Cascade fault analysis method for urban infrastructure based on high-order network model

Abstract

The invention relates to the technical field of urban construction, and provides an urban infrastructure cascade fault analysis method based on a high-order network model. According to the method, a multi-layer network model of an urban infrastructure system is constructed, and interaction among a plurality of network nodes in the multi-layer network model is represented by adopting a simple replica structure, so that a high-order network model of the urban infrastructure system is obtained; then, setting a node fault mechanism and a region fault mechanism of the high-order network model, and performing cascade fault simulation on the high-order network model under a preset cascade failure situation; and finally, on the basis of the network comprehensive factors of the cascade faults of the defined high-order network model, according to a cascade fault simulation result, identifying high-risk nodes in the high-order network model so as to improve the elasticity of the urban infrastructure system corresponding to the high-risk nodes. Therefore, the high-risk nodes of the urban infrastructure are identified more effectively, and support and basis are provided for improving the elastic anti-risk capability of an urban infrastructure system.

Description

Technical Field

[0001] The present application relates to the field of urban construction technology, and in particular to a method for analyzing cascading failures of urban infrastructure based on a high-order network model. Background Art

[0002] Critical urban infrastructure such as power grids, water supply systems, natural gas systems and transportation networks are important components for maintaining social stability. These systems form a highly complex multi-layer network with extensive and deep interdependence. The failure of a single node or component may trigger a cascade effect through inter-layer coupling, leading to interruption and functional failure of the entire system. These effects propagate in a nonlinear and unpredictable manner, making risk assessment and management increasingly challenging. Summary of the invention

[0003] The purpose of this application is to provide a method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model to solve or alleviate the problems existing in the above-mentioned prior art.

[0004] In order to achieve the above objectives, this application provides the following technical solutions: The present application provides a method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model, comprising: step S101, constructing a multi-layer network model of an urban infrastructure system, and using a simple complex structure to characterize the interaction between multiple network nodes in the multi-layer network model to obtain a high-order network model of the urban infrastructure system; wherein the connection between different network nodes in the high-order network model represents the functional dependency relationship between different urban infrastructure systems; Step S102: setting a node failure mechanism and a regional failure mechanism of the high-order network model, and performing a cascading failure simulation on the high-order network model under a preset cascading failure scenario; Step S103: Based on the defined network comprehensive factor of the cascading failure of the high-order network model and according to the cascading failure simulation result, identify the urban infrastructure system corresponding to the high-risk node in the high-order network model.

[0005] Preferably, in step S101, the key components of the urban infrastructure system are described as the network nodes, and the interactions between different network nodes are described based on the power supply relationship; According to the function of the urban infrastructure system, each of the network nodes is classified into a different network layer, and the functional dependency between different urban infrastructure systems is represented by the connection between different network layers; Geographic coordinates are assigned to each of the network nodes, and all of the network nodes are projected onto a geographic base layer to construct the multi-layer network model.

[0006] Preferably, in step S102, in response to a single network node in the high-order network model failing due to an internal failure or failure of other dependent network nodes in the network layer where the single network node is located, the node failure mechanism is triggered; In response to multiple network nodes in a region failing synchronously due to external factors in the high-order network model, the regional failure mechanism is triggered.

[0007] Preferably, in step S102, in response to triggering the node failure mechanism and the failure of the network node corresponding to the substation, the cascading failure of the high-order network model under the traditional first-order interaction and the high-order network interaction is simulated, and the number of faulty nodes at each time step is tracked; In response to triggering the regional failure mechanism, multiple network nodes in the high-order network model fail simultaneously, and the dynamic changes of fault propagation and node recovery in each time step are simulated respectively, and the number of failed nodes in each time step and the distribution of failed nodes within the network layer of the high-order network model and between the network layers are recorded to determine the fault propagation range and fault propagation rate in the high-order network model.

[0008] Preferably, in step S102, in the node failure mechanism, according to the formula: Determine the network nodes when the high-order network model performs cascading failure simulation At the moment The probability of cascading failure ; In the formula, For the network node Cascade failure rate under traditional first-order interactions, For the network node Propagation rates under high-order network interactions; For the network node The number of failed first-order neighbor nodes, For the network node The number of failed high-order neighbor nodes; In the regional failure mechanism, according to the formula: Determine the network nodes when the high-order network model performs cascading failure simulation At the moment The regional failure probability ; In the formula, For the network node geographical coordinates; To simulate the affected area when external factors affect the synchronization of nodes in a specific area based on the regional failure mechanism, Affected areas outside the area.

[0009] Preferably, in step S102, according to the formula: Determining a fault propagation index when simulating cascading failures for the high-order network model ; Wherein, the fault propagation index is used to quantify the propagation range and recovery speed of cascading faults in the high-order network model; In the formula, is the cumulative number of faulty network nodes when cascading failure simulation is performed on the high-order network model, is the time required for network nodes to recover stability and no longer change when cascading failure simulation is performed on the high-order network model. is the maximum value of the time step under different simulation conditions when performing cascading failure simulation on the high-order network model.

[0010] Preferably, in step S103, according to the formula: Determine the network integration factor ; In the formula, is the network node in the high-order network model The total number of direct connections in all said network layers, is the total number of network nodes in the high-order network model; is the network node in the high-order network model With the network node The shortest path length between is the network node in the high-order network model With the network node The adjacency matrix between them, is the adjacency matrix The maximum eigenvalue of Preferably, in step S103, the network comprehensive factor of each of the network nodes in the high-order network model is calculated according to the cascading failure simulation result, and the network node corresponding to the largest network comprehensive factor is determined as a high-risk node in the high-order network model.

[0011] Preferably, it also includes: according to the formula: Determining the self-repair probability of the urban infrastructure system corresponding to the network node in the high-order network model ; In the formula, is the intrinsic recovery rate of the network node, is the failure duration of the cascading failure of the high-order network model.

[0012] Preferably, the method further includes: verifying the rationality and effectiveness of the high-order network model through Jaccard similarity of different fault modes in the high-order network model.

[0013] Beneficial effects: In the method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model provided in the embodiment of the present application, a multi-layer network model of the urban infrastructure system is first constructed, and a simple complex structure is used to characterize the interaction between multiple network nodes in the multi-layer network model to obtain a high-order network model of the urban infrastructure system; then, the node failure mechanism and the regional failure mechanism of the high-order network model are set, and the high-order network model is simulated for cascading failures under a preset cascading failure scenario; finally, based on the network comprehensive factor of the cascading failure of the defined high-order network model, according to the cascading failure simulation results, the high-risk nodes in the high-order network model are identified to improve the resilience of the urban infrastructure system corresponding to the high-risk nodes. Thus, through the propagation of cascading failures of the urban infrastructure system, the high-risk nodes of the urban infrastructure can be more effectively identified, providing support and basis for the cascading failure analysis of the key urban infrastructure, mitigating the impact of cascading failures, shortening the network recovery time, and improving the resilience and risk resistance of the urban infrastructure system. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The drawings constituting part of the present application are used to provide a further understanding of the present application. The exemplary embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. Among them: Figure 1 A schematic diagram of a flow chart of a method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to some embodiments of the present application; Figure 2 A logical schematic diagram of a method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to some embodiments of the present application; Figure 3 A schematic diagram of a multi-layer network model of an urban infrastructure system provided according to some embodiments of the present application; Figure 4 A schematic diagram of a node failure mechanism provided according to some embodiments of the present application; Figure 5A schematic diagram based on a regional failure mechanism provided according to some embodiments of the present application; Figure 6 A comparative schematic diagram of fault propagation of network nodes under high-order interactions provided according to some embodiments of the present application; Figure 7 A schematic diagram of the number of failed nodes with different short time periods provided according to some embodiments of the present application; Figure 8 A schematic diagram of the robustness of different network node combinations under the self-healing mechanism provided according to some embodiments of the present application. DETAILED DESCRIPTION

[0015] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. Each example is provided by way of explanation of the present application and does not limit the present application. In fact, it will be clear to those skilled in the art that modifications and variations may be made in the present application without departing from the scope or spirit of the present application. For example, a feature shown or described as a part of an embodiment may be used in another embodiment to produce yet another embodiment. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the embodiments of the present invention should belong to the scope of protection of the embodiments of the present invention.

[0016] In the risk effect analysis of urban infrastructure systems, traditional risk analysis methods are mostly based on pairwise interaction models, which only consider direct connections between nodes and are difficult to accurately describe the complex dynamic relationships between multiple nodes. High-order network models, by introducing multi-node interactions, can reflect the behavioral characteristics of complex systems and their multi-layer dependencies, and can reveal the propagation laws of faults at a higher level, providing an important tool for accurately predicting systemic risks.

[0017] Based on this, an embodiment of the present application proposes a method for analyzing cascading failures of urban infrastructure based on a high-order network model, which converts the urban infrastructure system into a high-order network model as the basic framework for cascading failure analysis; compares the behavior of the traditional first-order model with the behavior of the high-order model, and more effectively identifies high-risk nodes by analyzing changes in the cascading failure rate, propagation speed, and overall system impact, providing theoretical support for cascading failure analysis and self-healing mechanism optimization of critical urban infrastructure.

[0018] like Figures 1 to 8 As shown, the urban infrastructure cascading failure analysis method based on the high-order network model includes: Step S101: construct a multi-layer network model of the urban infrastructure system, and use a simple complex structure to characterize the interaction between multiple network nodes in the multi-layer network model to obtain a high-order network model of the urban infrastructure system.

[0019] Among them, the connections between different network nodes in the high-order network model represent the functional dependencies between different urban infrastructure systems.

[0020] In this application, the functional data and geographic information of key urban infrastructure are collected, including key nodes and connection relationships of power, transportation, communication and water supply systems, and the key components of the urban infrastructure system are described as network nodes, and the interaction between different network nodes is described based on the power supply relationship. According to the function of the urban infrastructure system, each network node is classified into different network layers (such as power layer, transportation layer, water supply layer, etc.), and the functional dependency relationship between different urban infrastructure systems is characterized by the connection between different network layers. In other words, the key urban infrastructure is represented as a multi-layer directed graph, and each node in the multi-layer directed graph corresponds to a key infrastructure system, such as a power generator, a gas station or a water treatment plant, etc. The edges connecting the nodes represent the functional dependency relationship between the nodes, and the interaction relationship between different urban infrastructure systems is described by the inter-layer connection. Here, it is mainly the power supply relationship (such as the power plant needs gas supply and the water system depends on electricity); at the same time, each network node is assigned a geographic coordinate, and all network nodes are projected to the geographic base layer, and finally a multi-layer network model containing multiple network nodes and their connections is constructed.

[0021] Furthermore, a simple complex structure is used to characterize the interaction between multiple network nodes, and a high-dimensional geometric structure (such as a triangle for the interaction of three network nodes, a tetrahedron for the connection of four network nodes, etc.) is used to simulate the complex dynamic characteristics of the interconnection in the urban infrastructure system, and the impact of group-level interaction on the overall behavior of the network is analyzed. After completing the configuration of the internal connection of each network layer, the establishment of cross-network layer edges represents the interdependence between various urban infrastructure systems. For example, the power grid, as the core of urban infrastructure, transmits energy from power generation facilities through the power grid to the end user. In addition, while maintaining their own internal connections, other infrastructure systems obtain energy from the power grid through the substation network to ensure the normal operation of their equipment.

[0022] Step S102: setting a node failure mechanism and a regional failure mechanism of the high-order network model, and performing a cascading failure simulation on the high-order network model under a preset cascading failure scenario.

[0023] In a multi-layer high-order network model, the state of a network node is jointly affected by its directly connected neighbors (i.e., first-order neighbors) within the network layer in which it is located, the higher-order neighbors connected through multi-network node interactions, and the network nodes from other network layers through inter-network layer connections. On this basis, node-based failure mechanisms (node ​​failure mechanisms) and region-based failure mechanisms (regional failure mechanisms) are defined, and the urban infrastructure system is analyzed through a high-order network model.

[0024] When a single network node fails due to internal failure or failure of other dependent network nodes in the network layer where the single network node is located, the node failure mechanism is triggered, which causes a cascading effect through the direct connection between network nodes. When multiple network nodes in a region fail synchronously due to external factors, the regional failure mechanism is triggered. In other words, the regional failure mechanism affects multiple network nodes in a specific area at the same time, and the triggering of the regional failure mechanism is caused by external factors (such as natural disasters or large-scale system failures), which will cause the synchronous failure of multiple network nodes in the region.

[0025] In this application, a high-order network model is simulated under a preset cascading failure scenario (high-order reinforcement and self-healing mechanism). In the high-order network model, more complex interdependencies of second-order or higher-order connections between network nodes are considered through high-order reinforcement. These connections involve the interaction of more than two network nodes, and the state changes of regional and traditional network nodes are manifested as the superposition of multiple network nodes on the state changes of one network node.

[0026] The failure of a network node directly causes the failure of its directly connected neighboring network nodes. This direct fault propagation is defined as a first-order interaction. The failure of a network node causes the failure of other network nodes through a more complex path (which may involve multiple intermediate network nodes). This fault propagation is defined as a higher-order network interaction (i.e., higher-order reinforcement). In other words, under the first-order interaction, only the influence of two directly connected network nodes is involved; under the higher-order network interaction, the interaction involving more than two network nodes can capture more complex interdependencies in the network.

[0027] When simulating cascading failures through a high-order network model, when the node failure mechanism is triggered and the network node corresponding to the substation fails, the evolution of the cascading failure of the high-order network model under traditional first-order interactions (i.e., first-order neighbors) and high-order network interactions (i.e., high-order neighbors connected through multiple network nodes) is simulated, and the number of faulty nodes at each time step is tracked.

[0028] For multi-layer high-order network models, the cascading failure dynamics and node criticality are analyzed based on probability and centrality methods. The failure probability is determined by the first-order propagation probability and the higher-order propagation probability. The probability of a network node switching from a functional state to a faulty state depends on the faulty state of its neighboring nodes, which is affected by direct connections and higher-order group interactions. Specifically, when a high-order network model triggers a node failure mechanism, according to the formula: Determine the network nodes when performing cascading failure simulation in a high-order network model At the moment The probability of cascading failure ; In the formula, For network nodes Cascade failure rate under traditional first-order interactions, For network nodes Propagation rates under high-order network interactions; For network nodes The number of failed first-order neighbor nodes, For network nodes The number of failed high-order neighbor nodes.

[0029] When cascading failures are simulated through a high-order network model, when the regional failure mechanism is triggered, multiple network nodes in the high-order network model fail synchronously. The dynamic changes of fault propagation and node recovery at each time step are simulated respectively, and the number of failed nodes (faulty network nodes) in each time step and the distribution of failed nodes within and between network layers in the high-order network model are recorded to determine the fault propagation range and fault propagation rate in the high-order network model.

[0030] The synchronous impact of external factors on nodes in a specific area is simulated by a regional failure mechanism (regional failure mechanism). The failure probability of network nodes in the affected area is set to 1, and the failure probability of network nodes outside the affected area is set to 0. Specifically, when the high-order network model triggers the regional failure mechanism, according to the formula: Determine the network nodes for cascading failure simulation in high-order network models At the moment The regional failure probability ; In the formula, For network nodes The geographical coordinates of To simulate the affected area when external factors affect the synchronization of nodes in a specific area based on the regional failure mechanism, Affected Areas outside the area.

[0031] In the cascading failure scenario of high-order reinforcement and self-healing mechanism in the cascade, the cascading failure of the urban infrastructure system is simulated through a high-order network model. In this case, a self-healing mechanism is introduced (the network node recovers from the fault state to the functional state and remains stable during the cascading failure simulation), and the transition of the network node from failure (fault state) to functional state is quantified by the recovery probability. Specifically, according to the formula: Determine the self-repair probability of urban infrastructure systems corresponding to network nodes in high-order network models In the formula, is the intrinsic recovery rate of the network nodes, The failure duration of a cascading failure in a high-order network model.

[0032] At the same time, in order to comprehensively evaluate the fault status, the cascading failures in the urban infrastructure system are evaluated through the stable time and the total number of failures during the cascading failure simulation. Among them, the stable time step (Stable TimeNormlized) represents the number of time steps required for the cascading failure to reach a stable state during the cascading failure simulation (the time required for the network nodes to recover stability and no longer change when cascading failure simulation is performed on the high-order network model), at which time no further fault propagation will occur; the total number of failures (Total Failures Normalized) is the cumulative number of failed network nodes (faulty network nodes) during the fault propagation process; it reflects the overall degree of disruption of the entire system in the high-order network model. Here, for the entire high-order network model, the fault propagation index is used To quantify the propagation range and recovery speed of cascading failures, specifically, according to the formula: Determining the fault propagation exponent when simulating cascading failures for high-order network models In the formula, is the cumulative number of faulty network nodes when simulating cascading failures for high-order network models, It is the time required for network nodes to recover stability and no longer change when cascading failure simulation is performed on high-order network models. It is the maximum value of the time step under different simulation conditions when simulating cascading failures for high-order network models.

[0033] Step S103: Based on the network comprehensive factor of the cascading failure of the defined high-order network model and according to the cascading failure simulation result, identify the urban infrastructure system corresponding to the high-risk node in the high-order network model.

[0034] In this application, degree centrality is used to measure the number of direct connections between network nodes and other network nodes in a high-order network model, closeness centrality is used to measure whether a network node is located on the shortest path between other network nodes, and eigenvector centrality is used to measure the connection between a network node and other high-centrality network nodes. Furthermore, the network comprehensive factor is calculated based on degree centrality, closeness centrality, and eigenvector centrality. , used to identify key network nodes. Specifically, according to the formula: Determine the network integration factor ; In the formula, is the network node in the high-order network model The total number of direct connections in all network layers, is the total number of network nodes in the high-order network model; is the network node in the high-order network model With network nodes The shortest path length between is the network node in the high-order network model With network nodes The adjacency matrix between the connections, is the adjacency matrix The maximum eigenvalue of .

[0035] Then, based on the results of the cascading failure simulation, the network comprehensive factor of each network node in the high-order network model is calculated, and the network node corresponding to the largest network comprehensive factor is identified as the high-risk node in the high-order network model. The resilience of the urban infrastructure system corresponding to the high-risk node is improved. For example, the capabilities of key components such as substations, water treatment plants, and data centers are strengthened to effectively reduce the risk of cross-system failure propagation.

[0036] In a specific application scenario, the node P3-1 (substation node) is selected to fail, and the evolution of cascading failures under traditional first-order interactions and high-order network interactions is analyzed by tracking the number of faulty nodes at each time step. Since high-order interactions in urban infrastructure systems are usually indirect and receive a buffering effect, the propagation rate of network nodes under high-order network interactions is calculated. It is set to 0.5 to prevent high-order effects from excessively affecting cascade propagation. After introducing high-order interactions in the high-order network model, the propagation speed and range of cascading failures are greatly accelerated. Among them, the dependencies between interconnected network nodes such as substations, energy storage systems, and data centers have aggravated the system pressure and further promoted the cascade effect.

[0037] For regional faults, we simulate external disasters (such as earthquakes) that cause multiple network nodes in the region to fail simultaneously, and analyze their spread. The fault propagation process is discretized into multiple short time steps, and each time step simulates the dynamic changes of fault propagation and node recovery. In each time step, the number of failed nodes and their distribution within and between network layers are recorded to analyze the scope and rate of fault propagation.

[0038] For the self-healing mechanism and its role in fault recovery, the recovery probability and the first repair delay time are defined as the key parameters of the self-healing mechanism. The self-healing capabilities of network nodes are classified according to the defined key parameters, and the recovery probability of each network node is listed ( : first-order recovery probability, : high-order recovery probability) and repair delay time, as shown in Table 1. Artificial repair intervention was introduced after the 50th time step of the simulation. Before that, it only relied on the black start capability of the network node (self-healing mechanism). The results show that the urban infrastructure system corresponding to the network node recovered faster under higher recovery probabilities, and the number of faulty network nodes decreased rapidly, indicating that the self-healing mechanism can effectively alleviate the cascade effect. As shown in Table 2, when the recovery probability (μ) of the network node is between 0.3 and 0.5, due to the complex dependencies between urban infrastructure systems, the self-healing mechanism is accompanied by large fluctuations. For example, after the substation restores power, the restoration of the transportation system may increase power demand and affect power restoration.

[0039] Table 1 System propagation parameters and repair delay Table 2 Curve integral area under different μ values By analyzing the impact of self-healing network nodes on the propagation of cascading faults, setting the black start (self-healing mechanism) substation level, and performing robust monitoring in the first 50 time steps, the results show that the black start capability of the substation can maintain basic operation, but cannot restore the initial robustness. The robustness of network node combinations with different network comprehensive factors at different times is different, indicating that different network node combinations have different strengths in the recovery process.

[0040] In this application, in order to further verify the rationality and effectiveness of the high-order network model of the urban infrastructure system, the Jaccard similarity of different fault modes in the high-order network model is calculated for evaluation. Specifically, the cascade propagation data in multiple accidents are abstracted into network nodes and connected edges, and the Jaccard similarities of different fault modes are compared (as shown in Table 3). Among them, the similarity of node failures is about 88%, and the similarity of regional failures is about 80%. The higher similarity indicates that the model can accurately simulate local failures, while the slightly lower regional failure similarity reflects the complexity of the model. Here, the 80% similarity indicates that the model can effectively reproduce large-scale regional cascade effects.

[0041] Table 3 Jaccard similarity of accident cases In this application, we effectively capture complex multi-node interactions based on high-order networks, so as to have a deeper understanding of the characteristics of cascading failures in urban infrastructure systems, and apply them to urban infrastructure systems. By building a multi-layer network model of urban infrastructure and combining the node status influence relationship of the multi-layer network model, we use node-based failure mechanisms and region-based failure mechanisms, and through simulation models, we can comprehensively understand the probability of cascading failures. , Failure probability based on region , self-repair probability , network comprehensive factor (NSF), fault propagation index and other indicators to comprehensively evaluate the dynamic behavior of cascading failures in urban infrastructure systems, identify high-risk nodes that have a significant impact on fault propagation through analysis, and improve the overall resilience and risk resistance of the system.

[0042] In the description of the present invention, the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0043] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model, characterized in that: include: Step S101, constructing a multi-layer network model of an urban infrastructure system, and using a simple complex structure to characterize the interaction between multiple network nodes in the multi-layer network model to obtain a high-order network model of the urban infrastructure system; Step S102: setting a node failure mechanism and a regional failure mechanism of the high-order network model, and performing a cascading failure simulation on the high-order network model under a preset cascading failure scenario; Step S103: Based on the defined network comprehensive factor of the cascading failure of the high-order network model and according to the cascading failure simulation result, identify the urban infrastructure system corresponding to the high-risk node in the high-order network model.

2. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to claim 1 is characterized in that: In step S101, Describing the key components of the urban infrastructure system as network nodes, and describing the interactions between different network nodes based on power supply relationships; According to the function of the urban infrastructure system, each of the network nodes is classified into a different network layer, and the functional dependency between different urban infrastructure systems is represented by the connection between different network layers; Geographic coordinates are assigned to each of the network nodes, and all of the network nodes are projected onto a geographic base layer to construct the multi-layer network model.

3. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to claim 1 is characterized in that: In step S102, In response to a single network node in the high-order network model failing due to an internal failure or failure of other dependent network nodes in the network layer where the single network node is located, triggering the node failure mechanism; In response to multiple network nodes in a region failing synchronously due to external factors in the high-order network model, the regional failure mechanism is triggered.

4. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to claim 1 is characterized in that: In step S102, In response to triggering the node failure mechanism and the failure of the network node corresponding to the substation, simulating the evolution of the cascading failure of the high-order network model under traditional first-order interaction and high-order network interaction, and tracking the number of failed nodes at each time step; In response to triggering the regional failure mechanism, multiple network nodes in the high-order network model fail simultaneously, and the dynamic changes of fault propagation and node recovery in each time step are simulated respectively, and the number of failed nodes in each time step and the distribution of failed nodes within the network layer of the high-order network model and between the network layers are recorded to determine the fault propagation range and fault propagation rate in the high-order network model.

5. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to claim 4 is characterized in that: In step S102, In the node failure mechanism, according to the formula: Determine the network nodes when the high-order network model performs cascading failure simulation At the moment The probability of cascading failure ; In the formula, For the network node Cascade failure rate under traditional first-order interactions, For the network node Propagation rates under high-order network interactions; For the network node The number of failed first-order neighbor nodes, For the network node The number of failed high-order neighbor nodes; In the regional failure mechanism, according to the formula: Determine the network nodes when the high-order network model performs cascading failure simulation At the moment The regional failure probability ; In the formula, For the network node geographical coordinates; To simulate the affected area when external factors affect the synchronization of nodes in a specific area based on the regional failure mechanism, Affected areas outside the area.

6. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to claim 1 is characterized in that: In step S102, according to the formula: Determining a fault propagation index when simulating cascading failures for the high-order network model ; Wherein, the fault propagation index is used to quantify the propagation range and recovery speed of cascading faults in the high-order network model; In the formula, is the cumulative number of faulty network nodes when cascading failure simulation is performed on the high-order network model, is the time required for network nodes to recover stability and no longer change when cascading failure simulation is performed on the high-order network model. is the maximum value of the time step under different simulation conditions when performing cascading failure simulation on the high-order network model.

7. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to claim 1 is characterized in that: In step S103, According to the formula: Determine the network integration factor ; In the formula, is the network node in the high-order network model The total number of direct connections in all network layers, is the total number of network nodes in the high-order network model; is the network node in the high-order network model With the network node The shortest path length between is the network node in the high-order network model With the network node The adjacency matrix between the connections, is the adjacency matrix The maximum eigenvalue of .

8. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to claim 1 is characterized in that: In step S103, According to the cascading failure simulation result, the network comprehensive factor of each of the network nodes in the high-order network model is calculated, and the network node corresponding to the largest network comprehensive factor is determined as a high-risk node in the high-order network model.

9. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to any one of claims 1 to 8, characterized in that: Also includes: According to the formula: Determining the self-repair probability of the urban infrastructure system corresponding to the network node in the high-order network model ; In the formula, is the intrinsic recovery rate of the network node, is the failure duration of the cascading failure of the high-order network model.

10. The method for analyzing cascading failures of urban infrastructure equipment based on a high-order network model according to any one of claims 1 to 8, characterized in that: Also includes: The rationality and effectiveness of the high-order network model are verified by using the Jaccard similarity of different failure modes in the high-order network model.

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