connection network to further mine key features; in the loss optimization stage, the simulation results of the SIR propagation model are used as the supervision signal to continuously optimize the parameters by minimizing the loss function, realizing the efficient identification of key nodes.

[0053] 1.1 Feature matrix construction

[0054] In the power communication network, let G = (V, E) be the graph structure, where: V = {i = 1, 2, …, N} is the node set, and N is the number of nodes; E is the edge set. Based on this graph structure, the corresponding adjacency matrix A and node feature matrix X are generated.

[0055] 1.1.1 Adjacency matrix A

[0056] The adjacency matrix A represents the connection relationship between nodes in the CPPS. Nodes can represent power equipment (such as substations, generators) or communication equipment (such as routers), and edges represent physical or communication connections between them. Adjacency matrix A is an N × N matrix, where N is the number of nodes, defined as:

[0057]

[0058] 1.1.2 Node feature matrix X

[0059] The node feature matrix X is an N × d matrix, where N is the number of nodes and d is the feature dimension of each node. This matrix combines topological information and physical characteristics to provide a comprehensive representation of nodes for the GCN-IDDA model. To further optimize the node feature matrix construction process of the model, this study introduces the degree, clustering coefficient, and physical characteristics of nodes to enhance the perception of local structure in the power communication network and improve the comprehensiveness and accuracy of feature representation.

[0060] The physical characteristics Physical(i) of node i can be composed of electrical parameters (such as voltage, current, power, etc.) of the power grid and communication parameters (such as bandwidth, latency, data transmission rate, etc.) of the information network, aiming to capture the physical essence and functional characteristics of nodes in the CPPS, and to give nodes rich representation dimensions beyond the topological structure, deepening the model's understanding of the nature of nodes.

[0061] Physical(i) = [V(i), I(i), P(i), B(i), D(i), R(i),…]

[0062] where V(i) is the voltage, I(i) is the current, P(i) is the power, B(i) is the bandwidth, D(i) is the delay, and R(i) is the data transmission rate.

[0063] Node degree k(i): the number of connections of node i. It is defined as:

[0064]

[0065] where A ij is the adjacency matrix element.

[0066] Clustering coefficient C(i): reflects the tightness of connections between the neighbors of a node, defined as:

[0067]

[0068] where M(i) is the number of triangles containing node i.

[0069] Concatenate physical features and topological features to form the feature vector of each node. The corresponding node feature matrix X is:

[0070]

[0071] In the construction of the feature matrix, the introduction of physical features significantly enhances the model's ability to represent node characteristics. By effectively concatenating physical features with topological features, a more comprehensive feature vector is constructed for each node, thereby improving the model's ability to perceive complex structures.

[0072] 1.2 GCN-IDDA model construction

[0073] GCN-IDDA model is a cutting-edge graph convolutional network architecture designed to enhance the identification of key nodes in power communication networks. By integrating multi-scale feature extraction, deformable convolution, depth separable convolution, and attention mechanisms, the model fully explores and integrates local and global features of nodes to achieve more accurate node identification.

[0074] 1.2.1 Inception

[0075] By using different sizes of convolution kernels in parallel, different scale features can be captured. This structure can enhance the model's ability to capture multi-scale features, thereby improving the model's expression ability.

[0076] H (l+1) = Concat(Conv 3×3 (H(l) ),Conv 5×5 (H (l) ))

[0077] where Conv 3×3 (H (l) ),Conv 5×5 (H (l) ) denote 3x3 and 5x5 convolution operations respectively, and Concat denotes concatenating the results of these convolutions in the channel dimension.

[0078] 1.2.2 Deformable Convolution

[0079] By introducing offsets to adjust the position of the convolution kernel, the model can adaptively focus on important regions in the input feature map, thus better capturing the local features of the node. The model uses convolution kernels of different sizes to capture features of different ranges. Denoted as:

[0080]

[0081] where σ is a nonlinear activation function, φ(i) is the set of neighbor nodes of node i, w j is the weight corresponding to neighbor node j, H (l) (i+ΔP (l) (i,j)) represents that in the l-th layer, the features of node i are sampled after adding the offset ΔP (l) (i,j), ΔP (l) (i,j) is the offset from node i to neighbor node j in the l-th layer, which is obtained by learning, and b (l) is the bias term of the l-th layer.

[0082] 1.2.3 Depthwise Separable Convolution

[0083] DSC is divided into two stages: depthwise convolution and pointwise convolution. Among them, depthwise convolution is responsible for performing n x n convolution operation on each input channel independently in the spatial dimension, realizing fine spatial feature capture; pointwise convolution uses a 1x1 convolution kernel to upgrade on the basis of depthwise convolution, obtaining feature maps with information fusion between different channels. As shown in Figure 2 .

[0084] 1.2.4 Attention Mechanism

[0085] By calculating the attention coefficients between nodes to dynamically allocate weights, weighted aggregation of features is realized. The calculation process of attention mechanism is as follows.

[0086] H (l+1) = σ(αH (l) W (l) )

[0087] where σ is a nonlinear activation function, a is an attention coefficient, W (l) is the weight matrix of the attention layer.

[0088] 1.3 Model training

[0089] In this study, the pycharm environment is developed, and the PyTorch deep learning framework is built. In the process of model training, the training data is constructed based on the BA scale-free network generation mechanism, which can effectively simulate the power-law distribution characteristics of real-world networks. The model architecture adopts a multi-scale feature fusion strategy, which extracts node features at different scales through 3x3 and 5x5 graph convolution kernels, and combines DCN and DSC technologies to enhance the model's ability to capture the topological relationship of nodes at different spatial scales. The model structure is designed as a two-layer graph convolution network, with an input channel number of 5, an output channel number of 32 in the first layer, and an output channel number of 64 in the second layer. The fully connected layer is responsible for mapping the fused multi-scale features to the output space, ultimately realizing the prediction of node influence. The number of channels in the hidden layer of the model is set to 16, and the output channel number is 1, adopting a multi-head attention mechanism with 2 heads to enhance the feature expression ability, and setting the dropout rate to 0.1 to prevent overfitting. The mean square error (MSE) is used as the loss function in the training process, combined with the Adam optimization algorithm for parameter optimization, with a learning rate of 0.001. In each training period, the model performs forward propagation calculation on the input node feature matrix and edge index, and after obtaining the prediction result, it calculates the mean square error loss between it and the true label. Through the back propagation mechanism, the model parameters are updated, and the training process continues for 2000 periods until the model converges.

[0090] 2 Experimental results and analysis

[0091] 2.1 Experimental data set

[0092] In this study, 6 artificial networks are constructed using the BA model, and 4 representative CPPS networks are selected as test networks, named Network 1, Network 2, Network 3, and Network 4. Among them, Network 1 is a typical high-voltage urban network, focusing on describing the process of high-voltage power transmission and distribution in urban environments; Network 2 is a high-voltage-medium voltage urban network, which can reveal the interaction mechanism and synergistic effect between high-voltage and medium-voltage power systems in cities; Network 3 is a high-voltage-ultra-high voltage hybrid network, which fully demonstrates the operation rules of high-voltage and ultra-high voltage power systems in hybrid scenarios; Network 4 is a more comprehensive high-voltage-medium voltage hybrid full-type network, which integrates various power equipment and connection modes, fully reflecting the complexity of actual CPPS. In order to deeply understand and analyze the topological structure characteristics of these networks, this paper describes the topological characteristics of the network by calculating the following key parameters: N represents the number of nodes in the network, M represents the number of edges, k represents the average degree of the network, kmax denotes the maximum degree value of the network, D denotes the network density, denotes the average clustering coefficient.

[0093] Table 1 Network statistics

[0094]

[0095]

[0096] 2.2 Evaluation criteria SIR model

[0097] The SIR model clearly shows the role of each node in the propagation chain by tracking the propagation path of security threats in the power network. In particular, those nodes that can efficiently propagate security threats to other nodes are identified as key nodes, which is consistent with the mechanism of infected nodes propagating threats in the SIR model. The propagation dynamics of the SIR model provides a benchmark for key node identification for the GCN-IDDA model, enabling the model to quantitatively assess the importance of each node based on its infection and propagation capabilities. By setting different infection rates β and recovery rates γ, the propagation is simulated randomly from a certain node, and the infection size and recovery size are recorded to assess the influence of the node on the propagation, and accordingly label its importance. The GCN-IDDA model then uses these label data for testing to achieve accurate identification of key nodes.

[0098] 2.2.2 Evaluation index

[0099] To evaluate the effectiveness of the GCN-IDDA model in identifying key nodes, this study uses the Kendall correlation coefficient as an evaluation index. The Kendall correlation coefficient is a non-parametric statistical method used to measure the ordinal correlation between two variables, and is particularly suitable for comparing the similarity of node importance rankings generated by different methods. In this study, the Kendall correlation coefficient between the ranking of key nodes predicted by the GCN-IDDA model and the actual propagation influence ranking obtained by the SIR model simulation is calculated to quantify the accuracy of the model in identifying key nodes. Its value range is [-1, 1], the closer the value is to 1, the higher the consistency between the predicted ranking and the actual ranking, thus reflecting the excellent performance of the model.

[0100] 2.3 Experimental analysis

[0101] 2.3.1 Ablation experiment

[0102] To verify the effectiveness of each component in the proposed GCN-IDDA model, we conduct ablation experiments. We systematically analyze the contribution of Inception module, DCN, DSC, and attention mechanism to the model performance. Experiments are conducted on four representative CPPS networks (Network 1, Network 2, Network 3, and Network 4), and Kendall’s Tau is used as the evaluation metric to compare the consistency between the node importance ranking of different model variants and the actual ranking simulated by the SIR propagation model. The experimental results are shown in Table 2.

[0103] Table 2. Results of network ablation experiments

[0104]

[0105] As can be seen from Table 2, in the key node identification task of networks 1 to 4, the performance of the basic GCN model is relatively poor, which shows that the traditional GCN has limitations in dealing with the complex network structure and dynamic characteristics of CPPS, and it is difficult to accurately capture the features of key nodes. When the attention mechanism is added to form the GAT model, the performance in the network does not improve significantly, because GAT simply introduces the attention mechanism and does not effectively improve the convolution operation itself, which limits the improvement of its ability to capture node spatial features. After introducing DCN, the performance of the model is significantly improved in the four networks. This shows that DCN enhances the model's ability to capture non-uniform node spatial features by adjusting the position of the convolution kernel through the introduction of the offset, and can better adapt to the complex spatial distribution of nodes in the CPPS network, thereby improving the accuracy of key node identification. The addition of DSC also improves the performance of the model to some extent, which shows that DSC separates spatial feature extraction and inter-channel information fusion, reduces the complexity of the model while improving the ability to mine node features, which helps to more efficiently identify key nodes. Finally, the GCN-IDDA model that integrates the Inception network structure, deformable convolution, deep separable convolution and attention mechanism all achieves the best performance in the four networks. This fully shows that the components in the GCN-IDSCA model cooperate with each other and form a complementary advantage. The multi-scale feature extraction capability of the Inception module provides rich feature information for the model, the spatial adaptive capability of DCN enables the model to accurately locate the features of key nodes, DCS reduces the complexity of the model and improves the feature mining efficiency, and the attention mechanism further highlights the importance of key features. This comprehensive feature extraction and weighting mechanism enables the GCN-IDDA model to more comprehensively and accurately depict the influence of nodes, thereby exhibiting excellent performance in the CPPS key node identification task and effectively solving the shortcomings of traditional methods when facing the complex characteristics of CPPS networks. It provides a reliable solution for actual CPPS key node detection, and performs well in different types of CPPS networks, further verifying the generalization ability of the model.

[0106] 2.3.2 Different algorithm comparison experiments

[0107] To comprehensively evaluate the performance of the GCN-IDDA model in the task of identifying key nodes in CPPS, we conducted comparative experiments with various traditional and deep learning algorithms. The experiments compared the performance of different algorithms in the task of ranking the importance of nodes in CPPS, verifying the effectiveness and superiority of the GCN-IDDA model. The comparison algorithms include traditional machine learning methods (Linear Regression, KNN, Random Forest, SVR), network topology-based centrality methods (Degree Centrality, Betweenness Centrality), basic graph neural networks (GCN), improved graph neural network variants (GAT), and the GCN-IDDA model proposed in this study. The Kendall correlation coefficient was used as the evaluation indicator to measure the consistency between the predicted node importance ranking and the actual ranking simulated by the SIR propagation model.

[0108] Figure 3 The performance of different node influence prediction algorithms in networks 1 to 4 is shown. The horizontal axis is the ratio of the propagation rate to the threshold, which measures the strength of information propagation between nodes; the vertical axis is the Kendall correlation coefficient, which measures the consistency between the model's prediction results and the actual propagation results. From the four graphs, it can be seen that the GCN-IDDA model has the highest Kendall correlation coefficient under different networks and different ratios of propagation rate to threshold, and its performance is stable and superior to other algorithms. This indicates that the GCN-IDDA model has a significant advantage in the task of identifying key nodes in CPPS, and can more accurately identify key nodes in the network.

[0109] For the GCN-IDDA model, the Kendall correlation coefficient shows an upward trend as the ratio of propagation rate to threshold value increases. This is because when the ratio of propagation rate to threshold value is low, the network propagation ability is weak, and only a few highly connected key nodes can effectively spread information, at which time the model may be more susceptible to noise. As the ratio of propagation rate to threshold value increases, the network propagation ability is enhanced, and the model can more accurately capture the influence of nodes, thereby improving the consistency of the prediction results and the actual results, and the Kendall correlation coefficient also rises. Traditional algorithms (such as Linear Regression, KNN, Random Forest, etc.) mostly show a downward trend in Kendall correlation coefficient as the ratio of propagation rate to threshold value increases. These algorithms usually make predictions based on simple linear relationships or local features, and cannot effectively capture the non-linear relationships and global structural information in complex networks. When the ratio of propagation rate to threshold value is low, the network propagation process is relatively simple, and these algorithms may still be able to obtain relatively good results. However, as the ratio of propagation rate to threshold value increases, the complexity of network propagation increases, and the limitations of traditional algorithms gradually appear, making it difficult to accurately identify key nodes, resulting in a decrease in the consistency of prediction results and actual results, and a decrease in the Kendall correlation coefficient. In addition, the centrality methods based on network topology (such as degree centrality, betweenness centrality, etc.) have relatively stable Kendall correlation coefficients when the ratio of propagation rate to threshold value changes, but the overall Kendall correlation coefficients are low. This is because they only rely on the static topological structure of the network, and cannot dynamically adapt to changes in the network propagation process, and cannot fully reflect the actual influence of nodes under different propagation intensities.

[0110] Network 1 is a typical high-voltage urban network. The network structure is relatively compact, the connection relationship between nodes is clear, and the influence of key nodes is more easily captured by the model. At the same time, the number of nodes in network 1 is 81, and the structure of networks with a larger number of nodes (such as network 4 with 1566 nodes) is more complex. During the training process, the model may learn the features of key nodes more quickly for small networks, thereby exhibiting a higher correlation coefficient in the initial stage.

[0111] 3 Conclusion

[0112] This study proposes a key node identification model GCN-IDDA based on improved graph convolution network (GCN), which innovatively integrates multi-scale feature extraction and deformable convolution. Experimental results show that the GCN-IDDA model performs superiorly in the key node identification tasks of networks 1 to 4, with a stable Kendall correlation coefficient of 0.93 or above, far exceeding traditional methods and basic graph neural networks, and showing strong robustness and generalization ability. In the future, the model architecture and parameters can be further optimized, and its application in larger-scale and more complex networks and different key infrastructure fields can be expanded, and its potential in dynamic network analysis can be explored to cope with the challenges of network dynamic changes on key node identification. In summary, the GCN-IDDA model provides an efficient and accurate new method for CPPS key node identification, which is of great significance for the optimization of CPPS structure, the improvement of reliability and attack resistance.

[0113] The above description is only a description of the preferred embodiments of the present application, and is not any limitation on the scope of the present application. Any modification or modification made by a person skilled in the art according to the above disclosure is within the protection scope of the claims.

Claims

1. A method for identifying key nodes in power cyber-physical systems based on GCN-IDDA, characterized by: The following steps are involved: S1. Construct a node feature matrix that integrates topological information and physical features, and form a rich feature representation by splicing the physical features of the node with the network topological features; S2. Build a graph convolutional neural network model that integrates multi-scale feature extraction through the Inception module, enhances spatial adaptability through deformable convolution, reduces model complexity through depthwise separable convolution, and dynamically weights key features through the attention mechanism. S3. Use the PyTorch framework to train a graph convolutional neural network model. The model architecture consists of a two-layer graph convolutional network. The first layer has 32 output channels, and the second layer has 64 output channels. A fully connected layer is used to map the fused multi-scale features to the output space. S4. Use the trained model to identify key nodes in the power cyber-physical system.

2. The method for identifying key nodes of a power cyber-physical system based on GCN-IDDA according to claim 1 is characterized in that: In step S1, in the power communication network, a graph G = (V, E) is set, where V = {i = 1, 2, ..., N} is a node set and N is the number of nodes; E is an edge set. Based on this graph structure, the corresponding adjacency matrix A and node feature matrix X are generated. S1.

1. Adjacency Matrix A The adjacency matrix A represents the connection relationship between nodes in the power cyber-physical system. Nodes can represent power equipment or communication equipment, and edges represent the physical or communication connections between them. The adjacency matrix A is an N×N matrix, where N is the number of nodes and is defined as: S1.2, node feature matrix X The node feature matrix X is an N×d matrix, where N is the number of nodes and d is the feature dimension of each node. This matrix integrates topological information and physical features to provide a comprehensive representation of nodes for the graph convolutional neural network model. It introduces node degree, clustering coefficient, and physical characteristics to enhance the perception of local structure in the power communication network, thereby improving the comprehensiveness and accuracy of feature expression. The physical characteristics of node i include the electrical parameters of the power grid and the communication parameters of the information network. They aim to capture the physical nature and functional characteristics of nodes in the power cyber-physical system, endowing nodes with a rich representation dimension beyond topology, and deepening the model's understanding of the node's nature. Physical(i)=[V(i),I(i),P(i),B(i),D(i),R(i),…] Where V(i) is voltage, I(i) is current, P(i) is power, B(i) is bandwidth, D(i) is delay, and R(i) is data transmission rate. Node degree k(i): the number of connections of node i, defined as: Among them, A ij is the adjacency matrix element; Clustering coefficient C(i): reflects the degree of connection between node neighbors and is defined as: Where M(i) is the number of triangles containing i; The physical features and topological features are spliced ​​together to form the feature vector of each node. The corresponding node feature matrix X is: By effectively combining physical features with topological features, a richer feature vector is constructed for each node, thereby improving the model's perception of complex structures.

3. The method for identifying key nodes of a power cyber-physical system based on GCN-IDDA according to claim 1 is characterized in that: Step S2 specifically includes the following steps: S2.1, introduce the Inception module, which captures features of different scales by using convolution kernels of different sizes in parallel, expressed as: H (l+1) =Concat(Conv 3×3 (H (l) ),Conv 5×5 (H (l) )) Among them, Conv 3×3 (H (l) ),Conv 5×5 (H (l) ) represent 3×3 and 5×5 convolution operations respectively, and Concat represents concatenating these convolution results in the channel dimension; S2.

2. Introducing deformable convolution, by introducing an offset to adjust the position of the convolution kernel, the model can adaptively focus on the important areas in the input feature map, thereby better capturing the local features of the node. The model uses convolution kernels of different sizes to capture features of different ranges, which can be expressed as: Among them, σ is a nonlinear activation function, φ(i) is the set of neighbor nodes of node i, and w j is the weight corresponding to neighbor node j, H (l) (i+ΔP (l) (i,j)) indicates that in layer l, the feature of node i is obtained by adding the offset ΔP (l) (i, j) and then sample, ΔP (l) (i, j) is the offset from node i to neighbor node j in layer l. These offsets are learned. (l) is the bias term of the lth layer; S2.

3. Introducing depthwise separable convolution, which is divided into two stages: depthwise convolution and pointwise convolution. Depthwise convolution is responsible for performing n×n convolution operations on each input channel independently in the spatial dimension to achieve fine spatial feature capture; pointwise convolution uses a 1×1 convolution kernel to increase the dimension based on depthwise convolution to obtain feature maps that fuse information between different channels; S2.

4. Introduce the attention mechanism to dynamically allocate weights by calculating the attention coefficients between nodes to achieve weighted aggregation of features. The calculation process of the attention mechanism is as follows: H (l+1) =σ(αH (l) W (l) ) Among them, σ is the nonlinear activation function, α is the attention coefficient, and W (l) is the weight matrix of the attention layer.

4. The method for identifying key nodes of a power cyber-physical system based on GCN-IDSCA according to claim 1, characterized in that: In step S3, the model architecture adopts a multi-scale feature fusion strategy, extracting node features of different scales through 3x3 and 5x5 graph convolution kernels, and combining deformable convolution and depthwise separable convolution techniques to enhance the model's ability to capture the topological relationships of nodes at different spatial scales; The model structure is designed as a two-layer graph convolutional network with 5 input channels, 32 output channels in the first layer, and 64 output channels in the second layer. The fully connected layer is responsible for mapping the fused multi-scale features to the output space, ultimately achieving the prediction of node influence. The model has 16 hidden layer channels and 1 output channel. A multi-head attention mechanism is used with 2 heads to enhance feature expression. The dropout rate is set to 0.1 to prevent overfitting. The mean square error is used as the loss function in the training process. The Adam optimization algorithm is used for parameter optimization. The learning rate is set to 0.

001. In each training cycle, the model performs forward propagation calculations on the input node feature matrix and edge index. After obtaining the prediction results, it calculates the mean square error loss between them and the true labels, and updates the model parameters through the backpropagation mechanism. The training process continues for 2000 cycles until the model converges.

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