Cascade failure prediction method and device based on interdependent infrastructure network

Abstract

The invention relates to the technical field of infrastructure cascade failure prediction, and provides a cascade failure prediction method and device based on an interdependent infrastructure network, and the method comprises the steps: obtaining single infrastructure network embedding and coupled infrastructure network embedding based on a given interdependent infrastructure network and an initial failure node; predicting target node embedding of the interdependent infrastructure network after cascade failure propagation based on single infrastructure network embedding and coupled infrastructure network embedding; and according to the target node embedding, predicting to obtain a cascade failure prediction result. According to the method, topological structure features of interdependent infrastructure networks are captured through link prediction embedding, high-order dynamic and global evolution features in the infrastructure networks are captured through global pooling embedding, and excessive smoothness in a graph convolutional neural network is avoided through initial node enhanced embedding. And the accuracy and the fine granularity of the cascade failure prediction in the infrastructure network are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of infrastructure cascading failure prediction, and in particular to a cascading failure prediction method and device based on an interdependent infrastructure network. Background Art

[0002] Cascading failure prediction is an important and widely studied issue in urban infrastructure networks. Cascading failure in infrastructure networks refers to the process in which the failure of one or several infrastructures causes the failure of other infrastructures, thus causing a cascading chain reaction. Cascading failures may be caused by earthquakes, typhoons, or failure of infrastructure components due to network aging. This process often brings catastrophic damage to cities, leading to the collapse of urban services and functions, and even threatening the lives of citizens. Accurately predicting cascading failures in infrastructure networks can help understand the key interconnections and vulnerabilities in infrastructure networks to improve system reliability, or minimize the impact of infrastructure failures through early intervention.

[0003] In the field of infrastructure cascading failure prediction, some methods are currently available for reference for single networks or coupled networks. For the prediction of cascading failures on a single infrastructure network, existing research has taken into account the prediction of cascading failures on power grids, road networks, and communication networks. For example, for power grids, DC-based models such as OPA (Operational Amplifier) ​​can be used for prediction, or AC-based models such as the Manchester model can be used for prediction. In addition, there are many existing machine learning methods to achieve cascading failure prediction on a single infrastructure network. In addition, there are methods that treat the infrastructure network as a dependent network and consider the correlation between different networks to predict cascading failures in multiple infrastructure networks.

[0004] However, most of these models are rule- or mechanism-based models, which are originally intended to explain a certain phenomenon or law in the real world, but they perform poorly in prediction tasks.

[0005] It has been observed that there are three challenges in predicting cascading failures in existing infrastructure networks: On the one hand, when predicting cascading failures in a single infrastructure network, the dynamics of cascading failures of the same infrastructure are affected by higher-order global dynamics. Interactions in infrastructure networks are usually not one-to-one connected, for example, for two connected nodes, the failure of one node does not necessarily mean that the other node will also fail. In addition, there are higher-order dynamics, namely multi-hop dynamics in the network, and network resilience during cascading failures.

[0006] On the other hand, when predicting infrastructure cascading failures in coupled infrastructure networks, the dependencies between different types of infrastructure are diverse and complex. Because the real-world infrastructure network is a combination of multiple infrastructure networks, i.e., interdependent networks, different types of infrastructure have different dependencies and coupling mechanisms, and modeling such diverse dependencies is often difficult.

[0007] Finally, for the data-driven approach to cascading failure prediction on infrastructure networks, the dynamics of the initial failure nodes are noisy due to oversmoothing when using graph convolutional neural networks. Most existing data-driven methods use graph convolutional neural network structures, which suffer from oversmoothing. When urban infrastructure fails, the number of initial faulty nodes is often much smaller than the number of normal nodes. This results in that when using graph convolutional neural networks for convolution, as the network deepens and the structure becomes more complex, the original small amount of information about the faulty nodes is gradually submerged in the large amount of information about the normal nodes, resulting in poor performance in cascading failure prediction on infrastructure networks.

[0008] In summary, existing related work has the following limitations: (1) It is unable to capture the high-order dynamics and global evolution in a single infrastructure network; (2) For coupled infrastructure networks, the diverse coupling relationships between different infrastructures are not considered; (3) The accuracy and granularity of cascading failure prediction in infrastructure networks are not high enough.

[0009] Therefore, how to solve the problem that the existing infrastructure network cascading failure prediction methods are unable to capture the high-order dynamics and global evolution in a single infrastructure network, and do not consider the diverse coupling relationships between different infrastructure networks in the coupled infrastructure network, and the cascading failure prediction accuracy and granularity are not high, is an important issue that needs to be urgently addressed in the field of infrastructure cascading failure prediction. Summary of the invention

[0010] The present invention provides a cascading failure prediction method and device based on interdependent infrastructure networks, so as to overcome the defects of the existing cascading failure prediction methods of infrastructure networks that cannot capture the high-order dynamics and global evolution in a single infrastructure network, and do not consider the diverse coupling relationships between different infrastructure networks in a coupled infrastructure network, and the low accuracy and granularity of cascading failure prediction. The method and device can not only capture the high-order dynamics and global evolution characteristics in the infrastructure network, but also take into account the diverse coupling relationships between different infrastructure networks, and can effectively improve the accuracy and granularity of cascading failure prediction in the infrastructure network.

[0011] On the one hand, the present invention provides a cascading failure prediction method based on an interdependent infrastructure network, comprising: based on a given interdependent infrastructure network and an initial failure node, obtaining a single infrastructure network embedding and a coupled infrastructure network embedding; based on the single infrastructure network embedding and the coupled infrastructure network embedding, predicting a target node embedding of the interdependent infrastructure network after cascading failure propagation; according to the target node embedding, predicting a cascading failure prediction result; wherein the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhanced embedding.

[0012] Furthermore, the method of obtaining a single infrastructure network embedding and a coupled infrastructure network embedding based on a given interdependent infrastructure network and an initial failure node includes: representing the interdependent infrastructure network as a heterogeneous graph, and determining the node input according to the initial failure node; based on a pre-trained link prediction model, obtaining the link prediction embedding of the coupled infrastructure network and the link prediction embedding of the single infrastructure network according to the heterogeneous graph and the node input; based on a pre-trained global pooling model, obtaining the global pooling embedding of the coupled infrastructure network and the global pooling embedding of the single infrastructure network according to the heterogeneous graph and the node input; based on a pre-trained initial node enhancement model, obtaining the initial node enhancement embedding of the coupled infrastructure network and the initial node enhancement embedding of the single infrastructure network according to the heterogeneous graph and the node input.

[0013] Furthermore, the heterogeneous graph includes a heterogeneous graph of a coupled infrastructure network and a heterogeneous graph of a single infrastructure network, and the node input includes an initial node state; accordingly, the pre-trained link prediction model obtains the link prediction embedding of the coupled infrastructure network and the link prediction embedding of the single infrastructure network according to the heterogeneous graph and the node input, including: inputting the node input and the heterogeneous graph of the coupled infrastructure network into the pre-trained link prediction model to obtain the link prediction embedding of the coupled infrastructure network; inputting the node input and the heterogeneous graph of the single infrastructure network into the pre-trained link prediction model to obtain the link prediction embedding of the single infrastructure network; wherein the link prediction model is obtained by training and optimizing through an edge loss function, and the link prediction embedding characterizes the topological structure characteristics of the single infrastructure network or the coupled infrastructure network.

[0014] Furthermore, the global pooling model is a differentiable pooling network, the heterogeneous graph includes a heterogeneous graph of a coupled infrastructure network and a heterogeneous graph of a single infrastructure network, and the node input includes an initial node state and a shortest path length from an initial failed node to a current node; accordingly, the pre-trained global pooling model obtains a global pooling embedding of the coupled infrastructure network and a global pooling embedding of a single infrastructure network according to the heterogeneous graph and the node input, including: inputting the node input and the heterogeneous graph of the coupled infrastructure network into the differentiable pooling network, and obtaining the state of all nodes in the differentiable pooling network. The average shortest path length corresponding to each network layer of the differentiable pooling network is obtained, and the difference between the average shortest path length and the true path length is used as the global pooling embedding of the coupled infrastructure network; the node input and the heterogeneous graph of the single infrastructure network are input into the differentiable pooling network to obtain the average shortest path length corresponding to all nodes in each network layer of the differentiable pooling network, and the difference between the average shortest path length and the true path length is used as the global pooling embedding of the single infrastructure network; wherein the global pooling embedding characterizes the high-order dynamic-global evolution characteristics of different levels of a single infrastructure network or a coupled infrastructure network.

[0015] Further, the initial node enhancement model is a graph Markov network, the heterogeneous graph includes a heterogeneous graph of a coupled infrastructure network and a heterogeneous graph of a single infrastructure network, and the node input includes an initial node state; accordingly, the initial node enhancement model based on pre-training obtains the initial node enhancement embedding of the coupled infrastructure network and the initial node enhancement embedding of the single infrastructure network according to the heterogeneous graph and the node input, including: inputting the node input and the heterogeneous graph of the coupled infrastructure network into the graph Markov network, optimizing the dependency between node labels using the expectation maximization algorithm, and using the hidden layer embedding corresponding to the final output of the E step in the expectation maximization algorithm as the initial node enhancement embedding of the coupled infrastructure network; inputting the node input and the heterogeneous graph of the single infrastructure network into the graph Markov network, optimizing the dependency between node labels using the expectation maximization algorithm, and using the hidden layer embedding corresponding to the final output of the E step in the expectation maximization algorithm as the initial node enhancement embedding of the single infrastructure network; wherein, the initial node enhancement embedding characterizes the initial failure node characteristics in the single infrastructure network or the coupled infrastructure network.

[0016] Furthermore, the predicting of target node embeddings of the interdependent infrastructure network after cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding includes: encoding the single infrastructure network embedding and the coupled infrastructure network embedding respectively to obtain corresponding single infrastructure network coded embedding and coupled infrastructure network coded embedding; connecting the single infrastructure network coded embedding and the coupled infrastructure network coded embedding according to the type of infrastructure network to obtain the target infrastructure network coded embedding; and predicting the target node embedding of the interdependent infrastructure network after cascading failure propagation based on the target infrastructure network coded embedding based on a relational graph convolutional neural network.

[0017] Furthermore, predicting a cascading failure prediction result based on the target node embedding includes: decoding the target node embedding based on a single infrastructure network decoder to obtain a single infrastructure network feature; decoding the target node embedding based on a coupled infrastructure network decoder to obtain a coupled infrastructure network feature; based on a relational graph convolutional neural network, predicting a cascading failure prediction result based on the single infrastructure network feature and the coupled infrastructure network feature; wherein the cascading failure prediction result includes the failure probability corresponding to each node in the interdependent infrastructure network.

[0018] Furthermore, it also includes: obtaining different numbers of initial failure nodes and their corresponding cascading failure prediction results, and drawing a curve of the final number of failure nodes changing with the number of initial failure nodes; performing resilience analysis on the curve to obtain the phase change point of the interdependent infrastructure network; and issuing an infrastructure network collapse warning based on the phase change point of the interdependent infrastructure network.

[0019] In a second aspect, the present invention also provides a cascading failure prediction device based on an interdependent infrastructure network, comprising: an infrastructure network embedding acquisition module, used to acquire a single infrastructure network embedding and a coupled infrastructure network embedding based on a given interdependent infrastructure network and an initial failure node; a node embedding prediction module, used to predict a target node embedding of the interdependent infrastructure network after cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding; a cascading failure prediction result prediction module, used to predict a cascading failure prediction result based on the target node embedding; wherein the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhancement embedding.

[0020] In a third aspect, the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the cascading failure prediction method based on an interdependent infrastructure network as described in any one of the above is implemented.

[0021] The cascading failure prediction method based on the interdependent infrastructure network provided by the present invention obtains the single infrastructure network embedding and the coupled infrastructure network embedding based on the given interdependent infrastructure network and the initial failure node; wherein the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhanced embedding; and based on the single infrastructure network embedding and the coupled infrastructure network embedding, the target node embedding of the interdependent infrastructure network after the cascading failure propagation is predicted; and then the cascading failure prediction result is predicted based on the target node embedding. The method captures the topological structure characteristics of the interdependent infrastructure network through link prediction embedding, considers the diverse coupling relationships between different infrastructure networks, captures the high-order dynamic and global evolution characteristics in the infrastructure network through global pooling embedding, avoids over-smoothing in the graph convolutional neural network through initial node enhanced embedding, and effectively improves the accuracy and granularity of cascading failure prediction in the infrastructure network. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0023] Figure 1 It is a flow chart of a cascading failure prediction method based on an interdependent infrastructure network provided by an embodiment of the present invention.

[0024] Figure 2 is a schematic diagram of an interdependent infrastructure network provided by an embodiment of the present invention.

[0025] Figure 3 It is a schematic diagram of the overall process of a cascading failure prediction method based on an interdependent infrastructure network provided by an embodiment of the present invention.

[0026] Figure 4 It is a schematic diagram of the structure of a cascading failure prediction device based on an interdependent infrastructure network provided by an embodiment of the present invention.

[0027] Figure 5 It is a schematic diagram of the physical structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0028] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] It should be noted that there are three challenges in predicting cascading failures in existing infrastructure networks: On the one hand, when predicting cascading failures in a single infrastructure network, the dynamics of cascading failures of the same infrastructure are affected by higher-order global dynamics. Interactions in infrastructure networks are usually not one-to-one connected, for example, for two connected nodes, the failure of one node does not necessarily mean that the other node will also fail. In addition, there are higher-order dynamics, namely multi-hop dynamics in the network, and network resilience during cascading failures.

[0030] On the other hand, when predicting infrastructure cascading failures in coupled infrastructure networks, the dependencies between different types of infrastructure are diverse and complex. Because the real-world infrastructure network is a combination of multiple infrastructure networks, i.e., interdependent networks, different types of infrastructure have different dependencies and coupling mechanisms, and modeling such diverse dependencies is often difficult.

[0031] Finally, for the data-driven approach to cascading failure prediction on infrastructure networks, the dynamics of the initial failure nodes are noisy due to oversmoothing when using graph convolutional neural networks. Most existing data-driven methods use graph convolutional neural network structures, which suffer from oversmoothing. When urban infrastructure fails, the number of initial faulty nodes is often much smaller than the number of normal nodes. This results in that when using graph convolutional neural networks for convolution, as the network deepens and the structure becomes more complex, the original small amount of information about the faulty nodes is gradually submerged in the large amount of information about the normal nodes, resulting in poor performance in cascading failure prediction on infrastructure networks.

[0032] In view of this, the present invention proposes a cascading failure prediction method based on an interdependent infrastructure network. Specifically, Figure 1 A schematic flow chart of a cascading failure prediction method based on an interdependent infrastructure network provided by an embodiment of the present invention is shown.

[0033] like Figure 1As shown, the method includes steps S110-S130, and these steps and related steps will be described in detail below.

[0034] S110, based on the given interdependent infrastructure network and the initial failed node, obtain a single infrastructure network embedding and a coupled infrastructure network embedding; wherein the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhanced embedding.

[0035] It is understood that the goal of this embodiment is to give an interdependent infrastructure network and the set of nodes that failed in the initial situation, predicting the set of nodes that failed after the cascade failure propagation. A heterogeneous graph representing an interdependent infrastructure network. Represents nodes / vertices in a heterogeneous graph, i.e., infrastructure in an infrastructure network. Represents the edge in the heterogeneous graph, that is, the connection between infrastructures in the infrastructure network.

[0036] To achieve this goal, in this step S110, based on the given interdependent infrastructure network and the initial failed node, a plurality of pre-set pre-training tasks are used to extract the feature embedding of a single infrastructure network (single infrastructure network embedding) and the feature embedding of a coupled infrastructure network (coupled infrastructure network embedding).

[0037] Among them, the interdependent infrastructure network is a combination of multiple infrastructure networks, including power grids , Road Network , Communication Network and building network For details, please refer to Figure 2 , Figure 2 A schematic diagram of an interdependent infrastructure network provided by an embodiment of the present invention is shown.

[0038] exist Figure 2 In the context of the Internet of Things (IoT), a single infrastructure network includes any one of the electric network, road network, communication network and building infrastructure, and a coupled infrastructure network includes the electric network, road network, communication network and building network at the same time.

[0039] It should be noted that coupled infrastructure networks not only include single infrastructure networks such as power grids, road networks, communication networks, and building networks, but also include the interdependencies between different single infrastructure networks. This dependency can be physical (for example, communication towers rely on power supply) or logical (for example, the operation of transportation networks relies on information transmission in communication networks).

[0040] The initial failed node is a faulty / failed node in the interdependent infrastructure network in the initial situation.

[0041] The pre-set pre-training tasks include but are not limited to link prediction pre-training tasks, global pooling pre-training tasks, and initial node enhancement pre-training tasks.

[0042] The link prediction pre-training task is used to obtain link prediction embeddings, which characterize the topological structure characteristics in the interdependent infrastructure network. The global pooling pre-training task is used to obtain global pooling embeddings, which characterize the high-order dynamic and global evolution characteristics in the interdependent infrastructure network. The initial node enhancement pre-training task is used to obtain the initial node enhancement embeddings, which characterize the characteristics of the initial failed nodes.

[0043] It should be noted that the single infrastructure network embedding and coupled infrastructure network embedding in this step both include link prediction embedding, global pooling embedding, and initial node enhancement embedding. In other words, a total of six embeddings are obtained in this step, namely, link prediction embedding, global pooling embedding, and initial node enhancement embedding corresponding to the single infrastructure network, and link prediction embedding, global pooling embedding, and initial node enhancement embedding of the coupled infrastructure network.

[0044] S120, predicting target node embeddings of the interdependent infrastructure network after cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding.

[0045] It can be understood that based on obtaining the single infrastructure network embedding and the coupled infrastructure network embedding in step S110, further, step S120 will predict the node embedding of the interdependent infrastructure network after the cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding.

[0046] Specifically, first, the single infrastructure network embedding and the coupled infrastructure network embedding are encoded respectively to obtain the single infrastructure network coded embedding and the coupled infrastructure network coded embedding. Then, according to the type of infrastructure network, the single infrastructure network coded embedding and the coupled infrastructure network coded embedding are connected. Finally, according to the connected target infrastructure network coded embedding, the target node embedding of the interdependent infrastructure network after cascading failure propagation is predicted by the relational graph convolutional neural network.

[0047] S130: predicting a cascading failure prediction result according to the node embedding.

[0048] It can be understood that, based on the prediction of the target node embedding of the interdependent infrastructure network after the cascading failure propagation in step S120, further, step S130 will predict the cascading failure prediction result according to the target node embedding.

[0049] Specifically, the target node embedding needs to be decoded first, and then the relational graph convolutional neural network is used to predict the cascading failure prediction result based on the decoded target node embedding.

[0050] Among them, the cascading failure prediction results include the failure probability corresponding to each node in the interdependent infrastructure network.

[0051] Furthermore, nodes with a failure probability higher than a set probability can be identified as failed nodes, and nodes with a failure probability lower than a set probability can be identified as normal nodes. Thus, the total number of failed nodes in the interdependent infrastructure network after cascading failure propagation can be counted.

[0052] In this embodiment, based on a given interdependent infrastructure network and an initial failure node, a single infrastructure network embedding and a coupled infrastructure network embedding are obtained; wherein, the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding, and initial node enhancement embedding; and based on the single infrastructure network embedding and the coupled infrastructure network embedding, the target node embedding of the interdependent infrastructure network after the cascading failure propagation is predicted; and then, based on the target node embedding, the cascading failure prediction result is predicted. This method captures the topological structure characteristics of the interdependent infrastructure network through link prediction embedding, considers the diverse coupling relationships between different infrastructure networks, captures the high-order dynamic and global evolution characteristics in the infrastructure network through global pooling embedding, avoids over-smoothing in the graph convolutional neural network through initial node enhancement embedding, and effectively improves the accuracy and granularity of cascading failure prediction in the infrastructure network.

[0053] On the basis of the above embodiments, the process of acquiring single infrastructure network embedding and coupled infrastructure network embedding will be described in detail below.

[0054] Based on a given interdependent infrastructure network and an initial failure node, a single infrastructure network embedding and a coupled infrastructure network embedding are obtained, including: representing the interdependent infrastructure network as a heterogeneous graph, and determining the node input according to the initial failure node; based on a pre-trained link prediction model, obtaining the link prediction embedding of the coupled infrastructure network and the link prediction embedding of the single infrastructure network according to the heterogeneous graph and the node input; based on a pre-trained global pooling model, obtaining the global pooling embedding of the coupled infrastructure network and the global pooling embedding of the single infrastructure network according to the heterogeneous graph and the node input; based on a pre-trained initial node enhancement model, obtaining the initial node enhancement embedding of the coupled infrastructure network and the initial node enhancement embedding of the single infrastructure network according to the heterogeneous graph and the node input.

[0055] It can be understood that for a given interdependent infrastructure network, it is represented as a heterogeneous graph, which means that different types of infrastructure will be regarded as different node types of the heterogeneous graph, and different types of infrastructure dependencies will be regarded as different edge types of the heterogeneous graph. At the same time, according to the given initial failure node, the status of all nodes in the initial state is determined, including valid node status and invalid node status, to obtain the node input. Then, the node input can be embedded into the heterogeneous graph as the attribute of the node in the heterogeneous graph.

[0056] In a heterogeneous graph, graph nodes can be represented as vectors, which may include the attributes and type information of the nodes, and graph edges can be represented as weight matrices to reflect the strength of interdependence between different node types.

[0057] Then, based on the link prediction pre-training task, the global pooling pre-training task and the initial node enhancement pre-training task, the link prediction embedding, the global pooling embedding and the initial node enhancement embedding are obtained.

[0058] Specifically, the heterogeneous graph and node input are used as the input of the link prediction pre-training task, the global pooling pre-training task, and the initial node enhancement pre-training task, respectively, to obtain the corresponding output.

[0059] For example, in one embodiment, a detailed description is provided for a process of acquiring link prediction embedding.

[0060] Heterogeneous Graph Heterogeneous graphs including coupled infrastructure networks and heterogeneous graphs of single infrastructure networks , the node input includes the initial node state.

[0061] Accordingly, based on the pre-trained link prediction model, according to the heterogeneous graph and the node input, the link prediction embedding of the coupled infrastructure network and the link prediction embedding of the single infrastructure network are obtained, including: inputting the node input and the heterogeneous graph of the coupled infrastructure network into the pre-trained link prediction model to obtain the link prediction embedding of the coupled infrastructure network; inputting the node input and the heterogeneous graph of the single infrastructure network into the pre-trained link prediction model to obtain the link prediction embedding of the single infrastructure network; wherein the link prediction model is obtained by training and optimizing through the edge loss function, and the link prediction embedding characterizes the topological structure characteristics of the single infrastructure network or the coupled infrastructure network.

[0062] It can be understood that link prediction embedding includes link prediction embedding of a single infrastructure network and link prediction embedding of a coupled infrastructure network. The acquisition process of the two is only different in input (one is the heterogeneous graph and node input of a single infrastructure network, and the other is the heterogeneous graph and node input of a coupled infrastructure network). Therefore, the following will not distinguish between a single infrastructure network or a coupled infrastructure network, and will describe the same acquisition process.

[0063] The cascading failure propagation on the interdependent infrastructure network is affected by the topological structure of the interdependent infrastructure network. In order to capture the network topological structure characteristics, this embodiment applies the link prediction pre-training task. This is because the topological structure of the network reveals the similarity and correlation information between nodes, which can be used as a supervisory signal to generate link prediction embedding. Therefore, this process can be considered as a link prediction task.

[0064] The purpose of the link prediction task is to estimate the possibility of the existence of edges between nodes based on the observed attributes of edges and nodes. Specifically, this embodiment samples all edges existing in the interdependent infrastructure network as positive sets and all non-existent edges as negative sets to form a negative graph. Then, the score corresponding to the link prediction task can be defined as the following formula (1).

[0065] (1).

[0066] In formula (1), represents the link prediction model, Representation Node The corresponding link prediction embedding, A heterogeneous graph representing a network of interdependent infrastructures, and Representing heterogeneous graphs The nodes in represents the edge between node n and node m, Represents the set of connected edges of a heterogeneous graph.

[0067] Compute a given heterogeneous graph The inner product of the embedding vectors of the two nodes on each existing edge is used as the prediction weight. Then the edge loss function is used to obtain the representation of the node, as shown in the following formula (2).

[0068] (2).

[0069] In formula (2), represents the marginal loss function value, It means to find the average value, It means to find the maximum value, is a constant, Represented by the existence of heterogeneous graph The positive graph obtained by edge sampling in , Represents that the The negative image obtained by edge sampling in is the L2 regularization term.

[0070] Optimize the loss function by pre-training on different heterogeneous graphs , we can get an embedding for each node about the similarity between nodes In this embodiment, the final embedding obtained after optimization is used as the link prediction embedding and .in, Representing link prediction embeddings for coupled infrastructure networks, Representing link prediction embeddings for a single infrastructure network.

[0071] For another example, in another embodiment, a process for obtaining a global pooling embedding is described in detail.

[0072] The global pooling model is a differentiable pooling network. The heterogeneous graph includes the heterogeneous graph of the coupled infrastructure network and the heterogeneous graph of the single infrastructure network. The node input includes the initial node state and the shortest path length from the initial failed node to the current node.

[0073] Accordingly, based on the pre-trained global pooling model, according to the heterogeneous graph and node input, the global pooling embedding of the coupled infrastructure network and the global pooling embedding of the single infrastructure network are obtained, including: inputting the node input and the heterogeneous graph of the coupled infrastructure network into the differentiable pooling network, obtaining the average shortest path length corresponding to all nodes in each network layer of the differentiable pooling network, and taking the difference between the average shortest path length and the true path length as the global pooling embedding of the coupled infrastructure network. Inputting the node input and the heterogeneous graph of the single infrastructure network into the differentiable pooling network, obtaining the average shortest path length corresponding to all nodes in each network layer of the differentiable pooling network, and taking the difference between the average shortest path length and the true path length as the global pooling embedding of the single infrastructure network; wherein, the global pooling embedding characterizes the high-order dynamic-global evolution characteristics of different levels of the single infrastructure network or the coupled infrastructure network.

[0074] It can be understood that the global pooling embedding includes the global pooling embedding of a single infrastructure network and the global pooling embedding of a coupled infrastructure network. The acquisition process of the two is only different in input (one is the heterogeneous graph and node input of a single infrastructure network, and the other is the heterogeneous graph and node input of a coupled infrastructure network). Therefore, the following will not distinguish between a single infrastructure network or a coupled infrastructure network, and will describe the same acquisition process.

[0075] The cascading failure dynamics in interdependent infrastructure networks are not only affected by the local topology, but also by higher-order dynamics such as multi-hop interactions and global evolution. Therefore, this embodiment needs to obtain another embedding that models global features.

[0076] Specifically, this embodiment designs a global pooling pre-training task to extract the global pooling embedding and This embodiment uses the DiffPool network (differentiable pooling network) to perform end-to-end pre-trained regression tasks to extract global pooling features. In order to extract global information, this embodiment constructs a heterogeneous graph or Heterogeneous graphs with the same graph structure , but their node characteristics are different.

[0077] In heterogeneous graph In , the node attributes include the state of the node in the initial situation and the shortest path length from the initial fault node to the current node. The prediction target of the global pooling pre-training task is the heterogeneous graph The average value of the shortest distance from all nodes to the initial failure node .

[0078] The DiffPool network in this embodiment is stacked The graph neural network GNN of the layer The layer applies the first layer, and learn how to assign nodes to the Clusters in a layer. Definition For the The cluster assignment matrix learned by the layer, then the embedding of each cluster after assignment can be obtained by the following formula (3).

[0079] (3).

[0080] In formula (3), Indicates The cluster embedding of the layer, Indicates The cluster assignment matrix learned by the layer, Indicates The cluster feature matrix learned by the layer, Indicates The number of clusters in the layer, Indicates the feature dimension. At layer 0, the input Heterogeneous Graph The node feature matrix of (that is, the aforementioned node input).

[0081] The adjacency matrix between new clusters can be generated by the following equation (4).

[0082] (4).

[0083] In DiffPool, the present embodiment uses two GNNs to generate the first The cluster feature matrix and cluster assignment matrix of the layer can be expressed as follows (5)-(6) respectively.

[0084] (5).

[0085] (6).

[0086] The loss function used in training and optimizing the DiffPool network in this embodiment is the RMSE of the predicted value of the shortest distance from all nodes to the initial failed node and the average value of the labels, which can be expressed as the following formula (7).

[0087] (7).

[0088] After pre-training, the trained DiffPool network should be able to capture the global characteristics of the network given the initial failed nodes.

[0089] In order to better capture high-order interactions at different levels, it is necessary to construct a global pooling embedding and , the global pooling is embedded as a The matrix of Heterogeneous graph The number of nodes in Indicates the number of GNN layers in the DiffPool network. Line Elements of a column represents a difference, which can be found in the following formula (8).

[0090] (8).

[0091] In formula (8), Indicates Nodes in the Diffpool network The average shortest path length of the cluster to which the layer belongs, Indicates the real path length. Thus, this embodiment can obtain embedded representations of high-order dynamics and global dynamics at different levels of coupled infrastructure networks and single infrastructure networks, respectively.

[0092] In yet another embodiment, a process for obtaining enhanced embedding of an initial node is described in detail.

[0093] The initial node enhancement model is a graph Markov network, the heterogeneous graph includes the heterogeneous graph of coupled infrastructure networks and the heterogeneous graph of single infrastructure networks, and the node input includes the initial node state.

[0094] Accordingly, based on the pre-trained initial node enhancement model, the initial node enhancement embedding of the coupled infrastructure network and the initial node enhancement embedding of the single infrastructure network are obtained according to the heterogeneous graph and the node input, including: inputting the node input and the heterogeneous graph of the coupled infrastructure network into the graph Markov network, optimizing the dependency between the node labels using the expectation-maximization algorithm, and using the hidden layer vector corresponding to the final output of the E-step in the expectation-maximization algorithm as the initial node enhancement embedding of the coupled infrastructure network; inputting the node input and the heterogeneous graph of the single infrastructure network into the graph Markov network, optimizing the dependency between the node labels using the expectation-maximization algorithm, and using the hidden layer vector corresponding to the final output of the E-step in the expectation-maximization algorithm as the initial node enhancement embedding of the single infrastructure network; wherein the initial node enhancement embedding characterizes the initial failure node characteristics in the single infrastructure network or the coupled infrastructure network.

[0095] It can be understood that the initial node enhanced embedding includes the initial node enhanced embedding of a single infrastructure network and the initial node enhanced embedding of a coupled infrastructure network. The acquisition process of the two is only different in input (one is the heterogeneous graph and node input of a single infrastructure network, and the other is the heterogeneous graph and node input of a coupled infrastructure network). Therefore, the following will not distinguish between a single infrastructure network or a coupled infrastructure network, and will describe the same acquisition process.

[0096] When using graph convolutional neural network GCN for convolution, the network will have the problem of over-smoothing due to the imbalance between the initial normal nodes and the failed nodes. To solve this problem, this embodiment uses another semi-supervised pre-training task GMNN (Graph Markov Neural Networks), which is a method of fusing node label relevance based on the idea of ​​label propagation.

[0097] Specifically, GMNN uses CRF (Conditional Random Field) to model the joint distribution between node labels through object attributes (node ​​features) and optimizes it using the pseudo-likelihood variational EM algorithm (Expectation-Maximization algorithm). In this case, GNN is used in the M step to model the dependencies between node labels, and another GNN is used in the E step to learn the feature representation of the node to predict the node label attributes.

[0098] In the M step, it can be regarded as a The learning process of labeling unlabeled nodes. , and update the parameters using the following formula (9) .

[0099] (9).

[0100] In formula (9), represents the optimization goal of the M step, represents the conditional probability, Represents a node collection The predicted labels of all nodes in (e.g., valid or invalid), The label representing the set of neighbors of node n, For Node The neighbor set of Representing heterogeneous graphs Properties of midpoints (node ​​inputs), Is a set of unknown label nodes The predicted label of .

[0101] GNN can be used to parameterize the , please refer to the following formula (10) for details.

[0102] (10).

[0103] In formula (10), represents the label of node n, Indicates the use of heterogeneous graphs The GNN embedding obtained by graph structure optimization is represents node embedding (initial node enhanced embedding), It is a subscript with no actual physical meaning. Indicates the node number.

[0104] Step E is a and The reasoning process of labeling unlabeled nodes can be updated using the following formula (11): .

[0105] (11).

[0106] certainly, The update can also be achieved through GNN, as shown in the following formula (12).

[0107] (12).

[0108] In formula (12), Indicates the use of heterogeneous The GNN embedding obtained by graph structure optimization is is the node embedding (initial node enhanced embedding), It is a subscript with no actual physical meaning.

[0109] The above E-step and M-step can be optimized by alternately optimizing the evidence lower bound (ELBO). This process can be expressed as follows (13).

[0110] (13).

[0111] In formula (13), A collection of node labels representing nodes with known labels.

[0112] By continuously optimizing the M-step and E-step through formula (13), we can obtain the node embedding containing the initial failed node information, that is, the enhanced embedding of the initial node. Specifically, the last E-step training The hidden layer embedding of the GNN is extracted as the initial node enhanced embedding and , where each initial node is enhanced to embedding information containing the initial failed node.

[0113] In this embodiment, the interdependent infrastructure network is represented as a heterogeneous graph, and the node input is determined according to the initial failure node. Then, based on the pre-trained link prediction model, the global pooling model, and the initial node enhancement model, the single infrastructure network embedding and the coupled infrastructure network embedding are obtained according to the heterogeneous graph and the node input. Then, based on the single infrastructure network embedding and the coupled infrastructure network embedding, the target node embedding of the interdependent infrastructure network after the cascading failure propagation is predicted; thus, according to the target node embedding, the cascading failure prediction result is predicted. This method captures the topological structure characteristics of the interdependent infrastructure network through link prediction embedding, considers the diverse coupling relationships between different infrastructure networks, captures the high-order dynamic and global evolution characteristics in the infrastructure network through global pooling embedding, avoids over-smoothing in the graph convolutional neural network through initial node enhancement embedding, and effectively improves the accuracy and granularity of cascading failure prediction in the infrastructure network.

[0114] On the basis of the above-mentioned embodiments, the process of predicting node embedding of an interdependent infrastructure network after cascading failure propagation will be described in detail below.

[0115] Based on the single infrastructure network embedding and the coupled infrastructure network embedding, the node embedding of the interdependent infrastructure network after the cascading failure propagation is predicted, including: encoding the single infrastructure network embedding and the coupled infrastructure network embedding respectively to obtain the corresponding single infrastructure network coded embedding and coupled infrastructure network coded embedding; connecting the single infrastructure network coded embedding and the coupled infrastructure network coded embedding according to the type of infrastructure network to obtain the target infrastructure network coded embedding; based on the relational graph convolutional neural network, according to the target infrastructure network coded embedding, predicting the target node embedding of the interdependent infrastructure network after the cascading failure propagation.

[0116] It can be understood that after obtaining the single infrastructure network embedding (link prediction embedding, global pooling embedding and initial node enhancement embedding of the single infrastructure network) and the coupled infrastructure network embedding (link prediction embedding, global pooling embedding and initial node enhancement embedding of the coupled infrastructure network) respectively, this embodiment obtains the single infrastructure network coding embedding and the coupled infrastructure network coding embedding respectively through two graph autoencoders.

[0117] Specifically, the graph autoencoder includes a single infrastructure network encoder and a coupled infrastructure network encoder. The single infrastructure network encoder is used to encode the single infrastructure network embedding to obtain a single infrastructure network coded embedding. The coupled infrastructure network encoder is used to encode the coupled infrastructure network embedding to obtain a coupled infrastructure network coded embedding. For details, see the following equations (14)-(15).

[0118] (14).

[0119] (15).

[0120] in, Represents coupled infrastructure network coding embedding, represents the coupled infrastructure network encoder, , , They represent the link prediction embedding, global pooling embedding, and initial node enhancement embedding of the coupled infrastructure network, respectively. represents a single infrastructure network coding embedding, represents a single infrastructure network encoder, , , They represent the link prediction embedding, global pooling embedding, and initial node enhanced embedding of a single infrastructure network respectively.

[0121] After obtaining the coupled infrastructure network coding embedding and the single infrastructure network coding embedding, since the real-world urban infrastructure network is composed of multiple infrastructures coupled, it is very important to distinguish different infrastructures when modeling.

[0122] This embodiment uses a relational graph convolutional neural network (RGCN) to model different types of infrastructure. Specifically, first, according to the type of infrastructure network, the coupled infrastructure network coding embedding and the single infrastructure network coding embedding are connected, as shown in the following formula (16).

[0123] (16).

[0124] In formula (16), Representation Node The target infrastructure network coding is embedded. All nodes correspond to The combination can get the target infrastructure network coding embedding .

[0125] Since this embodiment only cares about the set of nodes that eventually fail during the cascading failure propagation process, this embodiment uses RGCN to predict the target node embedding of the interdependent infrastructure network after the cascading failure propagation. , please refer to the following formula (17) for details.

[0126] (17).

[0127] RGCN is a graph convolutional network for heterogeneous graphs. For each node, the aggregation process of RGCN considers the contribution of different types of edges and neighbors to the node. , its node embedding can be expressed as follows (18).

[0128] (18).

[0129] In formula (18), Representation Node In the The node embeddings in the layer, represents the sigmoid function, Indicates the type of edge, Representation Node With edge type The neighbor set of represents the normalization parameter, represents the neural network parameters, Representation Node In the The node embeddings in the layer, represents the neural network parameters, Representation Node In the Node embeddings in a layer.

[0130] For edge type , which includes homogeneous edges (such as the edge between two power stations) and heterogeneous edges (such as the edge between a base station and a building).

[0131] The target node embedding predicted by RGCN contains information about different types of nodes and edges, which can be used to model the propagation of collaborative filtering in heterogeneous networks.

[0132] In this embodiment, by encoding the single infrastructure network embedding and the coupled infrastructure network embedding respectively, the corresponding single infrastructure network code embedding and coupled infrastructure network code embedding are obtained, and the single infrastructure network code embedding and the coupled infrastructure network code embedding are connected according to the type of infrastructure network to obtain the target infrastructure network code embedding, and then based on the relationship graph convolutional neural network, the target node embedding of the interdependent infrastructure network after the cascading failure propagation is predicted according to the target infrastructure network code embedding, so that the cascading failure prediction result is predicted according to the target node embedding. This method captures the topological structure characteristics of the interdependent infrastructure network through link prediction embedding, considers the diverse coupling relationships between different infrastructure networks, captures the high-order dynamic and global evolution characteristics in the infrastructure network through global pooling embedding, avoids over-smoothing in the graph convolutional neural network through initial node enhancement embedding, and effectively improves the accuracy and granularity of cascading failure prediction in the infrastructure network.

[0133] On the basis of the above-mentioned embodiment, the process of predicting the cascading failure prediction result will be described in detail below.

[0134] According to the target node embedding, the cascading failure prediction result is predicted, including: decoding the target node embedding based on the single infrastructure network decoder to obtain the single infrastructure network characteristics; decoding the target node embedding based on the coupled infrastructure network decoder to obtain the coupled infrastructure network characteristics; based on the relationship graph convolutional neural network, according to the single infrastructure network characteristics and the coupled infrastructure network characteristics, the cascading failure prediction result is predicted; wherein the cascading failure prediction result includes the failure probability corresponding to each node in the interdependent infrastructure network.

[0135] It is understood that this embodiment uses two decoders, a coupled infrastructure network decoder and a single infrastructure network decoder. The coupled infrastructure network decoder is used to decode the target node embedding to obtain the corresponding coupled infrastructure network features. The single infrastructure network decoder is used to decode the target node embedding to obtain the corresponding single infrastructure network features.

[0136] After decoding, the obtained single infrastructure network features and coupled infrastructure network features are cascaded, and the cascade failure prediction results are obtained through RGCN prediction, that is, the final failure probability of each node in the interdependent infrastructure network. This process can be expressed as follows (19).

[0137] (19).

[0138] In formula (19), represents the failure probability of a node, represents the coupled infrastructure network decoder, Single infrastructure network decoder.

[0139] It should be noted that the relational graph convolutional neural network can be trained and optimized through the cross entropy loss function, and the expression of the cross entropy loss function is as follows (20).

[0140] (20).

[0141] In formula (20), It refers to the actual node status. It refers to the probability that each node is predicted to fail during the training process.

[0142] In this embodiment, the target node embedding is decoded based on a single infrastructure network decoder to obtain a single infrastructure network feature, and the target node embedding is decoded based on a coupled infrastructure network decoder to obtain a coupled infrastructure network feature, and then based on a relationship graph convolutional neural network, according to the single infrastructure network feature and the coupled infrastructure network feature, a cascading failure prediction result is predicted; wherein the cascading failure prediction result includes the failure probability corresponding to each node in the interdependent infrastructure network. This method captures the topological structure characteristics of the interdependent infrastructure network through link prediction embedding, considers the diverse coupling relationships between different infrastructure networks, captures the high-order dynamic and global evolution characteristics in the infrastructure network through global pooling embedding, avoids over-smoothing in the graph convolutional neural network through initial node enhancement embedding, and effectively improves the accuracy and granularity of cascading failure prediction in the infrastructure network.

[0143] On the basis of the above-mentioned embodiment, the process of estimating the phase change point will be described in detail below.

[0144] Obtain different numbers of initial failure nodes and their corresponding cascading failure prediction results, and draw a curve showing the change in the number of final failure nodes versus the number of initial failure nodes; perform resilience analysis on the curve to obtain the phase transition point of the interdependent infrastructure network; and issue an infrastructure network collapse warning based on the phase transition point of the interdependent infrastructure network.

[0145] It can be understood that, based on the cascading failure prediction method based on an interdependent infrastructure network provided by the above embodiments, cascading failure prediction results corresponding to different numbers of initial failure nodes can be obtained.

[0146] According to the different numbers of initial failure nodes and their corresponding cascading failure prediction results, a change curve between the final number of failure nodes and the initial number of failure nodes can be drawn. By performing resilience analysis on the change curve, the phase change point in the interdependent infrastructure network can be obtained. The phase change point refers to the number of failure nodes that will cause the interdependent infrastructure network to collapse.

[0147] After estimating the phase transition point of the interdependent infrastructure network, an infrastructure network collapse warning can be carried out based on the phase transition point to avoid network collapse in the interdependent infrastructure network.

[0148] In some embodiments, Figure 3 The overall flow chart of the cascading failure prediction method based on an interdependent infrastructure network provided by an embodiment of the present invention is shown.

[0149] like Figure 3 As shown, in order to capture the high-order dynamic and global evolution characteristics within the same infrastructure network, this embodiment designs a dual GAE (Graph Autoencodes) skeleton and a global pooling. In addition, this embodiment also uses heterogeneous graph structures to capture the dynamic relationship between different types of infrastructure networks to model the unique characteristics of interdependent infrastructure networks; and adds an initial node enhancement pre-training task based on the idea of ​​label propagation to overcome the over-smoothing problem when using graph convolutional neural networks.

[0150] Specifically, a dual-GAE framework consisting of a multi-pre-trained task encoding module and an RGCN-enhanced decoding module is used to extract features of coupled infrastructure networks and single infrastructure networks, respectively.

[0151] First, the features in different infrastructure networks are encoded; during the encoding process, this embodiment designs three different pre-training tasks to obtain three embeddings. Link prediction embedding using link prediction pre-training and To capture the topological structure characteristics of the heterogeneous graph corresponding to the interdependent infrastructure network, we use the global pooling embedding pre-trained with global pooling and To extract high-order dynamic and global features, and introduce the initial node enhancement pre-training task to obtain the initial node enhanced embedding and To avoid over-smoothing in graph convolutional neural networks.

[0152] Then, RGCN is used to predict the propagation of cascading failures and decode the final set of failed nodes.

[0153] It should be noted that in Figure 3In the text, coupled network is the abbreviation of coupled infrastructure network, and single network is the abbreviation of single infrastructure network. Similarly, coupled network encoder is coupled infrastructure network encoder, single network encoder is single infrastructure network encoder, coupled network embedding is coupled infrastructure network embedding, single network embedding is single infrastructure network embedding, coupled network decoder is coupled infrastructure network decoder, and single network decoder is single infrastructure network decoder.

[0154] Corresponding to the cascading failure prediction methods based on an interdependent infrastructure network described in the above embodiments, the present invention also proposes a cascading failure prediction device based on an interdependent infrastructure network.

[0155] Specifically, Figure 4 A schematic diagram of the structure of a cascading failure prediction device based on an interdependent infrastructure network provided by an embodiment of the present invention is shown.

[0156] like Figure 4 As shown, the device includes: an infrastructure network embedding acquisition module 410, which is used to acquire a single infrastructure network embedding and a coupled infrastructure network embedding based on a given interdependent infrastructure network and an initial failure node; a node embedding prediction module 420, which is used to predict a target node embedding of the interdependent infrastructure network after cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding; a cascading failure prediction result prediction module 430, which is used to predict a cascading failure prediction result based on the target node embedding; wherein the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhanced embedding.

[0157] In this embodiment, the infrastructure network embedding acquisition module 410 acquires the single infrastructure network embedding and the coupled infrastructure network embedding based on the given interdependent infrastructure network and the initial failure node; the node embedding prediction module 420 predicts the target node embedding of the interdependent infrastructure network after the cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding; the cascading failure prediction result prediction module 430 predicts the cascading failure prediction result according to the target node embedding; wherein the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhanced embedding. The device captures the topological structure characteristics of the interdependent infrastructure network through link prediction embedding, takes into account the diverse coupling relationships between different infrastructure networks, captures the high-order dynamic and global evolution characteristics in the infrastructure network through global pooling embedding, avoids over-smoothing in the graph convolutional neural network through initial node enhanced embedding, and effectively improves the accuracy and granularity of cascading failure prediction in the infrastructure network.

[0158] It should be noted that the cascading failure prediction device based on an interdependent infrastructure network provided in this embodiment and the cascading failure method based on an interdependent infrastructure network provided in the above embodiments can be referred to each other, and will not be described in detail here.

[0159] Figure 5 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 5 As shown, the electronic device may include: a processor 510, a communication interface 520, a memory 530 and a communication bus 540, wherein the processor 510, the communication interface 520 and the memory 530 complete mutual communication through the communication bus 540. The processor 510 may call the logic instructions in the memory 530 to execute the cascading failure prediction method based on the interdependent infrastructure network, the method comprising: based on the given interdependent infrastructure network and the initial failure node, obtaining a single infrastructure network embedding and a coupled infrastructure network embedding; based on the single infrastructure network embedding and the coupled infrastructure network embedding, predicting the target node embedding of the interdependent infrastructure network after the cascading failure propagation; according to the target node embedding, predicting the cascading failure prediction result; wherein the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhanced embedding.

[0160] In addition, the logic instructions in the above-mentioned memory 530 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0161] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0162] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A cascading failure prediction method based on an interdependent infrastructure network, characterized in that: include: Based on the given interdependent infrastructure networks and initial failure nodes, obtain the single infrastructure network embedding and coupled infrastructure network embedding; Predicting target node embeddings of the interdependent infrastructure networks after cascading failure propagation based on the single infrastructure network embeddings and coupled infrastructure network embeddings; According to the target node embedding, a cascading failure prediction result is predicted; Wherein, the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhancement embedding.

2. The cascading failure prediction method based on an interdependent infrastructure network according to claim 1, characterized in that: The method of obtaining a single infrastructure network embedding and a coupled infrastructure network embedding based on a given interdependent infrastructure network and an initial failure node includes: Representing the interdependent infrastructure network as a heterogeneous graph and determining node inputs based on the initial failed nodes; Based on the pre-trained link prediction model, obtaining link prediction embeddings of the coupled infrastructure network and link prediction embeddings of the single infrastructure network according to the heterogeneous graph and the node input; Based on the pre-trained global pooling model, obtaining a global pooling embedding of the coupled infrastructure network and a global pooling embedding of the single infrastructure network according to the heterogeneous graph and the node input; Based on the pre-trained initial node enhancement model, the initial node enhancement embedding of the coupled infrastructure network and the initial node enhancement embedding of the single infrastructure network are obtained according to the heterogeneous graph and the node input.

3. The cascading failure prediction method based on an interdependent infrastructure network according to claim 2, characterized in that: The heterogeneous graph includes a heterogeneous graph of a coupled infrastructure network and a heterogeneous graph of a single infrastructure network, and the node input includes an initial node state; Accordingly, the pre-trained link prediction model obtains the link prediction embedding of the coupled infrastructure network and the link prediction embedding of the single infrastructure network according to the heterogeneous graph and the node input, including: Inputting the node input and the heterogeneous graph of the coupled infrastructure network into a pre-trained link prediction model to obtain a link prediction embedding of the coupled infrastructure network; Inputting the node input and the heterogeneous graph of the single infrastructure network into a pre-trained link prediction model to obtain a link prediction embedding of the single infrastructure network; The link prediction model is obtained by training and optimizing the edge loss function, and the link prediction embeds the topological structure characteristics that characterize a single infrastructure network or a coupled infrastructure network.

4. According to the cascading failure prediction method based on interdependent infrastructure networks as described in claim 2, the global pooling model is a differentiable pooling network, the heterogeneous graph includes a heterogeneous graph of a coupled infrastructure network and a heterogeneous graph of a single infrastructure network, and the node input includes an initial node state and a shortest path length from an initial failure node to a current node; Accordingly, the pre-trained global pooling model obtains the global pooling embedding of the coupled infrastructure network and the global pooling embedding of the single infrastructure network according to the heterogeneous graph and the node input, including: Inputting the node input and the heterogeneous graph of the coupled infrastructure network into the differentiable pooling network, obtaining the average shortest path length corresponding to all nodes in each network layer of the differentiable pooling network, and taking the difference between the average shortest path length and the true path length as the global pooling embedding of the coupled infrastructure network; Inputting the node input and the heterogeneous graph of the single infrastructure network into the differentiable pooling network, obtaining the average shortest path length corresponding to all nodes in each network layer of the differentiable pooling network, and taking the difference between the average shortest path length and the true path length as the global pooling embedding of the single infrastructure network; Therein, the global pooling embeds high-order dynamic-global evolution features at different levels that characterize a single infrastructure network or coupled infrastructure networks.

5. The cascading failure prediction method based on an interdependent infrastructure network according to claim 2, characterized in that: The initial node enhancement model is a graph Markov network, the heterogeneous graph includes a heterogeneous graph of a coupled infrastructure network and a heterogeneous graph of a single infrastructure network, and the node input includes an initial node state; Accordingly, the pre-trained initial node enhancement model obtains the initial node enhancement embedding of the coupled infrastructure network and the initial node enhancement embedding of the single infrastructure network according to the heterogeneous graph and the node input, including: Inputting the node input and the heterogeneous graph of the coupled infrastructure network into a graph Markov network, optimizing the dependency between node labels using an expectation maximization algorithm, and using the hidden layer embedding corresponding to the final output of step E in the expectation maximization algorithm as the initial node enhanced embedding of the coupled infrastructure network; Inputting the node input and the heterogeneous graph of the single infrastructure network into a graph Markov network, optimizing the dependency between node labels using an expectation maximization algorithm, and using the hidden layer embedding corresponding to the final output of step E in the expectation maximization algorithm as the initial node enhanced embedding of the single infrastructure network; The initial node enhancement embedding characterizes the initial failure node characteristics in a single infrastructure network or a coupled infrastructure network.

6. The cascading failure prediction method based on an interdependent infrastructure network according to claim 1, characterized in that: The predicting target node embedding of the interdependent infrastructure network after cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding includes: Encoding the single infrastructure network embedding and the coupled infrastructure network embedding respectively to obtain corresponding single infrastructure network coded embedding and coupled infrastructure network coded embedding; Connect the single infrastructure network code embedding and the coupled infrastructure network code embedding according to the type of infrastructure network to obtain the target infrastructure network code embedding; Based on a relational graph convolutional neural network, target node embeddings of the interdependent infrastructure network after cascading failure propagation are predicted according to the target infrastructure network code embeddings.

7. The cascading failure prediction method based on an interdependent infrastructure network according to claim 1, characterized in that: The predicting of a cascading failure prediction result according to the target node embedding includes: Decoding the target node embedding based on a single infrastructure network decoder to obtain a single infrastructure network feature; Decoding the target node embedding based on a coupled infrastructure network decoder to obtain a coupled infrastructure network feature; Based on the relationship graph convolutional neural network, according to the single infrastructure network characteristics and the coupled infrastructure network characteristics, a cascading failure prediction result is predicted; The cascading failure prediction result includes the failure probability corresponding to each node in the interdependent infrastructure network.

8. The cascading failure prediction method based on an interdependent infrastructure network according to any one of claims 1 to 7, characterized in that: Also includes: Obtain different numbers of initial failure nodes and their corresponding cascading failure prediction results, and draw a curve showing the change of the number of final failure nodes with the number of initial failure nodes; Conducting resilience analysis on the curves, we obtain the phase transition points of the interdependent infrastructure network; According to the phase transition points of the interdependent infrastructure networks, an infrastructure network collapse warning is performed.

9. A cascading failure prediction device based on an interdependent infrastructure network, characterized in that: include: An infrastructure network embedding acquisition module, used for acquiring a single infrastructure network embedding and a coupled infrastructure network embedding based on a given interdependent infrastructure network and an initial failure node; a node embedding prediction module for predicting target node embeddings of an interdependent infrastructure network after cascading failure propagation based on the single infrastructure network embedding and the coupled infrastructure network embedding; A cascading failure prediction result prediction module, used to predict and obtain a cascading failure prediction result according to the target node embedding; Wherein, the coupled infrastructure network embedding and the single infrastructure network embedding both include link prediction embedding, global pooling embedding and initial node enhancement embedding.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the cascading failure prediction method based on an interdependent infrastructure network according to any one of claims 1 to 8 is implemented.

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