A method for identifying a source node of a cross-domain cascading failure of a mutual dependence network

Abstract

The application provides a method for identifying a source node of cross-domain cascading failure in an interdependent network, comprising the following steps: step one, decomposing the interdependent network into a set of interdependent functional subgraphs; step two, evaluating the function of a shortest control loop with a weighted distance between a resource supply node and a resource demand node; step three, evaluating the function of an interdependent functional subgraph; step four, evaluating the function of an interdependent network; and step five, evaluating the criticality of the resource supply node and non-resource supply node and arranging them in descending order. The interdependent functional subgraph of the application is more in line with the actual situation of resource transmission, the identification method of the application avoids the problem of low accuracy of the existing identification methods based on the maximum connected subgraph, the maximum performance subgraph and the interdependent functional subgraph, and can prevent the occurrence of cross-domain cascading failure in the interdependent network at a lower cost.

Description

Technical Field

[0001] This invention belongs to the field of interdependent network technology and relates to fault identification, specifically to a method for identifying cross-domain cascading fault source nodes in interdependent networks. Background Technology

[0002] Interdependent networks, formed by the mutual coupling of physical networks and information networks, are widely distributed in modern society, such as smart grids. Interdependent networks utilize information systems to allocate resources, enabling more efficient and rational distribution to users. For example, in smart grids, the control and allocation of information networks allows for safer and more efficient delivery of electricity to users. In interdependent networks, resource supply nodes and resource demand nodes in the physical network are connected through resource relay nodes, while control nodes in the information network connect information acquisition nodes and execution nodes through information relay nodes. Nodes in the physical and information networks are coupled through analog-to-digital (A / D) and analog-to-digital (A / D) transformations. The A / D transformations of information acquisition nodes in the information network sense the states of nodes in the physical network, thus influencing the discrete state evolution of nodes in the information network. Control decisions issued by control nodes in the information network drive the continuous state transitions of nodes in the physical network through the A / D transformations of execution nodes. Furthermore, nodes in the information network sometimes require power from nodes in the physical network. This tight coupling and interdependence between the physical and information networks creates a potential risk of cross-domain cascading failures propagating across both the information and physical networks. Although research indicates that the probability of such cross-domain cascading failures is low, their occurrence can lead to the collapse of the entire network system, causing incalculable losses to the economic development of modern society. There are two ways to prevent cross-domain cascading failures: one is to identify the starting node of the cascading failure propagation chain and then focus on protecting it to prevent the spread of subsequent chains; the other is to block the further extension of the propagation chain during the propagation process of the cross-domain cascading failure. The first method can prevent cross-domain cascading failures at a lower cost; therefore, it is necessary to provide a method for identifying the source node of cross-domain cascading failures in interdependent networks.

[0003] Methods for identifying cascading fault source nodes based on maximally connected subgraphs assume that nodes in the network are functioning normally only when they belong to maximally connected subgraphs; however, this assumption does not consider the influence of useful connected subgraphs. Methods for identifying cascading fault source nodes based on maximally efficient subgraphs assume that nodes in the network are functioning normally only when they belong to maximally efficient subgraphs; this assumption does not consider the influence of the interdependence between physical and information networks. Both of these methods are applicable to single physical or information networks and do not address the prevention of cross-domain cascading fault propagation chains, resulting in low identification accuracy. Therefore, they are not suitable for identifying cross-domain cascading fault source nodes in interdependent networks. Existing methods for identifying cross-domain cascading fault source nodes based on mutually functional subgraphs, while overcoming the shortcomings of the above two methods, still suffer from low identification accuracy. Therefore, the problem of how to more accurately identify the starting node of a cross-domain cascading fault propagation chain in interdependent networks remains. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for identifying cross-domain cascading fault source nodes in interdependent networks, thereby solving the technical problem that the identification accuracy of existing identification methods needs further improvement.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for identifying cross-domain cascading fault source nodes in interdependent networks, comprising the following steps:

[0007] Step 1: Decompose the interdependent network into a set of interdependent functional subgraphs.

[0008] Step 2: Evaluate the functionality of the control loop with the shortest weighted distance between a resource supply node and a resource demand node.

[0009] Step 3: Evaluate the functionality of an interdependent functional subgraph.

[0010] Step four: Evaluate the functionality of an interdependent network.

[0011] Step 5: Assess the criticality of resource supply nodes and non-resource supply nodes and rank them in descending order.

[0012] Compared with the prior art, the present invention has the following technical effects:

[0013] (I) The identification method of the present invention evaluates the criticality of nodes in a mutually dependent network based on the interdependent functional subgraph, which can more accurately identify the source node of a cross-domain cascading fault propagation sequence.

[0014] (II) This invention establishes a mutually dependent functional subgraph containing a resource supply node and a resource demand node by analyzing the weighted shortest distance control loop between a resource supply node and a resource demand node. The invention then uses a shortest path traversal method to decompose a mutually dependent network, thereby obtaining the set of mutually dependent functional subgraphs corresponding to the system. Next, the functionality of the weighted shortest distance control loop between a resource supply node and a resource demand node is evaluated, and the functionality of a mutually dependent functional subgraph is evaluated based on the functionality of the weighted shortest distance control loop. Then, the functionality of a mutually dependent network is evaluated based on the functionality of a mutually dependent functional subgraph. Finally, the criticality of resource supply nodes and non-resource supply nodes is evaluated separately, and all nodes in the mutually dependent network are sorted in descending order according to node criticality, thereby obtaining the source node of the cross-domain cascading failure propagation sequence in the mutually dependent network.

[0015] (III) The interdependent functional subgraphs of the present invention are more in line with the actual situation of resource transmission (e.g., power transmission in smart grids). The identification method of the present invention avoids the problem of low accuracy of identification methods based on maximally connected subgraphs, maximally efficient subgraphs and existing interdependent functional subgraphs, and can prevent cross-domain cascading failures in interdependent networks at a lower cost. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of an interdependent functional subgraph.

[0017] Figure 2 For a resource supply node n N1 With a resource demand node n N2 A schematic diagram of a weighted shortest distance control loop.

[0018] Figure 3 This is a flowchart of the method for identifying cross-domain cascading fault source nodes in interdependent networks according to the present invention.

[0019] Figure 4 The flowchart shows the process of decomposing a mutually dependent network into a set of mutually dependent functional subgraphs.

[0020] Figure 5 The flowchart for evaluating the function of the weighted shortest distance control loop c.

[0021] Figure 6 A flowchart illustrating the procedure for evaluating and ranking the criticality of nodes in an interdependent network.

[0022] The specific content of the present invention will be further explained in detail below with reference to the embodiments. Detailed Implementation

[0023] It should be noted that, unless otherwise specified, all algorithms in this invention are algorithms known in the prior art.

[0024] This invention relates to a technical solution for identifying the source node of a cross-domain cascading failure propagation chain in an interdependent network composed of a physical network and an information network using network science theory and technology. The improvement is that it overcomes the problem of low identification accuracy that exists in existing identification methods based on maximally connected subgraphs, maximally efficient subgraphs, and interdependent functional subgraphs.

[0025] The purpose of this invention is to propose a more accurate method for identifying the starting node of a cross-domain cascading failure propagation chain based on interdependent functional subgraphs. This method fully considers both the influence of resource supply nodes in the physical network and the close interdependence between the physical network and the information network to more effectively solve the problem of identifying the starting node of a cross-domain cascading failure propagation chain in interdependent networks. It can prevent the initiation of a cross-domain cascading failure propagation chain in interdependent networks from the source in a cost-effective manner.

[0026] The flowchart of the method for identifying cross-domain cascading fault source nodes in interdependent networks of the present invention is as follows: Figure 3 As shown, the entire method is divided into five steps, namely, connecting the interdependent network G... N Decomposed into multiple interdependent functional subgraphs (G IIS A set of ) is given, which evaluates an interdependent functional subgraph G. IIS Given a functional metric from a resource supply node to a resource demand node, provide an evaluation of the interdependent network G. N A mutually dependent functional subgraph G IIS A functional metric is provided to evaluate an interdependent network G. N Functional metrics are provided to evaluate interdependent networks G. N The criticality of resource supply nodes and non-resource supply nodes is ranked in descending order.

[0027] Following the above technical solutions, specific embodiments of the present invention are given below. It should be noted that the present invention is not limited to the following specific embodiments, and all equivalent modifications made based on the technical solutions of this application fall within the protection scope of the present invention.

[0028] Example:

[0029] This embodiment provides a method for identifying cross-domain cascading fault source nodes in interdependent networks, which includes the following steps:

[0030] Step 1: Decompose the interdependent network into a set of interdependent functional subgraphs:

[0031] The shortest path traversal method is used to traverse the interdependent network G.N Decomposed into a set G containing multiple interdependent functional subgraphs. IISs ,

[0032] Specifically, the definition of a mutually dependent functional subgraph is as follows: In a mutually dependent network, a mutually dependent functional subgraph refers to a minimally connected, mutually dependent, directed weighted graph in which a resource-supplying node provides services to a resource-demanding node at a certain time.

[0033] Furthermore, the interdependent functional subgraph can be modeled as a triple G. IIS =(V IIS E IIS W IIS ), including:

[0034] First constraint. V N =V N1 ∪V N2 ∪V N3 ∪V N4 ∪V N5 ∪V N6 ∪V N7 It is an interdependent network G N The set of all nodes in V N1 V represents the set of resource-supplying nodes in a physical network within an interdependent network (e.g., hydropower, thermal power, wind power, etc. in a smart grid). N2 V represents the set of resource-demanding nodes in a physical network within an interdependent network (e.g., power loads in a smart grid). N3 V represents the set of resource relay nodes in the physical network of an interdependent network (e.g., power distribution nodes in a smart grid); N4 V represents the set of sensor nodes (corresponding to the nodes in the physical network that collect information) in an interdependent network. N5 V represents the set of control nodes (corresponding to decision-making devices such as controllers) in an interdependent network. N6 V represents the set of actuator nodes in the information network of an interdependent network (corresponding to actions that affect the states of nodes in the physical network). N7 This represents an information relay node in an interdependent network. The set of nodes V of an interdependent functional subgraph is also represented. IIS There is one and only one resource supply node n. IIS1 ∈V N1 and at least one resource demand node n IIS2 ∈V N2 And V IIS It contains at least one sensor node n IIS4 ∈V N4A control node n IIS5 ∈V N5 and an actuator node n IIS6 ∈V N6 A schematic diagram of an interdependent functional subgraph is shown below. Figure 1 As shown.

[0035] Second constraint, (interdependent network G) N The set of all edges in a functional subgraph is the set of all edges contained in the interdependent functional subgraph. One type is a weighted shortest distance control loop consisting of a resource supply node in the physical network, a connected resource demand node, and the necessary information network nodes (control nodes, sensor nodes, and actuator nodes) and edges required for sensing and controlling the resource demand node and the resource supply node. Another type is also a weighted shortest distance control loop consisting of a resource supply node in the physical network, a connected resource demand node, and the necessary information network nodes (control nodes, sensor nodes, and actuator nodes) and edges required for controlling and sensing the resource demand node and the resource supply node. For example, a resource supply node n... IIS1 With a resource demand node n IIS2 The weighted shortest distance control loop is formed as c = (n IIS1 ,n IIS3 ,n IIS2 ,n IIS4 ,n IIS5 ,n IIS6 ,n IIS1 ).

[0036] The third constraint is the edge weight mapping W. IIS :E IIS →[0,1].

[0037] Interdependent functional subgraph G IISs The set {G} is a set containing m interdependent functional subgraphs. IIS1 G IIS2 ,…G IISm}, where m≤|V N1 |,and|V N1 | is set V N1 The model.

[0038] Furthermore, step one specifically includes the following steps:

[0039] Step 101: Transform the directed weighted interdependent network into an undirected interdependent graph with a weight of 1, wherein the weight of the interdependent edges between the physical network (PN) and the information network (CN) (including the sensor edges of the information network collecting data from the physical network and the interdependent edges of the information network driving the physical network) is also set to 1.

[0040] Step 102: Divide the nodes in the undirected, mutually dependent graph with a weight of 1 generated in step 101 into two categories: the resource supply node set V. Supply and the set of non-resource supply nodes V Demand The resource supply node set V Supply For V N1 The set of non-resource supply nodes V Demand For V N -V N1 ; Node n in the resource supply node set N1 out-degree O(n) N1 ) is greater than zero, and the in-degree I(n) N1 The value is zero.

[0041] Step 103: Sequentially retrieve the resource supply node set V. Supply Each node n in Si Determine node n Si Whether it is connected to the execution node or sensor node in the information network through a dependency edge; if not connected, discard the current node and select the resource supply node set V. Supply The next node in; if connected, then node n Si Put into set V IISi Then, iterate through the set V of non-resource-supplying nodes in sequence. Demand Each node n in Dj If resource supply node n Si With non-resource supply node n Dj If a shortest path exists between them, then the non-resource-supplying node n is removed. Dj Put into set V IISi If resource supply node n Si With non-resource supply node n Dj If no shortest path exists between them, then the non-resource-supplying node n is discarded. Dj Next, from the set of non-resource supply nodes V Demand Take the next node and repeat the judgment process until all nodes n have been judged. Si With the set of non-resource supply nodes V Demand Any node n in Dj The goal is to determine if there is a shortest path between them.

[0042] Generate an edge set E according to the weights and directions of the original edges in the directed weighted interdependent network. IISi Determine the connected subgraph G IISi =(V IISi E IISiDoes it satisfy the definition of a mutually dependent functional subgraph (specifically, the first and second constraints)? If so, continue to determine the connected subgraph G. IISi =(V IISi E IISi Does the normal operation condition of the nodes and edges satisfy the condition? If it does, then the interdependent connected subgraph G is considered normal. IISi Add to set G IISs If the definition of a mutually dependent functional subgraph is not satisfied (specifically, the first and second constraints), then the connected subgraph G is discarded. IISi =(V IISi E IISi If the definition of a mutually dependent functional subgraph is met (specifically, the first and second constraints), but the normal operation conditions are not met, then the corresponding nodes in the information network and physical network are removed; then, the resource supply node set V is selected. Supply The next node in the process repeats the determination process, eventually generating a mutually dependent functional subgraph G. IISs A set of.

[0043] in:

[0044] V N1 G represents a mutually dependent network N Set of resource supply nodes in China;

[0045] V N G represents a mutually dependent network N The set of all nodes in the set;

[0046] V IISi G represents the set of interdependent functional subgraphs. IISs The i-th interdependent functional subgraph G IISi The set of nodes;

[0047] E IISi G represents the set of interdependent functional subgraphs. IISs The i-th interdependent functional subgraph G IISi The set of edges.

[0048] In this embodiment, the flowchart for decomposing the interdependent network into a set of interdependent functional subgraphs is as follows: Figure 4 As shown.

[0049] Step 2: Evaluate the functionality of the control loop with the shortest weighted distance between a resource supply node and a resource demand node.

[0050] Evaluate an interdependent functional subgraph G according to Equation I. IIS =(V IIS E IIS W IISA resource supply node n in ) IIS1 ∈V N1 To a resource demand node n IIS2 ∈V N2 Function F c (n IIS1 ,n IIS2 ).

[0051]

[0052] In the formula:

[0053] V N1 G represents a mutually dependent network N Set of resource supply nodes in China;

[0054] V N2 G represents a mutually dependent network N Set of resource demand nodes in China;

[0055] V IIS Represents the interdependent functional subgraph G IIS The set of all nodes contained therein;

[0056] E IIS Represents the interdependent functional subgraph G IIS The set of all edges contained therein;

[0057] W IIS Represents the interdependent functional subgraph G IIS Weight mapping of edges;

[0058] circle(n IIS1 ,n IIS2 ) represents all nodes n containing a resource supply node. IIS1 ∈V N1 To a resource demand node n IIS2 ∈V N2 node n IIS1 With node n IIS2 The set of rings; and circle(n IIS1 ,n IIS2 All nodes in the ring are functioning normally, which meets the normal operating conditions of nodes and edges in an interdependent network.

[0059] c represents the control loop with the shortest weighted distance;

[0060] In this embodiment, c = (n IIS1 →n IIS3 →n IIS2 →n IIS4 →n IIS5 →n IIS6 →n IIS1 ) / (nIIS1 ←n IIS3 ←n IIS2 ←n IIS4 ←n IIS5 ←n IIS6 ←n IIS1 )——circle(n IIS1 ,n IIS2 The loop with the smallest weight in the control loop, i.e., the control loop with the shortest weighted distance, such as... Figure 2 As shown; in this control loop c, sensor node n IIS4 ∈V N4 Collect resource demand nodes n IIS2 ∈V N2 The information is then collected and transmitted to the control node n. IIS5 ∈V N5 Control node n IIS5 ∈V N5 The given decision is passed through executor node n IIS6 ∈V N6 Control resource supply node n IIS1 ∈V N1 .

[0061] d(c) represents the weight of the shortest weighted control loop c;

[0062] In this embodiment, the edge weights are derived from the interdependent functional subgraph G. IIS Edge weight mapping W in IIS When resource supply node n IIS1 ∈V N1 With a resource demand node n IIS2 ∈V N2 When there is no weighted shortest control loop c between them, we have d(c)=∞, that is, F c (n IIS1 ,n IIS2 ) = 0; when resource supply node n IIS1 ∈V N1 With a resource demand node n IIS2 ∈V N2 When there exists a weighted shortest control loop c, we have d(c)=∑W IIS (e), e∈E IIS e is an edge in control loop c. Function F c (n IIS1 ,n IIS2 This corresponds to the reciprocal of the weight of the shortest control loop c in the weighted distance calculation.

[0063] In this embodiment, as Figure 1 As shown, at two nodes n IISi With n IISjThe shortest cycle c contains at least one control node n. IIS5 ∈V N5 And contains one sensor node n IIS4 ∈V N4 An executor node n IIS6 ∈V N6 This cycle c is divided into two parts: one part is the shortest path (path(n)). IIS1 ,n IIS2 Located in the physical network, a portion contains the shortest path (path(n)) to the controller. IIS4 ,n IIS5 ) and path(n IIS5 ,n IIS6 It is located in the information network.

[0064] In this embodiment, a specific evaluation is performed on a resource supply node n. IIS1 With a resource demand node n IIS2 The flowchart of the control loop c with the shortest weighted distance between the two loops is as follows: Figure 5 As shown.

[0065] Step 3: Evaluate the functionality of an interdependent functional subgraph:

[0066] Evaluate an interdependent functional subgraph G according to Equation II. IIS =(V IIS E IIS W IIS ) Function F IIS (G IIS );

[0067]

[0068] In the formula:

[0069] Δ represents a very small positive number;

[0070] G φ This indicates that the interdependent functional subgraph does not exist, meaning that there are no nodes or edges in the graph;

[0071] Step 4: Evaluate the functionality of an interdependent network:

[0072] According to Equation III, the interdependent network G N Each interdependent functional subgraph G contained therein IISi =(V IISi E IISi W IISi The functions of ) are summed to evaluate an interdependent network G. N Function F N (G N ).

[0073]

[0074] In the formula:

[0075] G IISs Represents the set of interdependent functional subgraphs; it is derived from the interdependent network G. N The interdependent functional subgraph G obtained after running the shortest path algorithm; considering the normal operation of the interdependent network abstracted from reality. IISs The set is non-empty.

[0076] V IISi G represents the set of interdependent functional subgraphs. IISs The i-th interdependent functional subgraph G IISi The set of nodes;

[0077] E IISi G represents the set of interdependent functional subgraphs. IISs The i-th interdependent functional subgraph G IISi The set of edges;

[0078] W IISi G represents the set of interdependent functional subgraphs. IISs The i-th interdependent functional subgraph G IISi Edge weight mapping.

[0079] Step 5: Assess the criticality of resource-supplying nodes and non-resource-supplying nodes and rank them in descending order:

[0080] Step 501, evaluate the interdependent network G N Keyness measurement of resource supply nodes:

[0081] Since a resource supply node may provide resources to multiple resource demand nodes, from a resource supply node n N1 ∈V N1 The search algorithm will obtain the resource supply node n. N1 ∈V N1 The corresponding interdependent functional subgraph G IIS .

[0082] Evaluate the interdependent network G according to Formula IV. N A resource supply node n N1 ∈V N1 criticality Imp N (n N1 );

[0083]

[0084] In the formula:

[0085] V N1 G represents a mutually dependent network N Set of resource supply nodes in China;

[0086] F IIS (G IIS ) represents the interdependent functional subgraph G IIS Functions;

[0087] F N (G N ) represents a mutually dependent network G N Functions;

[0088] This formula uses the resource to supply node n N1 The corresponding interdependent functional subgraph G IIS Functions divided by interdependent network G N Function F N (G N ).

[0089] Step 502, evaluate the interdependent network G N Criticality measurement of resource supply nodes between China and Africa:

[0090] Evaluate the interdependent network G according to equations VI to XI. N The criticality of the China-Africa resource supply node Imp N ;

[0091] Due to the interdependent network G N A non-resource supply node n i It may be shared by multiple different interdependent functional subgraphs, thus the non-resource supply node n i Corresponding to the set of interdependent functional subgraphs G IIS_ni If a resource-supplying node n j If a node n belongs to multiple different interdependent functional subgraphs, then the node n j This is very important for interdependent networks, node n j Failures can affect the functionality of interdependent networks (e.g., energy transfer).

[0092] As shown in Equation V, the interdependent network G N A non-resource supply node n i Function F n (n i ) refers to node n i The corresponding set of interdependent functional subgraphs G IIS_ni The sum of functions and interdependent network functions F N (G N The ratio of )

[0093]

[0094] In the formula:

[0095] V N G represents a mutually dependent network N The set of all nodes in the set;

[0096] As shown in Equation VI, the interdependent network G N A non-resource supply node n i criticality Imp N (n i () refers to the importance of non-resource-providing nodes in the network, which is related to node n. i Function F n (n i ), node n i BC's centrality N (n i ), harmonic centrality HC N (n i ), load center degree LC N (n i ) and node n i PageRank (PR) N (n i These indicators are positively correlated and are defined as the arithmetic mean of these indicators;

[0097]

[0098] In the formula:

[0099] norm(HC N (n i )) indicates the harmonic centrality HC N (n i Normalization is performed.

[0100] Interdependent network G N A node n i BC's centrality N (n i ), harmonic centrality HC N (n i ), load center degree LC N (n i ) and PageRank (PR) N (n i The definition of ) is shown in Equations VII, VIII, IX and XI;

[0101] As shown in Equation VII, nodes n in an interdependent network i BC's centrality N (ni ) refers to passing through a node n i The number of shortest paths;

[0102]

[0103] In the formula:

[0104] σ st This represents the number of shortest paths between nodes s and t;

[0105] σ st (n i () indicates that the shortest path in the node pair (s,t) passes through node n. i Quantity;

[0106] |V N | represents set V N The model.

[0107] As shown in Equation VIII, nodes n in an interdependent network i Harmonicity of HC N (n i ) refers to all nodes in an interdependent network that are connected to node n. i The sum of the reciprocals of the shortest paths;

[0108]

[0109] In the formula:

[0110] path(n,n i ) represents nodes n and n i The shortest path between;

[0111] W N (n,n i ) represents the distance from node n to node n i The shortest path between path(n,n) i The weight value of ).

[0112] As shown in Equation IX, nodes n in an interdependent network i Load centrality LC N (n i ) refers to all nodes that pass through the same node n. i The score of the shortest path;

[0113]

[0114] In the formula:

[0115] B s (v) represents a variable that assists in the calculation;

[0116] As shown in Equation X, the variable used for auxiliary calculation is defined as follows:

[0117] For a fixed s∈V N :

[0118] initial:

[0119] According to W N (s,t) updated from longest to shortest:

[0120] As shown in Equation XI, nodes n in an interdependent network i PageRank (PR) N (n i ) refers to node n in an interdependent network. i The neighboring nodes of node n i The effect is shown in equation (XI).

[0121]

[0122] In the formula:

[0123] α represents a value range of 0 to 1, and is usually set to 0.85;

[0124] O(n) represents the out-degree of node n in an interdependent network;

[0125] inDegree N (n i ) represents the interdependent network where node n is given a specific information. i Provides the set of neighboring nodes with in-degree.

[0126] Step 503, sort in descending order:

[0127] Following the sequence of steps 1 to 502, calculate the interdependent network G. N The criticality of each node is determined, and then the corresponding nodes are sorted in descending order according to their criticality. Thus, the source node of the cross-domain cascading failure propagation sequence in the interdependent network can be identified based on the criticality.

[0128] In this embodiment, the flowchart for evaluating and ranking the criticality of nodes in an interdependent network is as follows: Figure 6 As shown.

Claims

1. A method for identifying cross-domain cascading fault source nodes in interdependent networks, characterized in that, The method includes the following steps: Step 1: Decompose the interdependent network into a set of interdependent functional subgraphs: The shortest path traversal method is used to traverse interdependent networks. Split into a set containing multiple interdependent functional subgraphs. G IISs ; The definition of the aforementioned interdependent functional subgraph: In an interdependent network, an interdependent functional subgraph refers to a minimally connected interdependent directed weighted graph in which a resource supply node provides services to a resource demand node at a certain time. Step 2: Evaluate the functionality of the control loop with the shortest weighted distance between a resource supply node and a resource demand node; Step 3: Evaluate the functionality of an interdependent functional subgraph; Step four: Evaluate the functionality of an interdependent network; Step 5: Assess the criticality of resource-supplying nodes and non-resource-supplying nodes and rank them in descending order: Step 501, Evaluate the interdependent network Keyness measurement of resource supply nodes in China: Evaluate interdependent networks according to Formula IV. A resource supply node n N1 ∈ V N1 criticality Imp N ( n N1 ); Formula IV; In the formula: V N1 Represents interdependent networks Set of resource supply nodes in China; F IIS ( G IIS ) represents a mutually dependent functional subgraph G IIS Functions; Represents interdependent networks Functions; Step 502, Evaluate the interdependent network Criticality measurement of resource supply nodes between China and Africa: Evaluate interdependent networks according to formulas VI to XI. The criticality of China-Africa resource supply nodes Imp N ; As shown in Equation V, interdependent networks A non-resource supply node n i Functions F n ( n i ) refers to a node n i The corresponding set of interdependent functional subgraphs G IIS_ni All interdependent functional subgraphs G IIS The sum of functions and interdependent network functions The ratio; Formula V; In the formula: V N Represents interdependent networks The set of all nodes in; As shown in Equation VI, interdependent networks A non-resource supply node n i criticality Imp N ( n i This refers to the importance of non-resource-providing nodes in the network, which is related to the node's importance. n i Functions F n ( n i ),node n i The centrality of the intermediaries BC N ( n i ), harmonic centrality HC N ( n i ), load centrality LC N ( n i ) and nodes n i Page ranking PR N ( n i These indicators are positively correlated and are defined as the arithmetic mean of these indicators; Formula VI; In the formula: norm ( HC N ( n i )) indicates harmonic centrality HC N ( n i Normalization was performed. Interdependent networks A node n i The centrality of the intermediaries BC N ( n i ), harmonic centrality HC N ( n i ), load centrality LC N ( n i ) and webpage ranking PR N ( n i The definition of ) is shown in Equations VII, VIII, IX and XI; As shown in Equation VII, nodes in an interdependent network n i The centrality of the intermediaries BC N ( n i () refers to passing through a node n i The number of shortest paths; Formula VII; In the formula: σ st Represents a node s and t The number of shortest paths between them; σ st ( n i ) represents a node pair ( s , t The shortest path passes through the nodes in the () n i Quantity; | V N | represents a set V N The model; As shown in Equation VIII, nodes in an interdependent network n i Harmonic centrality HC N ( n i This refers to all nodes in an interdependent network that are connected to that node. n i The sum of the reciprocals of the shortest paths; Formula VIII; In the formula: W N ( n , n i ) represents a node n To the node n i The shortest path between path ( n , n i The weight value of ); As shown in Equation IX, nodes in an interdependent network n i Load centrality LC N ( n i () refers to all nodes that pass through the same node n i The score of the shortest path; Formula IX; In the formula: Represents a node n i Variables used in auxiliary calculations; As shown in Equation X, the variables that aid in the calculation B s ( v The definition of ) is: Formula X; As shown in Equation XI, nodes in an interdependent network n i Page ranking PR N ( n i () refers to nodes in an interdependent network n i The neighboring nodes of this node n i The impact; Formula XI; In the formula: α This indicates a value range of 0 to 1, and is usually set to 0.85; O ( n ) represents nodes in an interdependent network n The degree of departure; inDegree N ( n i ) represents the nodes in an interdependent network. n i Provides the set of neighbor nodes with in-degree; Step 503, sort in descending order: Following the order of steps 1 to 502, calculate the interdependent network. The criticality of each node is determined, and then the corresponding nodes are sorted in descending order according to their criticality. Thus, the source node of the cross-domain cascading failure propagation sequence in the interdependent network can be identified based on the criticality.

2. The method for identifying cross-domain cascading fault source nodes in interdependent networks as described in claim 1, characterized in that, Step one specifically includes the following steps: Step 101, the directed weighted interdependent network It is transformed into an undirected interdependent graph with a weight of 1, where the weight of the interdependent edge between the physical network and the information network is also set to 1; Step 102: Divide the nodes in the undirected, mutually dependent graph with a weight of 1 generated in Step 101 into two categories: a set of resource supply nodes and a set of resource supply nodes. V Supply and non-resource supply node set V Demand The set of resource supply nodes V Supply for V N1 Non-resource supply node set V Demand for V N - V N1 ; Nodes in the resource supply node set n N1 out of degree O ( n N1 ) is greater than zero and has an in-degree I ( n N1 The value is zero; Step 103: Sequentially retrieve the resource supply node set. V Supply Each node in n Si Determine the node n Si Whether it is connected to the execution node or sensor node in the information network through a dependency edge; if not connected, discard the current node and select the resource supply node set. V Supply The next node in; if connected, then the node n Si Add to collection V IISi Then, iterate through the set of non-resource-supplying nodes in sequence. V Demand Each node in n Dj If resource supply nodes n Si Non-resource supply nodes n Dj If a shortest path exists, then the node that requires the resource is... n Dj Add to collection V IISi If resource supply nodes n Si Non-resource supply nodes n Dj If no shortest path exists between them, then the node requiring the resource is discarded. n Dj Next, from the set of resource demand nodes... V Demand Take the next node and repeat the judgment process until all nodes have been judged. n Si Set of non-resource supply nodes V Demand any node in n Dj Until there is a shortest path between them; According to the directed weighted interdependent network The weights and directions of the edges in the original text generate the edge set. E IISi Determine connected subgraphs G IISi =( V IISi , E IISi Does it satisfy the definition of a mutually dependent functional subgraph? If it does, then continue to determine the connected subgraph. G IISi =( V IISi , E IISi Does the normal operation condition of the nodes and edges meet the requirements? If both are met, convert the interdependent connected subgraph to a valid one. G IISi Add to collection G IISs If the definition of a mutually dependent functional subgraph is not met, the connected subgraph is discarded. G IISi =( V IISi , E IISi If the definition of a mutually dependent functional subgraph is satisfied, but the normal operation conditions of nodes and edges are not met, then the corresponding nodes in the information network and physical network are removed; then a set of resource supply nodes is selected. V Supply The next node in the process repeats the determination process, ultimately generating a mutually dependent functional subgraph. G IISs A set; in: V N1 Represents interdependent networks Set of resource supply nodes in China; V N Represents interdependent networks The set of all nodes in; V IISi Represents a set of interdependent functional subgraphs G IISs The Middle i Interdependent functional subgraphs G IISi The set of nodes; E IISi Represents a set of interdependent functional subgraphs G IISs The Middle i Interdependent functional subgraphs G IISi The set of edges.

3. The method for identifying cross-domain cascading fault source nodes in interdependent networks as described in claim 1, characterized in that, In step two, an interdependent functional subgraph is evaluated according to Equation I. G IIS =( V IIS , E IIS , W IIS A resource supply node in ) n IIS1 ∈ V N1 To a resource demand node n IIS2 ∈ V N2 Functions F c ( n IIS1 , n IIS2 ); Formula I; In the formula: V N1 Represents interdependent networks Set of resource supply nodes in China; V N2 Represents interdependent networks Set of resource demand nodes in China; V IIS Representing interdependent functional subgraphs G IIS The set of all nodes contained therein; E IIS Representing interdependent functional subgraphs G IIS The set of all edges contained therein; W IIS Representing interdependent functional subgraphs G IIS Weight mapping of edges; circle ( n IIS1 , n IIS2 ) represents all nodes that contain a resource supply node. n IIS1 ∈ V N1 To a resource demand node n IIS2 ∈ V N2 nodes n IIS1 With nodes n IIS2 The set of rings; and circle ( n IIS1 , n IIS2 All nodes in the ring are functioning normally, which meets the normal operating conditions of nodes and edges in an interdependent network. c This represents the control loop with the shortest weighted distance. d ( c () indicates the control loop with the shortest weighted distance. c The weight.

4. The method for identifying cross-domain cascading fault source nodes in interdependent networks as described in claim 1, characterized in that, In step three, an interdependent functional subgraph is evaluated according to Equation II. G IIS =( V IIS , E IIS , W IIS ) function F IIS ( G IIS ); Formula II; In the formula: Represents a very small positive number; This indicates that the interdependent functional subgraph does not exist, meaning that there are no nodes or edges in the graph.

5. The method for identifying cross-domain cascading fault source nodes in interdependent networks as described in claim 1, characterized in that, In step four, the interdependent network is analyzed according to Equation III. Each interdependent functional subgraph contained therein G IISi =( V IISi , E IISi , W IISi The functions of ) are summed to evaluate an interdependent network. Functions ; Formula III; In the formula: G IISs Represents a set of interdependent functional subgraphs; V IISi Represents a set of interdependent functional subgraphs G IISs The Middle i Interdependent functional subgraphs G IISi The set of nodes; E IISi Represents a set of interdependent functional subgraphs G IISs The Middle i Interdependent functional subgraphs G IISi The set of edges; W IISi Represents a set of interdependent functional subgraphs G IISs The Middle i Interdependent functional subgraphs G IISi Edge weight mapping.

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