Method and system for modeling resilience degradation of a cluster system based on functional higher-order networks

Abstract

The application discloses a kind of cluster system resilience degradation modeling methods based on function high-order network, this method is first obtained cluster node, communication relay, task target and task constraint parameter, communication cluster, collaborative perception group and task execution unit are abstracted as function hyperedge, and function high-order network is constructed;Second, based on correlation matrix and the projection network calculated high-order shortest path induced by current available communication, perception hyperedge, and according to collaborative scale, load demand, coverage radius and relay reachability determine the availability of three types of hyperedge;Finally, the task retention rate, communication retention rate, perception retention rate, high-order reachability and hyperdegree entropy are calculated, and the high-order function resilience sequence parameter is obtained by geometric average, and the resilience degradation curve, curve area and critical failure threshold are output.The application can avoid overestimating the cluster function retention capability of pair network connectivity by retaining the high-order closed condition that multiple nodes meet the task constraint together.

Description

Technical Field

[0001] This invention belongs to the field of cluster system resilience modeling and complex network analysis technology, and specifically relates to a method and system for cluster system resilience degradation modeling based on functional high-order networks. Background Technology

[0002] When performing tasks such as area search, collaborative coverage, emergency communication, target tracking, or payload delivery, the functionality of a cluster system depends not only on the connectivity between any two nodes, but also on whether multiple nodes can simultaneously meet constraints such as task coverage, payload capacity, communication relay reachability, and collaborative scale. Existing complex network resilience analyses often describe structural robustness using indicators such as nodes, paired edges, maximum connected components, degree distribution, or average path length. These indicators can reflect the topological connectivity after link or node failures, but they are insufficient to indicate whether the functional units formed by multiple nodes remain usable.

[0003] In typical engineering systems such as UAV swarms, a task often requires multiple UAVs, communication relay nodes, and the task target to jointly form a task execution unit; communication clusters and cooperative sensing groups also have obvious multi-entity cooperative attributes. If the above relationships are completely projected into ordinary pairwise networks, although pairwise connections can be obtained, the closure condition that "multiple nodes must simultaneously satisfy task constraints" will be lost, which may overestimate the actual functional retention capability of the system while the communication structure remains connected. Summary of the Invention

[0004] This invention addresses the technical problems of existing pairwise network resilience modeling, which struggles to explicitly characterize multi-body functional constraints in cluster systems and is prone to misinterpreting structural connectivity as functional preservation. It provides a cluster system resilience degradation modeling method and system based on high-order functional networks. This method simultaneously preserves high-order functional relationships, task constraints, and reachability constraints, characterizing the transition of a cluster system from a functionally ordered state to a functionally disordered state. It outputs resilience degradation curves, curve areas, and critical failure thresholds that can be used to compare different failure modes and improvement strategies.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The first aspect is a method for modeling the resilience degradation of cluster systems based on high-order functional networks, which includes the following steps:

[0007] S1. Obtain cluster system data and construct a high-order functional network including a set of nodes, a set of functional hyperedges, and a set of hyperedge weights;

[0008] S2. Divide the node set into the execution node set, the communication relay node set, and the task target node set; divide the functional hyperedge set into the communication cluster hyperedge set, the collaborative perception hyperedge set, and the task execution hyperedge set; construct an association matrix based on the membership relationship between nodes and hyperedges;

[0009] S3. Form a counting-type projective adjacency matrix based on the correlation matrix; use the counting-type projective adjacency matrix as the adjacency basis for constructing the projected network, calculate the higher-order shortest path on the projected network induced by the current set of live nodes and the current available communication cluster hyperedge and cooperative sensing hyperedge, and use it to evaluate the higher-order reachability of the UAV to the communication relay layer.

[0010] S4. Determine the availability of communication cluster hyperedge, collaborative sensing hyperedge, and task execution hyperedge;

[0011] S5. Calculate the task retention rate, communication retention rate, perception retention rate, higher-order reachability, and hyperextension based on the availability of the three types of hyperedges.

[0012] S6. Perform geometric averaging on task retention rate, communication retention rate, perception retention rate, higher-order reachability and super-entropy to obtain the higher-order functional resilience order parameters of the cluster system. Output the resilience degradation curve, resilience curve area and critical failure threshold under different failure ratios to complete the resilience degradation modeling of the cluster system.

[0013] Preferably, in S2, the communication cluster hyperedge represents a communication functional unit consisting of a communication relay node and a UAV that can form a stable communication relationship; the collaborative perception hyperedge represents a perception functional unit consisting of UAVs that can jointly cover the same area or form complementary observations; and the task execution hyperedge represents a task functional unit consisting of a task target node and UAVs participating in the task.

[0014] Preferably, S3 includes:

[0015] Select the currently available communication cluster hyperedges and cooperative sensing hyperedges, and project the node pairs within them as unweighted edges to obtain the projected network. :

[0016]

[0017] in, , These are its node set and edge set, respectively. For execution node set, For a set of communication relay nodes, Let be the set of surviving nodes at time t;

[0018] As a preferred option, S3 also includes:

[0019] Calculate the set of live and working communication relay nodes from the UAV node u on the projection network. higher-order shortest path :

[0020]

[0021] in, Represents projection network Middle node To relay node The shortest path length; if An empty or unmanned node u cannot reach any surviving communication relay node, causing It is positive infinity.

[0022] Preferably, S4 includes:

[0023] The current set of surviving candidate drones is determined based on the spatial location of the mission objective, the spatial location of the drones, the mission coverage radius, and the initial candidate set. If the number of drones in the current set of surviving candidate drones is not less than the minimum collaborative scale required by the mission, the total payload capacity of the candidate drones is not less than the mission payload requirement, and each candidate drone satisfies the condition that the higher-order shortest path is less than or equal to the higher-order hop count threshold, then the mission execution superedge is deemed available.

[0024] As a preferred option, S4 also includes:

[0025] If the relay node of the communication cluster superedge belongs to the set of working communication relay nodes, and the number of surviving UAV members in the communication cluster is not less than the minimum number of working members, the communication cluster superedge is determined to be usable; if the number of surviving UAV members of the collaborative sensing superedge is not less than the minimum collaborative sensing scale, the collaborative sensing superedge is determined to be usable.

[0026] As a preferred embodiment, S5 includes:

[0027] Task retention rate Communication retention rate Perception retention rate The calculation is as follows:

[0028]

[0029] in, , , These are the sets of initial task execution hyperedges, communication cluster hyperedges, and collaborative sensing hyperedges, respectively. For super-edge The weights;

[0030] Higher-order reachability is calculated as follows:

[0031]

[0032] in, Represents projection network The number of nodes in the largest connected component. This represents the total number of currently active drone nodes and communication relay nodes;

[0033] The entropy of transcendence is calculated as follows:

[0034]

[0035]

[0036] in, For surviving nodes The normalized percentage of super-degrees, For nodes The number of available functional superedges participating at time t.

[0037] As a preferred option, it also includes:

[0038] Calculate the function exposure score And according to the functional exposure score A descending order is used to generate a node failure sequence to simulate node failure scenarios that simultaneously perform high-order functional loads and communication bridging functions.

[0039]

[0040] in, The normalized value of node superdegree. For the betweenness centrality normalized value on the projection communication skeleton, This is the normalized value of the high-order functional resilience loss caused by a single node failure.

[0041] Secondly, a cluster system resilience degradation modeling system based on high-order functional networks includes:

[0042] The high-order functional network construction module is used to acquire cluster system data and construct a high-order functional network that includes a set of nodes, a set of functional hyperedges, and a set of hyperedge weights.

[0043] The node partitioning module is used to divide the node set into an execution node set, a communication relay node set, and a task target node set.

[0044] The hyperedge partitioning module is used to divide the functional hyperedge set into a communication cluster hyperedge set, a collaborative sensing hyperedge set, and a task execution hyperedge set;

[0045] The association matrix construction module is used to construct an association matrix based on the membership relationship between nodes and hyperedges;

[0046] The higher-order shortest path calculation module is used to form a counting projected adjacency matrix based on the correlation matrix; it calculates higher-order shortest paths on the projection network induced by the current set of surviving nodes and the current available communication cluster hyperedges and cooperative sensing hyperedges, and is used to evaluate the higher-order reachability of UAVs to the communication relay layer.

[0047] The hyperedge availability determination module is used to determine the availability of communication cluster hyperedges, collaborative sensing hyperedges, and task execution hyperedges;

[0048] The category-specific functional component calculation module is used to calculate the task retention rate, communication retention rate, perception retention rate, higher-order reachability, and hyper-entropy based on the availability of three types of hyperedges.

[0049] The resilience degradation modeling module is used to perform geometric averaging on task retention rate, communication retention rate, perception retention rate, higher-order reachability and super-entropy to obtain the higher-order functional resilience order parameters of the cluster system. It also outputs the resilience degradation curve, the area of ​​the resilience curve and the critical failure threshold under different failure ratios, thus completing the resilience degradation modeling of the cluster system.

[0050] The system for modeling the resilience degradation of cluster systems based on higher-order functional networks is used to implement the method and steps for modeling the resilience degradation of cluster systems based on higher-order functional networks in the first aspect.

[0051] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0052] This invention integrates the communication, sensing, and task execution relationships in a cluster system into a higher-order functional network, preserving the closed-loop condition that multiple nodes must jointly satisfy task constraints to form a usable functional unit, thus avoiding the loss of higher-order information caused by projecting the entire system into a pairwise network.

[0053] This invention introduces task coverage radius, minimum collaboration scale, load requirements and higher-order relay reachability into the hyperedge availability determination, so that whether a task function can be executed is jointly determined by spatial location, capability constraints and higher-order reachability, rather than simply determined by the number of nodes or pair connectivity.

[0054] This invention uses the geometric mean of task retention rate, communication retention rate, perception retention rate, higher-order reachability and super-entropy as a higher-order functional resilience order parameter, which can remain sensitive to the degradation of any bottleneck functional component, thereby more accurately identifying the functional collapse and critical degradation process of the cluster system.

[0055] This invention outputs a toughness degradation curve, a toughness curve area, and a critical failure threshold, which can be used to compare different disturbance mechanisms such as random failure, projection-priority failure, over-precision failure, and functional exposure-priority failure. It can also provide quantitative basis for redundant node deployment, communication relay enhancement, and task grouping adjustment. Attached Figure Description

[0056] Figure 1 This is a flowchart of the cluster system resilience degradation modeling method based on functional high-order networks of the present invention, which is used to illustrate the processing sequence from cluster system data acquisition, functional high-order network construction, node and hyperedge classification, association matrix and projection network generation, high-order shortest path calculation, hyperedge availability determination to resilience degradation result output.

[0057] Figure 2 This is a high-order network diagram of a UAV swarm with task constraints. It is used to show that the execution node, communication relay node and task target node form a functional unit in which multiple nodes jointly satisfy the constraints through communication cluster hyperedge, collaborative perception hyperedge and task execution hyperedge.

[0058] Figure 3 The curves represent the higher-order resilience degradation caused by different failure strategies under different cluster sizes, and are used to illustrate the decrease in higher-order functional resilience order parameters as the failure rate increases.

[0059] Figure 4 This is a comparison chart of critical failure thresholds under different failure modes, used to compare the differences in critical degradation of the system triggered by random failure, projection-priority failure, over-precision failure, and function exposure-priority failure.

[0060] Figure 5 This is a comparison chart of high-order functional resilience and baseline metrics under different failure mechanisms, used to illustrate that ordinary pairwise network metrics may overestimate the functional maintenance capability of cluster systems in some scenarios.

[0061] Figure 6 The functional resilience order parameter and structure-function component degradation diagrams under different failure mechanisms are used to illustrate the contributions of components such as task retention rate, communication retention rate, perception retention rate, higher-order reachability and super-entropy to the overall degradation.

[0062] Figure 7 A heatmap showing the correlation between different node metrics and single-node failure loss is used to illustrate the relationship between metrics such as excess, projection degree, and functional exposure score and the key node identification effect.

[0063] Figure 8 This is a graph showing the relationship between hyperedge overlap and higher-order functional resilience, used to illustrate the impact of the degree of overlap between functional hyperedges on the system's resilience degradation.

[0064] Figure 9 This is a comparison chart of different resilience enhancement strategies and baseline methods, used to demonstrate the improvement effects of strategies such as random redundancy, degree centrality redundancy, structural high-order hardening, and functional high-order hardening.

[0065] Figure 10The matrix and profile diagrams represent the resilience gains of different enhancement strategies, illustrating the distribution of resilience gains under different parameters and strategy combinations.

[0066] Figure 11 This is a parameter sensitivity plot showing the impact of communication radius, coverage radius, and load requirements on resilience degradation, used to illustrate the effect of changes in engineering constraints on the trunking system's ability to maintain functionality and the rate of degradation. Detailed Implementation

[0067] To make the technical means, inventive features, objectives, and effects of the invention readily understandable, the invention is further described below with reference to specific illustrations. However, the invention is not limited to the embodiments described below.

[0068] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0069] Example 1:

[0070] This embodiment uses a drone swarm as an example to illustrate the implementation process of the present invention. First, data such as swarm size, drone node locations, communication relay node locations, mission target locations, drone payload capacity, remaining energy, mission coverage radius, mission payload requirements, minimum coordination scale, and high-order hop count thresholds are collected. Execution nodes can be drone nodes, communication relay nodes can be relay drones, ground relay stations, or mobile communication nodes, and mission target nodes can be spatial targets to be covered, sensed, or serviced.

[0071] like Figure 1 As shown, the method flow of the present invention includes the following steps: cluster system data acquisition, construction of functional high-order network, classification of node and hyperedge types, generation of association matrix and projection network, determination of high-order shortest path and hyperedge availability, calculation of functional components, and output of resilience degradation results. Figure 1 This is used to explain the sequential relationship between each processing step and the data transfer relationship.

[0072] like Figure 2 As shown, in UAV swarm applications, execution nodes, communication relay nodes, and task target nodes form a functional unit where multiple nodes jointly satisfy constraints through communication cluster hyperedges, collaborative perception hyperedges, and task execution hyperedges. Figure 2 This invention is used to illustrate that it does not model solely based on pairwise connectivity, but rather uses the functional constraints formed by the combined action of multiple nodes as the object of resilience evaluation.

[0073] A system for modeling the resilience degradation of cluster systems based on high-order functional networks includes the following steps:

[0074] Step 1: Obtain node data, task target data, communication relay data, and task constraint parameters of the cluster system, and abstract the cluster system into a high-order functional network with hyperedge weights. ;

[0075] in, This represents the constructed high-order functional network. For a set of nodes, For a set of functional superedges, This is the set of weights corresponding to each functional hyperedge; this formula is used to give the overall representation of the modeling object of this invention.

[0076] Step 2: Divide the node set into execution node sets. Set of communication relay nodes and task target node set The hyperedge set is divided into communication cluster hyperedge sets. Collaborative sensing hyperedge set and task execution superedge set And construct an association matrix based on the membership relationship between nodes and hyperedges. ;

[0077]

[0078] in, For nodes With super-edge The elements of the correlation matrix; when belong When the value is 1, it does not belong to The value is set to 0, which is used to record the membership relationship between nodes and functional superedges.

[0079] A communication cluster hyperedge represents a communication functional unit consisting of a communication relay node and several UAVs that can form a stable communication relationship; a collaborative sensing hyperedge represents a sensing functional unit consisting of UAVs that can jointly cover the same area or form complementary observations; and a task execution hyperedge represents a task functional unit consisting of a task target node and the UAVs participating in the task.

[0080] Step 3: Form a counting type projective adjacency matrix based on the correlation matrix. And the projection network induced by the current set of surviving nodes and the currently available communication cluster hyperedges and cooperative sensing hyperedges. Calculate higher-order shortest paths ;

[0081] Step 3.1: When calculating paths and pairwise network baselines, a counting-type projective adjacency matrix Aij(t) is formed based on the correlation matrix. Aij(t) is not directly used as the final resilience index, but rather as the adjacency basis for constructing the projective network GH(t): when Aij(t) > 0, it indicates that node i and node j co-occur in at least one currently available communication cluster hyperedge or cooperative sensing hyperedge, and an unweighted projective edge is set in GH(t); when Aij(t) = 0, no edge is set. Therefore, the higher-order shortest path dGH(t)(u,r) is searched on the projective network induced by Aij(t) > 0, and Aij(t) participates in edge generation, adjacency determination, and reachability determination in path calculation. The counting-type projective adjacency matrix can also be used for projection degree and pairwise network baseline calculation, but it does not replace the higher-order information used for hyperedge availability determination and functional component calculation in the original functional higher-order network.

[0082]

[0083] in, For nodes With nodes Counting projected adjacent elements between them and Represents a node , Do they belong to the same superedge? This formula is used to count the number of superedges jointly participated in by two nodes, and sets the diagonal elements... It is 0.

[0084] In specific calculations, the projection network edge set EH(t) = {(i,j)|i,j∈VH(t),i≠j,Aij(t)>0} can be formed from Aij(t)>0. Then, dGH(t)(u,r) is calculated on GH(t) = (VH(t),EH(t)) using breadth-first search or equivalent shortest path algorithm. Thus, the role of Aij(t) is to convert the currently available high-order functional hyperedges into the adjacency relations required for path search, so that the reachability from the UAV node to the communication relay node can be quantified into the high-order shortest hop count.

[0085] Step 3.2: At time t, let... For the set of surviving nodes, This invention represents a set of surviving and operational communication relay nodes. First, it filters currently usable communication cluster hyperedges and cooperative sensing hyperedges, then projects the node pairs within these hyperedges as unweighted edges, resulting in a projected network. :

[0086]

[0087] in, Let be the projection network induced by the currently available communication cluster hyperedges and cooperative sensing hyperedges at time t. , These are its node set and edge set, respectively. Let be the set of surviving nodes at time t;

[0088] Step 3.3: Calculate the set of communication relay nodes from UAV node u to the UAV node u on the projection network. higher-order shortest path :

[0089]

[0090] in, Indicates drone node To the set of surviving and working communication relay nodes The higher-order shortest jump number, Represents projection network middle To relay node The shortest path length; if If node u is empty or a drone cannot reach any surviving communication relay node, then let Positive infinity. Higher-order shortest path. Used to evaluate the higher-order reachability of UAVs to the communication relay layer.

[0091] Step 4: Determine the availability of communication cluster superedge, collaborative sensing superedge, and task execution superedge based on the communication relay working status, collaborative sensing scale, task coverage radius, minimum collaborative scale, load requirements, and higher-order shortest path threshold, respectively.

[0092] For the task execution hyperedge e, firstly, based on the spatial location of the task target... UAV spatial location Task coverage radius and the initial candidate set Determine the current set of surviving candidate drones :

[0093]

[0094] in, Indicates the superedge of task execution at time t. The corresponding set of currently surviving candidate drones, For the task The initial candidate set, For the set of surviving nodes, and drones and mission objectives Spatial location, The radius is the mission coverage radius; this formula is used to filter candidate UAVs that still meet the spatial coverage conditions.

[0095] when The number of drones in the process shall not be less than the minimum coordination scale required by task e. Total payload capacity of candidate UAVs Not less than the mission payload requirement And each candidate drone meets the following requirements. ≤ At that time, it is determined that the task execution superedge e is available.

[0096]

[0097] in, Superedge for task execution Availability indicator at time t, For indicator functions, For the number of candidate drones, For the task Minimum required collaboration size For the total payload capacity of the candidate drones, To meet mission payload requirements, This is a high-order hop count threshold; the formula requires that the scale, load, and relay reachability be satisfied simultaneously for the task execution superedge to be available.

[0098] For a communication cluster superedge e, if its relay node belong Furthermore, the number of surviving drone members in the communication cluster is not less than the minimum number of working members. Then, the communication cluster's superedge is determined to be available:

[0099]

[0100] in, For communication cluster superedge Availability indicator at time t, For communication cluster superedge relay nodes, A set of working communication relay nodes. This refers to the set of drone members within the communication cluster. This represents the minimum number of working members; this formula is used to determine whether the communication cluster function can still provide communication support.

[0101] For a collaborative sensing hyperedge e, if the number of surviving drone members is not less than the minimum collaborative sensing scale... If the collaborative sensing hyperedge is found to be available, then it is determined that the hyperedge is usable. Therefore, communication, sensing, or task functional units that are no longer usable after a node fails will no longer provide false functional support for resilience assessment.

[0102]

[0103] in, For collaborative sensing of hyperedge Availability indicator at time t, Let UAV members be the set of members in this collaborative sensing hyperedge. This represents the minimum scale of collaborative sensing; this formula is used to determine whether the collaborative sensing function is still available.

[0104] Step 5: Calculate the task retention rate based on the availability of the three types of hyperedges. Communication retention rate Perception retention rate Higher-order accessibility and transcendence entropy ;

[0105] After obtaining the availability of the three types of hyperedges, this invention calculates the task retention rate for each. Communication retention rate and perception retention rate The retention rates mentioned above all use the sum of the weights of the initial set of similar hyperedges as the denominator and the sum of the weights of the currently available similar hyperedges as the numerator. Therefore, they represent the proportion of the initial functional requirements that are still maintained in the current state.

[0106]

[0107] in, , , These represent the task retention rate, communication retention rate, and perception retention rate, respectively. , , These are the sets of initial task execution hyperedges, communication cluster hyperedges, and collaborative sensing hyperedges, respectively. For super-edge The weights; this formula measures the degree of preservation of the three types of functions by the proportion of the currently available hyperedge weights to the sum of the initial hyperedge weights.

[0108] Furthermore, in projection networks induced by available communication cluster hyperedges and cooperative sensing hyperedges... Calculate the percentage of the largest connected component. :

[0109]

[0110] in, As a high-order accessibility metric, Represents projection network The number of nodes in the largest connected component. This represents the total number of currently surviving drone nodes and communication relay nodes; this formula is used to measure the overall connectivity of the current communication projection network.

[0111] Simultaneously, the normalized superdegree ratio is calculated based on the number of available superedges participated in by surviving nodes. and transcendence entropy When higher-order functional workloads are evenly distributed across the surviving nodes, Approaching 1; when a large number of functional hyperedges rely on a few key nodes, Close to 0.

[0112]

[0113] in, For surviving nodes The normalized percentage of super-degrees, For nodes The number of available functional superedges participating at time t. The number of surviving nodes is represented by this formula, which normalizes the high-order functional load borne by each surviving node into a probability distribution.

[0114]

[0115] in, To reduce entropy, To normalize the percentage of deliverance, The value represents the number of surviving nodes. This formula is used to characterize the degree of dispersion of high-order functional workloads among surviving nodes. The lower the value, the more concentrated the functionality depends on a few nodes.

[0116] Step 6: Task retention rate Communication retention rate Perception retention rate Higher-order accessibility and transcendence entropy Geometric averaging is performed to obtain the higher-order functional resilience order parameters of the cluster system. The system outputs toughness degradation curves, toughness curve areas, and critical failure thresholds under different failure ratios, thus completing the toughness degradation modeling of the cluster system.

[0117]

[0118] in, For higher-order functional toughness order parameters. express Category Functional Components Pick , , , , These correspond to the task, communication, perception, reachability, and hyperentropy components, respectively. To avoid the extremely small positive number that causes product degradation due to zero value, this formula integrates the five functional components through normalized geometric mean to reflect the overall functional resilience of the cluster system.

[0119] This invention will , , , and Add the smallest positive number Then, a normalized geometric mean was performed to obtain the higher-order functional toughness order parameter. Geometric mean causes the overall order parameter to decrease when any functional component degrades significantly, which can reflect the complementary deficiencies among task execution, communication coordination, perception coordination, higher-order reachability, and load balancing.

[0120] In the resilience degradation simulation, a node failure sequence is generated according to random failure, projection-priority failure, hyperedge-priority failure, or functional exposure-priority failure, and a corresponding node is removed for each failure proportion f. After each removal, the availability of the three types of hyperedges is reassessed, and the projection network is reconstructed. Calculate the resilience of higher-order functions ordinary pairwise network resilience Compared with traditional connectivity metrics Finally, for Integrating the curve yields the area of ​​the toughness curve. :

[0121]

[0122] in, The area under the toughness curve is... Failure rate The higher-order functional toughness order parameter. To maximize the failure rate, this formula quantifies the overall resilience of the system throughout the entire failure process by integrating the toughness degradation curve.

[0123] And record First time below the degradation threshold Critical failure threshold at time :

[0124]

[0125] in, This is the critical failure threshold. To preset the degradation threshold, Failure rate The higher-order functional resilience order parameter is used to determine the failure rate when the system resilience first falls below the threshold.

[0126] like Figures 3 to 6 As shown, RH(f) degradation curves, critical failure thresholds, and degradation curves of each functional component can be plotted under different cluster sizes and different failure strategies. Figure 3 Used to demonstrate the decay trend of higher-order toughness as the failure rate increases; Figure 4 Used to compare the differences in thresholds that trigger critical degradation under different perturbation modes; Figure 5 This is used to illustrate that paired network baselines may overestimate the system's ability to retain functionality in certain scenarios; Figure 6 Used to demonstrate the contribution of components such as task, communication, perception, accessibility, and hyperentropy to the overall degradation.

[0127] Example 2: Evaluation of Functional Exposure Priority Failure and Improvement Strategies

[0128] To identify critical nodes more likely to trigger critical degradation, this invention can calculate a functional exposure score based on the node's superdegree normalized value, the betweenness centrality normalized value on the projected communication framework, and the normalized value of higher-order functional resilience loss caused by single-node failure. and in accordance with Node failure sequences are generated in descending order. Functional exposure priority failure can simulate node failure scenarios that simultaneously undertake high-order functional loads and communication bridging functions.

[0129]

[0130] in, For nodes Functional exposure score, The normalized value of node superdegree. For the betweenness centrality normalized value on the projection communication skeleton, This is a normalized value for the loss of high-order functional resilience caused by a single node failure; this formula is used to identify critical nodes that simultaneously undertake high-order functional loads and communication bridging functions.

[0131] This invention can also compare different resilience enhancement strategies under the same redundancy budget. The stochastic redundancy strategy does not use network structure information; the degree-centrality-only strategy selects nodes with high projectivity based on ordinary pairwise projective networks; the structural high-order hardening strategy uses node excess, curvature exposure, and high-order functional participation to identify structural bottlenecks; the functional high-order hardening strategy further combines task location, load capacity, remaining energy, and relay reachability. By comparing different strategies... , and This can provide quantitative basis for backup drone deployment, task grouping adjustment, and communication relay enhancement.

[0132] like Figures 7 to 11 As shown, the node index heatmap, hyperedge overlap relationship, comparison of improvement strategies, resilience benefit matrix and parameter sensitivity results can be used to explain the failure of key nodes and the mechanism of resilience improvement. Figure 7 Used to compare the correlation between node metrics such as extent, projection, and functional exposure score and single-node failure loss; Figure 8 Used to illustrate the effect of hyperedge overlap on functional high-order toughness; Figure 9 and Figure 10 Used to compare the resilience gains of different redundancy and hardening strategies; Figure 11 This is used to illustrate the impact of changes in communication radius, coverage radius, and payload requirements on the degradation process, thereby providing a basis for relay enhancement, backup UAV configuration, and mission parameter adjustments.

[0133] Example 3:

[0134] A cluster system resilience degradation modeling system based on high-order functional networks includes:

[0135] The high-order functional network construction module is used to acquire cluster system data and construct a high-order functional network that includes a set of nodes, a set of functional hyperedges, and a set of hyperedge weights.

[0136] The node partitioning module is used to divide the node set into an execution node set, a communication relay node set, and a task target node set.

[0137] The hyperedge partitioning module is used to divide the functional hyperedge set into a communication cluster hyperedge set, a collaborative sensing hyperedge set, and a task execution hyperedge set;

[0138] The association matrix construction module is used to construct an association matrix based on the membership relationship between nodes and hyperedges;

[0139] The higher-order shortest path calculation module is used to form a counting projected adjacency matrix based on the correlation matrix; it calculates higher-order shortest paths on the projection network induced by the current set of live nodes and the current available communication cluster hyperedges and cooperative sensing hyperedges, and is used to evaluate the higher-order reachability of UAVs to the communication relay layer.

[0140] The hyperedge availability determination module is used to determine the availability of communication cluster hyperedges, collaborative sensing hyperedges, and task execution hyperedges;

[0141] The category-specific functional component calculation module is used to calculate the task retention rate, communication retention rate, perception retention rate, higher-order reachability, and hyper-entropy based on the availability of three types of hyperedges.

[0142] The resilience degradation modeling module is used to perform geometric averaging on task retention rate, communication retention rate, perception retention rate, higher-order reachability and super-entropy to obtain the higher-order functional resilience order parameters of the cluster system. It also outputs resilience degradation curves, resilience curve area and critical failure thresholds under different failure ratios to complete the resilience degradation modeling of the cluster system.

Claims

1. A method for modeling the resilience degradation of cluster systems based on high-order functional networks, characterized in that, Includes the following steps: S1. Obtain cluster system data and construct a high-order functional network including a set of nodes, a set of functional hyperedges, and a set of hyperedge weights; S2. Divide the node set into the execution node set, the communication relay node set, and the task target node set; divide the functional hyperedge set into the communication cluster hyperedge set, the collaborative perception hyperedge set, and the task execution hyperedge set; construct an association matrix based on the membership relationship between nodes and hyperedges; S3. Form a counting-type projective adjacency matrix based on the correlation matrix; use the counting-type projective adjacency matrix as the adjacency basis for constructing the projected network, calculate the higher-order shortest path on the projected network induced by the current set of live nodes and the current available communication cluster hyperedge and cooperative sensing hyperedge, and use it to evaluate the higher-order reachability of the UAV to the communication relay layer. S4. Determine the availability of communication cluster hyperedge, collaborative sensing hyperedge, and task execution hyperedge; S5. Calculate the task retention rate, communication retention rate, perception retention rate, higher-order reachability, and hyperextension based on the availability of the three types of hyperedges. S6. Perform geometric averaging on task retention rate, communication retention rate, perception retention rate, higher-order reachability and super-entropy to obtain the higher-order functional resilience order parameters of the cluster system. Output the resilience degradation curve, resilience curve area and critical failure threshold under different failure ratios to complete the resilience degradation modeling of the cluster system.

2. The method for modeling the resilience degradation of cluster systems based on functional high-order networks according to claim 1, characterized in that, In S2, the communication cluster hyperedge represents a communication functional unit consisting of a communication relay node and a UAV that can form a stable communication relationship; the collaborative perception hyperedge represents a perception functional unit consisting of UAVs that can jointly cover the same area or form complementary observations; and the task execution hyperedge represents a task functional unit consisting of a task target node and UAVs participating in the task.

3. The method for modeling the resilience degradation of cluster systems based on functional high-order networks according to claim 1, characterized in that, S3 includes: Select the currently available communication cluster hyperedges and cooperative sensing hyperedges, and project the node pairs within them as unweighted edges to obtain the projected network. : ； in, , These are its node set and edge set, respectively. For execution node set, For a set of communication relay nodes, Let be the set of surviving nodes at time t.

4. The method for modeling the resilience degradation of cluster systems based on functional high-order networks according to claim 3, characterized in that, S3 also includes: Calculate the set of live and working communication relay nodes from the UAV node u on the projection network. higher-order shortest path : ； in, Represents projection network Middle node To relay node The shortest path length; if An empty or unmanned node u cannot reach any surviving communication relay node, causing It is positive infinity.

5. The method for modeling the resilience degradation of cluster systems based on functional high-order networks according to claim 1, characterized in that, S4 includes: The current set of surviving candidate drones is determined based on the spatial location of the mission objective, the spatial location of the drones, the mission coverage radius, and the initial candidate set. If the number of drones in the current set of surviving candidate drones is not less than the minimum collaborative scale required by the mission, the total payload capacity of the candidate drones is not less than the mission payload requirement, and each candidate drone satisfies the condition that the higher-order shortest path is less than or equal to the higher-order hop count threshold, then the mission execution superedge is deemed available.

6. The method for modeling the resilience degradation of cluster systems based on functional high-order networks according to claim 5, characterized in that, S4 also includes: If the relay node of the communication cluster superedge belongs to the set of working communication relay nodes, and the number of surviving UAV members in the communication cluster is not less than the minimum number of working members, the communication cluster superedge is determined to be usable; if the number of surviving UAV members of the collaborative sensing superedge is not less than the minimum collaborative sensing scale, the collaborative sensing superedge is determined to be usable.

7. The method for modeling the resilience degradation of cluster systems based on functional high-order networks according to claim 1, characterized in that, S5 include: Task retention rate Communication retention rate Perception retention rate The calculation is as follows: ； in, , , These are the sets of initial task execution hyperedges, communication cluster hyperedges, and collaborative sensing hyperedges, respectively. For super-edge The weights; Higher-order reachability is calculated as follows: ； in, Represents projection network The number of nodes in the largest connected component. This represents the total number of currently active drone nodes and communication relay nodes; The entropy of transcendence is calculated as follows: ； ； in, For surviving nodes The normalized percentage of super-degrees, For nodes The number of available functional superedges participating at time t.

8. The method for modeling the resilience degradation of cluster systems based on functional high-order networks according to claim 1, characterized in that, Also includes: Calculate the function exposure score And according to the functional exposure score A descending order is used to generate a node failure sequence to simulate node failure scenarios that simultaneously perform high-order functional loads and communication bridging functions. ； in, The normalized value of node superdegree. For the betweenness centrality normalized value on the projection communication skeleton, This is the normalized value of the high-order functional resilience loss caused by a single node failure.

9. A cluster system resilience degradation modeling system based on high-order functional networks, characterized in that, include: The high-order functional network construction module is used to acquire cluster system data and construct a high-order functional network that includes a set of nodes, a set of functional hyperedges, and a set of hyperedge weights. The node partitioning module is used to divide the node set into an execution node set, a communication relay node set, and a task target node set. The hyperedge partitioning module is used to divide the functional hyperedge set into a communication cluster hyperedge set, a collaborative sensing hyperedge set, and a task execution hyperedge set; The association matrix construction module is used to construct an association matrix based on the membership relationship between nodes and hyperedges; The higher-order shortest path calculation module is used to form a counting projected adjacency matrix based on the correlation matrix; it calculates higher-order shortest paths on the projection network induced by the current set of surviving nodes and the current available communication cluster hyperedges and cooperative sensing hyperedges, and is used to evaluate the higher-order reachability of UAVs to the communication relay layer. The hyperedge availability determination module is used to determine the availability of communication cluster hyperedges, collaborative sensing hyperedges, and task execution hyperedges; The category-specific functional component calculation module is used to calculate the task retention rate, communication retention rate, perception retention rate, higher-order reachability, and hyper-entropy based on the availability of three types of hyperedges. The resilience degradation modeling module is used to perform geometric averaging on task retention rate, communication retention rate, perception retention rate, higher-order reachability and super-entropy to obtain the higher-order functional resilience order parameters of the cluster system. It also outputs the resilience degradation curve, the area of ​​the resilience curve and the critical failure threshold under different failure ratios, thus completing the resilience degradation modeling of the cluster system. The cluster system resilience degradation modeling system based on functional high-order networks is used to implement the cluster system resilience degradation modeling method and steps based on functional high-order networks as described in claim 1.

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