A method for evaluating infrastructure network invulnerability based on three-phase dynamic mechanism

Abstract

The application discloses a kind of infrastructure network invulnerability evaluation methods based on three-phase dynamics mechanism, it is related to complex network reliability and security analysis technical field, this method is first by constructing damaged network topology model, calculates mesoscopic intensity index to quantify network vulnerability;Then based on the scaling behavior of the index, the network state is divided into three dynamic phase regions of linear phase, complex phase and backbone phase, to identify different vulnerability mechanisms;Subsequently trace the structural defects of connected group, and take optimization strategy for different phase state: for backbone phase network, verify and converge guide based on universal constant ln2, for linear phase and complex phase network, it is driven to jump to backbone phase by ring perception strategy;Finally, simulation verification is carried out under multi-mode attack scene, to ensure that the network has stable power law behavior and ln2 critical threshold under backbone phase;The application realizes the accurate identification of network cascading failure critical condition and invulnerability enhancement.

Description

Technical Field

[0001] This invention relates to the field of reliability and security analysis technology for complex networks, and in particular to a method for assessing the resilience of infrastructure networks based on a three-phase dynamics mechanism. Background Technology

[0002] With the acceleration of global economic integration and digital transformation, various critical infrastructures, represented by supply chain networks (and also including power grids, transportation networks, and the Industrial Internet), have become the cornerstone of ensuring the stable operation of the social economy. These networks are typically characterized by their large scale, complex topology, cross-regional collaboration, and multi-stage coupling. However, in reality, these network systems are constantly threatened by various uncertainties, including natural disasters, public emergencies, equipment failures, and malicious attacks (such as network intrusions). Due to the tight physical or logical connections between network nodes, the failure of a local node often triggers cascading failures through coupling relationships, causing the fault to spread rapidly throughout the network, resulting in incalculable economic losses and social impacts.

[0003] To address the aforementioned vulnerabilities, existing technologies primarily enhance network robustness through physical redundancy or topology optimization. Common methods include: (1) Node redundancy: dispersing single-point risks by adding backup suppliers, production nodes, or server replicas; (2) Critical node protection: identifying important nodes based on degree centrality or betweenness centrality and implementing key protection or capacity expansion; (3) Edge weight and path optimization: alleviating congestion by adjusting transport paths, rerouting, or redistributing load ratios; (4) Multi-source backup strategy: establishing multiple supply channels or backup links to reduce the probability of connection interruption. However, existing technologies have the following drawbacks: lack of accurate assessment based on dynamic mechanisms, relying heavily on static indicators, making it difficult to reveal phase transition mechanisms and quantify critical thresholds, and failing to achieve early warning; insufficient utilization of structural features, ignoring the contribution of higher-order structures to resilience, blind and costly redundancy construction, and potentially introducing interference; insufficient universality verification, existing methods are mostly effective under single failure modes, and the protection effect decreases when facing intelligent attacks or mixed disturbances, lacking theoretically universal robustness assurance schemes.

[0004] Therefore, there is an urgent need for an infrastructure network resilience assessment method based on a three-phase dynamics mechanism. This method needs to be able to accurately identify the critical conditions for network cascading failure and use this as a guide to explore key topological features in the network, thereby achieving a significant improvement in the robustness and resilience of critical infrastructure networks such as supply chains while ensuring cost control. Summary of the Invention

[0005] The purpose of this invention is to provide an infrastructure network resilience assessment method based on a three-phase dynamic mechanism, which solves the problems of unclear dynamic mechanisms, lack of quantitative critical thresholds, blind redundant design, and cost-efficiency contradictions in existing critical infrastructure resilience assessment and enhancement technologies.

[0006] To achieve the above objectives, this invention provides a method for assessing the resilience of infrastructure networks based on a three-phase dynamic mechanism, comprising the following steps: Step 1: Quantify network status: Construct a topology model of the critical infrastructure network under damage, and calculate the mesoscopic strength index to quantify the vulnerability of the network's mesoscopic structure by statistically analyzing its connectivity characteristics. Step 2: Divide the dynamic phases: Based on the scaling behavior of the mesoscopic strength index, the current state of the network is divided into three dynamic phase regions that characterize different vulnerability mechanisms: linear phase (FC), composite phase (Com), and backbone phase (Bb). Step 3: Tracing the root cause of vulnerability: Based on the results of the dynamic phase division, trace the defects of the connected group characteristics that lead to insufficient network robustness; Step 4: Calibrate and optimize the safety boundary: For networks in the backbone phase, use universal constants... As the absolute benchmark for theoretically optimal robustness, the network state is verified and guided to converge to this benchmark. For networks in the linear or composite phases, optimization is performed based on diagnostic results using a loop-aware strategy, driving them to transition to the backbone phase and anchoring them to it. Feature region; Step 5, Robustness Comprehensive Verification: Under multi-mode attack scenarios, simulate and test the optimized network to verify its power-law dominant behavior in the backbone phase. Stability of the critical threshold.

[0007] Preferably, the construction of the topology model of the critical infrastructure network under damage in step 1 specifically involves: obtaining the node data and edge data of the infrastructure network under damage, and constructing an undirected graph model. ,in For a set of nodes, Let the set of edges contain the total number of nodes. .

[0008] Preferably, the calculation process of the mediator strength index in step 1 is as follows: S1. Traverse the network using Breadth-First Search (BFS) or Depth-First Search (DFS) algorithms. Identify all connected groups in the network and sort them in descending order by the number of nodes, specifically: S11. Define the largest connected group ranked first as the giant connected group, whose size is... Let its relative size relative to all nodes in the network be denoted as . ; S12. Define all remaining groups as finitely connected groups, denoted as the... The size of a finitely connected group is ,in ; S13. Define the network final recovery curve as follows: ,use Characterize the recovery curve after random seeding is applied to the damaged network; S2. Based on the arrangement results in S1, calculate the normalized second moment of the size of the finite connected group. The expression is as follows: ; S3, Computational network mesoscopic strength index The expression is as follows: .

[0009] Preferably, the specific process of step 2 is as follows: S21. Parameter setting and threshold calculation, including: S211, Calculate the low-intensity cutoff threshold Based on finite size scaling theory, an upper threshold for identifying linear phases is defined, and the calculation formula is as follows: ; In the formula, The total number of network nodes. This is a preset constant (adjustment parameter). The maximum probability of recovery from random seeding is denoted as the effective recovery strength. The threshold The scaling behavior dynamically decreases as the network size increases, conforming to the limits of the physical system. S212, Set the critical threshold for backbone personnel : Set a critical threshold for determining whether the MegaConnect Group has taken shape ,and Scale-dependent; S213. Calculate the robustness deviation index. : The expression used to quantify the deviation of the current dynamic characteristics of the network from the ideal backbone phase is as follows: ; S22. Three-phase division and determination: based on the mesoscopic strength index. Critical threshold with the backbone and the size of the Giant Connect Group The relationship between the network states is used to divide the network state into three dynamic phase regions.

[0010] Preferably, the division and determination of the three dynamic phase regions are as follows: Linear phase: if and The extremely low value indicates that the network connectivity is broken, dominated by a large number of discrete finite groups, and lacks a global backbone; Skeletal phase: If and ,in A minimal constant is set for the backbone critical threshold. In order to Being in a stable range indicates that the network has formed a robust mega-connected backbone with low structural volatility; Composite phase: In addition to the two cases above, there is a special transition state. In this transition state, it is indicated that the network is in the oscillation window of phase transition and has not yet formed stable global connectivity. The transition state is: (1) Although it exceeded But it didn't reach that goal. This indicates that the network connectivity is not strong enough; (2) Very satisfied ,but (The deviation is too large, and the network is unstable.) In this phase region, the network is constrained by the "squeeze effect" between the mesoscopic structure and the backbone structure, and is in a period of violent oscillation. Although there are large groups, they are extremely fragile and do not meet the requirements. Robustness characteristics.

[0011] Preferably, in step 3, based on the results of the dynamic phase state division, the specific defects in the connected group features that lead to insufficient network robustness are as follows: For linear phase networks: connectivity is lacking, and mesoscopic groups are too discrete; For complex phase networks: structural squeeze and topological bottleneck exist. In this phase network, by mining key node pairs that can close long chains and form stable triangular or quadrilateral loop structures, the squeeze constraint can be relieved and the group integration can be promoted. For backbone network: The structure is relatively robust, and we enter the feature verification stage.

[0012] Preferably, in step 4, for networks in the backbone phase, a universal constant is used. As the absolute benchmark for theoretically optimal robustness, verifying and guiding the network state to converge to this benchmark specifically involves: for networks in the backbone phase, simulating cascading failure processes (such as randomly removing nodes) and plotting the network performance recovery law curve; monitoring the key characteristic parameter values ​​when the recovery law reaches 0.5; and if this characteristic parameter stably converges to... If the value is approximately 0.693, the network is considered to have reached its theoretically optimal robust state; if this feature parameter deviates from... This indicates that although the backbone structure has been formed, its internal density or redundancy still needs to be optimized.

[0013] Preferably, in step 4, for networks in the linear or composite phase, optimization is performed based on the diagnostic results using a loop-aware strategy, driving them to transition to the diaphragmatic phase and anchoring them to [the target area]. The specific feature region is: by mining key node pairs that can close long chains and form stable triangular or quadrilateral cycle structures, the squeeze constraint is removed, thereby reducing the normalized second moment of finite connected groups. This increases the size of the mesoscopic interconnects, thereby significantly reducing the mesoscopic strength exponent, driving the network to transition from the linear / composite phase to the backbone phase, and ultimately anchoring it in the [unclear context]. Feature region.

[0014] The preferred optimization using a circle-aware strategy is as follows: In the topology of the infrastructure network obtained from the modeling, two different nodes are randomly selected. and Furthermore, there is no direct edge connection between the two in the current network, so the node pair... As a candidate edge; for candidate edges First determine the node and In the damaged network Determine if the two paths are reachable; if so, calculate the shortest path length. and average clustering coefficient If neither can be reached, then a new candidate edge is selected; if the conditions are met... and If the candidate edge meets the condition, it is temporarily added to the edge list. It then checks whether the edge causes a new cycle to form in the network: if a new cycle is formed, the edge is accepted and kept in the network, and the edge count is updated. If no new cycle is formed, discard the candidate edge and resample. This represents the lower bound of the shortest path length for candidate edges. This represents the upper bound of the shortest path length of the candidate edges. This represents the threshold value for the set clustering coefficient; values ​​below this threshold meet the selection criteria.

[0015] Preferred multi-mode attack scenarios include random edge attacks, random point attacks, and randomness attacks.

[0016] Therefore, the present invention employs the above-mentioned infrastructure network resilience assessment method based on a three-phase dynamic mechanism, which has the following beneficial effects: (1) This invention innovatively introduces the mesoscopic strength index, breaking through the limitations of existing technologies that only focus on microscopic (node ​​degree) or macroscopic (connectivity) indicators; by quantifying the interaction between the second moment of connected groups and giant connected groups, this invention can profoundly reveal the intrinsic physical mechanism of network cascading failure, accurately capture the "structural leverage effect" of broken mesoscopic structures in the network relative to the backbone, and provide a more physically deep order parameter for resilience assessment. (2) Based on the finite size scaling theory, this invention innovatively establishes a system based on the finite size scaling theory. This invention provides a standard for defining critical points in key phase regions. Compared to traditional methods that rely on static determination based on empirical values, this invention achieves dynamic and adaptive partitioning of phase transition boundaries for networks of different sizes. This provides a rigorous mathematical basis for defining linear phases, composite phases, and backbone phases, significantly improving the scientific rigor of the evaluation results. (3) This invention can accurately identify “composite phases” in the critical region of phase transition; unlike the coarse evaluation of traditional binary (connected / disconnected) systems, this invention can further distinguish the deep topological sources that cause network fragility: whether it is due to the mesoscopic clusters being too fragmented (linear phase) or due to the squeeze effect constraining the network into an oscillating period (composite phase); this refined diagnosis can avoid blind optimization and guide managers to adopt targeted loop perception strategies (such as connecting fragmented clusters or removing structural bottlenecks). (4) This invention reveals the unique characteristics of the backbone network. "Universal characteristic"; that is, when the network forms a robust backbone, its cascade recovery law reaches... The key feature number at time will be stably anchored at The proximity provides an absolute physical indicator for the supply chain and critical infrastructure; managers do not need to rely on complex simulations, but only need to monitor the offset of this feature number to directly determine whether the network has reached the theoretically optimal robust state. (5) Based on the universal network dynamics phase transition mechanism and finite size scaling theory, this method has a high degree of cross-domain transferability. It is not only applicable to complex supply chain systems (covering high-end manufacturing, energy supply, and emergency logistics), but can also be directly applied to fields such as the power energy Internet, integrated three-dimensional transportation network (aviation and railway), industrial Internet, and critical information infrastructure. This method provides a general theoretical tool for cascading failure early warning, survivability quantitative assessment, and defense architecture design of various complex systems when facing sudden disturbances. It has significant practical value for ensuring the stable operation of the social economy.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1This is an overall flowchart of an infrastructure network resilience assessment method based on a three-phase dynamics mechanism according to the present invention. Figure 2 The network three-phase dynamic response curve and backbone region ln 2 characteristic number state diagram are shown in the embodiment of the present invention, wherein (a) is the linear phase recovery curve, (b) is the composite phase recovery curve, (c) is the backbone phase recovery curve, and (d) is the ln 2 characteristic point state diagram. Figure 3 To ensure the universality of the generated network structure and the uniformity of the ignition phase diagram in the embodiments of the present invention; Figure 4 The diagrams shown are for verifying the robustness of the three-phase dynamics and the ln 2 feature number of the backbone region under multiple attack scenarios in this embodiment of the invention. (a) is a planar diagram of the random network after suffering different damage intensities, and (b) is a robustness verification diagram of the ln 2 feature number of the backbone region. Figure 5 This is a three-phase dynamic diagram of a real network under the attack scenario of this invention embodiment. Detailed Implementation

[0019] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] Please see Figure 1 A method for assessing the resilience of infrastructure networks based on a three-phase dynamic mechanism includes the following steps: Step 1: Quantify Network State: Obtain node data (e.g., suppliers, factories, distributors) and edge data (e.g., logistics routes, supply relationships) of the target supply chain network. Construct a topology model of the critical infrastructure network under damage. Calculate the mesoscopic strength index, used to quantify the vulnerability of the network's mesoscopic structure, by statistically analyzing its connectivity characteristics. Specifically, constructing the topology model of the critical infrastructure network under damage involves: obtaining node and edge data of the infrastructure network under damage, and constructing an undirected graph model. ,in For a set of nodes, Let the set of edges contain the total number of nodes. .

[0021] The calculation process for the mesoscopic strength index is as follows: S1. Traverse the network using Breadth-First Search (BFS) or Depth-First Search (DFS) algorithms. Identify all connected groups in the network and sort them in descending order by the number of nodes, specifically: S11. Define the largest connected group ranked first as the giant connected group, whose size is... Let its relative size relative to all nodes in the network be denoted as . ; S12. Define all remaining groups as finitely connected groups, denoted as the... The size of a finitely connected group is ,in ; S13. Define the network final recovery curve as follows: ,use Characterize the recovery curve after random seeding is applied to a damaged network; such as Figure 2 As shown, Figure 2 In Figure (a), the linear phase (FC) recovery curve of the random network (ER) is shown when n=4000, damage intensity p=0.0056, and S=0.002. Figure 2 (b) in the figure is the recovery curve of the mixed phase (Com) when n=4000, damage strength p=0.1885, and S=0.236; Figure 2 (c) in the figure is the diaphysis (Bb) recovery curve when n=4000, damage strength p=0.2554, and S=0.614; Figure 2 (d) in the figure represents the ln2 feature point corresponding to the "half-recovery point"; S2. Based on the arrangement results in S1, calculate the normalized second moment of the size of the finite connected group. The expression is as follows: ; S3, Computational network mesoscopic strength index The expression is as follows: .

[0022] Step 2: Delineate the dynamic phase states: Based on the scaling behavior of the mesoscopic strength index, the current state of the network is divided into three dynamic phase regions representing different vulnerability mechanisms: linear phase (FC), composite phase (Com), and backbone phase (Bb); the specific process is as follows: S21. Parameter setting and threshold calculation, including: S211, Calculate the low-intensity cutoff threshold Based on finite size scaling theory, an upper threshold for identifying linear phases is defined, and the calculation formula is as follows: ; In the formula, The total number of network nodes. This is a preset constant (adjustment parameter). The maximum probability of recovery from random seeding is denoted as the effective recovery strength. The threshold The scaling behavior dynamically decreases as the network size increases, conforming to the limits of the physical system. S212, Set the critical threshold for backbone personnel : Set a critical threshold for determining whether the MegaConnect Group has taken shape ,and Scale-dependent; S213. Calculate the robustness deviation index. : The expression used to quantify the deviation of the current dynamic characteristics of the network from the ideal backbone phase is as follows: ; S22. Three-phase division and determination: based on the mesoscopic strength index. Critical threshold with the backbone and the size of the Giant Connect Group The relationship between these factors divides the network state into three dynamic phase regions; specifically: Linear phase: if and The extremely low value indicates that the network connectivity is broken, dominated by a large number of discrete finite groups, and lacks a global backbone; Skeletal phase: If and ,in A minimal constant is set for the backbone critical threshold. In order to Being in a stable range indicates that the network has formed a robust mega-connected backbone with low structural volatility; Composite phase: In addition to the two cases above, there is a special transition state. In this transition state, it is indicated that the network is in the oscillation window of phase transition and has not yet formed stable global connectivity. The transition state is: (1) Although it exceeded But it didn't reach that goal. This indicates that the network connectivity is not strong enough; (2) Very satisfied ,but (The deviation is too large, and the network is unstable.) In this phase region, the network is constrained by the "squeeze effect" between the mesoscopic structure and the backbone structure, and is in a period of violent oscillation. Although there are large groups, they are extremely fragile and do not meet the requirements. Robustness characteristics. For example... Figure 3 As shown, the effectiveness of the three-phase partitioning and determination was verified in multiple generator networks. Specifically, it characterizes the different damage intensities experienced by random networks (ER), scale-free networks (BA), small-world networks (WS), and modular networks (MOD) with n=4000. The planar diagram dynamically changes with the network structure as the damage intensity increases.

[0023] Step 3: Tracing the root cause of vulnerability: Based on the dynamic phase state division results, trace the defects in the connected group characteristics that lead to insufficient network robustness; specifically: For linear phase networks: connectivity is lacking, and mesoscopic groups are too discrete; For complex phase networks: structural squeeze and topological bottleneck exist. In this phase network, by mining key node pairs that can close long chains and form stable triangular or quadrilateral loop structures, the squeeze constraint can be relieved and the group integration can be promoted. For backbone network: The structure is relatively robust, and we enter the feature verification stage.

[0024] Step 4: Calibrate and optimize the safety boundary: For networks in the backbone phase, use universal constants... As the absolute benchmark for theoretically optimal robustness, the network state is verified and guided to converge to this benchmark. For networks in the linear or composite phases, optimization is performed based on diagnostic results using a loop-aware strategy, driving them to transition to the backbone phase and anchoring them to it. Feature regions; where, for networks in the backbone phase, a universal constant is used. As the absolute benchmark for theoretically optimal robustness, verifying and guiding the network state to converge to this benchmark specifically involves: for networks in the backbone phase, simulating cascading failure processes (such as randomly removing nodes) and plotting the network performance recovery law curve; monitoring the key characteristic parameter values ​​when the recovery law reaches 0.5; and if this characteristic parameter stably converges to... If the value is approximately 0.693, the network is considered to have reached its theoretically optimal robust state; if this feature parameter deviates from... This indicates that although the basal structure has been formed, its internal density or redundancy still needs to be optimized. For networks in the linear or complex phases, optimization is performed based on diagnostic results using a loop-aware strategy to drive them to transition to the basal phase and anchor them to [the desired network]. The specific feature region is: by mining key node pairs that can close long chains and form stable triangular or quadrilateral cycle structures, the squeeze constraint is removed, thereby reducing the normalized second moment of finite connected groups. This increases the size of the mesoscopic interconnects, thereby significantly reducing the mesoscopic strength exponent, driving the network to transition from the linear / composite phase to the backbone phase, and ultimately anchoring it in the [unclear context]. Feature region.

[0025] The optimization using the circle-aware strategy specifically involves: In the topology of the infrastructure network obtained from the modeling, two different nodes are randomly selected. and Furthermore, there is no direct edge connection between the two in the current network, so the node pair... As a candidate edge; for candidate edges First determine the node and In the damaged network Determine if the two paths are reachable; if so, calculate the shortest path length. and average clustering coefficient If neither can be reached, then a new candidate edge is selected; if the conditions are met... and If the candidate edge meets the condition, it is temporarily added to the edge list. It then checks whether the edge causes a new cycle to form in the network: if a new cycle is formed, the edge is accepted and kept in the network, and the edge count is updated. If no new cycle is formed, discard the candidate edge and resample. This represents the lower bound of the shortest path length for candidate edges. This represents the upper bound of the shortest path length of the candidate edges. This represents the threshold value for the set clustering coefficient; values ​​below this threshold meet the selection criteria.

[0026] Step 5, Robustness Comprehensive Verification: Under multi-mode attack scenarios, simulate and test the optimized network to verify its power-law dominant behavior in the backbone phase. Stability of the critical threshold; among which, multi-mode attack scenarios include random edge attacks (random removal ratio is...). (connecting edges), random point attacks (randomly removing a proportion of...) (Nodes), degree attacks (removal ratio based on node degree value from largest to smallest) The verification of power-law dominant behavior specifically involves: verifying whether the size distribution of the remaining network's connected groups maintains a power-law characteristic during the attack process, which is a typical indicator of the existence of a backbone phase; and verifying the threshold stability by recording the critical threshold at the moment of network collapse and verifying whether this threshold remains robustly maintained under different attack modes. Near the baseline. For example... Figure 4 The results demonstrate the network structure changes and robustness under random node attack (RNA), random edge attack (REA), and degree-specific attack (DTA) with an attack strength of q=0.15. Figure 4 (a) in the figure depicts the ER network after suffering different levels of damage. The planar diagram dynamically changes with the network structure of the damaged area. Figure 4 (b) in the figure verifies the robustness of the ln 2 feature number in the backbone region.

[0027] Example To verify the effectiveness of the proposed resilience-aware enhancement architecture in real-world industrial scenarios, we applied the method to a regional infrastructure network and conducted systematic stress tests on its topology response under heterogeneous threats. Figure 5 As shown, we examined the critical behavior of the network under three typical attack modes and mapped the physical attack scenarios to specific industrial internet contexts: random point attacks simulate random failures of edge devices due to aging or environmental factors; random edge attacks correspond to communication fiber optic cable interruptions or unexpected disruptions to logistics transportation paths; and targeted attacks simulate the worst-case scenario where an adversary with high destructive intent prioritizes attacking high-connectivity hub nodes (such as core data centers or backbone switches) under budget constraints.

[0028] Experimental results reveal the significant advantages of the defensive architecture in maintaining core network functions. In the phase diagram, we introduce theoretical eigenvalues. This serves as a physical baseline for measuring the "semi-recovery robustness" of a network. In this context, It doesn't just represent the connectivity threshold of the topology; it has a deeper physical meaning: it signifies that after defensive mechanisms intervene, the core backbone of the network can maintain at least 50% of its functionality or connectivity. This threshold verifies whether the network has the ability to restore critical business flows to an acceptable operating level (i.e., a "half-recovery" state) after suffering a severe attack, preventing the system from falling into an irreversible total shutdown.

[0029] observe Figure 5 It is evident that the infrastructure network backbone exhibits robustness. Even when faced with highly destructive targeted attacks (red data points, attack strength q=0.05), the network's key structural indicators did not experience vertical collapse. More importantly, the vast majority of critical evolution points remained above or within the effective recovery strength In2 threshold. This robustness to the In2 threshold confirms that the architecture can effectively suppress cascading failures, ensuring that the Industrial Internet retains the ability to "degrade operation" rather than "complete shutdown" under extreme attacks.

[0030] Therefore, this invention employs the aforementioned infrastructure network resilience assessment method based on a three-phase dynamic mechanism. This method starts by quantifying the network state, constructing a damaged network topology, and calculating a mesoscopic strength index to reveal the vulnerability of the network's mesoscopic structure. Based on the scaling behavior of this index, the network is dynamically divided into a linear phase, a composite phase, and a backbone phase, each corresponding to a different vulnerability mechanism: the linear phase exhibits connectivity breakdown, the composite phase is in a state of structural squeeze and oscillation, and the backbone phase has formed a robust, giant connected backbone. For different phase states, this invention implements differentiated optimization: for the backbone phase network, the universal constant ln2 is used as the theoretical optimal value. The robustness benchmark is used to verify and guide the network towards this characteristic. For linear and composite phases, a loop-aware strategy—that is, identifying and adding key edges that can form a stable loop structure—is used to remove topological bottlenecks, promote cluster integration, and drive the network to transition to the backbone phase. Finally, simulation tests under multi-mode attack scenarios (such as random point attacks, edge attacks, and degree attacks) are used to verify the power-law behavior and stability of the ln2 threshold of the optimized network in the backbone phase. This method breaks through the limitations of traditional static evaluation, realizes dynamic diagnosis and targeted enhancement of network resilience, and is applicable to various critical infrastructure networks such as supply chain, power, and transportation.

[0031] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for assessing the resilience of infrastructure networks based on a three-phase dynamic mechanism, characterized in that, Includes the following steps: Step 1: Quantify network status: Construct a topology model of the critical infrastructure network under damage, and calculate the mesoscopic strength index to quantify the vulnerability of the network's mesoscopic structure by statistically analyzing its connectivity characteristics. Step 2: Divide the dynamic phase state: Based on the scaling behavior of the mesoscopic strength index, the current state of the network is divided into three dynamic phase regions that characterize different vulnerability mechanisms: linear phase, composite phase and backbone phase. Step 3: Tracing the root cause of vulnerability: Based on the results of the dynamic phase division, trace the defects of the connected group characteristics that lead to insufficient network robustness; Step 4: Calibrate and optimize the safety boundary: For networks in the backbone phase, use universal constants... As the absolute benchmark for theoretically optimal robustness, the network state is verified and guided to converge to this benchmark. For networks in the linear or composite phases, optimization is performed based on diagnostic results using a loop-aware strategy, driving them to transition to the backbone phase and anchoring them to it. Feature region; Step 5, Robustness Comprehensive Verification: Under multi-mode attack scenarios, simulate and test the optimized network to verify its power-law dominant behavior in the backbone phase. Stability of the critical threshold.

2. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 1, characterized in that, Step 1, which involves constructing the topology model of the damaged critical infrastructure network, specifically involves: obtaining the node and edge data of the damaged infrastructure network and constructing an undirected graph model. ,in For a set of nodes, Let the set of edges contain the total number of nodes. .

3. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 2, characterized in that, The calculation process for the mediator strength index in step 1 is as follows: S1. Traverse the network using breadth-first search or depth-first search algorithms. Identify all connected groups in the network and sort them in descending order by the number of nodes, specifically: S11. Define the largest connected group ranked first as the giant connected group, whose size is... Let its relative size relative to all nodes in the network be denoted as . ; S12. Define all remaining groups as finitely connected groups, denoted as the... The size of a finitely connected group is ,in ; S13. Define the network final recovery curve as follows: ,use Characterize the recovery curve after random seeding is applied to the damaged network; S2. Based on the arrangement results in S1, calculate the normalized second moment of the size of the finite connected group. The expression is as follows: ； S3, Computational network mesoscopic strength index The expression is as follows: 。 4. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 3, characterized in that, The specific process of step 2 is as follows: S21. Parameter setting and threshold calculation, including: S211, Calculate the low-intensity cutoff threshold Based on finite size scaling theory, an upper threshold for identifying linear phases is defined, and the calculation formula is as follows: ； In the formula, The total number of network nodes. As a preset constant, The maximum probability of recovery from random seeding is denoted as the effective recovery strength. ; S212, Set the critical threshold for backbone personnel : Set a critical threshold for determining whether the MegaConnect Group has taken shape ,and Scale-dependent; S213. Calculate the robustness deviation index. : The expression used to quantify the deviation of the current dynamic characteristics of the network from the ideal backbone phase is as follows: ； S22. Three-phase division and determination: based on the mesoscopic strength index. Critical threshold with the backbone and the size of the Giant Connect Group The relationship between the network states is used to divide the network state into three dynamic phase regions.

5. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 4, characterized in that, The division and determination of the three dynamic phase regions are as follows: Linear phase: if and The extremely low value indicates that the network connectivity is broken, dominated by discrete finite groups, and lacks a global backbone; Skeletal phase: If and ,in The threshold value is the backbone critical threshold, indicating that the network has formed a robust giant connected backbone with low structural volatility. Composite phase: In addition to the two cases above, there is a transitional state. In this transitional state, it is indicated that the network is in the oscillation window of phase transition and has not yet formed stable global connectivity. The transitional state is: (1) Although it exceeded But it didn't reach that goal. This indicates that the network connectivity is not strong enough; (2) satisfy ,but In this phase region, the network is constrained by the "squeeze effect" between its mesoscopic and backbone structures, and is in a period of violent fluctuation. Although there are large groups, they are extremely fragile and do not meet the requirements. Robustness characteristics.

6. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 5, characterized in that: In step 3, based on the results of the dynamic phase state division, the specific defects of the connected group features that lead to insufficient network robustness are as follows: For linear phase networks: connectivity is lacking, and mesoscopic groups are too discrete; For complex phase networks: structural squeeze and topological bottleneck exist. In this phase network, by mining key node pairs that can close long chains and form stable triangular or quadrilateral loop structures, the squeeze constraint can be relieved and the group integration can be promoted. For backbone network: The structure is relatively robust, and we enter the feature verification stage.

7. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 6, characterized in that: In step 4, for networks in the backbone phase, a universal constant is used. As the absolute benchmark for theoretically optimal robustness, verifying and guiding the network state to converge toward this benchmark specifically involves: for networks in the backbone phase, simulating the cascading failure process and plotting the recovery law curve of the network performance; monitoring the key characteristic parameter values ​​when the recovery law reaches 0.5; If the characteristic parameter is stable and converges to If the network reaches its theoretically optimal robust state, then it is determined that the network has reached the optimal robust state; if the feature parameter deviates from this state... This indicates that although the backbone structure has been formed, its internal density or redundancy still needs to be optimized.

8. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 7, characterized in that: In step 4, for networks in the linear or complex phases, optimization is performed based on the diagnostic results using a loop-aware strategy, driving them to transition to the diaphragmatic phase and anchoring them to [the target area]. The specific feature region is: by mining key node pairs that can close long chains and form stable triangular or quadrilateral cycle structures, the squeeze constraint is removed, thereby reducing the normalized second moment of finite connected groups. This increases the size of the mesoscopic interconnects, thereby significantly reducing the mesoscopic strength exponent, driving the network to transition from the linear / composite phase to the backbone phase, and ultimately anchoring it in the [unclear context]. Feature region.

9. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 8, characterized in that: The optimization using the circle-aware strategy specifically involves: In the topology of the infrastructure network obtained from the modeling, two different nodes are randomly selected. and Furthermore, there is no direct edge connection between the two in the current network, so the node pair... As a candidate edge; for candidate edges First determine the node and In the damaged network Determine if the two paths are reachable; if so, calculate the shortest path length. and average clustering coefficient ; If neither can be reached, then a new candidate edge is selected; if the conditions are met... and If the candidate edge meets the condition, it is temporarily added to the edge list. It then checks whether the edge causes a new cycle to form in the network: if a new cycle is formed, the edge is accepted and kept in the network, and the edge count is updated. If no new cycle is formed, discard the candidate edge and resample. This represents the lower bound of the shortest path length for candidate edges. This represents the upper bound of the shortest path length of the candidate edges. This represents the threshold value for the set clustering coefficient; values ​​below this threshold meet the selection criteria.

10. The infrastructure network resilience assessment method based on a three-phase dynamic mechanism according to claim 9, characterized in that: Multi-mode attack scenarios include random edge attacks, random point attacks, and randomness attacks.

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