Electric power communication network key node identification method based on graph neural network

Abstract

The invention discloses an electric power communication network key node identification method based on a graph neural network, and belongs to the technical field of intelligent power grid analysis. The method comprises the following steps: firstly, constructing an electric power communication network topological graph, generating an adjacent matrix from the topological graph, standardizing the adjacent matrix to generate a first input matrix, and encoding one-hot of nodes to obtain a second input matrix; inputting the first input matrix and the second input matrix into a trained GCN auto-encoder to obtain a node potential representation; and inputting the node potential representation and the adjacent matrix into a trained GNN node ranking prediction model, outputting node importance scores and sorting, and selecting the first k nodes as key nodes. During model training, a BA model is adopted to generate a synthetic network, an SIR propagation model is adopted to obtain the real importance of nodes, and a listMLE loss function and an Adam optimizer are combined to train an auto-encoder and a prediction model. The method can automatically extract the topology deep features, is high in calculation efficiency and generalization capability, and improves the key node recognition precision.

Description

Technical Field

[0001] This invention relates to the field of smart grid analysis, and more specifically, to a method for identifying key nodes in power communication networks based on graph neural networks. Background Technology

[0002] The power communication network is the nerve center of the power system, and its reliability directly affects the security of the power grid. With the rapid development of smart grids, the scale of power communication networks is constantly expanding, and the network topology is becoming increasingly complex. Identification of critical nodes has become an important technical means to ensure the safe operation of the network.

[0003] Traditional methods for identifying critical nodes have two major drawbacks: first, they rely on manually defined features (such as node degree, betweenness centrality, proximity centrality, etc.) and fail to fully explore the deep information in the network topology; second, they employ subjective evaluation methods (such as expert analysis), which have an error rate exceeding 10%, making it difficult to meet the needs of actual engineering projects.

[0004] Existing technologies, such as patent CN106375104A, propose a quantitative method based on network topology and device reliability, which identifies critical nodes by calculating network reliability indicators. This method involves calculating the overall network reliability, recalculating reliability changes after deleting nodes one by one, and ranking node importance according to the degree of reliability degradation. However, this method still requires manual design of evaluation indicators and suffers from high computational complexity and poor generalization ability in complex networks.

[0005] While Graph Convolutional Networks (GCNs) in deep learning can learn topological features, single models struggle to handle the relative ranking of node importance. Existing methods lack effective cross-network transfer capabilities, limiting their application in various power communication networks. Summary of the Invention

[0006] To address the issues that existing key node identification methods rely on manually defined features and have subjective evaluation methods, this invention proposes a key node identification method for power communication networks based on graph neural networks to overcome these problems.

[0007] According to one aspect of the present invention, a method for identifying key nodes in a power communication network based on a graph neural network is provided, comprising the following steps: S1: Constructing a topology graph G=(V,E) of the power communication network, where V={v1,v2,...,vn} is the set of nodes in the power communication network, E is the set of edges in the power communication network, and n is the total number of nodes in the power communication network; S2: Generating an adjacency matrix A of the power communication network based on the topology graph, adding self-loops to the adjacency matrix A and standardizing it to obtain a first input matrix. ; and, using one-hot encoding to generate the feature matrix of the node, using the feature matrix as the second input matrix X; S3: using the first input matrix The second input matrix X is input into the trained autoencoder to obtain the node latent representation Z, wherein the autoencoder is constructed based on the graph convolutional network GCN; S4: The node latent representation Z and the adjacency matrix A are input into the trained node ranking prediction model to output the importance score of the node, and the nodes are ranked according to the importance score, and the top k nodes are selected as the key nodes of the power communication network, wherein the node ranking prediction model is constructed based on the graph neural network GNN.

[0008] In the above respects, more specifically, the trained autoencoder in step S3 and the trained node ranking prediction model in step S4 are obtained through joint training via the following steps: S10: Generate the synthetic network using the BA model and construct the topology graph of the synthetic network. =( , ),in ={ 1, 2,..., } represents the set of nodes in the synthetic network. Let the set of edges of the synthetic network be . This represents the total number of nodes in the synthetic network. S20: Generating the adjacency matrix of a synthetic network based on its topology graph. To the adjacency matrix Add self-loops and normalize to obtain the third input matrix. The feature matrix of the generated node is used as the fourth input matrix; one-hot encoding is used. ; S30: Transfer the third input matrix and the fourth input matrix Input the original autoencoder to obtain the node latent representation. The original autoencoder mentioned therein is built based on the graph convolutional network GCN; S40: Use the SIR propagation model to obtain the true importance index of each node in the synthetic network. This allows us to obtain the true ranking of each node. ; S50: Represent the potential node representation and adjacency matrix Input the original node ranking prediction model to output the predictive importance score of the nodes. This leads to the predicted ranking of the nodes, where the original node ranking prediction model is built based on a graph neural network (GNN). S60: Generate a scalar loss value based on the difference between the predicted and actual rankings of nodes using a loss function. ; S70: Employ the Adam optimizer based on the scalar loss value. By adaptively adjusting the parameters of the original autoencoder and the original node ranking prediction model through backpropagation, the trained autoencoder and the trained node ranking prediction model are finally obtained.

[0009] More specifically, in the foregoing, the SIR propagation model in step S40 includes three state nodes and two parameters. The state nodes include a susceptible node S, an infected node I, and a recovery node R. The two parameters include the propagation probability. and recovery probability The information propagation process is simulated using the SIR propagation model as follows: (1) At time t=0, node vi is set as infected node I, and other nodes are set as susceptible nodes S; (2) At each time step, infected node I propagates with probability Infect its neighboring nodes; (3) Infect node I with recovery probability (4) Calculate the number of infected nodes I and recovered nodes R when the SIR propagation model reaches a steady state. (5) Select The average of a certain number of simulation results is used as an indicator of the true importance of node vi. Among them, the propagation probability = 1.5 , The infection probability threshold is calculated using the following formula:

[0010] in, Indicates node degree. This indicates taking the average value.

[0011] In the foregoing, more specifically, the loss function is the listMLE loss function based on the Plackett-Luce model, and the scalar loss value is calculated using the following formula. :

[0012] in, It is the predictive importance score of the node. It represents the true ranking of the nodes, where P represents the Plackett-Luce model, and its formula is as follows: .

[0013] In the foregoing, more specifically, the first input matrix It is obtained through the following formula:

[0014] Where A is the adjacency matrix of the topological graph G, I is the identity matrix of the adjacency matrix A, and D is the degree matrix of the adjacency matrix A.

[0015] More specifically, in the foregoing, the autoencoder includes an encoder and a decoder, wherein the encoder employs a 2-layer GCN and the decoder employs a 2-layer fully connected layer.

[0016] More specifically, the node ranking prediction model, from top to bottom, comprises: a first graph neural network layer, used to receive the latent node representation Z and adjacency matrix A generated by the autoencoder, and to extract and transform graph structure features from them; a first batch normalization layer, used to standardize the features output by the first graph neural network layer; a first ReLU activation layer, used to introduce nonlinear transformations into the batch-normalized features; a second graph neural network layer, used to perform deeper graph structure feature extraction and transformation on the features after nonlinear activation; a second batch normalization layer, used to standardize the features output by the second graph neural network layer; a second ReLU activation layer, used to introduce nonlinear factors again to further optimize the feature distribution; a Dropout layer, used to randomly discard a portion of the neuron outputs according to a preset probability during model training; a fully connected layer, used to map the high-dimensional features extracted by the preceding layers into a preliminary one-dimensional node importance score; a third ReLU activation layer, used to apply nonlinear rectification to the node importance score output by the fully connected layer; and a Flatten layer, used to flatten the final output node importance score tensor into a one-dimensional vector.

[0017] In the foregoing, additionally, Kendall's The coefficients and monotonicity index MI are used to test the performance of the trained node ranking prediction model, among which Kendall's... The formula for calculating the coefficient is:

[0018] Where c is the number of consistent logarithms, d is the number of inconsistent logarithms, and n is the number of nodes; The formula for calculating the monotonicity index MI is as follows:

[0019] in, R This represents a ranking list. This represents a value in the ranking list. This indicates that the value in the ranking list is... The number of values, N This represents the total number of values ​​in the ranking list.

[0020] According to another aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the computer program, when executed by the processor, implements a graph neural network-based method for identifying key nodes in a power communication network according to the above aspects.

[0021] According to another aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method for identifying key nodes in a power communication network based on a graph neural network according to the above aspects.

[0022] The beneficial effects of this invention are as follows: 1. This invention uses graph convolution operations based on GCN to autonomously capture deep information such as node connection patterns and neighbor dependencies from the network topology structure without the need for manually designing features such as "degree" and "betweenness". This completely avoids the limitations of manual features in traditional methods.

[0023] 2. This invention uses a forward propagation method that extracts features based on a GCN-based autoencoder and predicts node rankings using a GNN-based node ranking prediction model. Compared with the existing technology's "delete nodes and recalculate" mode, this greatly reduces computational complexity and is more suitable for the current reality of increasingly large-scale and complex smart grids.

[0024] 3. This invention uses a synthetic network generated by the BA model as input when training the autoencoder and node ranking prediction model. The network generated by this model is highly consistent with the topology of the real power communication network. Therefore, in application, no matter how the number of nodes and link density of the real network change, as long as the adjacency matrix and feature matrix are generated in a unified format, the identification can be completed by the trained node ranking prediction model. There is no need to retrain for each network, which completely solves the core pain point of "poor generalization ability" of the existing technology.

[0025] 4. This invention obtains true labels through the SIR propagation model, and the label error is far less than 10% compared with the traditional "subjective evaluation". In addition, this invention uses the listLME loss function based on the Plackett-Luce model to optimize the relative relationship between the predicted ranking and the true ranking, rather than just optimizing the absolute value of the score. This ensures that the node ranking prediction model focuses on the differences in importance between nodes and avoids "fuzzy scores and unclear rankings". Moreover, this invention uses Kendall's τ coefficient and monotonicity index MI to quantify and verify the model output, ensuring the consistency between the predicted ranking and the true ranking and the absence of ranking duplication or ambiguity. Compared with the subjective judgment of traditional methods, the accuracy is quantifiable and verifiable, fully meeting the needs of practical engineering. Attached Figure Description

[0026] Figure 1 This is a flowchart of the key node identification method for power communication networks based on graph neural networks according to the present invention.

[0027] Figure 2 This is a schematic diagram of the structure of a GCN-based autoencoder.

[0028] Figure 3 This is a schematic diagram of the structure of a node ranking prediction model based on GNN. Detailed Implementation

[0029] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0030] In one embodiment of the present invention, a method for identifying key nodes in a power communication network based on a graph neural network is provided, comprising the following steps: S1: Constructing a topology graph G=(V,E) of the power communication network, where V={v1,v2,...,vn} is the set of nodes in the power communication network, E is the set of edges in the power communication network, and n is the total number of nodes in the power communication network; S2: Generating an adjacency matrix A of the power communication network based on the topology graph; Adding self-loops to the adjacency matrix A and standardizing it to obtain a first input matrix. S3: Use one-hot encoding to generate the feature matrix of the node as the second input matrix X; The second input matrix X is input into the trained autoencoder to obtain the node latent representation Z, wherein the autoencoder is based on a graph convolutional network (GCN); S4: The node latent representation Z and the adjacency matrix A are input into the trained node ranking prediction model to output the importance score of the node. The nodes are ranked according to the importance score, and the top k nodes are selected as key nodes of the power communication network, wherein the node ranking prediction model is based on a graph neural network (GNN).

[0031] In the above embodiments, the specific process of generating the original adjacency matrix A based on the constructed topological graph G is as follows: (1) Node numbering mapping: Number all nodes in the network topology graph G, establish a mapping relationship between nodes and matrix indices, and ensure that each node vi corresponds to the i-th row and i-th column in the matrix; (2) Adjacency matrix initialization: Create an n×n adjacency matrix A, where n is the total number of nodes; (3) Edge relationship transformation: Traverse each edge (vi, vj) in the edge set E, and set A[i][j]=1 and A[j][i]=1 in the adjacency matrix A to indicate that there is a connection relationship between nodes vi and vj; (4) Matrix storage: The generated adjacency matrix A is stored in the form of a numerical array for easy use in subsequent graph neural network calculations.

[0032] Through the above process, the topology of the power communication network can be converted into a standard adjacency matrix representation. The matrix element A[i][j]=1 indicates that there is a direct connection between nodes vi and vj, and A[i][j]=0 indicates that there is no direct connection between the two nodes. This adjacency matrix provides a standardized input format for feature learning in subsequent deep learning networks.

[0033] In the above embodiment, the trained autoencoder in step S3 and the trained node ranking prediction model in step S4 are obtained through joint training by the following steps: S10: Generate a synthetic network using the BA (Barabási-Albert) model and construct the topology graph of the synthetic network. =( , ),in ={ 1, 2,..., } represents the set of nodes in the synthetic network. Let the set of edges of the synthetic network be . S20: Generate the adjacency matrix of the synthesized network based on its topology graph. (This represents the total number of nodes in the synthesized network.) To the adjacency matrix Add self-loops and normalize to obtain the third input matrix. The feature matrix of the generated node is used as the fourth input matrix; one-hot encoding is used. S30: The third input matrix and the fourth input matrix Input the original autoencoder to obtain the node latent representation. The original autoencoder is based on a graph convolutional network (GCN); S40: The true importance index of each node is obtained using the SIR propagation model. This allows us to obtain the true ranking of each node. S50: Represent the potential of nodes and adjacency matrix Input the original node ranking prediction model to output the predictive importance score of the nodes. This leads to the predicted ranking of the nodes, where the original node ranking prediction model is based on a graph neural network (GNN); S60: A scalar loss value is generated based on the difference between the predicted and actual rankings of the nodes using a loss function. S70: Employ the Adam optimizer based on the scalar loss value. By adaptively adjusting the parameters of the original autoencoder and the original node ranking prediction model through backpropagation, the trained autoencoder and the trained node ranking prediction model are finally obtained.

[0034] In the above embodiments, the present invention uses a synthetic network generated by a BA model as training data. The scale-free network generated by the BA model is highly similar to the topology of real power communication networks, and the synthetic network can generate training samples of different sizes as needed. Furthermore, if the node ranking prediction model is trained and tested only on a specific real network, it is prone to overfitting. However, by training on a synthetic network and testing on a real network, the model's cross-domain generalization ability can be effectively verified. When obtaining a large amount of real power communication network data is difficult, using a synthetic network as training data is a better choice.

[0035] In one embodiment of the present invention, such as Figure 2 As shown, the GCN-based autoencoder of the present invention includes an encoder and a decoder, wherein the encoder adopts a 2-layer GCN and the decoder adopts a 2-layer fully connected layer.

[0036] The encoder's input is the one-hot encoding of the node. It can be calculated using the following formula:

[0037]

[0038] in, To add self-loops and normalize the adjacency matrix, Let A be the adjacency matrix of the topological graph G, I be the identity matrix of the adjacency matrix A, and D be the degree matrix of the adjacency matrix A. The degree matrix D is a diagonal matrix, and the diagonal element D[i][i] = the sum of the elements in the i-th row of the adjacency matrix A (i.e., the degree of node i). and It is a learnable parameter matrix; ReLU is the activation function; Let d be the latent representation of the node, and d be the latent dimension.

[0039] weight matrix and The method for determining it is as follows: (1) Determining the matrix dimension: First layer weight matrix The input dimension is n (the one-hot encoding dimension of the corresponding node), and the output dimension is set to 256 (the feature dimension of the first hidden layer). Second layer weight matrix The input dimension is 256 (first-level output dimension), and the output dimension is d (latent representation dimension, which is d=48 in the preferred embodiment). (2) Parameter initialization: The weight matrix is ​​initialized using a Xavier uniform distribution; (3) Parameter learning mechanism: weight matrix and As a learnable parameter of type torch.nn.Parameter, the gradient is automatically calculated through the backpropagation algorithm during model training, and the parameter is updated using an optimizer (the Adam optimizer is used in this embodiment, and the learning rate is set to 0.001) to minimize the target loss function. (4) Network structure implementation: In the specific implementation, the first layer GCN is constructed by GNN(n, 256), and the second layer GCN is constructed by GNN(256, d), where n is the node one-hot encoding dimension and d is the latent representation dimension. In the preferred embodiment, d=48 is used.

[0040] The decoder maps the node's latent representation Z to an importance score: H_dec = Linear(Z, 256) / / First layer fully connected: d → 256 A = Linear(H_dec, 1) / / Second-level fully connected layer: 256 → 1 in, This is the reconstructed output of the decoder. The training objective of the autoencoder in this invention is to learn the low-dimensional latent representation of nodes through the encoder-decoder structure. The node latent representation Z output by the encoder will serve as the input feature of the node ranking prediction model of this invention.

[0041] In the above embodiments of the present invention, the SIR propagation model in step S40 includes three state nodes: susceptible node S, infected node I, and recovered node R, and has two parameters: propagation probability. and recovery probability The information propagation process is simulated using the SIR propagation model as follows: (1) At time t=0, node vi is infected node I, and the other nodes are susceptible nodes S; (2) At each time step, infected node I is propagated with probability. Infect its neighboring nodes; (3) Infected node I with recovery probability Recover and acquire immunity; (4) Calculate the number of infected nodes I and recovered nodes R when the SIR propagation model reaches a steady state. ; (5) Selection The average of a certain number of simulation results is used as an indicator of the true importance of node vi. In one instance, 100 simulation results are selected, among which... Propagation probability = 1.5 , The infection probability threshold is calculated using the following formula:

[0042] in, Indicates node degree. This indicates taking the average value.

[0043] It is worth mentioning that although the SIR propagation model can obtain the influence index of nodes and identify key nodes, it is still necessary to construct the node ranking prediction model of this invention for the following reasons: (1) Computational efficiency problem: The SIR model requires propagation simulation for each node separately. For a network with n nodes, n complete propagation processes need to be executed. Each propagation requires multiple time steps until a stable state is reached. Taking the 5715 nodes in Embodiment 2 of this invention as an example, 5715 propagation simulations need to be executed, and the computational complexity is O(n×T×|E|), where T is the number of propagation time steps and |E| is the number of edges. The computational overhead is huge.

[0044] (2) Real-time requirements: In actual power communication network operation and maintenance, it is necessary to respond quickly to network topology changes and update the ranking of key nodes in real time. The multiple simulation processes of the SIR model cannot meet the real-time requirements, while the prediction model can obtain the importance ranking of all nodes through one forward propagation, reducing the computational complexity to O(|E|).

[0045] (3) Generalization considerations: Propagation parameters of the SIR model ( , It needs to be adjusted for different network characteristics and lacks cross-network generalization ability. The prediction model learns a general topological feature representation through pre-training on synthetic networks and can adapt to power communication networks of different sizes and topologies.

[0046] (4) Model training strategy: In this invention, the SIR model is mainly used to generate training labels, providing a real node importance standard for the supervised learning of the prediction model. The prediction model achieves the transformation from "computation-intensive" to "inference-efficient" by learning the output pattern of the SIR model.

[0047] In one embodiment of the present invention, the node ranking prediction model comprises, from top to bottom: a first graph neural network layer, used to receive the latent node representation Z and adjacency matrix A generated by an autoencoder, and to extract and transform graph structure features from them; a first batch normalization layer, used to standardize the features output by the first graph neural network layer; a first ReLU activation layer, used to introduce nonlinear transformations into the batch-normalized features; a second graph neural network layer, used to perform deeper graph structure feature extraction and transformations into the features after nonlinear activation; a second batch normalization layer, used to standardize the features output by the second graph neural network layer; a second ReLU activation layer, used to introduce nonlinear factors again to further optimize the feature distribution; a Dropout layer, used to randomly discard a portion of the neuron outputs according to a preset probability during model training; a fully connected layer, used to map the high-dimensional features extracted by the preceding layers into a preliminary one-dimensional node importance score; a third ReLU activation layer, used to apply nonlinear rectification to the node importance score output by the fully connected layer; and a Flatten layer, used to flatten the final output node importance score tensor into a one-dimensional vector.

[0048] Specifically, the node ranking prediction model constructed in this invention has the following structure: (1) First layer GNN: Input dimension: 48-dimensional node features Output dimension: 6-dimensional hidden representation Parameter initialization: Initialization is performed using the Kaiming normal distribution, adapted to the leaky_relu activation function. (2) First-level batch normalization: Batch normalization is performed on the 6-dimensional features to stabilize the training process. (3) First-level activation function: ReLU activation function (4) Second-layer GNN: Input dimension: 6-dimensional hidden features Output dimension: 12-dimensional representation Kaiming initialization is also used. (5) Second-level batch normalization: Batch normalization of the 12-dimensional features. (6) Second-level activation function: ReLU activation function (7) Dropout layer: The dropout rate is set to 0.5 to prevent overfitting. (8) Fully connected layer: Input dimension: 12-dimensional Output dimension: 1-dimensional (node ​​importance score) The weights are initialized using Kaiming, and the bias is initialized to 0.5. (9) Output processing: The ReLU activation function ensures that the score is non-negative. Use flatten() to flatten the output into a one-dimensional vector. It should be noted that the input dimension of 48 for the first layer is determined by the dimension of the node latent representation Z generated by the autoencoder. Since the node latent representation Z generated by the autoencoder serves as the input feature of the node ranking prediction model, the two should maintain consistency in dimension. Similarly, the input dimension of the second layer should be consistent with the output dimension of the first layer. The choice of the number of output dimensions for the first and second layers is not unique and can be adjusted according to the specific task and data characteristics. After trying the first layer output dimensions of [4, 6, 8, 12, 16] and the second layer output dimensions of [8, 12, 16, 24, 32], the inventors found that choosing a first layer GNN output dimension of 6 dimensions and a second layer GNN output dimension of 12 dimensions resulted in the best prediction performance.

[0049] The forward propagation process of the node ranking prediction model of this invention is as follows: H1 = GNN_layer1(Z, A) H1_norm = LayerNorm(H1) H1_relu = relu(H1) H2 = GNN_layer2(H1_relu, A) H2_norm = LayerNorm(H2) H2_relu = relu(H2_norm) H_drop = Dropout(H2_relu) H_fc = FC(H_drop) H3_relu = relu(H_fc) scores = flatten(H3_relu) In one embodiment of the present invention, the loss function used is the listMLE (Maximum LikelihoodEstimation) loss function, and the scalar loss value is calculated by the following formula. :

[0050] in, It is the predictive importance score of the node. The true ranking is formed based on the actual value y of the node (y = [y1, y2,..., yn]ᵀ), where P represents the Plackett-Luce model, and its formula is as follows: .

[0051] The listMLE loss function considers the relative ranking relationships between nodes, optimizing the overall ranking quality. The listMLE loss function is responsible for calculating the difference between the model's predicted ranking and the actual ranking, generating a scalar loss value. The Adam optimizer adaptively adjusts the parameters of the autoencoder and the node ranking prediction model to minimize the loss based on the gradient calculated by backpropagation of the listMLE loss function.

[0052] In a further embodiment of the invention, Kendall's The coefficients and monotonicity index MI are used to test the performance of the trained node ranking prediction model, among which Kendall's... The formula for calculating the coefficient is:

[0053] Where c is the number of consistent logarithms, d is the number of inconsistent logarithms, and n is the number of nodes. For example, for ( , (), , This data, if and or and If they are a pair, then they are called a consistent pair; otherwise, they are not a consistent pair. The closer the coefficient is to 1, the more consistent the predicted ranking of the trained node ranking prediction model is with the actual ranking, and the better the training effect.

[0054] The formula for calculating the monotonicity index MI is as follows:

[0055] Where 𝑅 represents the ranking list. This represents a value in the ranking list. This indicates that the value in the ranking list is... The number of values, MI represents the total number of values ​​in the ranking list; MI is between 0 and 1, and the higher the value, the higher the degree of uniqueness of the ranking list and the better the performance of the node ranking prediction model.

[0056] In one embodiment of the present invention, an electronic device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the computer program, when executed by the processor, implements the graph neural network-based key node identification method for power communication networks of the present invention.

[0057] In one embodiment of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the graph neural network-based key node identification method for power communication networks of the present invention.

[0058] Specifically, memory can be random access memory, read-only memory, non-volatile memory, programmable ROM, erasable PROM, electrically erasable memory, flash memory, optical memory, and registers, etc.

[0059] A processor can be an integrated circuit chip with signal processing capabilities. In implementation, the steps of the above methods can be completed through integrated logic circuits in the processor's hardware or through software instructions. The processor can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor.

[0060] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a solid-state drive (SSD), etc.

[0061] In addition, the present invention also designed experiments to verify the effectiveness of the identified key nodes, specifically including the following steps: (1) Design evaluation metrics for the communication topology network; (2) Calculate the evaluation metrics for the original, undamaged communication topology network; (3) Identify and record the top k critical nodes of the power communication network; (4) Destroy the top k critical nodes of the identified power communication network, delete these critical nodes and all edges connected to them, and calculate the evaluation metrics for the communication network after deletion; (5) Destroy the top k inefficient nodes of the identified power communication network, i.e., the last k nodes (inefficient bottleneck nodes that reduce network performance, such as nodes that may introduce redundant paths or inefficient connections), delete these critical nodes and all edges connected to them, and calculate the evaluation metrics for the communication network after deletion; (6) Randomly delete the same number of network nodes and all edges connected to them, and calculate the evaluation metrics for the communication network after deletion; (7) Compare the evaluation metrics of the original, undamaged communication topology network with those of the communication topology network after deleting nodes in three different ways, and determine the effectiveness of the critical nodes.

[0062] The evaluation metrics for the designed communication topology network are as follows: 1. Limiting path length efficiency ( First, let's define the global efficiency of a graph: it's the sum of the efficiencies between all pairs of nodes. Efficiency is defined as the reciprocal of the distance between two nodes. The higher the global efficiency of a network, the higher its overall information transmission or communication efficiency. Since removing some key nodes can cause some nodes to become isolated, resulting in zero global efficiency and making it impossible to analyze efficiency differences, the inventors designed a path length-limited efficiency mechanism based on global efficiency, setting a maximum path length threshold. Twice the diameter of the original network, limiting path length efficiency:

[0063] Where N is the total number of nodes. Let be the distance between node i and node j.

[0064] 2. Maximum connected subgraph proportion ( The maximum connected subgraph is defined as the ratio of the number of nodes in the maximum connected subgraph to the total number of nodes in the original network. The number of nodes in the maximum connected subgraph refers to the number of nodes in the maximum connected component after deleting some nodes, and the total number of nodes in the original network refers to the total number of nodes in the original network. The higher the ratio of the maximum connected subgraph to the maximum connected subgraph, the stronger the connectivity and the better the robustness of the graph.

[0065] 3. Natural connectivity λ is a topological robustness index based on graph eigenvalues. It quantifies the redundancy strength of a network through the eigenvalue distribution of the adjacency matrix. The more alternative paths in the network, the stronger the fault tolerance and the higher the λ value. The formula is as follows:

[0066] in, Let A be the eigenvalue of the adjacency matrix A of graph G.

[0067] 4. Fracture sensing path length ( Because deleting certain nodes in the network causes the graph to become disconnected, the average shortest path length becomes infinite, making it impossible to analyze efficiency differences. Therefore, we designed a break-aware path length based on the average shortest path length. The core idea is to penalize network breaks by combining the proportion of connected subgraphs and path lengths, as shown in the following formula:

[0068] in, Let G be the average shortest path length of the subgraph containing the nodes of the largest connected component. Let G be the proportion of the largest connected subgraph in graph G. If the network is broken ( (Decrease), the indicator value will increase, while retaining the path information of the connected parts. Specific Implementation Example 1: Taking a municipal-level power communication backbone network as an example, this network contains 300 communication nodes and 878 links. According to the identification method of this invention: (1) Construct the network topology graph and adjacency matrix ; (2) Set the latent dimension of the autoencoder to d=48; (3) Construct a composite graph neural network (CGNN) ranking prediction model. The specific structure is as follows: First GNN layer (48→6 dimensions) → Batch normalization layer → ReLU activation layer → Second GNN layer (6→12 dimensions) → Batch normalization layer → ReLU activation layer → Dropout layer (dropout rate 0.5) → Fully connected layer (12→1 dimension) → ReLU activation layer → Flattened output; (4) Set SIR model parameters =1, calculated using the formula in step S40. =0.26; (5) Use the Adam optimizer with a learning rate of 0.001 and train for 3000 epochs; (6) Pre-train on the network generated by the BA model and then test it on the target network.

[0070] Experimental results show that the key nodes identified by the method of this invention are consistent with Kendall's calculation results of the SIR model. The coefficient reached 0.78, and the monotonicity index (MI) reached 1.0. The results of the key node effectiveness verification experiment are shown in Table 1. Table 1. Results of the Experiment Validating Key Nodes

[0071] The term "original network" refers to the original, undamaged power communication backbone network, containing 300 communication nodes and 878 links. Various indicators were calculated based on the original power communication backbone network. "Critical nodes" refer to the top 5% of nodes identified by the node ranking prediction model. These nodes were removed from the original power communication backbone network, and various indicators were calculated accordingly. "Inefficient nodes" refer to the bottom 5% of nodes identified by the node ranking prediction model. These nodes were removed from the original power communication backbone network, and various indicators were calculated accordingly. "Random destruction" refers to randomly destroying the same number of nodes from the original network. These nodes were then removed from the original power communication backbone network, and various indicators were calculated accordingly. Table 1 shows that deleting the critical nodes identified by the method of this invention significantly reduced network performance indicators, and the decline was more pronounced than randomly deleting the same number of nodes. This verifies the effectiveness of critical node identification. Deleting inefficient nodes improved network performance indicators, suggesting that these inefficient nodes may be bottlenecks limiting network performance, and their removal could be considered in practice.

[0072] Example 2: Taking a provincial power communication backbone network as an example, this network contains 5715 communication nodes and 19794 links. According to the identification method of this invention: (1) Construct the network topology graph and adjacency matrix ; (2) Set the latent dimension of the autoencoder to d=48; (3) Construct a composite graph neural network (CGNN) ranking prediction model. The specific structure is as follows: First GNN layer (48→6 dimensions) → Batch normalization layer → ReLU activation layer → Second GNN layer (6→12 dimensions) → Batch normalization layer → ReLU activation layer → Dropout layer (dropout rate 0.5) → Fully connected layer (12→1 dimension) → ReLU activation layer → Flattened output; (4) Set SIR model parameters =1, calculated using the formula in step S40. =0.07; (5) Use the Adam optimizer with a learning rate of 0.001 and train for 3000 epochs; (6) Pre-train on the network generated by the BA model and then test it on the target network.

[0073] Experimental results show that the key nodes identified by the method of this invention are consistent with Kendall's calculation results of the SIR model. The coefficient reached 0.80, and the monotonicity index (MI) reached 0.99. The results of the key node effectiveness verification experiment are shown in Table 2. Table 2 Results of the Experiment Validation of Key Nodes

[0074] The term "original network" refers to the original, undamaged power communication backbone network, containing 5715 communication nodes and 19794 links. Various indicators were calculated based on the original power communication backbone network. "Critical nodes" refer to the top 5% of nodes identified by the node ranking prediction model. These nodes were removed from the original power communication backbone network, and various indicators were calculated accordingly. "Inefficient nodes" refer to the bottom 5% of nodes identified by the node ranking prediction model. These nodes were removed from the original power communication backbone network, and various indicators were calculated accordingly. "Random destruction" refers to randomly destroying the same number of nodes from the original network. These nodes were removed from the original power communication backbone network, and various indicators were calculated accordingly. Table 2 shows that deleting the critical nodes identified in this invention significantly reduced network performance indicators, and the decline was more pronounced than randomly deleting the same number of nodes. This verifies the effectiveness of critical node identification. Deleting inefficient nodes improved network performance indicators, suggesting that these inefficient nodes may be bottlenecks limiting network performance, and their removal could be considered in practice.

[0075] The above description is merely a selection of preferred embodiments of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for identifying key nodes in a power communication network based on graph neural networks, characterized in that, Includes the following steps: S1: Construct the topology graph G=(V,E) of the power communication network, where V={v1,v2,...,vn} is the set of nodes in the power communication network, E is the set of edges in the power communication network, and n is the total number of nodes in the power communication network; S2: Generate an adjacency matrix A for the power communication network based on the topology graph, add self-loops to adjacency matrix A and normalize it to obtain the first input matrix. ; and, using one-hot encoding to generate the feature matrix of the node, and using the feature matrix as the second input matrix X; S3: Transfer the first input matrix The second input matrix X is input into the trained autoencoder to obtain the node latent representation Z, wherein the autoencoder is constructed based on the graph convolutional network GCN. S4: Input the node latent representation Z and adjacency matrix A into the trained node ranking prediction model to output the importance score of the node. Rank the nodes according to the importance score and select the top k nodes as key nodes of the power communication network. The node ranking prediction model is built based on graph neural network (GNN).

2. The method for identifying key nodes in a power communication network based on a graph neural network according to claim 1, characterized in that, The trained autoencoder in step S3 and the trained node ranking prediction model in step S4 are obtained through joint training using the following steps: S10: Generate the synthetic network using the BA model and construct the topology graph of the synthetic network. =( , ),in ={ 1, 2,..., } represents the set of nodes in the synthetic network. Let the set of edges of the synthetic network be . This represents the total number of nodes in the synthetic network. S20: Generating the adjacency matrix of a synthetic network based on its topology graph. To the adjacency matrix Add self-loops and normalize to obtain the third input matrix. The feature matrix of the generated node is used as the fourth input matrix; one-hot encoding is used. ; S30: Transfer the third input matrix and the fourth input matrix Input the original autoencoder to obtain the node latent representation. The original autoencoder mentioned therein is built based on the graph convolutional network GCN; S40: Use the SIR propagation model to obtain the true importance index of each node in the synthetic network. This allows us to obtain the true ranking of each node. ; S50: Represent the potential node representation and adjacency matrix Input the original node ranking prediction model to output the predictive importance score of the nodes. This leads to the predicted ranking of the nodes, where the original node ranking prediction model is built based on a graph neural network (GNN). S60: Generate a scalar loss value based on the difference between the predicted and actual rankings of nodes using a loss function. ; S70: Employ the Adam optimizer based on the scalar loss value. By adaptively adjusting the parameters of the original autoencoder and the original node ranking prediction model through backpropagation, the trained autoencoder and the trained node ranking prediction model are finally obtained.

3. The method for identifying key nodes in a power communication network based on a graph neural network according to claim 2, characterized in that, The SIR propagation model in step S40 includes three state nodes and two parameters. The state nodes include susceptible nodes S, infected nodes I, and recovered nodes R. The two parameters include the propagation probability. and recovery probability ; The information propagation process is simulated using the SIR propagation model as follows: (1) At time t=0, node vi is set as infected node I, and other nodes are set as susceptible nodes S; (2) At each time step, infected node I is propagated with probability. Infect its neighboring nodes; (3) Infected node I with recovery probability Recover and acquire immunity; (4) Calculate the number of infected nodes I and recovered nodes R when the SIR propagation model reaches a steady state. ; (5) Selection The average of a certain number of simulation results is used as an indicator of the true importance of node vi. ,in, Propagation probability = 1.5 , The infection probability threshold is calculated using the following formula: in, Indicates node degree. This indicates taking the average value.

4. The method for identifying key nodes in a power communication network based on a graph neural network according to claim 2, characterized in that, The loss function is the listMLE loss function based on the Plackett-Luce model, and the scalar loss value is calculated using the following formula. : in, It is the predictive importance score of the node. It represents the true ranking of the nodes, where P represents the Plackett-Luce model, and its formula is as follows: 。 5. The method for identifying key nodes in a power communication network based on a graph neural network according to claim 1, characterized in that, The first input matrix It is obtained through the following formula: Where A is the adjacency matrix of the topological graph G, I is the identity matrix of the adjacency matrix A, and D is the degree matrix of the adjacency matrix A.

6. The method for identifying key nodes in a power communication network based on a graph neural network according to claim 2, characterized in that, The autoencoder includes an encoder and a decoder, wherein the encoder uses a 2-layer GCN and the decoder uses a 2-layer fully connected layer.

7. The method for identifying key nodes in a power communication network based on a graph neural network according to any one of claims 2 to 6, characterized in that, The node ranking prediction models, from top to bottom, are as follows: The first graph neural network layer is used to receive the node latent representation Z and adjacency matrix A generated by the autoencoder, and to extract and transform the graph structure features of them. The first batch normalization layer is used to standardize the features output by the first graph neural network layer; The first ReLU activation layer is used to introduce a non-linear transformation into the batch-normalized features; The second graph neural network layer is used to perform deeper graph structure feature extraction and transformation on the features after nonlinear activation. The second batch normalization layer is used to standardize the features output by the second graph neural network layer; The second ReLU activation layer is used to introduce nonlinear factors again to further optimize the distribution of features; Dropout layers are used to randomly discard a portion of the outputs of neurons according to a preset probability during model training. Fully connected layers are used to map the high-dimensional features extracted by the preceding layers into preliminary results of one-dimensional node importance scores; The third ReLU activation layer is used to apply nonlinear rectification to the node importance score output of the fully connected layer; The Flatten layer is used to flatten the final output node importance score tensor into a one-dimensional vector.

8. The method for identifying key nodes in a power communication network based on a graph neural network according to any one of claims 2 to 6, characterized in that, Further utilize Kendall's The coefficients and monotonicity index MI are used to test the performance of the trained node ranking prediction model, among which Kendall's... The formula for calculating the coefficient is: Where c is the number of consistent logarithms, d is the number of inconsistent logarithms, and n is the number of nodes; The formula for calculating the monotonicity index MI is as follows: in, R This represents a ranking list. This represents a value in the ranking list. This indicates that the value in the ranking list is... The number of values, N This represents the total number of values ​​in the ranking list.

9. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program that, when executed by the processor, implements the method for identifying key nodes in a power communication network based on a graph neural network according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the method for identifying key nodes in a power communication network based on any one of claims 1 to 8.

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