Unmanned system toughness analysis and improvement method based on multi-level flow betweenness and adjacency entropy

Abstract

The invention discloses an unmanned system toughness analysis and improvement method based on multi-level flow betweenness and adjacency entropy, and the method comprises the steps: firstly constructing a function dependence network model, so as to accurately describe the dependency relationship between detection, control and execution in an unmanned system and each function level of a target; then, a multi-layer flow betweenness-adjacency information entropy fusion algorithm is provided, and key nodes in the system are accurately identified by comprehensively calculating the multi-layer flow betweenness, interlayer entropy, intra-layer entropy and cross-layer connection coefficients of the nodes; and finally, constructing an anti-recovery oriented toughness enhancement framework which adopts a Lagrangian damping non-smooth Newton method to optimally allocate protection resources in a resistance stage so as to strengthen key nodes, and adopts a network block decomposition method to dynamically reconstruct a damaged network in a recovery stage so as to quickly recover task capability. According to the method, the key nodes can be comprehensively and accurately identified, and the overall toughness of the unmanned system under confrontation disturbance is systematically improved.

Description

Technical Field

[0001] This invention belongs to the field of unmanned systems and complex network technology, specifically relating to a method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy. Background Technology

[0002] With the continuous improvement of the intelligence and clustering of unmanned systems, Unmanned Systems of Business (USoS) have become a core force in performing complex tasks such as rescue operations. This system forms a closed-loop "detection-control-execution-evaluation" mission circuit through the functional collaboration of heterogeneous unmanned platforms to achieve mission objectives. However, USoS are highly susceptible to multi-source disturbances such as interference in complex adversarial environments, leading to the failure of critical nodes, interruption of the mission circuit, and severely weakening the overall mission execution efficiency of the system. Therefore, accurately identifying the critical nodes that maintain the system's functionality and effectively improving their resilience and recovery capabilities after being disturbed are key to ensuring the continuous and reliable operation of USoS.

[0003] Currently, there are some studies on the identification of key nodes and the improvement of resilience in USoS, but there are still obvious limitations:

[0004] In identifying critical nodes, existing methods are mostly based on traditional network centrality metrics, such as degree centrality, betweenness centrality, and proximity centrality. These methods primarily rely on the static topology of the network and fail to fully consider the dynamic information flow characteristics of nodes in multi-layered functional networks and the functional dependencies across layers. In systems like USoS with clear functional layers (such as the probe layer, control layer, execution layer, and target layer), the importance of a node depends not only on the number of its connections but also on its ability to relay information, transmit instructions, and cooperate between different layers. Traditional single topology metrics are insufficient to comprehensively characterize the functional roles and dynamic contributions of nodes in multi-layered networks, resulting in inaccurate identification results that often overlook or misjudge critical nodes that play a decisive role in the integrity of the task loop.

[0005] Regarding resilience enhancement, existing strategies largely separate node-level hardening (protection resource allocation) from network-level reconstruction (topology restoration), lacking an integrated resilience enhancement framework. During the disturbance resistance phase, existing resource allocation methods often lack efficient solutions for optimizing protection resource allocation, making it difficult to maximize the system's expected performance under resource-constrained conditions. During the recovery phase, existing reconstruction strategies primarily focus on restoring local connectivity, neglecting the need for rapid reconstruction of the complex task loop structure composed of multiple functional nodes in the USoS. This results in slow system recovery after multiple node failures, or even an inability to recover to a state capable of performing basic tasks.

[0006] In summary, the current field lacks a method for identifying key nodes that can systematically integrate multi-layer network topology, dynamic information flow, and functional collaboration relationships. It also lacks a resilience enhancement framework that organically integrates proactive protection and dynamic recovery, thus hindering further improvements in the survivability and adaptive recovery capabilities of USoS in complex adversarial environments. Therefore, a more comprehensive, accurate, and efficient resilience analysis and enhancement method is urgently needed to support the resilient design and resource optimization of USoS under uncertain disturbance environments. Summary of the Invention

[0007] To address the limitations of existing technologies in accurately quantifying the performance maintenance and recovery capabilities of unmanned systems under multiple disturbances, and in comprehensively characterizing their functionally dependent structures and dynamic resilience, this invention delves into the topological functions and information flow characteristics of nodes in multi-layer networks. It proposes a method for analyzing and enhancing the resilience of unmanned systems based on multi-layer flow betweenness and adjacency entropy. By integrating the topological structure of multi-layer networks with dynamic information flow characteristics, it accurately identifies key nodes and constructs an integrated anti-recovery enhancement framework, thereby significantly improving the overall resilience of unmanned systems under complex disturbance environments.

[0008] The concept and principle of this invention:

[0009] First, to address the functional heterogeneity of USoS, a Function Dependent Network (FDN) model is constructed to accurately describe the interaction relationships between the functional levels of "detection-control-execution-target". Then, considering the multidimensional representation of node criticality, a critical node identification method based on Multilayer Flow Betweenness-Adjacency Information Entropy (MLFB-AIE) is proposed, integrating topology structure and information dynamics, to accurately quantify the contribution of nodes to network stability and information transmission. Finally, based on the above evaluation and identification results, a resilience enhancement framework oriented towards recovery (RR-REF) is constructed: in the resistance phase, the Lagrange damped nonsmooth Newton (L-DNSN) method is used to solve for the optimal resource allocation solution to strengthen critical nodes; in the recovery phase, the Network Block Decomposition (NBD) method is used to dynamically reconstruct the damaged topology and quickly restore the operational loop.

[0010] The technical solution of this invention is as follows:

[0011] A method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy includes the following steps:

[0012] Step S1: Construct the functional dependency network model of the unmanned system;

[0013] Step S2: Based on the functionally dependent network model, calculate the comprehensive centrality of nodes by fusing the multi-level flow betweenness and adjacency information entropy to identify key nodes;

[0014] Step S3: Based on the key node identification results, the unmanned system is reinforced using an anti-recovery-oriented resilience enhancement framework. The framework includes a resource allocation strategy based on the Lagrange damped non-smooth Newton method during the resistance phase, and a dynamic reconstruction strategy based on network block decomposition during the recovery phase.

[0015] Furthermore, in step S1, constructing the functional dependency network model of the unmanned system specifically includes:

[0016] Step S1.1: The detection nodes in the unmanned system Control Node Execution Node and target node They are each constructed as independent network layers;

[0017] Step S1.2: Construct directed edges between the nodes, including intra-layer edges and inter-layer edges, wherein the inter-layer edges include at least... , , and Four types, with at least the inner edge of the layer including , and Three types.

[0018] Furthermore, in step S2, the specific process for identifying key nodes is as follows:

[0019] Step S2.1: Define and calculate the multi-level flow betweenness of the node;

[0020] Step S2.2: Based on the multi-layer flow betweenness, calculate the inter-layer entropy and intra-layer entropy of the node respectively; the inter-layer entropy is used to quantify the distribution balance of information interaction between the node and its upper and lower layer neighbors; the intra-layer entropy is used to quantify the distribution balance of collaborative cooperation between the node and its same-layer neighbors;

[0021] Step S2.3: Calculate the cross-layer connection coefficient of the node. The cross-layer connection coefficient comprehensively reflects the node's ability to receive and issue instructions in the vertical direction, as well as its collaborative ability in the horizontal direction.

[0022] Step S2.4: Normalize the interlayer entropy and intralayer entropy, and apply a gain function to the normalized intralayer entropy to amplify the synergistic effect it represents, and obtain the synergistic gain coefficient.

[0023] Step S2.5: Based on the normalized inter-layer entropy, the cooperative gain coefficient, and the cross-layer connectivity coefficient, the final comprehensive centrality of the node is obtained through a comprehensive calculation function.

[0024] Furthermore, in step S2.1, the multi-level flow betweenness of a node is calculated through the following process: setting the maximum number of propagation steps related to the number of network layers; initializing each node as an information source in sequence; simulating the multi-step propagation process in which information is evenly distributed from the node carrying the information to all its outgoing neighbor nodes in each step; counting the total amount of information received by each node after all propagation is completed; and calculating the ratio of the total amount of information to the initial total amount of information in the entire network as the multi-level flow betweenness of the node.

[0025] Furthermore, in step S2.2, the method for calculating the interlayer entropy is as follows:

[0026]

[0027] in It is the input-output centrality weighting adjustment coefficient. and These represent the probability distributions of inbound and outbound information, respectively; the method for calculating the layer entropy is as follows:

[0028]

[0029] in This represents the probability distribution of collaborative information within the layer.

[0030] Furthermore, in step S2.3, the cross-layer connection coefficient of the node The calculation method is as follows:

[0031]

[0032] in, , and These represent the number of neighbors on the upper and lower floors and on the same floor, respectively. To maximize the network's extent, used for normalization; and The weighting coefficients and ; The function is used to prevent numerical saturation.

[0033] Furthermore, in step S2.4, the cooperative gain coefficient The calculation method is as follows:

[0034]

[0035] in To normalize the layer entropy, This is the gain function.

[0036] Furthermore, in step S2.5, the comprehensive calculation function is:

[0037]

[0038] in, This is the normalized interlayer entropy. For the cooperative gain coefficient, This represents the cross-layer connectivity coefficient.

[0039] Furthermore, in step S3, the resource allocation strategy based on the Lagrange damped non-smooth Newton method in the resistance phase specifically involves: establishing an optimization model with the goal of maximizing the expected network performance after an attack and constrained by total protection resources; using the Lagrange multiplier method to process the constraints and construct the Lagrange function; and using the damped non-smooth Newton method to iteratively solve for the optimal solution that satisfies the KKT conditions to obtain the optimal resource allocation scheme for key nodes.

[0040] Furthermore, in step S3, the dynamic reconstruction strategy based on network block decomposition in the recovery phase specifically includes:

[0041] Block destructuring identifies and removes failed nodes and their associated edges;

[0042] Block reconstruction involves relocating available nodes from redundant network blocks to damaged network blocks.

[0043] Block switching involves sorting and merging damaged blocks based on their target value when block reconstruction is not feasible, thereby redistributing tasks.

[0044] Beneficial effects

[0045] The advantages of this invention are:

[0046] 1. This invention provides a complete resilience management solution from accurate identification and scientific evaluation to proactive enhancement, providing systematic theoretical and technical guidance for the resilient design and resource allocation of USoS under uncertain disturbance environments.

[0047] 2. The critical node identification method (MLFB-AIE) proposed in this invention breaks through the limitations of traditional topological centrality indicators. By innovatively integrating "multi-layer flow betweenness" and "adjacency information entropy", it not only considers the global topological hub role of nodes, but also characterizes their interaction balance and intra-layer synergy among multiple layers. It breaks through the limitations of traditional single structural indicators, and the identification results are more comprehensive and accurate. It can effectively reveal nodes that play a decisive role in the functional loop of the system. Under deliberate attacks, it can more quickly dismantle the opponent's network or more effectively protect one's own network.

[0048] 3. The resilience enhancement framework (RR-REF) constructed in this invention organically combines proactive hardening with dynamic recovery, forming a closed loop of resilience management covering the entire disturbance process. The optimal resource allocation model in the resistance phase improves protection efficiency; the network block decomposition and reconstruction strategy in the recovery phase enables rapid recovery of task-oriented capabilities. Case studies have verified that it can significantly improve the overall system resilience and elasticity factors at each stage, demonstrating good applicability and superiority for various failure modes.

[0049] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0050] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0051] Figure 1 : The hierarchical structure of a function-dependent network model;

[0052] Figure 2 : The edge structure of the function-dependent network model;

[0053] Figure 3 : The internal topology of a network block; (1) basic network block, (2) redundant network block, (3) damaged network block;

[0054] Figure 4 : Topology reconstruction process based on NBD;

[0055] Figure 5 A typical USoS network topology;

[0056] Figure 6 Node centrality correlation metrics based on MFLB-AIE;

[0057] Figure 7 Distribution of node importance across different nodes;

[0058] Figure 8 Under sequential deliberate attacks, the network performance degradation after different methods identify key nodes;

[0059] Figure 9 Under rule-based deliberate attacks, the network performance degradation after different methods identify key nodes;

[0060] Figure 10 Performance trajectory of USoS before and after reinforcement strategy in random failure scenarios;

[0061] Figure 11 Performance trajectory of USoS before and after hardening strategy in a deliberate attack scenario;

[0062] Figure 12 Performance trajectory of USoS before and after reinforcement strategy in mixed fault scenarios;

[0063] Figure 13 Performance curves of USoS under different optimization methods in random failure scenarios;

[0064] Figure 14 Performance curves of USoS under different optimization methods in intentional attack scenarios;

[0065] Figure 15 Performance curves of USoS under different optimization methods in mixed fault scenarios. Detailed Implementation

[0066] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0067] This embodiment proposes a method for resilience analysis and enhancement of unmanned systems based on multi-level flow betweenness and adjacency entropy. By integrating multi-level network topology and dynamic information flow characteristics, it accurately identifies key nodes and constructs an integrated anti-recovery enhancement framework, thereby significantly improving the overall resilience of unmanned systems in complex disturbance environments. Specifically, it includes the following steps:

[0068] Step S1: Construct the functional dependency network model of the unmanned system.

[0069] To address the functional heterogeneity of unmanned systems, a multi-layered directed functional dependency network model is constructed. The entity nodes in the system are divided into four independent layers based on their functions: detection nodes, control nodes, execution nodes, and target nodes. By defining intra-layer edges (such as information sharing between detection nodes, command interaction between control nodes, and collaborative cooperation between execution nodes) and inter-layer edges (such as detection nodes reporting information to control nodes and control nodes issuing commands to execution nodes), the functional dependencies and information flow relationships between nodes in the "detection-control-execution-target" task loop are accurately described, laying a structural foundation for subsequent analysis.

[0070] Step S1.1: Node Definition and Hierarchy. Entities in USoS are divided into four functional types and placed at different levels: the probe nodes... Control Node Execution Node and target node Each layer is constructed as an independent network layer, with the function depending on the hierarchical structure of the network model, as follows: Figure 1 As shown.

[0071] Step S1.2: Construct directed edges between the nodes, including intra-layer edges and inter-layer edges, wherein the inter-layer edges include at least... , , and Four types, with at least the inner edge of the layer including , and The three types and the specific meanings of these seven types of directed edges are shown in Table 1 below. The edge structure of the function-dependent network model is as follows: Figure 2 As shown.

[0072] Table 1 Directed edges of nodes

[0073]

[0074] Step S2: Based on the functionally dependent network model, calculate the comprehensive centrality of nodes by fusing the multi-level flow betweenness and adjacency information entropy to identify key nodes.

[0075] Step S2.1: Multi-level Flow Betweenness Number (MLFB) Calculation. MLFB measures a node's hub capacity in the network information diffusion process. Its calculation process is a multi-step information propagation simulation, simulating the process of information propagating in a multi-level network in a multi-step and uniform manner. It counts the proportion of the total amount of information received by each node during propagation, thereby quantifying the global importance of the node as an information flow hub.

[0076] Step S2.1.1: Initialization. Set the maximum propagation steps D. Each node acts as an information source in turn, holding the initial amount of information. .

[0077] Step S2.1.2: Propagation Simulation. For each step, each node carrying information distributes its current total information equally among all its outgoing neighbor nodes, and then resets its own information to 0.

[0078] Step S2.1.3: Result Statistics. After completing a maximum of D propagation steps, perform statistics for each node. The total amount of information received from all source nodes.

[0079] Step S2.1.4: Calculate the multi-level flow betweenness number (MLFB). Node The multi-level flow betweenness is the sum of the total amount of received information and the total amount of initial information in the entire network ( The ratio of ) to . The calculation formula is as follows:

[0080] (1)

[0081] in, Represents a node The set of all neighboring nodes, This represents the initial total amount of network information. Represents a node The total amount of source information received from all neighboring nodes.

[0082] Step S2.2: Calculate the adjacency information entropy based on the multi-layer flow betweenness of nodes. From the perspective of information theory, calculate the inter-layer entropy (quantifying the distribution balance of information interaction with upper and lower layer neighbors) and intra-layer entropy (quantifying the distribution balance of collaborative cooperation with same-layer neighbors) of nodes to characterize the diversity of node connections and the intensity of functional cooperation.

[0083] Step S2.2.1: Calculate the inter-layer entropy, which is used to quantify the distribution balance of nodes and their upstream and downstream neighbors when exchanging information. The calculation formula is as follows:

[0084] (2)

[0085] in, It is the input-output centrality weight adjustment coefficient. and Let be the probability distributions of the incoming and outgoing information, respectively, and expressed as:

[0086] (3)

[0087] (4)

[0088] in, and These are nodes The set of neighbors on the upper and lower levels.

[0089] Step S2.2.2: Calculate the intra-layer entropy, which is used to quantify the distribution balance of nodes and their peers during collaborative cooperation. The calculation formula is as follows:

[0090] (5)

[0091] in, The probability distribution of intra-layer collaborative information is expressed as:

[0092] (6)

[0093] in, It is a node The set of neighbors on the same floor.

[0094] Step S2.3: Calculate the cross-layer connectivity coefficient of the node. Based on the number of topological connections between the node and its neighbors in the upper, lower, and same layers, this coefficient quantifies the node's connectivity advantage from a purely topological perspective. The calculation formula is as follows:

[0095] (7)

[0096] in, , and These represent the number of neighbors on the upper and lower floors and on the same floor, respectively. To maximize the network's extent, used for normalization; and The weighting coefficients and ; The function is used to prevent numerical saturation.

[0097] Step S2.4: Normalize the interlayer entropy and intralayer entropy, and apply a gain function to the normalized intralayer entropy to amplify the synergistic effect it represents, obtaining the synergistic gain coefficient:

[0098] interlayer entropy and intralayer entropy Perform min-max normalization to obtain and As shown below:

[0099] (8)

[0100] (9)

[0101] Subsequently, a sigmoid gain function is applied to the entropy within the normalized layer: The cooperative gain coefficient is obtained. This step aims to amplify the elasticity gains brought about by high-level synergy.

[0102] Step S2.5: Based on the normalized inter-layer entropy, the cooperative gain coefficient, and the cross-layer connectivity coefficient, the final comprehensive centrality of the node is obtained through a comprehensive calculation function. Based on this value, the critical nodes essential for maintaining network stability and task loop integrity can be accurately identified. The comprehensive calculation function is:

[0103] (10)

[0104] according to By sorting the nodes, the key nodes in USoS can be identified.

[0105] Step S3: Based on the key node identification results, the unmanned system is reinforced using an anti-recovery-oriented resilience enhancement framework. The framework includes a resource allocation strategy based on the Lagrange damped non-smooth Newton method during the resistance phase, and a dynamic reconstruction strategy based on network block decomposition during the recovery phase.

[0106] In the resistance phase, an optimal resource allocation strategy based on the Lagrange-damped non-smooth Newton's method is adopted: an optimization model is established with the goal of maximizing the expected network performance after an attack, constrained by total protection resources. The Lagrange-damped non-smooth Newton's method is used to solve the model, yielding the optimal protection resource allocation scheme for critical nodes. This scheme, under limited resource conditions, scientifically allocates resources to the nodes that most affect overall performance, maximizing the system's survivability in the disturbance resistance phase, as detailed below:

[0107] Step S3.1: Resistance Phase: Resource allocation strategy based on Lagrange-damped nonsmooth Newton's method (L-DNSN). This step aims to optimally allocate limited protection resources to critical nodes to maximize the expected performance of the unmanned system after an attack. The specific implementation steps are as follows:

[0108] Step S3.1.1: Establish the optimization model. First, determine the optimization objective: maximize the expected performance of the network. The expression is:

[0109] (11)

[0110] in, For nodes The network performance loss caused by the failure is determined by the aforementioned comprehensive centrality or its contribution in the task loop; For nodes The inherent failure probability depends on the attack strength and the vulnerability of the node itself; For nodes The protection efficiency represents the efficiency with which resources improve the survival probability of the node. For the pending, assigned to the node The amount of protective resources.

[0111] In addition, constraints need to be set, including total resource constraints and boundary constraints for individual nodes:

[0112] (12)

[0113] in The total amount of available resources, This sets the upper limit for allocating resources to nodes.

[0114] Step S3.1.2: The constrained optimization problem is transformed into an unconstrained form using the Lagrange multiplier method, and then the improved nonsmooth Newton method is used to solve the nonlinear equations. The specific steps are as follows:

[0115] Step S3.1.2.1: Introduce a Lagrange multiplier To handle total resource constraints, the Lagrange function The following is given:

[0116] (13)

[0117] According to the KKT conditions, the optimal solution must satisfy the following conditions:

[0118] (14)

[0119] (15)

[0120] Solving equation (13), we get The explicit solution is:

[0121] (16)

[0122] Step S3.1.2.2: Combining equations (13) and (14), we can obtain 1 containing variables and A system of nonlinear equations. The function corresponding to each KKT condition. The components are given in the following form:

[0123] (17)

[0124] (18)

[0125] (19)

[0126] in, This represents the i-th component of the residual vector function, which means... These are the conditions for the solution.

[0127] Step S3.1.2.3: In the L-DNSN... In the next iteration, let the current estimate be... .right Perform Newton linearization and solve for the increment that satisfies the following conditions. :

[0128] (20)

[0129] in, It is the first The Jacobian matrix of the next iteration; This represents the update vector for resource allocation. This represents the updated value of the Lagrange multiplier; It can be considered as the Newtonian direction. The elements are The partial derivative of each component with respect to each variable:

[0130] (twenty one)

[0131] for Based on equation (15) about Find the partial derivative:

[0132] (twenty two)

[0133] akin, , , Substituting these partial derivatives into equation (19), we can obtain... Structural form:

[0134] (twenty three)

[0135] make

[0136] (twenty four)

[0137] The linear system in equation (19) can be extended as follows:

[0138] (25)

[0139] (26)

[0140] Substituting equation (24) into equation (25), we get:

[0141] (27)

[0142] (28)

[0143] During the iterative update process In the meantime, it is necessary to ensure and If the truncated variable is fixed at its boundary, then equations (15) to (28) are used to continue iterating over the remaining variable until convergence is achieved and all KKT conditions are satisfied.

[0144] Step S3.1.3: Put the optimal allocation scheme obtained from the solution into practice. This scheme can ensure that, under resource-constrained conditions, the survivability and mission support capabilities of the unmanned system during the attack resistance phase are maximized.

[0145] During the recovery phase, a dynamic topology reconstruction strategy based on network block decomposition is adopted, treating the system as a set of multiple basic functional blocks (containing the minimum complete task loop). When a node failure causes damage to a functional block, the dynamic reconstruction strategy is initiated: firstly, it attempts to schedule available nodes with the same function from redundant functional blocks for block reconstruction, directly repairing the damaged loop; if no available redundant resources are available, the damaged blocks are sorted according to task value, and residual resources are integrated through block merging or resource reallocation (block switching) to prioritize the recovery of high-value task capabilities, thereby achieving rapid network self-healing and task sustainability, as detailed below:

[0146] Step S3.2: Recovery Phase: Dynamic Reconstruction Strategy Based on Network Block Decomposition (NBD). The core of this strategy is to view the system as a collection of multiple functional blocks. By manipulating these functional blocks, the network topology is quickly reconstructed, restoring task capabilities. The specific steps are as follows:

[0147] Step S3.2.1: Network block classification and definition, dividing the functional blocks in the network into three categories:

[0148] 1. Basic network block: It contains a complete and minimal "probe (S)-control (D)-execute (E)-target (T)" task loop and is the basic unit for executing tasks.

[0149] 2. Redundant network blocks: Based on the basic functional blocks, multiple nodes (such as D1, D2) are present in the same functional layer, forming node redundancy and providing stronger anti-disturbance capabilities.

[0150] 3. Damaged network block: A functional block that cannot form a complete combat loop due to the failure of one or more nodes, and has lost its mission capability.

[0151] Step S3.2.2: Network block deconstruction, as follows Figure 4 As shown in (2). The system first monitors the node status in real time, and once the node is confirmed... If a node fails, immediately locate all functional blocks to which that node belongs. Then remove the failed node from the network topology. and all its associated edges Finally, these functional blocks containing failed nodes are marked as "damaged blocks".

[0152] Step S3.2.3: Network block reconstruction, as shown in the appendix. Figure 4 -(3) shows. The system traverses all functional blocks and checks whether there are redundant functional blocks (i.e., functional blocks with spare nodes at the same level). If a redundant block is found... Then, block reconstruction will be performed. Specifically:

[0153] From redundant blocks In the middle, remove a usable node with the same function type as the failed node in the damaged block. and its necessary internal connections, to this node Dynamically added to damaged blocks In the process, connections are established with its new upper and lower level nodes to restore the complete task loop.

[0154] Step S3.2.4: Network block switching, specifically including the following steps:

[0155] Switching condition judgment: When there are no redundant resources available for block refactoring in the system, block switching is initiated.

[0156] Task priority ranking: The system reads the pre-set task values ​​of all damaged blocks. The damaged blocks are sorted by value from highest to lowest, with the most valuable damaged blocks having priority for recovery.

[0157] Resource integration and redistribution: as attached Figure 4 -(4) shows two possible refactoring actions: merging two or more low-value damaged blocks, integrating their remaining nodes with different functions, to form one or more new, complete functional blocks; or deconstructing the lowest-value damaged block, releasing its intact nodes as free resources, and then redistributing these resources to higher-value damaged blocks.

[0158] Implementation Cases and Results Analysis:

[0159] To verify the effectiveness of the method described in this invention, a simulation experiment was conducted in a typical unmanned system scenario. (See attached diagram.) Figure 5 As shown, the network scenario adopts a four-layer FDN model, consisting of 90 unmanned entities, including 25 probe nodes, 20 control nodes, 25 execution nodes, and 20 target nodes, and there are various information flow edges.

[0160] The table below shows the parameter configurations for the simulation experiment.

[0161] Table 2 Configuration of relevant parameters for simulation experiment

[0162]

[0163] It should be noted that the core of this invention lies in providing a general framework for critical node identification and resilience enhancement, the effectiveness of which does not depend on the specific quantification method of node or operational loop performance; therefore, the performance values ​​involved in the embodiments are only examples, and the specific calculation process is not the focus of this invention, so it will not be described in detail.

[0164] Analysis of the effectiveness of key node identification.

[0165] Regarding the comprehensiveness of identification, as shown in the appendix Figure 6 As shown, the MLFB-AIE method integrates multiple dimensions such as multi-layer flow betweenness, inter-layer entropy, and intra-layer entropy. The results show that although control layer nodes have high flow betweenness, after entropy correction, the importance distribution of nodes across layers is more balanced, proving that this method can more comprehensively capture the combined contribution of nodes in topology and information interaction.

[0166] In terms of superiority in discriminative ability: such as Figure 7 As shown, compared with traditional methods (such as degree centrality, betweenness centrality, PageRank, etc.), the node importance values ​​obtained by the method of the present invention are more dispersed and have stronger distinguishability. It can clearly separate key nodes from ordinary nodes and avoid the problem of a large number of nodes having similar importance values ​​and being difficult to sort in traditional methods.

[0167] Regarding the effectiveness of the attack: (Appendix) Figure 8 This demonstrates the network performance degradation after identifying key nodes using different methods under a sequential, deliberate attack. When 20% of the nodes are removed, attacks targeting nodes identified using the method of this invention cause the network capability to drop to 0.073 and network connectivity to drop to 0.077, a performance degradation exceeding 91%. Its destructive efficiency is comparable to betweenness centrality and far surpasses other methods. (Appendix) Figure 9 The method of this invention also performs well under rule-based deliberate attacks (dynamically recalculating and attacking the most critical nodes at each step), continuously and rapidly weakening network performance, demonstrating its robustness in identifying critical nodes in dynamic adversarial environments.

[0168] Effectiveness analysis of node hardening strategies.

[0169] Figure 10 , Figure 11 , Figure 12 The performance trajectories of USoS before and after applying the hardening strategy of this invention are shown in random failure, intentional attack, and mixed failure scenarios.

[0170] In all scenarios, after applying the L-DNSN optimization strategy of this invention (red curve), the minimum system performance and overall performance trajectory are significantly higher than in the unhardened case (blue curve). Specifically, in intentional attack scenarios ( Figure 11 Under random fault conditions, the minimum network performance improved from 0.58 to 0.81, representing an absolute performance improvement of up to 39.7%. Figure 10 ) and mixed faults ( Figure 12 In the aforementioned scenarios, performance improvements of 23.9% and 8.2% were achieved, respectively. This demonstrates that the resource allocation model of this invention can accurately allocate resources to key nodes that contribute the most to network performance, thereby maximizing the overall benefits of protection resources.

[0171] Analysis of the overall superiority of the toughness-enhanced framework.

[0172] Appendix Figure 13 , 14 Figure 15 shows the performance change curves of USoS under three fault scenarios, using different optimization methods (including PSO, greedy algorithm, and the RR-REF of this invention). It can be observed that the performance curves under the RR-REF framework of this invention show the following: the performance degradation is minimal during the resistance phase (performance degradation period); the performance recovery speed is the fastest and the level is the highest during the recovery phase; throughout the entire process, the system performance can be maintained above the operating baseline, ensuring basic task capabilities.

[0173] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy, characterized in that: Includes the following steps: Step S1: Construct the functional dependency network model of the unmanned system; Step S2: Based on the functionally dependent network model, calculate the comprehensive centrality of nodes by fusing the multi-level flow betweenness and adjacency information entropy to identify key nodes; Step S3: Based on the key node identification results, the unmanned system is reinforced using an anti-recovery-oriented resilience enhancement framework. The framework includes a resource allocation strategy based on the Lagrange damped non-smooth Newton method during the resistance phase, and a dynamic reconstruction strategy based on network block decomposition during the recovery phase.

2. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 1, characterized in that: In step S1, constructing the functional dependency network model of the unmanned system specifically includes: Step S1.1: The detection nodes in the unmanned system Control Node Execution Node and target node They are each constructed as independent network layers; Step S1.2: Construct directed edges between the nodes, including intra-layer edges and inter-layer edges, wherein the inter-layer edges include at least... , , and Four types, with at least the inner edge of the layer including , and Three types.

3. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 1, characterized in that: In step S2, the specific process of identifying key nodes is as follows: Step S2.1: Define and calculate the multi-level flow betweenness of the node; Step S2.2: Based on the multi-layer flow betweenness, calculate the inter-layer entropy and intra-layer entropy of the node respectively; the inter-layer entropy is used to quantify the distribution balance of information interaction between the node and its upper and lower layer neighbors; the intra-layer entropy is used to quantify the distribution balance of collaborative cooperation between the node and its same-layer neighbors; Step S2.3: Calculate the cross-layer connection coefficient of the node. The cross-layer connection coefficient comprehensively reflects the node's ability to receive and issue instructions in the vertical direction, as well as its collaborative ability in the horizontal direction. Step S2.4: Normalize the interlayer entropy and intralayer entropy, and apply a gain function to the normalized intralayer entropy to amplify the synergistic effect it represents, and obtain the synergistic gain coefficient. Step S2.5: Based on the normalized inter-layer entropy, the cooperative gain coefficient, and the cross-layer connectivity coefficient, the final comprehensive centrality of the node is obtained through a comprehensive calculation function.

4. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 3, characterized in that: In step S2.1, the multi-layer flow betweenness of a node is calculated through the following process: setting the maximum number of propagation steps related to the number of network layers; initializing each node as an information source in sequence; simulating the multi-step propagation process in which information is evenly distributed from the node carrying the information to all its outgoing neighbor nodes in each step; and counting the total amount of information received by each node after all propagation is completed. The ratio of the total amount of information to the initial total amount of information in the entire network is calculated and used as the multi-layer flow betweenness number of the node.

5. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 3, characterized in that: In step S2.2, the interlayer entropy is calculated as follows: in It is the input-output centrality weighting adjustment coefficient. and These represent the probability distributions of inbound and outbound information, respectively; the method for calculating the layer entropy is as follows: in This represents the probability distribution of collaborative information within the layer.

6. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 3, characterized in that: In step S2.3, the cross-layer connection coefficient of the node The calculation method is as follows: in, , and These represent the number of neighbors on the upper and lower floors and on the same floor, respectively. To maximize the network's extent, used for normalization; and The weighting coefficients and ; The function is used to prevent numerical saturation.

7. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 3, characterized in that: In step S2.4, the cooperative gain coefficient The calculation method is as follows: in To normalize the layer entropy, This is the gain function.

8. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 3, characterized in that: In step S2.5, the comprehensive calculation function is: in, This is the normalized interlayer entropy. For the cooperative gain coefficient, This represents the cross-layer connectivity coefficient.

9. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 1, characterized in that: In step S3, the resource allocation strategy based on the Lagrange damped non-smooth Newton method in the resistance phase specifically involves: establishing an optimization model with the goal of maximizing the expected network performance after an attack and constrained by total protection resources; using the Lagrange multiplier method to process the constraints and construct the Lagrange function; and using the damped non-smooth Newton method to iteratively solve for the optimal solution that satisfies the KKT conditions to obtain the optimal resource allocation scheme for key nodes.

10. The method for resilience analysis and improvement of unmanned systems based on multi-level flow betweenness and adjacency entropy as described in claim 1, characterized in that: In step S3, the dynamic reconstruction strategy based on network block decomposition in the recovery phase specifically includes: Block destructuring identifies and removes failed nodes and their associated edges; Block reconstruction involves relocating available nodes from redundant network blocks to damaged network blocks. Block switching involves sorting and merging damaged blocks based on their target value when block reconstruction is not feasible, thereby redistributing tasks.

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