Unmanned aerial vehicle cluster information exchange capability resilience analysis method based on multi-state network

Abstract

The present application relates to a kind of unmanned aerial vehicle cluster information exchange capability resilience analysis method based on multi-state network, comprising: constructing multi-state unmanned aerial vehicle cluster IE network model;Introducing the conditional probability distribution and IE network performance measurement index of IE network link;Unmanned aerial vehicle cluster resilience model for the unmanned aerial vehicle cluster is constructed;Wherein, the unmanned aerial vehicle cluster resilience model includes: the cluster formation transformation resilience submodel and unmanned aerial vehicle redeployment resilience submodel constructed using the conditional probability distribution and the IE network performance measurement index;Set the recovery strategy of unmanned aerial vehicle cluster in the process of cluster task, based on the recovery strategy and the unmanned aerial vehicle cluster resilience model, the information exchange capability of the multi-state unmanned aerial vehicle cluster IE network model is carried out resilience evaluation.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) swarms, and more particularly to a method for analyzing the resilience of UAV swarm information exchange capabilities based on multi-state networks. Background Technology

[0002] Drone swarms are capable of performing a variety of dangerous tasks in a self-organizing and adaptive manner, and efficient and stable information exchange between drones is crucial for mission success. Due to their flexibility and low cost, drones have been widely used in both civilian and military fields. In particular, drones can be used to perform tedious and dangerous tasks without posing a risk to humans. However, given the limited capabilities of a single drone, there is a growing focus on drone swarms to increase operational capabilities by combining multiple drones.

[0003] Unmanned aerial vehicle (UAV) swarms, consisting of a series of drones, can significantly improve the success rate of performing more complex missions. However, UAV swarms are typically used in hazardous and complex environments where unpredictable threats and unavoidable disruptive events may occur. Furthermore, UAV swarms operate in a self-organizing and adaptive manner, meaning they need to possess self-healing capabilities when interference occurs. For example, when a UAV swarm is performing a reconnaissance mission on a specific battlefield, it may be exposed to enemy air defense systems. External interference causing UAV functional impairment or degradation can lead to changes in the swarm's information exchange (IE) network topology, further deteriorating the overall swarm performance. In such cases, the UAV swarm needs to change formation to avoid danger and restore the performance of its IE network.

[0004] Resilience represents the ability of a drone swarm to resist interference, including predicting extreme events, assessing the impact of events, absorbing shocks, responding, adapting and recovering. Network resilience characterizes the ability to maintain and restore the required functions when an interruption occurs. Many scholars have used two-state networks to model the information interaction network of the swarm and analyze its resilience. However, due to various conditions such as communication distance and external noise, the data flow between drones can be in different states. Therefore, polymorphic networks are more suitable for characterizing the link capacity of the information interaction network. Reference [1] first modeled the IE network of the drone swarm as a polymorphic network and evaluated the reliability of the network, where the state probability distribution of the communication link is the proportion of the cumulative time of its distance in the task time.

[0005] To assess and analyze resilience, it is necessary to understand the changes in the link state distribution during resilience processes, rather than simply looking at statistics over the entire mission duration. UAV communication experiments demonstrate that IE links can operate in different states at a fixed communication distance. The state distribution can then be used to represent the performance of the IE link at that distance. Therefore, by analyzing the changes in these conditions, the performance of the IE network during the mission can be determined.

[0006] Furthermore, current research on swarm resilience primarily assumes that interference causes drones to lose functionality, reducing link capacity to zero. IE link recovery relies on reconnection between remaining drones. However, few studies investigate how drone swarms autonomously respond to external interference and its impact on swarm resilience. For example, when a swarm suffers internal failures or external disruptions, appropriate dispersal and / or aggregation behaviors can help the swarm resist and recover from interference. Therefore, it is necessary to consider dispersal actions to mitigate the risks of interference and aggregation actions in order to restore swarm performance.

[0007] References:

[0008] [1] Xu, B., Liu, T., Bai, G., Tao, J., Zhang, Y., & Fang, Y. (2021). A multistate network approach for reliability evaluation of unmanned swarms by considering information exchange capacity. Reliab. Eng. Syst. Saf., 219, 108221. Summary of the Invention

[0009] The purpose of this invention is to provide a method for analyzing the resilience of information exchange capabilities of unmanned aerial vehicle (UAV) swarms based on multi-state networks.

[0010] To achieve the above-mentioned objectives, this invention provides a method for resilience analysis of UAV swarm information exchange capabilities based on multi-state networks, comprising:

[0011] S1. Construct a multi-state drone swarm IE network model;

[0012] S2. Based on the multi-state UAV swarm IE network model, introduce the conditional probability distribution of IE network links and IE network performance metrics;

[0013] S3. Construct a drone swarm resilience model for the drone swarm based on the conditional probability distribution and the IE network performance metric; wherein, the drone swarm resilience model includes: a swarm formation transformation resilience sub-model and a drone redeployment resilience sub-model constructed using the conditional probability distribution and the IE network performance metric;

[0014] S4. Set the recovery strategy for the UAV cluster during the cluster task process, and evaluate the resilience of the information exchange capability of the multi-state UAV cluster IE network model based on the recovery strategy and the UAV cluster resilience model; wherein, the recovery strategy includes: cluster change formation strategy and cluster redeployment strategy;

[0015] If the cluster transformation formation strategy is adopted, the information exchange capability of the multi-state UAV cluster IE network model is evaluated based on the cluster formation transformation resilience sub-model.

[0016] If the cluster redeployment strategy is adopted, the resilience of the information exchange capability of the multi-state UAV cluster IE network model is evaluated based on the UAV redeployment resilience sub-model.

[0017] According to one aspect of the present invention, in step S1, the step of constructing a multi-state UAV swarm IE network model is a two-terminal multi-state network model composed of multiple network nodes and multiple components, which is represented as follows:

[0018] G(V,E)

[0019] Where V represents the set of network nodes in the two-terminal multistate network model, and E represents the set of components in the two-terminal multistate network model, expressed as: E={1,2,…,n}.

[0020] According to one aspect of the present invention, step S2, the step of introducing the conditional probability distribution of IE network links based on the multi-state UAV swarm IE network model, includes:

[0021] Let i represent the i-th component in the multi-state UAV swarm IE network model;

[0022] Using c i The various states of the components in the multi-state UAV swarm IE network model are represented as: c i ∈{0,1,…,m i}; where m i The maximum flow rate that the component can operate at;

[0023] The state probability distribution of the component is constructed as follows: in, It represents the probability that the component operates in various states;

[0024] The conditional probability distribution is constructed based on the state probability distribution, and it is expressed as follows:

[0025] p i (t)=pb i (t)*C i (t)

[0026] Among them, pb i (t) represents the condition vector of the component, C i (t) represents the conditional operation probability matrix of the component;

[0027] In the step of introducing IE network performance metrics based on the multi-state UAV swarm IE network model, the IE network performance metrics are expressed as follows:

[0028] QIE(t)=min(Q1(t),Q2(t),…,Q s (t))

[0029] Where Q1(t), Q2(t), ..., Q s (t) represents the node pair with the largest minimum multi-hop count and the same number of nodes.

[0030] According to one aspect of the present invention, the step of constructing the conditional probability distribution based on the state probability distribution includes:

[0031] For the component, multiple incompatible events are defined, and the events represent the operating conditions of the component.

[0032] The state c of the component's flow at time t is obtained using the law of total probability. i The probability is expressed as:

[0033]

[0034] in, This indicates that the flow of the i-th component is in state c under the condition that the event occurs at time t. i The probability, The event represents the condition that satisfies the following conditions. Ω represents the sample space;

[0035] Define the condition vector for the component, which is represented as follows:

[0036]

[0037] The conditional operation probability matrix of the component is defined as follows:

[0038]

[0039] The conditional probability distribution is obtained based on formulas (1), (2), and (3).

[0040] According to one aspect of the present invention, step S3, the step of constructing a drone swarm resilience model for the drone swarm based on the conditional probability distribution and the IE network performance metric, includes:

[0041] The resilient behavior of the UAV swarm during task execution is designed to obtain a resilient behavior scheme for the UAV swarm; wherein, the resilient behavior scheme includes: a swarm formation transformation resilient sub-scheme and a UAV redeployment resilient sub-scheme;

[0042] The resilience model of the drone swarm is constructed based on the aforementioned resilience behavior scheme.

[0043] According to one aspect of the present invention, the step of designing the resilient behavior of the drone swarm during task execution and obtaining a resilient behavior scheme for the drone swarm includes:

[0044] Three formation modes are set based on the distance between individual drones in the drone swarm, and each is represented by a variable MO; where MO=1 represents dense formation mode, MO=2 represents compact formation mode, and MO=3 represents sparse formation mode.

[0045] Based on the three formation modes, the cluster formation transformation resilience sub-scheme and the UAV redeployment resilience sub-scheme are set.

[0046] According to one aspect of the present invention, step S3, which involves constructing a cluster formation transformation resilience sub-model using the conditional probability distribution, includes:

[0047] Based on the cluster formation transformation resilience sub-scheme, the first state transition relationship of the components in the multi-state UAV cluster IE network model during the formation transformation process is obtained;

[0048] Based on the first state transition relationship and the semi-Markov model, a conditional vector is constructed to represent the state transitions of components in the multi-state UAV swarm IE network model during formation transformation, as follows:

[0049] pb i (t)=pb i (0)*Θ i (t)

[0050] Among them, pb i (0) represents the conditional probability distribution of the component at the initial time, Θ i(t) represents the state transition matrix obtained based on the semi-Markov model;

[0051] Based on the conditional vector generated by the component during the formation transformation, a conditional probability distribution of the UAV swarm separation behavior is constructed, which is expressed as:

[0052] p i (t)=pb i (0)*Θ i-d (t)*C i ;

[0053] Based on the conditional vector generated by the component during the formation transformation, a conditional probability distribution of the UAV swarm aggregation behavior is constructed, which is expressed as:

[0054] p i (t)=pb i (0)*Θ i-d (t)*Θ i-r (t)*C i ;

[0055] Based on the semi-Markov model, the probability distribution of the communication link state of the component during the formation transformation process is constructed as follows:

[0056]

[0057] in, This represents the transition probability matrix of the component during the toughness process.

[0058] According to one aspect of the present invention, step S3, the step of constructing the UAV redeployment resilience sub-model using the conditional probability distribution and the IE network performance metric, includes:

[0059] Based on the aforementioned drone redeployment resilience sub-scheme, the second state transition relationship of the components in the multi-state drone cluster IE network model during the redeployment process is obtained;

[0060] Based on the second state transition relationship, the conditional probability distribution of the recovered damaged components in the multi-state UAV swarm IE network model is defined as follows:

[0061]

[0062] Where e = (1, 0, ..., 0), This represents the probability distribution of the cluster under compact formation.

[0063] The objective function is constructed with the cluster resilience of the drone swarm as the optimization objective, and it is expressed as follows:

[0064]

[0065] Where Q(t) represents the performance of the drone swarm at time t; PQ(t) represents the minimum required performance of the UAV swarm at time t; PQ(t) represents the optimal (expected) performance of the UAV swarm at time t; [P] is an Iverson bracket, [P] = 1 only if P is true, otherwise [P] = 0; β is the system resilience emphasis factor, and 0 ≤ β ≤ 1.

[0066] According to one aspect of the present invention, the multi-state network modeling method employed can more realistically characterize the information interaction capabilities of UAV swarms. Based on this, further modeling the resilience behavior of UAV swarms can more accurately assess and analyze their resilience.

[0067] According to one aspect of the present invention, a resilience-based IE topology reconstruction method is proposed, which can more conveniently and quickly find the optimal candidate for damaged UAVs.

[0068] According to one aspect of the present invention, the use of multi-state network modeling considering conditional probabilities is closer to reality and has wider applications. Furthermore, the present invention fully considers the impact of cluster self-organizing behavior (aggregation and separation) on resilience and provides an effective resilience-based model for UAV formation changes. Attached Figure Description

[0069] Figure 1 This is a flowchart of a method for analyzing the resilience of unmanned aerial vehicle (UAV) swarm information exchange capabilities according to an embodiment of the present invention.

[0070] Figure 2 This is a diagram illustrating the formation transformation process of a drone swarm according to one embodiment of the present invention;

[0071] Figure 3 This is a diagram illustrating the drone swarm replacement process according to one embodiment of the present invention;

[0072] Figure 4 This is a conditional state transition diagram of a multi-state network component according to an embodiment of the present invention;

[0073] Figure 5 This is a diagram of a test scheme for unmanned aerial vehicle (UAV) information interaction throughput according to an embodiment of the present invention;

[0074] Figure 6 This is a test location map of an unmanned aerial vehicle (UAV) according to one embodiment of the present invention;

[0075] Figure 7This is an information interaction throughput curve of a UAV at various intervals according to an embodiment of the present invention, wherein (a) is an information interaction throughput curve at a interval of 10 meters, (b) is an information interaction throughput curve at a interval of 20 meters, (c) is an information interaction throughput curve at a interval of 30 meters, (d) is an information interaction throughput curve at a interval of 40 meters, (e) is an information interaction throughput curve at a interval of 50 meters, (f) is an information interaction throughput curve at a interval of 60 meters, and (g) is an information interaction throughput curve at a interval of 70 meters.

[0076] Figure 8 This is a rectangular formation diagram of a drone swarm according to an embodiment of the present invention, wherein (a) represents a rectangular formation of 20 drones performing a mission, and (b) represents the information interaction network topology of the drone swarm under the rectangular formation;

[0077] Figure 9 This is a network topology diagram of a drone swarm according to an embodiment of the present invention, wherein (a) represents the network topology of nodes 1-20 under the rectangular formation, and (b) represents the network topology of nodes 4-17 under the rectangular formation;

[0078] Figure 10 This is an information interaction link classification diagram according to an embodiment of the present invention, wherein (a) represents vertical classification and (b) represents horizontal classification;

[0079] Figure 11 This is a comparison diagram of the resilience of UAVs at different locations under different strategies when they are damaged, according to an embodiment of the present invention.

[0080] Figure 12 This is a network performance curve of a drone swarm according to an embodiment of the present invention, with the number of drones damaged being 1 when subjected to a second disturbance.

[0081] Figure 13 This is a toughness comparison chart of each group of drone swarms according to an embodiment of the present invention, with the number of damages when subjected to a second disturbance being 2.

[0082] Figure 14 This is a network performance curve when the number of damages is 2, according to one embodiment of the present invention.

[0083] Figure 15 This is a network performance curve of a drone swarm according to an embodiment of the present invention, with the number of damages when subjected to a second disturbance being 2, under different replacement schemes.

[0084] Figure 16 This is a comparison chart of the resilience of each group of drone swarms under the condition that the number of damages when subjected to a second disturbance is 3, according to an embodiment of the present invention.

[0085] Figure 17 This is a network performance curve of a drone swarm according to an embodiment of the present invention, with the number of damages during the second disturbance being 3.

[0086] Figure 18 This is a network performance curve of a drone swarm under different optimization objectives, with the number of damages during the second disturbance being 3, according to an embodiment of the present invention. Detailed Implementation

[0087] To more clearly illustrate the technical solutions of the embodiments of the present invention, a detailed description is provided below in conjunction with the accompanying drawings.

[0088] like Figure 1 As shown, according to one embodiment of the present invention, the method for resilience analysis of UAV swarm information exchange capability based on multi-state networks includes:

[0089] S1. Construct a multi-state drone swarm IE network model;

[0090] S2. Based on the multi-state UAV swarm IE network model, conditional probability distribution of IE network links and IE network performance metrics are introduced;

[0091] S3. Construct a drone swarm resilience model for drone swarms based on conditional probability distribution and IE network performance metrics; wherein, the drone swarm resilience model includes: a swarm formation transformation resilience sub-model and a drone redeployment resilience sub-model constructed using conditional probability distribution and IE network performance metrics;

[0092] S4. Set recovery strategies for the UAV swarm during swarm missions, and evaluate the resilience of the information exchange capability of the multi-state UAV swarm IE network model based on the recovery strategies and the UAV swarm resilience model; the recovery strategies include: swarm transformation formation strategy and swarm redeployment strategy.

[0093] If a cluster transformation formation strategy is adopted, the resilience of the information exchange capability of the multi-state UAV cluster IE network model is evaluated based on the cluster formation transformation resilience sub-model.

[0094] If a cluster redeployment strategy is adopted, the resilience of the information exchange capability of the multi-state UAV cluster IE network model is evaluated based on the UAV redeployment resilience sub-model.

[0095] According to one embodiment of the present invention, in step S1, the step of constructing a multi-state UAV swarm IE network model is a two-terminal multi-state network model composed of multiple network nodes and multiple components (edges), which is represented as follows:

[0096] G(V,E)

[0097] Where V represents the set of network nodes in the two-terminal multistate network model, and E represents the set of components in the two-terminal multistate network model, expressed as: E={1,2,…,n}, where,

[0098] According to one embodiment of the present invention, step S2, which involves introducing the conditional probability distribution of IE network links based on a multi-state UAV swarm IE network model, includes:

[0099] Let i represent the i-th component in the multi-state UAV swarm IE network model; where i∈E for any component.

[0100] Using c i The various states of components in a multi-state drone swarm IE network model are represented as: c i ∈{0, 1, ..., m i}; where m i This represents the maximum bandwidth that the component can handle.

[0101] The state probability distribution of the constructed component is represented as: in, It represents the probability of the i-th component operating in various states c; furthermore, for ease of description, the i-th component can be described as: component i in the following text;

[0102] Furthermore, a conditional probability distribution is constructed based on the state probability distribution, which is expressed as:

[0103] p i (t)=pb i (t)*C i (t)

[0104] Among them, pb i (t) represents the condition vector of the component, C i (t) represents the conditional operation probability matrix of the component;

[0105] In this embodiment, in the real world, the operating states of components in a multi-state UAV swarm IE network model are typically based on certain conditions. For example, the multi-state UAV swarm IE network model provides a certain data throughput between UAVs. The communication distance between UAVs is a crucial condition affecting the probability distribution of IE network link states. Furthermore, the availability of transceiver devices within the UAVs is another condition for normal data transmission between them. Therefore, the step of constructing a conditional probability distribution based on the state probability distribution includes:

[0106] For a component, multiple incompatible events are defined, and each event represents the component's runtime conditions; the multiple events defined are represented as follows:

[0107] The component is configured such that the flow is in state c under the condition that an event occurs at time t. i The probability of the component's flow at time t is obtained using the law of total probability. i The probability is expressed as:

[0108]

[0109] in, This indicates that the flow of component i is in state c given that an event occurs at time t. i The probability, Represents an event that satisfies Ω represents the sample space;

[0110] Define the condition vector for the component, which is represented as follows:

[0111]

[0112] The conditional execution probability matrix of the component is defined as follows:

[0113]

[0114] Based on formulas (2) and (3), formula (1) can be written in matrix form to obtain the aforementioned conditional probability distribution.

[0115] In this embodiment, in the step of introducing IE network performance metrics based on the multi-state UAV swarm IE network model, the IE network performance metrics are expressed as follows:

[0116] QIE(t)=min(Q1(t), Q2(t),...,Q s (t))

[0117] Where Q1(t), Q2(t), ..., Q s (t) represents the node pair with the largest minimum multi-hop count and the same number of nodes.

[0118] Definition of multi-hop: In a wireless multi-hop network, any wireless device can act as both an access point (AP) and a router simultaneously. Each node in the network can send and receive signals, and each node can communicate directly with one or more peer nodes. This type of network is called a multi-hop network. It can also be understood as information transmission being completed through forwarding from multiple nodes on a link. Each node can communicate directly with one or more peer nodes; multi-hop simply means multiple forwardings. Therefore, the aforementioned multi-hop count refers to the number of points traversed from one point to another.

[0119] In this embodiment, resilience describes the system's ability to resist and recover from disturbances. It is a process value. In a two-dimensional coordinate system, for a performance curve, the IE network performance metric is the vertical axis, and resilience describes the process of performance change when the system is subjected to disturbances. For example, the faster the performance recovers, the better the resilience, and the shorter the recovery time, the better the resilience.

[0120] In this embodiment, the performance of the multi-state UAV swarm IE network model is expressed as:

[0121]

[0122] Where d∈{1,2,...,M} represents the flow of the network from the source to the sink, and M is the maximum flow. d This represents the probability that traffic d flows from the source to the sink. For a multi-state drone swarm IE network model, network performance deteriorates as the number of communication hops between individual drones increases. Therefore, we define the source and sink nodes in the swarm as the two drones with the largest minimum number of hops, thus obtaining the aforementioned IE network performance metrics.

[0123] According to one embodiment of the present invention, step S3, the step of constructing a drone swarm resilience model for drone swarms based on conditional probability distribution and IE network performance metrics, includes:

[0124] The resilient behavior of the UAV swarm during task execution is designed to obtain a resilient behavior scheme for the UAV swarm; the resilient behavior scheme includes: a resilient sub-scheme for swarm formation transformation and a resilient sub-scheme for UAV redeployment.

[0125] A resilience model for drone swarms is constructed based on a resilience behavior scheme.

[0126] Combination Figure 2 and Figure 3 As shown, according to one embodiment of the present invention, the step of designing the resilient behavior of a drone swarm during task execution and obtaining a resilient behavior scheme for the drone swarm includes:

[0127] Three formation modes are defined based on the distance between individual drones in the drone swarm, each represented by the variable MO. MO=1 represents a dense formation mode, MO=2 a compact formation mode, and MO=3 a sparse formation mode. In this embodiment, reasonable separation and aggregation are typical self-organizing behaviors of intelligent swarms; therefore, three formation modes can be defined based on the distance between individual drones in the drone swarm. These three formation modes are applied to different combat situations: In dense formation mode, the drones are close together, resulting in strong swarm information interaction and the fastest swarm data sharing, but it is susceptible to enemy interference, potentially leading to the destruction of multiple drones. In compact formation mode, the drones are spaced appropriately, allowing for network reconfiguration measures such as position swapping. In sparse formation mode, the swarm spacing is large, making it difficult to transmit large amounts of information, but the swarm is less susceptible to enemy attacks. Based on these three formation modes, the drone swarm can change its formation according to the current situation.

[0128] Furthermore, based on the aforementioned three formation modes, we set up swarm formation transformation resilience sub-schemes and UAV redeployment resilience sub-schemes. The obtained resilience sub-schemes allow for further targeted modeling and analysis of the resilience behavior of UAV swarms.

[0129] According to one embodiment of the present invention, step S3, which involves constructing a cluster formation transformation resilience sub-model using conditional probability distribution and IE network performance metrics, includes:

[0130] The first state transition relationship of components in a multi-state UAV swarm IE network model during formation transformation is obtained based on a cluster formation transformation resilience sub-scheme; in this embodiment, see [link to implementation details]. Figure 2 and Figure 3 As shown, an example of a resilient sub-scheme for swarm formation transformation is presented. At the start of the mission, the UAV swarm operates in dense formation. In T... d Upon entering the enemy's air defense coverage area (i.e., the mission area) and encountering enemy fire (i.e., external disturbance), all drones will disperse and transition to a sparse formation to reduce the probability of individual drones being destroyed. After completing the formation transition, the drone swarm will maintain this formation for a period of time until it leaves the enemy's air defense coverage area; this flight time is recorded as h. Once out of the enemy's air defense coverage area, the drone swarm will... r The drone swarm can then transition to a tight formation mode to restore high-throughput information exchange capabilities. Furthermore, if the drone swarm remains intact, it can transition to a tight formation mode and continue performing its mission.

[0131] Therefore, the first state transition relationship of the corresponding components in the multi-state UAV swarm IE network model can be analyzed based on the above-mentioned swarm formation transformation resilience sub-scheme. In this embodiment, according to the aforementioned obtained conditional probability distribution formula (i.e., p... i (t)=pb i (t)*C i From (t) we can see that the IE network link capacity is based on the conditional running probability matrix C. i (t) and the condition vector pb of the component i The conditional running probability matrix C is determined by (t). i (t) mostly represents statistical results under various conditions, such as the distribution of the data stream within one second under certain intervals. Therefore, it is assumed that the conditional running probability matrix C i (t) does not change with time. However, external disturbances may cause the condition vector pb to change. i (t) changes, ultimately altering the state probability distribution p of component i. i (t). Therefore, it can be seen that the essence of formation change is the adjustment of the distance between UAVs.

[0132] Furthermore, assume component i has m i +1 state c, i.e., from 0 to m i The operating conditions of component i exist in u states, and its initial condition vector is pb. i (0); The initial conditional running probability matrix of component i is C i In the initial state, the states of component i follow the order I. i =pb i (0)*C i .

[0133] When component i experiences a disturbance or recovers during a task, its operating "conditions" may undergo a state transition. Similarly, with the handling of a fault or disturbance, component i's operating "conditions" recover to normal. Markov processes are memoryless, meaning the probability distribution of the current state is conditionally independent of past states. One property of Markov processes is that the dwell time (holding time) in any state follows an exponential distribution. This property limits the practical application of Markov models. Semi-Markov processes, as an extension of Markov processes, become a good choice for modeling component resilience processes because the dwell time distribution in any state can be arbitrary in semi-Markov processes.

[0134] like Figure 4 As shown, the running "conditions" (i.e., events) of component i. State transitions may occur at different stages of the resilience process. If the "conditions" are run... The subscript j represents the "conditions" under which component i operates at different performance levels. Assuming a larger subscript j, the smaller the spacing between drones, then when a disturbance occurs, the operating "conditions" will change. The running condition vector pb i (t) may be directed to the running "conditions". Run "Conditions" Equal-sized state transitions. Conversely, as recovery progresses, the condition vector pb... i (t) may be directed to the running "conditions". Small-interval state transitions are performed. As the state of the running "condition" transitions, the state probability distribution of component i also changes accordingly, thus obtaining the aforementioned first state transition relationship.

[0135] Furthermore, based on the first state transition relationship and the semi-Markov model, a condition vector is constructed to represent the state transitions of components in the multi-state UAV swarm IE network model during formation transformation, denoted as:

[0136] pb i (t)=pb i (0)*Θ i (t)

[0137] Among them, pb i (0) represents the conditional probability distribution of the component at the initial time, Θ i (t) represents the state transition matrix obtained based on the semi-Markov model;

[0138] In this embodiment, based on the aforementioned first state transition relationship, in order to model the resilience of the operational "conditions" (i.e., events) of component i using a semi-Markov process, a corresponding kernel matrix is ​​defined. Among them, the elements of the kernel matrix This represents the probability that component i's state transitions from state j to state l within the time interval [0, t]. Therefore:

[0139]

[0140]

[0141] in, ξ represents the probability that component i will remain in state j for a certain period of time under the "condition" and that the next state will be l.

[0142] Based on kernel matrix Φ i (t) can be further solved to obtain the state transition matrix Θ of the semi-Markov at time t. i (t), whose elements Let represent the probability that component i, starting in state j at initial time t = 0, will transition to state l at time t. This state transition matrix can be obtained by solving the following Markov equation:

[0143]

[0144] in, This equation can be solved by applying the Laplace transform and the inverse Laplace transform, thus obtaining the condition vector of component i after the state transition, i.e., pb. i (t)=pb i (0)*Θ i (t).

[0145] Furthermore, during the formation change process, individual drones in the drone swarm achieve corresponding distance changes through separation and aggregation behaviors. Moreover, in the separation behavior, a conditional probability distribution of the drone swarm's separation behavior is constructed based on the conditional vectors generated by the components during the state transition, which is expressed as:

[0146] p i (t)=pb i (0)*Θ i-d (t)*C i ;

[0147] Specifically, when the disturbance is T d At time T, the operating "conditions" of component i are affected, and a state transition begins. p To achieve the lowest performance. Let the kernel matrix of the semi-Markovnikov process at this stage be... If j < l, then we have At this point, the component's operational "condition" state transition matrix Θ can be obtained for this disturbance phase. i-d (t). Therefore, for any t∈[T] d T p The probability distribution of component i is as shown above.

[0148] In the aggregation behavior, the conditional probability distribution of the UAV swarm aggregation behavior is constructed based on the conditional vectors generated by the components during the formation transformation, and it is expressed as follows:

[0149] p i (t)=pb i (0)*Θ i-d (t)*Θ i-r (t)*C i ;

[0150] Specifically, from time T s Start to time T rUpon completion of the recovery process, as the recovery measures are implemented, the conditional probability distribution of the operating "conditions" of component i transitions towards the normal state, and consequently, the flow distribution of component i also changes over time. Let the kernel matrix of the semi-Markovnikov process in this stage be... If j > l, then we have Therefore, at any time t∈[T] s T r The state transition matrix Θ i-r After (t), the conditional probability distribution of the aggregation behavior of component i can be calculated, as shown above.

[0151] Furthermore, based on a semi-Markov model, the probability distribution of communication link states of the components during the resilience process (i.e., formation change process) is constructed as follows:

[0152]

[0153] in, This represents the transition probability matrix of the component during the resilience process.

[0154] Specifically, at any time t∈[T] in the component resilience process d [T], the semi-Markov kernel matrix for the entire process is defined as:

[0155]

[0156] Therefore, the transition probability matrix of the entire resilience process can be obtained in the following way:

[0157]

[0158] Based on this, the aforementioned communication link state probability distribution of component i during the resilience process can be obtained.

[0159] In this embodiment, the three formulas involved in obtaining the aforementioned communication link state probability distribution represent the change process of the component state distribution during resilience. When a disturbance occurs, based on the "conditional" state transition matrix Θ... i-d (t), the component's state distribution transitions to another low-level state. Then, before recovery begins, the conditional state transition probability matrix is ​​set to a constant Θ. i-d (T p Thus, the component's state distribution remains unchanged. As the component's "condition" state is restored, the component's state distribution is also restored. When the restoration is complete, the state transitions stop accordingly.

[0160] For each disturbed component i, the state probability distribution p of component i at any time can be obtained through the proposed resilient process model. i(t). Then, the overall state probability distribution matrix P(t) of the network is also determined. Therefore, the transition of the component state probability distribution ultimately translates into a change in the performance of the multi-state UAV swarm IE network model.

[0161] According to one embodiment of the present invention, step S3, which involves constructing a UAV redeployment resilience sub-model using conditional probability distribution and IE network performance metrics, includes:

[0162] Based on the UAV redeployment resilience sub-scheme, the second state transition relationship of components in the multi-state UAV swarm IE network model during the redeployment process is obtained. As mentioned earlier, if no UAVs are damaged during the execution of a mission, the corresponding mission process is only a UAV swarm formation change process. However, if UAVs are damaged, the corresponding mission process needs to add a UAV "replacement" process during the UAV swarm formation change process to constitute a UAV redeployment process. Specifically, after the swarm enters the enemy's air defense coverage area, individual UAVs may be damaged by the enemy, causing a decrease in the overall network performance level. In addition to the above-mentioned formation change behavior, UAV swarms can also improve system resilience by adjusting the topology. Figure 2 and Figure 3 As shown, after leaving the enemy's fire range, the drone swarm can first switch to a compact formation (MO=2), then carry out the corresponding drone "filling" behavior to adjust the network topology, and finally switch to a dense formation (MO=1) to continue to perform the mission.

[0163] In this embodiment, in addition to changing formations during the process of countering disturbances, the drone swarm can also adjust the network topology by adjusting the positions of existing drones according to the location of the damaged drones and mission requirements, so as to improve the performance level of the network after the damage.

[0164] Therefore, the steps to obtain the second state transition relationship are as follows:

[0165] Let Π be the set of damaged drones, and K be the set of remaining drones excluding the source and sink nodes. If drone u∈K is assigned to fill the position of v in Π, then the following process exists: First, drone v leaves its original position, such that all information interaction links (i.e., components i) i∈Γ connected to v are made possible. v First, it loses its function; second, assume that the shortest path between drones u and v in the original topology is l. uv It is then assumed that under the current compact formation, the drone v needs to fly relative to s*l uv Only then can they reach the substitute position. s is the distance between drones; then, assuming the flight time of drone v follows a normal distribution, its expected time is 20l. uv / v cWith a variance of 1, we can obtain the probability distribution of the state of the drone v reaching the specified position at any time t after the drone v begins its transfer, denoted as p. v (t). Finally, with the drone v in place, the previously damaged and dysfunctional component j∈Γ u Start restoring functionality, where Γ u Let j represent the set of components that were originally damaged and rendered inoperable, and let j represent an element in the set of components that were originally damaged and rendered inoperable, i.e., the component that rendered inoperable. Therefore, based on the second state transition relation, the conditional probability distribution of the recovered damaged components in the multi-state UAV swarm IE network model can be obtained, which is expressed as:

[0166]

[0167] Where e = (1, 0, ..., 0), This represents the probability distribution of the cluster under compact formation.

[0168] From the perspective of mission resilience, a key issue when a drone swarm executes a replacement strategy is how to select one drone from among many individuals to perform the replacement action in order to achieve the highest swarm resilience. To achieve this goal, the swarm resilience R(T) is taken as the optimization objective. Furthermore, an objective function is constructed with the swarm resilience of the drone swarm as the optimization objective, expressed as:

[0169]

[0170] Where Q(t) represents the performance of the drone swarm at time t; PQ(t) represents the minimum required performance of the UAV swarm at time t; PQ(t) represents the optimal (expected) performance of the UAV swarm at time t; [P] represents Iverson brackets, which are 1 only if P is true, otherwise [P] = 0; β is the system resilience factor, and 0 ≤ β ≤ 1.

[0171] In this embodiment, the impact of UAV swarm replacement behavior on swarm resilience R(T) is mainly reflected in the pairing of candidate UAVs and damaged UAVs. Therefore, the solution to this optimization problem can be set as the following matrix:

[0172]

[0173] Among them, u i and v i Let i ∈ {1, 2, ..., z} represent the damaged drone number and the drone number assigned to fill in the missing position, respectively, and z be the number of drones currently performing the filling operation. Therefore, the constraints of this optimization problem include:

[0174] u i ∈K

[0175] If i≠j, ui≠u j

[0176] v i ∈Π

[0177] 0≤z≤size(Π)

[0178] MO=2

[0179] The first and second constraints state that only drones from set K can participate in the replacement, and the same candidate drone can only fill the gap left by one destroyed drone. The fourth constraint states that the number of drones performing replacement cannot exceed the total number of destroyed drones, and there may be cases where no replacement is performed at any position. The fifth constraint states that replacement can only be performed in a compact formation.

[0180] To further illustrate the technical effects of the present invention, further examples are provided.

[0181] In this embodiment, in order to facilitate the resilience assessment of the information exchange capability of the multi-state UAV swarm IE network model, it is necessary to conduct further experiments on the information flow throughput of the UAV swarm information interaction network in advance to test the wireless information interaction capability between UAVs and obtain the state probability distribution of its information interaction link (i.e., IE network link).

[0182] Specifically, the throughput, response time, and latency parameters in the information exchange network were evaluated using the commercial Ixchariot software platform. This test platform consists of two parts: a console and an endpoint. The console is installed on a Windows operating system, while the endpoint can be installed on either Windows or mobile devices such as Android or iOS, providing a good hardware and software foundation for this experiment.

[0183] like Figure 5 As shown, in this embodiment, a test system is built using three rotary-wing unmanned aerial vehicles (UAV1, UAV2, and UAV3) for testing. This system consists of three wireless communication transceivers and a ground processing unit (PC) equipped with the Ixchariot test platform. The wireless communication transceivers are smartphones with an installed client (Endpoint APP). Each UAV carries one wireless transceiver to form a network and takes off. The Ixchariot control unit on the ground evaluates the information flow of each link.

[0184] In this embodiment, the information interaction capability of the UAV is tested at different distances. Due to the limited flight time of the UAV, to save experimental time, this experiment uses three UAVs networked together to test at multiple distances simultaneously. The specific test steps are as follows:

[0185] Step 1: Power on all devices on the ground and configure the relevant software.

[0186] Step 2: Press Figure 6 As shown, the drones were placed in the initial positions and remotely launched 10 meters into the air. The communication links of the two sets of rotorcraft UAV1 and UAV2, and rotorcraft UAV1 and UAV3 were tested at the ground control unit.

[0187] Step 3: Rotary-wing UAVs UVA2 and UVA3 each move 10 meters in their forward direction. At this distance, the throughput of the two information exchange links is evaluated again, and the data is recorded. Repeat the above process until both UAVs UVA2 and UVA3 reach their destination.

[0188] In this implementation, the data link was tested for one minute at each distance, and the throughput was recorded at each sampling time. Data loss is a common problem in engineering applications. After interpolating the missing parts of the initial data, the data throughput curves between UAVs at different distances were obtained, as shown below. Figure 7 As shown.

[0189] Depend on Figure 7 It can be seen that the throughput of UAV information interaction exhibits a certain degree of randomness over time at different distances, meaning it fluctuates randomly. Furthermore, the average throughput shows that the information interaction capability decreases as the distance between UAVs increases. Although an 80m distance scenario was designed in the experiment, it is practically impossible to achieve effective communication due to proximity to the communication range limit; therefore, the data does not include a distance of 80m.

[0190] In a multi-state network, the component states are represented by non-negative integers, indicating the component's operational capabilities. Therefore, a correspondence between information flow throughput and network component states is established, as shown in Table 1. Based on this correspondence, the probability distribution of different states is determined by obtaining their proportion within a one-minute test period. For example, at a communication distance of 10 meters, the total time for state 9 (i.e., information flow throughput greater than 45 Mbps) is 51.4 seconds, therefore the probability of state 9 is 51.4 / 60 = 0.856. Similarly, the probability distribution of UAV information interaction link states at various test distances can be statistically calculated, as shown in Table 2. At shorter test distances, information interaction capabilities are mainly concentrated in higher states, meaning the information flow fluctuates around higher throughput. As the test distance increases, the information flow states begin to concentrate towards intermediate states, while some disperse towards lower states. Further increasing the distance between UAVs significantly reduces the information interaction throughput, and the information flow states mainly converge towards lower states.

[0191] Table 1

[0192]

[0193]

[0194] Table 2

[0195]

[0196] Furthermore, the above-mentioned test experiment on the information flow throughput of the UAV swarm information interaction network was completed to further assess and analyze the resilience of information exchange capabilities in the UAV swarm information interaction network.

[0197] 1) Network Configuration

[0198] Suppose a swarm of 20 drones... Figure 8 As shown in (a), the rectangular formation performs a mission. Depending on the mission requirements, the cluster's information exchange network needs to maintain a certain information flow transmission capability during the mission. The information exchange network topology of this UAV cluster under the rectangular formation is as follows: Figure 8 As shown in (b), the network has 20 nodes. In this case, the shortest path length for node pairs 1-20 and 4-17 is 7, which is greater than the shortest path length for other node pairs in the network. Therefore, the performance of this cluster information exchange network is:

[0199] Q(t) = min(Q1(t), Q2(t))

[0200] Where Q1(t) and Q2(t) represent the expected task capabilities of node pairs 1-20 and 4-17 at time t, respectively. Taking node pair 1-20 as an example, considering that traffic is mainly transmitted to the sink, the network topology is as follows: Figure 9 As shown in (a), this multi-state network consists of 20 nodes and 40 components (links). Similarly, 9(b) is the network topology diagram for node pairs 4-17.

[0201] Assume that dense formation, compact formation, and sparse formation modes correspond to drone spacing of 20 meters, 30 meters, and 40 meters, respectively. This means that individual drones can only switch between these three spacings during mission execution. Due to the randomness of drone flight and formation switching, we assume the drone swarm is in formation at a certain distance if the probability of all individuals being at a certain spacing is greater than 0.95. For example, when the drone swarm transitions to sparse formation, it is determined to have transitioned to sparse formation mode only if the probability of all individuals being spaced at 40 meters is greater than 0.95, and MO = 3 is set. If the drone swarm is transitioning between the two formation modes, MO = 0.

[0202] Based on the aforementioned experiments on UAV information exchange throughput, the probability distribution of the information flow has been obtained. To reduce computational load, the states of the information flow are further integrated. State 0 is defined as throughput of 0 to 15 Mbps, state 1 as 15 to 35 Mbps, and state 2 as above 35 Mbps. Furthermore, the above data does not consider the reliability of individual UAVs; that is, information exchange can only occur when both the sending and receiving UAVs are in normal working order. Assuming the reliability of an individual UAV is 0.99, and since the normal operation of the link requires both sending and receiving UAVs to be in normal working order, the probability of a normal information exchange link is 0.98. Taking this assumption into account, the probability distribution of UAV information exchange capability (i.e., the throughput statistics at each distance) can be obtained under three formation distances, as shown in Table 3, which represents the probability distribution of the information flow under the "condition" of different distances.

[0203] Table 3

[0204]

[0205] Based on Table 3, for any information interaction link i (i.e., component i), its conditional operation probability matrix is ​​as follows:

[0206]

[0207] Assume that the probability distribution of the two drones corresponding to link i under the three spacing conditions is pb i (t), then the state probability distribution of the information exchange capability of this link is p i (t)=pb i (t)*C i .

[0208] 2) Determination of formation transformation parameters

[0209] During the process of countering disturbances, swarms may undergo formation changes, which are essentially adjustments to the spacing between individual swarm members. This case study assumes three possible formation spacings, and further assumes three possible scenarios (i.e., events) for the spacing between two UAVs corresponding to a certain information exchange link i. and This corresponds to three scenarios with drone spacing of 20m, 30m, and 40m, respectively. The state transition probability represents the probability that two drones will reach a designated position after a certain period of time from their initial positions. Therefore, this case assumes that F follows a normal distribution with mean μ and variance 1. Here, F describes the probability distribution, representing the probability that a drone will reach a designated position after a certain period of time from its initial position. When transitioning from a swarm to a dense formation, F... 12 =F 13 =F 23 =0; when the cluster transitions to compact formation, F = 0; 13 =F 31 =F 21 =F 23 =0; When transitioning from a cluster to a sparse formation, F = 0; 21 =F 31 =F 32 =0.

[0210] The parameter μ of the normal distribution represents the expected time required for the drone to reach the designated location. Taking the transition from dense to sparse swarm formation as an example, assume the drones expand outwards from the swarm center to increase spacing. Figure 10 As shown in (a), the upper and lower clusters divided by dashed line B move upward and downward by 10m respectively. Class I links are defined as links numbered 3, 11, 13, 21, 23, 31, 33, and 39. At this point, Class I links meet the UAV spacing requirements, and the expected time for UAV position movement is 10 / v. c , where v c Let be the relative velocity of the UAV during its position change, hence we have For drones located above and below dashed line A and C respectively, they need to move 20m up and down each, for a total displacement of 30m, to meet the drone spacing requirements. Therefore, Class II links are defined as links numbered 1, 5, 8, 10, 14, 16, 18, 20, 24, 26, 28, 30, 34, 36, 38, and 40.

[0211] After the longitudinal spacing is adjusted, consider the following: Figure 10 (b) shows the lateral spacing adjustment of the cluster. The drones on either side of the dashed lines E and F move 20m to each side. Class III links are defined as links numbered 12, 15, 22, and 25. For these links, the drones moved a total of 30m (including longitudinal adjustments) to achieve the required spacing. Therefore, there is... Class IV links are defined as links numbered 9, 17, 19, and 27. The drone traveled a total of 50 meters on these links, therefore... Finally, the drones on either side of dashed lines D and G need to move 20m to each side. Similarly, Class V links are defined, including links numbered 4, 6, 32, and 35. For these links, the drones move a total of 50m. Therefore, there are... Class VI links are defined as links numbered 2, 7, 29, and 37. The drone traveled a total of 70 meters on these links, therefore...

[0212] The transition from large-spaced formation to small-spaced formation can also be viewed as a reverse adjustment of the above process in both the longitudinal and lateral directions (i.e., various link state transition parameters). This yields the parameters, as shown in Table 4, which follow a normal distribution for different link spacing transitions.

[0213] Table 4

[0214]

[0215] 3) Simulation and Analysis

[0216] Based on the aforementioned cluster information interaction network model and adversarial behavior modeling, computer simulations are used to assess and analyze the cluster's resilience under different strategies during tasks. Two recovery strategies are considered during cluster tasks:

[0217] Cluster formation change strategy (strategy 1): The cluster only uses formation change to counteract disturbances.

[0218] Cluster redeployment strategy (Strategy 2): The cluster fills in the "vacant spots" of damaged drones while changing formation. The optimal selection of the replacement drone is determined using a genetic algorithm during the replacement operation. Furthermore, the relative flight path length l of the replacement drone is also considered. uv Obtained by the shortest path search algorithm.

[0219] The main simulation parameters are shown in Table 5. The ideal information exchange capability PQ(t) represents the information exchange capability of the entire network when the UAV swarm is in close formation and no individual UAVs are damaged. In this case, the state distribution of all links follows p... i= (0.02, 0.078, 0.902), the expected information interaction capability of the network under this ideal condition can be calculated to be 2.55. Assuming that the ideal information interaction capability does not change over time throughout the entire task, PQ(t) = 2.55. Furthermore, assuming that the cluster needs to share a large amount of real-time dynamic image data during the task, the required information interaction capability is set to 2. The cluster encountered two disturbances during the task, occurring at 300s and 600s respectively. The first disturbance did not cause damage to any individual drones in the cluster. The second disturbance caused varying degrees of damage to individual cluster members; specific settings are detailed in subsequent scenarios.

[0220] Table 5

[0221]

[0222] (a) Analysis of the two strategies with the damage number at the time of the second disturbance being 1.

[0223] This situation indicates that during the second disturbance in the drone swarm, one drone was damaged and lost all functionality. This case study simulates the damage scenarios for all drones except the source and sink nodes. The resilience statistics for different strategies at each location when damaged are shown in Table 6. Figure 11 As shown. The green dashed line represents the resilience of the cluster under formation changes caused only by disturbances, without any damage (0.787).

[0224] As shown in the chart, for individual drones damaged, whether or not the drones at positions 2, 3, 5, 8, 14, 16, 18, and 19 are damaged has a significant impact on the cluster's information exchange capabilities. Taking the case where the drone at position 2 is damaged as an example, the cluster's performance curve in this situation is as follows: Figure 12 As shown in the diagram, the first disturbance occurred at 300s, causing the cluster to transition to a sparse formation. At this point, the network performance only needed to decrease until the formation stabilized. After a period of observation and buffering (h), the cluster began to recover to a dense formation at 398s and completed the formation transition at 436s, at which point the network performance essentially returned to its initial state. After the second disturbance caused the drone at position 2 to fail, the network performance degradation was more severe compared to the first disturbance. At 735s, the cluster recovered to a compact formation. Strategy 1 continued to transition to a dense formation, but even after completing the transition, its expected mission capability was only 0.895, failing to meet the mission requirements. Strategy 2, at the beginning of the replacement phase, experienced a slight decrease in network performance due to the drone 6 leaving its original position. However, once the drone reached its designated position, the network performance recovered to 1.366, and as the cluster transitioned to a dense formation, the network performance recovered to 2.356, meeting the mission requirements.

[0225] For drones numbered 6, 7, 9, 10, 11, 12, 14, and 15, the optimization algorithm failed to find replacement drones with better resilience than strategy 1. That is, when these drones are damaged, on the one hand, the damage itself has little impact on the network performance; on the other hand, the best strategy is to keep the current topology unchanged, so that the network still has the ability to complete the task after the formation is restored.

[0226] Table 6

[0227]

[0228]

[0229] (b) Analyze the two strategies with the number of damages at the time of the second disturbance being 2.

[0230] In the second perturbation, two drones in the cluster were damaged and lost all functionality. Table 7 shows eight scenarios of drone damage at adjacent locations, and the resilience values ​​for each scenario and corresponding recovery strategies are recorded. The first number in the replacement scheme represents the drone number that replaces the position of the first damaged drone in the damage set. For example, in the first scenario, drone 10 is used to replace the position of the damaged drone 2. The table shows that compared to the scenario with only one damaged drone, increasing the number of damaged drones has a greater impact on network performance, and consequently, the resilience value decreases.

[0231] like Figure 13 As shown, among the eight damage scenarios, the damage in scenarios 6 and 7 (i.e., schemes numbered 6 and 7 in Table 7) did not significantly impact network resilience, and the optimization algorithm did not provide any further compensation schemes to improve resilience. The remaining damage scenarios severely impacted system performance; without compensation strategies, these scenarios could not be restored to the minimum task requirements. Taking scenario 4 as an example, the performance curves under the two strategies are shown below. Figure 14 As shown, Strategy 1 only achieves a performance of 1.94 after recovery, which fails to meet the minimum requirements of the task. Therefore, the recovery behavior after the second perturbation does not contribute to improving the resilience of the network. Although Strategy 2 reaches steady state later than Strategy 1 after the replacement, its performance level recovers to 2.24, meeting the task requirements, thus improving the resilience of the system.

[0232] like Figure 15As shown, for the damage set in Group 1 (i.e., scheme 1 in Table 7), the long dashed line represents the replacement scheme obtained using the optimization algorithm, where drone 10 replaces drone 2, and drone 6 replaces drone 3. The dotted dashed line represents another replacement scheme, the basic principle of which is to select two individuals from Table 6 whose damage has the least impact on network resilience as the replacement drones. It can be seen that the damage to drones 9, 10, 11, and 12 has the least impact on cluster resilience, therefore drone 11 is chosen to replace drone 2, and drone 10 to replace drone 3. As can be seen from the figure, although the final performance levels of both schemes meet the task requirements, the replacement scheme based on optimization enables the system performance to recover more quickly and reach the task requirements earlier, and the final performance level achieved is also higher than that of the replacement scheme represented by the blue curve, showing stronger resilience.

[0233] Table 7

[0234]

[0235] (c) Analyze the two strategies with the number of damages at the time of the second disturbance being 3.

[0236] Considering eight scenarios where disturbances to three adjacent components lead to complete functional loss, the corresponding combinations of damaged components are shown in Table 8. Simulation experiments reveal that when the number of damaged components reaches three, regardless of the recovery strategy, the resilience under the eight considered damage combinations cannot be improved; that is, the restored network performance cannot meet the original task requirements. At this point, the cluster is no longer able to effectively continue executing the original task, but in order to ensure the basic capabilities of the cluster, the task requirements can be changed to... This means ensuring basic information exchange capabilities between individual cluster members to prevent the cluster from disintegrating and to enable a safe return.

[0237] After reducing the task requirements following the second perturbation, the cluster's resilience under each strategy was evaluated again, and the results are shown in Table 9. Figure 16 As shown, based on changing task requirements, the resilience value before damage is 0.824. In cases 2 and 7, no optimal replacement solution was found, meaning the damaged drone has the least impact on resilience, and maintaining the current topology is the most resilient recovery measure. The damage in the other six cases all caused a significant drop in network performance. Strategy 1 is unlikely to effectively restore network performance, while Strategy 2, by changing the drone's position, restores it to basic information exchange capabilities.

[0238] Taking the first damage combination as an example, its network performance curve during the mission is as follows: Figure 17As shown, the network task requirement was initially set to 2. After the second disturbance, the task requirement changed to ensuring the basic information exchange capability of the cluster, so it was set to 1. Based on the new task requirement, the recovery performance of Strategy 1 eventually stabilized at 0.867, still not meeting the requirement. Strategy 2 met the new task requirement at 758 seconds and finally stabilized at 1.55. Therefore, Strategy 2 significantly improved the resilience of the system after the task requirement changed, ensuring the basic information exchange capability of the cluster. In this embodiment, the network performance curve refers to the performance change process under different optimization objectives (the aforementioned resilience optimization and performance).

[0239] Taking the first damage combination as an example, the optimization objective of strategy 2 is to achieve the highest system resilience. If the optimization objective is set to the highest network performance level, then the replacement scheme (7-11-15) can also restore the network performance level to 1.55. At this time, the performance curves under the two optimization strategies are as follows: Figure 18 As shown, although both schemes ultimately achieve the same performance level, the optimal resilience-based replacement scheme minimizes the relative movement distance of the drone, enabling it to reach the replacement position more quickly and allowing the network performance level to recover more promptly. Considering only performance level fails to take the time factor into account, further demonstrating the comprehensive resilience capabilities.

[0240] Table 8

[0241]

[0242] Table 9

[0243]

[0244]

[0245] The above description is merely an example of a specific solution of the present invention. For any devices and structures not described in detail herein, it should be understood that they are implemented using common devices and methods already available in the art.

[0246] The above description is merely one embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the resilience of UAV swarm information exchange capabilities based on multi-state networks, characterized in that, include: S1. Construct a multi-state drone swarm IE network model; S2. Based on the multi-state UAV swarm IE network model, introduce the conditional probability distribution of IE network links and IE network performance metrics; This includes: use i Representing the first in the multi-state UAV swarm IE network model i One component; use c i The various states of the components in the multi-state UAV swarm IE network model are represented as follows: ;in, m i The maximum flow rate that the component can operate at; The state probability distribution of the component is constructed as follows: ;in, p i c It represents the probability that the component operates in various states; The conditional probability distribution is constructed based on the state probability distribution, and it is expressed as follows: in, This represents the condition vector of the component. The conditional operating probability matrix represents the component. In the step of introducing IE network performance metrics based on the multi-state UAV swarm IE network model, the IE network performance metrics are expressed as follows: in, The pair of nodes with the largest minimum number of hops and equal minimum number of hops; S3. Construct a drone swarm resilience model for the drone swarm based on the conditional probability distribution and the IE network performance metric; wherein, the drone swarm resilience model includes: a swarm formation transformation resilience sub-model and a drone redeployment resilience sub-model constructed using the conditional probability distribution and the IE network performance metric; The step of constructing a cluster formation transformation resilience sub-model using the conditional probability distribution includes: Based on the cluster formation transformation resilience sub-scheme, the first state transition relationship of the components in the multi-state UAV cluster IE network model during the formation transformation process is obtained; Based on the first state transition relationship and the semi-Markov model, a conditional vector is constructed to represent the state transitions of components in the multi-state UAV swarm IE network model during formation transformation, as follows: in, This represents the conditional probability distribution of the component at the initial time. This represents the state transition matrix obtained based on the semi-Markov model; Based on the conditional vector generated by the component during the formation transformation, a conditional probability distribution of the UAV swarm separation behavior is constructed, which is expressed as: ； Based on the conditional vector generated by the component during the formation transformation, a conditional probability distribution of the UAV swarm aggregation behavior is constructed, which is expressed as: ； Based on the semi-Markov model, the probability distribution of the communication link state of the component during the formation transformation process is constructed as follows: in, This represents the transition probability matrix of the component during the resilience process; The step of constructing a drone redeployment resilience sub-model using the conditional probability distribution and the IE network performance metric includes: Based on the drone redeployment resilience sub-scheme, the second state transition relationship of the components in the multi-state drone cluster IE network model during the redeployment process is obtained; Based on the second state transition relationship, the conditional probability distribution of the recovered damaged components in the multi-state UAV swarm IE network model is defined as follows: in, , This represents the probability distribution of the cluster under compact formation. Let v represent the probability distribution of the state of the assumed drone v at any time t after it begins to move, and the drone reaches the specified location. The objective function is constructed with the cluster resilience of the drone swarm as the optimization objective, and it is expressed as follows: in, For the drone swarm in t Real-time performance; For the drone swarm in t Minimum performance requirements for the task at any given time; For the drone swarm in t Optimal performance of drone swarms at all times; For Iverson, brackets are only used when When true ,otherwise ; β As a system resilience-focusing factor, and ; S4. Set the recovery strategy for the UAV cluster during the cluster task process, and evaluate the resilience of the information exchange capability of the multi-state UAV cluster IE network model based on the recovery strategy and the UAV cluster resilience model; wherein, the recovery strategy includes: cluster change formation strategy and cluster redeployment strategy; If the cluster transformation formation strategy is adopted, the information exchange capability of the multi-state UAV cluster IE network model is evaluated based on the cluster formation transformation resilience sub-model. If the cluster redeployment strategy is adopted, the resilience of the information exchange capability of the multi-state UAV cluster IE network model is evaluated based on the UAV redeployment resilience sub-model.

2. The method for analyzing the resilience of UAV swarm information exchange capabilities according to claim 1, characterized in that, In step S1, the step of constructing a multi-state UAV swarm IE network model is a two-terminal multi-state network model composed of multiple network nodes and multiple components, which is represented as follows: in, V This represents the set of network nodes in a two-terminal, multi-state network model. E The set of components in a two-terminal multi-state network model is represented as: .

3. The method for analyzing the resilience of UAV swarm information exchange capabilities according to claim 2, characterized in that, The step of constructing the conditional probability distribution based on the state probability distribution includes: For the component, multiple incompatible events are defined, and the events represent the operating conditions of the component. The component is obtained from the law of total probability. t The flow rate is in a state at any given time. c i The probability is expressed as: （1） in, Indicates the first i The components are in t The flow is in a state when the event described occurs at a certain time. c i The probability, The event represents the condition that satisfies the following conditions. , For the sample space; Define the condition vector of the component as follows: （2） The conditional operation probability matrix of the component is defined as follows: （3） The conditional probability distribution is obtained based on formulas (1), (2) and (3).

4. The method for analyzing the resilience of UAV swarm information exchange capabilities according to claim 3, characterized in that, Step S3, the step of constructing a drone swarm resilience model for the drone swarm based on the conditional probability distribution and the IE network performance metric, includes: The resilient behavior of the UAV swarm during task execution is designed to obtain a resilient behavior scheme for the UAV swarm; wherein, the resilient behavior scheme includes: a swarm formation transformation resilient sub-scheme and a UAV redeployment resilient sub-scheme; The resilience model of the drone swarm is constructed based on the aforementioned resilience behavior scheme.

5. The method for analyzing the resilience of UAV swarm information exchange capabilities according to claim 4, characterized in that, The step of designing resilient behavior for the drone swarm during task execution and obtaining a resilient behavior scheme for the drone swarm includes: Three formation modes are set based on the distance between individual drones in the drone swarm, and each is defined by a variable. MO Indicates; among which, with Indicates dense formation mode, with Indicates compact formation mode, Indicates sparse formation mode; Based on the three formation modes, the cluster formation transformation resilience sub-scheme and the UAV redeployment resilience sub-scheme are set.

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