A method for evaluating group performance of unmanned aerial vehicle group based on flock intelligence cluster entropy metric

Abstract

The application discloses a kind of based on flock intelligence cluster entropy measure UAV group group efficiency evaluation method, comprising: step one: construct flock bionics mapping model, form the cross-domain mapping framework of four stages of flock intelligence to UAV group OODA ring;Step two: collect the cooperative state time series data in the process of UAV group execution task planning and carry out pre-processing;Step three: construct and calculate the structure entropy model of observation stage;Step four: build and calculate the information flow entropy model of judgment stage and so on eight steps in total.The method of the present application can realize the unified quantitative evaluation of UAV group in the whole process of task planning cooperation, stability and intelligence, reveal the coupling relationship between multi-dimensional indexes such as structure organization, information transmission, cooperative decision-making and action execution, improve the comprehensiveness, rationality and reliability of UAV group efficiency evaluation, suitable for multi-UAV task planning, cooperative decision analysis and group efficiency evaluation.

Description

Technical Field

[0001] This invention relates to a method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks, belonging to the field of UAV swarm intelligent evaluation and group collaboration analysis technology. Background Technology

[0002] With the rapid development of UAV swarm technology, multi-UAV systems have been widely applied in scenarios such as complex environment perception, collaborative reconnaissance, mission search, path planning, and formation flight. Compared to single-unit systems, UAV swarms, through information exchange, task division, and collaborative control among individuals, exhibit stronger robustness, self-organization, and mission adaptability in complex mission environments. Therefore, how to scientifically, uniformly, and quantitatively evaluate the overall effectiveness of UAV swarms throughout the entire mission planning and execution process has become a key issue in swarm intelligence research and engineering applications.

[0003] Existing methods for evaluating the effectiveness of drone swarms have explored the construction and comprehensive evaluation of indicator systems, primarily employing methods such as analytic hierarchy process (AHP) and fuzzy comprehensive evaluation to quantify drone swarm effectiveness. While these studies provide a reference for drone swarm effectiveness evaluation, they generally focus on single indicators or weighted comprehensive evaluations, making it difficult to uniformly depict the dynamic evolution of the swarm throughout the entire task planning process, including observation, judgment, decision-making, and action. Furthermore, they struggle to reveal the inherent coupling relationships between swarm structure organization, information dissemination, strategy formation, and action coordination. Additionally, they lack a holistic evaluation framework that can uniformly measure aspects such as swarm orderliness, causal transmission, decision consensus, and action rhythm.

[0004] From the perspective of biological group behavior, geese exhibit significant swarm intelligence characteristics during migration: they can spontaneously form V-formations during flight, achieving structural optimization and energy conservation through wingtip vortex upwash; the heading adjustment information of the lead goose can be transmitted directionally along the formation, demonstrating a clear information causal propagation mechanism; the leaders in the group can dynamically rotate based on energy depletion, reflecting mutually beneficial and equitable decision-making organization characteristics; simultaneously, migrating groups also exhibit multi-scale rhythmic control of flight-rest alternation and phase synchronization behavior among individuals. These behaviors have strong biomimetic correspondences with the structural organization, information interaction, collaborative decision-making, and task execution of UAV swarms during mission planning, providing a new approach for constructing a unified model for UAV swarm performance evaluation.

[0005] To address the aforementioned issues, this invention proposes a method for evaluating the effectiveness of UAV swarms based on goose-based intelligent swarm entropy measurement. This method constructs a goose-inspired mapping model, mapping the V-formation organization mechanism, information causal transmission mechanism, leadership rotation reciprocity mechanism, and flight rhythm synchronization mechanism of geese during migration to the structural entropy, information flow entropy, decision entropy, and action entropy of the UAV swarm's OODA loop (OODA Loop decision theory model, including four stages: observation, judgment, decision, and action) task planning process. By collecting and preprocessing time-series data of the UAV swarm's collaborative state, structural entropy models for the observation stage, information flow entropy models for the judgment stage, decision entropy models for the decision stage, and action entropy models for the action stage are established. The four entropy components are then fused using a weighted aggregation function with cross-coupling terms and a nonlinear modulation function based on the system state covariance matrix to obtain the total swarm entropy. This total swarm entropy is further mapped to a swarm effectiveness index. Simultaneously, an uncertainty quantification method based on a cloud model is used to output the confidence level of the evaluation results, thereby achieving a unified quantitative evaluation of the collaboration, stability, and intelligence of the UAV swarm throughout the entire task planning process. Summary of the Invention

[0006] This invention aims to propose a method for evaluating the effectiveness of UAV swarms based on the entropy metric of goose flock intelligence. The purpose is to address the problems of existing methods in evaluating UAV swarm effectiveness, such as fragmented evaluation dimensions, difficulty in reflecting the coupling relationships between multi-dimensional indicators, and uncertainty in evaluation results. The invention constructs a unified effectiveness evaluation method applicable to the entire process of UAV swarm mission planning, achieving comprehensive quantitative characterization of key capabilities such as swarm structure organization, information transmission, collaborative decision-making, and action execution. This improves the comprehensiveness, rationality, and credibility of UAV swarm effectiveness evaluation, providing a valid basis for optimizing UAV swarm mission planning, analyzing collaborative capabilities, and enhancing system performance.

[0007] This invention addresses the lack of a unified and quantitative evaluation method for the mission planning performance of unmanned aerial vehicle (UAV) swarms in existing technologies. Inspired by the structural organization, information dissemination, leadership rotation, and rhythmic coordination mechanisms of migratory goose flocks, it provides a UAV swarm performance evaluation method based on the intelligent swarm entropy measurement of goose flocks. The main implementation steps are as follows: Step 1: Construct a goose flock biomimetic mapping model to form a cross-domain mapping framework of four stages from goose flock intelligence to UAV swarm OODA loop. S11. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and structural entropy. During migration, geese spontaneously form a V-formation. Following geese gain additional lift by positioning their wingtips in the upwash region generated by the wingtip vortex of the leading goose. Optimal wingtip spacing of an individual relative to the individual in front satisfy ,in, For wingspan, formation size With the reduction rate of group-induced resistance Between satisfy ,in, Let be the wingtip overlap coefficient, and let this relationship exhibit a logarithmic decreasing characteristic; inspired by this, a structural mapping function is defined. In the formula, For structure mapping functions, for Structural entropy at time step For drones and The spacing, For the first The velocity vector of the drone As a communication topology diagram, the mapping maps the spatial order constraint of the goose V-formation to the structural entropy of the UAV swarm observation phase.

[0008] S12. Establish a mapping relationship between the intelligent behavioral characteristics of goose flocks and the entropy of information flow. During flight, the heading adjustment signal of the lead goose propagates directionally along the V-formation towards the follower birds; individual geese... For individuals The intensity of information influence is measured by transmission entropy and is defined as: (1) In the formula, Given the conditional Shannon entropy, For individuals exist The heading angle at any moment, For individuals The length is The heading history vector, For individuals The length is The heading history vector, and The propagation entropy is a predefined embedding dimension parameter with values ​​ranging from 1 to 5, and it exhibits asymmetry. This allows us to distinguish the causal direction of information between the lead goose and the follower geese; inspired by this, we define an information flow mapping function. In the formula, For information flow mapping functions, for Information flow entropy at any given moment For time window Sampling time within, For the first Time series of heading angle of a drone For a set of communication links, The mapping, defined as the time window length, maps the directionality and causality of goose information transmission to the information flow entropy during the drone swarm judgment phase.

[0009] S13. Establish a mapping relationship between the intelligent behavioral characteristics of goose flocks and decision entropy. Leader rotation in goose formations follows a direct reciprocity mechanism, with individual... In time period The cumulative time spent in the lead position is The cumulative time spent in the follower position to obtain the benefits of the wash is Then the two satisfy the positive correlation constraint. And the Gini coefficient for the group navigation time distribution is: (2) Its value approaching zero indicates fair rotation; inspired by this, a decision mapping function is defined. In the formula, For decision mapping function, for Decision entropy at any given moment Choose a vector for the strategy. For task load, For platform capability values, As a collaborative decision-making graph, the mapping maps the reciprocal fairness of goose leader rotation to the decision entropy of the drone swarm decision-making stage.

[0010] S14. Establish a mapping relationship between the intelligent behavioral characteristics of goose flocks and their action entropy. During goose migration, individuals in a V-formation maintain spatially in-phase wing flapping to track the upwash peak of the eddy current ahead. The wing flapping phase difference within the formation... satisfy ,in, The longitudinal spacing along the flight direction. Using the wingbeat wavelength as an example, this phase-matching relationship ensures the rhythmic synchronization of migration movements; inspired by this, a movement mapping function is defined. In the formula, For action mapping functions, for Action entropy at any moment For time window Sampling time within, For the first The actual flight path sequence of the drone. For the first The actual flight speed sequence of the drone. For the first The expected flight path sequence of the drone. To assess the window length, the mapping synchronizes the rhythm of goose migration with the action entropy of the drone swarm action phase.

[0011] Step 2: Collect and preprocess the time-series data of the collaborative status during the task planning process of the drone swarm. S21. Collect time-series data on the status of the drone group. Assume the group consists of... Composed of drones, the system uses a drone telemetry link to perform sampling at a preset period. For group number The drone's status is collected at various times; the collected status data includes the first... A drone in Position vector at time velocity vector Heading angle Remaining energy Sensor operating status indicator and communication link quality parameters .

[0012] S22. Preprocess the group status time-series data collected in step S21. For missing data, interpolation is performed using an AR(p) autoregressive model, where the autoregressive model is defined as... ,in, For a moment Status data, For the autoregressive parameter vector, White noise, model order Using Bayesian information criteria It is confirmed that, among them, The length of the sampled data. Least squares estimation of residual variance. The above process is used to time-synchronize and align the state data of each UAV, ensuring that all data are used for subsequent calculation of cluster entropy under a unified time reference.

[0013] Step 3: Construct and calculate the structural entropy model for the observation phase. S31. Construct a structural entropy modeling index system to extract structural features related to group spatial organization and communication topology. In the V-formation of geese, adjacent individuals maintain an optimal wingtip spacing of approximately 0.78 times the wingspan to maximize upwash airflow utilization; the velocity directions among individuals are highly consistent, and the overall formation exhibits polarized order. Inspired by this, from the aforementioned mapping function... Three types of input variables for drones and Spacing velocity vector and communication topology diagram Starting from this point, the parameters are decomposed into five sub-indicators: neighborhood velocity consistency, polarization order parameter, algebraic connectivity, cover distribution entropy, and structural convergence time.

[0014] S32. Based on the structural features described in S31, construct five sub-indices of structural entropy.

[0015] Based on the drones and their neighbors exist velocity vector at time t and Calculate neighborhood speed consistency Let the first The neighborhood set of the drone is ,in, For communication radius, Given the number of drones in the neighborhood set, the neighborhood speed consistency is... : (3) The closer the value is to 1, the more consistent the local velocity directions are, corresponding to the neighborhood velocity coupling characteristics in goose formation. Based on the first... A drone in velocity vector at time t Calculate polarization order parameters : (4) Its value ranges from 0 to 1, corresponding to completely disordered to completely ordered, respectively, which corresponds to the homogeneity of the global movement direction of the goose formation.

[0016] Based on communication topology input Construct the Laplace matrix Calculate its second smallest eigenvalue, i.e., its algebraic connectivity. A value greater than 0 indicates that the communication graph is connected, and the larger the value, the more stable the topology, corresponding to the stability of the visual perception link in the goose formation.

[0017] Based on spacing input and UAV position vector Discretize the task region into A uniform area grid cell, and at time... Select a length of for the endpoint The structural evaluation window. Let... This is the set of sampling times within the evaluation window. The number of sampling times. To evaluate whether all drone trajectory sampling points within the evaluation window fall into the first... The number of times the th grid cell is defined. The coverage percentage of each grid cell is Calculate the entropy of the coverage distribution: (5) The closer its value is to This indicates that the more uniform the trajectory coverage, the more uniform the spatial deployment of the V-formation of geese. Based on the temporal evolution of the above three types of inputs, the structural convergence time is defined as follows: (6) In the formula, , , The convergence time of the structure is a preset threshold. This corresponds to the time required for geese to go from taking off in a dispersed manner to forming a stable V-formation.

[0018] S33. Calculate structural entropy to characterize the degree of order in group spatial organization and communication topology. Let... ( Let represent the original values ​​of five structural entropy sub-indices: neighborhood velocity consistency, polarization order parameter, algebraic connectivity, cover distribution entropy, and structural convergence time. To eliminate the influence of different sub-indices' dimensions and values, each sub-indice is uniformly converted into a normalized entropy penalty term. For the large-scale index, where a larger value indicates a more ordered structural state, the following normalization method is adopted: (7) For smaller-valued indices, which indicate a more ordered structural state, the following normalization method is adopted: (8) In the formula, and The first The minimum and maximum values ​​of each structural entropy sub-index within the evaluation window or the preset range of the task scenario. The preset minimum positive number is used. Neighborhood velocity consistency, polarization order parameter, algebraic connectivity, and cover distribution entropy are indices for tending towards larger values, while structural convergence time is an index for tending towards smaller values. Let the weight of the structural entropy sub-index be... ,and , Then the structural entropy is expressed as , For the first The normalized entropy penalty term corresponds to each structural entropy sub-index. The decrease in structural entropy indicates that the group structure converges from loose randomness to ordered compactness, corresponding to the entropy reduction process of geese gradually forming a stable V-formation from dispersed takeoff.

[0019] Step 4: Construct and calculate the information flow entropy model for the judgment phase. S41. Construct an information flow entropy modeling index system to extract group heading information and communication link information. During migratory flight, goose formation information propagates directionally along the leader-follower link. Changes in the leader bird's heading have a causal impact on the follower birds, and this impact is asymmetric. Inspired by this, using transfer entropy as the core tool, from the aforementioned mapping function... Two types of input heading angle time series and communication link set Starting from this point, it is decomposed into four sub-indicators: spectral entropy of the transfer entropy matrix, information flow directionality index, group cognitive convergence degree, and information convergence time.

[0020] S42. Based on the judgment information described in S41, construct four types of sub-indices for information flow entropy. Based on the heading angle time series input. and communication link input For each pair of drones with a communication link Calculation from individual To individuals Transitive entropy: (9) In the formula, For individuals exist The heading angle at any moment, For individuals The length is The heading history vector, For individuals The length is The heading history vector, and The probability distribution is defined as follows: The embedding dimension parameter is a preset integer ranging from 1 to 5. Obtained by kernel density estimation method; for non-connected UAV pairs set up The asymmetry of the transfer entropy It can distinguish between information drivers and responders, corresponding to the causal direction of information between leaders and followers in a goose formation.

[0021] Construct a group information flow matrix For non-connected UAVs, assume the transit entropy is zero; perform singular value decomposition on the matrix to obtain singular values. (in, (where is the rank of the matrix), normalize each singular value to Calculate the spectral entropy of the transfer entropy matrix: (10) In the formula, Information flow matrix The A singular value, The percentage of singular values ​​after normalization; a lower spectral entropy indicates that information flow is concentrated in a few dominant causal links, corresponding to a clear hierarchical transmission structure in goose formations. The directionality index is calculated based on the information flow matrix: (11) In the formula, For individuals For individuals The propagation entropy, For individuals For individuals The propagation entropy, The total number of communication links. Preset minimum positive number to prevent division by zero; A value closer to 1 indicates a stronger directionality of information flow, corresponding to the unidirectional dominant transmission characteristic from the lead goose to the follower geese in a goose formation. Calculate the convergence degree of group cognition. : (12) In the formula, and For the first drones and their neighbors The situation estimation vector.

[0022] Define information convergence time for First time reaching the preset threshold The minimum moment.

[0023] S43. Calculate the information flow entropy to characterize the efficiency and consistency of information organization within the group. Let... ( The numbers () represent the original values ​​of four types of information flow entropy sub-indices: spectral entropy of the transfer entropy matrix, information flow directionality index, group cognitive convergence, and information convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, the spectral entropy of the transfer entropy matrix and the information convergence time are indicators of tending towards smaller values, while the information flow directionality index and the group cognitive convergence degree are indicators of tending towards larger values. Let the weight of the information flow entropy sub-indicator be... ,and , Then the information flow entropy is expressed as , For the first The normalized entropy penalty term corresponds to each information flow entropy sub-index. The decrease in information flow entropy indicates that the causal information chain converges from scattered and ambiguous to directional and clear, corresponding to the entropy reduction process in goose formation where information diffuses from disorder to effective convergence along the hierarchical chain.

[0024] Step 5: Construct and calculate the decision entropy model for the decision-making stage. S51. Construct a decision entropy modeling index system to extract strategy selection, task load, platform capability values, and collaborative decision-making graphs. In migratory goose formations, leader rotation is frequent and follows direct reciprocity; the group automatically adjusts leader roles based on individual energy depletion levels while maintaining overall directional stability. Inspired by this, from the aforementioned mapping function... Four types of input policy selection vectors Task load Platform capability value Collaborative Decision Diagram Starting from this point, the indicators are broken down into five categories: policy consistency, policy polarization order parameter, task assignment fairness, collaborative decision graph connectivity, and decision convergence time.

[0025] S52. Construct five sub-indicators of decision entropy based on the decision information described in S51.

[0026] To map the local consensus among adjacent individuals in a goose formation on directional decisions, and to obtain... Each drone and its neighbors Strategy selection vector and Calculate the consistency of group policies: (13) Based on policy selection vector input Calculate the strategy polarization order parameter: (14) Approaching 1 indicates that all individual strategies are concentrated in a few patterns, corresponding to the majority decision-making mechanism of the goose flock. Let the first... The mission payload of the drone is Platform capability value Calculate the fairness index of task assignment: (15) In the formula, The average load capacity ratio of the group; the fairness index directly corresponds to the Gini coefficient of the goose piloting time distribution. The reciprocal fairness constraint approaching zero A value closer to 1 indicates a more balanced task allocation. Construct a collaborative decision-making graph. And calculate the connectivity of the collaborative decision graph. This corresponds to the accessibility of decision-making information within a goose formation.

[0027] Define decision convergence time for First time reaching the preset threshold The minimum moment.

[0028] S53. Calculate the decision entropy to characterize the convergence degree of the group's strategy consensus. Let... ( The numbers () represent the original values ​​of five decision entropy sub-indices: policy consistency, policy polarization order parameter, task assignment fairness, collaborative decision graph connectivity, and decision convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, policy consistency, policy polarization order parameter, task assignment fairness, and collaborative decision graph connectivity are indicators of tendency towards larger scales, while decision convergence time is an indicator of tendency towards smaller scales. Let the weight of the decision entropy sub-indicator be... ,and , Then the decision entropy is expressed as , For the first The normalized entropy penalty term corresponds to each decision entropy sub-indicator. The decrease in decision entropy indicates that the group's strategy is converging from divergent fluctuations to consensus, corresponding to the entropy reduction process of the goose flock forming a unified migration decision through a reciprocal rotation mechanism.

[0029] Step Six: Construct and calculate the action entropy model for the action phase. S61. Construct an action entropy modeling index system to extract action state information such as actual trajectory, velocity vector, and expected trajectory. During goose migration, individual geese in formation maintain wingbeat frequency synchronization and spatial phase matching, ensuring rhythmic consistency and efficient energy utilization of the group's actions; inspired by this, from the aforementioned mapping function... The three types of input Actual flight sequence of the drone Actual speed sequence and expected track sequence The starting point is broken down into six sub-indicators: trajectory tracking deviation, velocity and attitude consistency, arrangement entropy, mission space coverage effectiveness, collision risk distribution, and action convergence time.

[0030] S62. Construct six sub-indicators of action entropy based on the action status information described in S61.

[0031] Based on the evaluation window of each drone Actual flight track sequence within With the expected track sequence Calculate the tracking deviation: (16) This corresponds to the degree to which an individual goose in a formation deviates from the ideal V-shaped position. Based on the first... drones and their neighbors Actual speed sequence and Calculate the group's velocity and attitude consistency: (17) This corresponds to the synchronization of the flight speed and direction of adjacent individuals in a goose formation. Based on actual flight path input. The time series of each drone's action mode are used to construct the first... The sequence of motion changes of the drone Used to characterize the The magnitude of the change in the motion state of a UAV between adjacent sampling times can be obtained by velocity vector difference or trajectory difference. (Based on embedding dimension) and time delay Constructing action embedding vectors And map the components in the vector to a permutation pattern according to their magnitude. ,remember For all A set of permutation patterns. Let... For the first Drones in the action assessment window Arrangement pattern appears inside Calculate the entropy of the drone swarm based on the relative frequencies: (18) The lower the permutation entropy, the more regular the movement rhythm, corresponding to the rhythmic order of wing phase synchronization during long-distance goose migration.

[0032] Based on actual flight path input Calculate the spatial coverage effectiveness of the task This is the ratio of the target area actually covered by the group to the total task area.

[0033] Based on the drones and their neighbors Actual track input and Calculate the collision risk distribution based on the instantaneous position in the data: (19) In the formula, To predetermine a safe distance, the spatial constraints are mapped to ensure that individuals in a goose formation maintain the optimal wingtip spacing to avoid collisions.

[0034] Define the action convergence time for First time below the preset threshold The minimum moment.

[0035] S63. Calculate action entropy to characterize the rhythmic stability and coordination of task execution. Let... ( The numbers () represent the original values ​​of six types of action entropy sub-indicators: track tracking deviation, velocity and attitude consistency, arrangement entropy, mission space coverage effectiveness, collision risk distribution, and action convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, velocity and attitude consistency and mission space coverage effectiveness are considered large-scale indicators, while trajectory tracking deviation, arrangement entropy, collision risk distribution, and action convergence time are considered small-scale indicators. Let the weight of the action entropy sub-indicator be... ,and , Then the action entropy is expressed as , For the first The normalized entropy penalty term corresponds to each action entropy sub-index. The decrease in action entropy indicates that the group's execution is converging from jittery chaos to rhythmic coordination, corresponding to the entropy reduction process of individual wingbeats in goose migration from desynchronization to precise phase matching.

[0036] Step 7: Combine and fuse the structural entropy, information flow entropy, decision entropy, and action entropy obtained in steps 3 to 6 to obtain the total cluster entropy. S71. Construct a composite function of total cluster entropy, which fuses a weighted aggregation function and a nonlinear modulation function. Define cluster entropy as a composite function of individual entropy and cooperative entropy: (20) In the formula, For weighted aggregation functions, It is a nonlinear modulation function. The weighted aggregation function is defined as: (twenty one) In the formula, For the first Entropy components of dimension ( Corresponding structural entropy , Corresponding information flow entropy , Corresponding decision entropy , Corresponding action entropy ), For the first First-order weights of the dimension For the first With the The cross-coupling coefficients between dimensions are used to characterize the cascading effects between adjacent stages of the OODA loop. The nonlinear modulation function is defined as follows: (twenty two) In the formula, for A drone at all times The joint state covariance matrix, for The covariance term is an identity matrix of order 1, which captures the overall statistical coupling strength of the system.

[0037] S72. The weights of each dimension are determined using a combined weighting method, and the total cluster entropy is obtained. The weights... The subjective weights are determined using a combined weighting method, specifically by employing the analytic hierarchy process (AHP). Determining objective weights using the entropy weight method The final comprehensive weight is obtained through relative entropy fusion. Corresponding to structural entropy Information flow entropy Decision entropy and action entropy For the evaluation window The sampling calculation is recorded as the nth... The dimension in the first The entropy component at the next sampling time is... The corresponding normalized percentage is In the formula, A preset minimum positive number is used to avoid fractions with zero denominators or undefined logarithmic terms. Based on the stated time percentage, the first... Normalized information entropy of each dimension indicator ,and ,but In the formula, For normalized summation index, Indicates the first Normalized information entropy of each dimension indicator, when At that time, take The subjective weight Determined by the analytic hierarchy process, satisfying and The objective weights satisfy and Construct a relative entropy optimization model for subjective and objective weights to solve for the aggregate weights: (twenty three) In the formula, For the first The final comprehensive weight of each dimension The subjective and objective weighting balance coefficient; when When the value is large, the final overall weighting places more emphasis on subjective factors. ,when When the weight is relatively small, the final overall weighting places more emphasis on objective weights. Solving the above relative entropy fusion model, the final comprehensive weight is obtained as follows: (twenty four) In the formula, For normalized summation index, Indicates the first Subjective weights of each dimension indicator, Indicates the first Objective weights of each dimension indicator.

[0038] Step 8: Convert the total cluster entropy into a group performance evaluation result and output the confidence level of the evaluation result. S81. Map the total cluster entropy to a group performance index, and output the sub-performance indices for each dimension. Define the group performance index as a negative exponential mapping of the total cluster entropy. ,in, , This corresponds to the ideal state of complete order where the total cluster entropy is zero. Approaching zero corresponds to a highly disordered degenerate state; output sub-efficiency indices for each dimension. , These correspond to the multi-dimensional effectiveness values ​​for the four stages of observation, judgment, decision-making, and action, respectively.

[0039] S82. Generate a normal cloud model from the sampled cluster entropy values ​​and output the confidence level of the evaluation results. Cluster entropy sampled values ​​obtained from sub-Monte Carlo simulation Generate a normal cloud model In the formula, the expectation is... Entropy is used to characterize the center level of cluster entropy sample values. Hyperentropy is used to characterize the degree of dispersion of cluster entropy sample values ​​relative to the expectation. The uncertainty used to characterize the degree of discreteness itself.

[0040] Specifically, the expectation In the formula For the first The cluster entropy sample value obtained from the Monte Carlo simulation, entropy hyperentropy In the formula, The sample variance of the cluster entropy sample values ​​and The confidence level is calculated using the cloud model: (25) In the formula, The entropy value of the cluster to be evaluated. For entropy For the expected value, the squared value of hyperentropy is a normally distributed random number with variance.

[0041] The advantages and beneficial effects of this invention are as follows: This invention proposes a method for evaluating the effectiveness of UAV swarms based on the intelligent swarm entropy measurement of goose flocks. This method addresses existing problems in UAV swarm effectiveness evaluation, such as fragmented evaluation dimensions, difficulty in reflecting the entire task planning process, inability to reveal the coupling relationships of multi-dimensional indicators, and insufficient representation of uncertainty in evaluation results. Its advantages are: First, it constructs a four-stage biomimetic mapping relationship of the UAV swarm's OODA loop, mimicking the formation organization, information transmission, leadership rotation, and rhythmic coordination behavior during goose migration, giving the evaluation model a clear biological inspiration basis. Second, it establishes separate models for structural entropy, information flow entropy, decision entropy, and action entropy, enabling a unified quantitative representation of the collaborative state of the UAV swarm throughout the entire process of observation, judgment, decision-making, and action. Third, it calculates the total swarm entropy using a weighted aggregation function with cross-coupling terms and a nonlinear modulation function, reflecting the mutual influence between various evaluation dimensions and improving the overall integrity and accuracy of swarm effectiveness evaluation. Fourth, it constructs a swarm effectiveness index based on the total swarm entropy and combines it with a cloud model to quantitatively represent the confidence level of the evaluation results, improving the credibility and engineering application value of the evaluation results. Attached Figure Description

[0042] Figure 1 This is a flowchart for evaluating the effectiveness of drone swarms based on the entropy metric of goose flocks.

[0043] Figure 2 This is a biomimetic mapping for evaluating the effectiveness of drone swarms based on the entropy metric of goose flock intelligence.

[0044] Figure 3 This is a mission scenario and flight path map for drone swarms and dynamic targets.

[0045] Figure 4 The time series curves represent structural entropy and its sub-indices.

[0046] Figure 5 This refers to the time series curves of information flow entropy and its sub-indices.

[0047] Figure 6 The time series curves represent the decision entropy and its sub-indices.

[0048] Figure 7 The time series curves of action entropy and its sub-indices.

[0049] Figure 8 The curves show the time series relationship between total cluster entropy and cluster performance index.

[0050] Figure 9 This is a comparison chart of the effectiveness indices of different evaluation schemes.

[0051] The labels and symbols in the diagram are explained as follows: —The x-coordinate in a two-dimensional plane; —The ordinate in a two-dimensional plane; meter — a unit of distance; Second—a unit of time; —Structural entropy; —Information flow entropy; —Decision entropy; —Action entropy; —Total cluster entropy; —Group effectiveness index; —Neighborhood speed consistency; —Polarization order parameter; —Algebraic connectivity; —Information flow directionality index; —Group cognitive convergence; —Strategic consistency; —Strategy polarization order parameter; —Fairness in task assignment; —Velocity and attitude consistency; —Collision risk distribution index; —Coverage effectiveness. Detailed Implementation

[0052] This invention addresses the lack of a cross-domain evaluation method for the task planning effectiveness of drone swarms, ranging from biological swarm intelligence to drone swarms. Inspired by the structural organization, information dissemination, leadership rotation, and rhythmic coordination mechanisms of migratory goose flocks, it provides a drone swarm effectiveness evaluation method based on goose flock intelligence swarm entropy measurement. The evaluation process flowchart is shown below. Figure 1 As shown, the implementation steps of the method proposed in this invention mainly include eight steps: constructing a goose flock biomimetic mapping model to form a cross-domain mapping framework of four stages from goose flock intelligence to UAV swarm OODA loop; collecting and preprocessing the collaborative state time series data of the UAV swarm during the task planning process; constructing and calculating the structural entropy model of the observation stage; and constructing and calculating the information flow entropy model of the judgment stage. The specific implementation steps are as follows: Step 1: Construct a goose flock biomimetic mapping model to form a cross-domain mapping framework of four stages from goose flock intelligence to UAV swarm OODA loop. S11. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and structural entropy. During migration, geese spontaneously form a V-formation. Following geese gain additional lift by positioning their wingtips in the upwash region generated by the wingtip vortex of the leading goose. Optimal wingtip spacing of an individual relative to the individual in front satisfy ,in, Let the wingspan be denoted by . Inspired by this, let the structure mapping function be denoted by . In the formula, For structure mapping functions, for The structural entropy at time point is used to map the spatial order constraint of the goose V-formation to the structural entropy during the observation phase of the UAV swarm.

[0053] S12. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and the entropy of information flow. During flight, the heading adjustment signal of the lead goose propagates directionally along the V-formation towards the follower birds; individual geese... For individuals The intensity of information influence is measured by transmission entropy, defined as follows: The transfer entropy is asymmetric. Inspired by this, we define an information flow mapping function. In the formula, For information flow mapping functions, for The information flow entropy at any given moment, the mapping maps the directionality and causality of goose information transmission to the information flow entropy of the drone swarm judgment stage.

[0054] S13. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and decision entropy. In goose formations, leader rotation follows a direct reciprocity mechanism, and the individual's leadership time is significantly positively correlated with the time of benefit from following. Inspired by this, define a decision mapping function. In the formula, For decision mapping function, for The decision entropy at any given moment is mapped to the reciprocal fairness of goose leader rotation to the decision entropy of the drone swarm decision-making stage.

[0055] S14. Establish a mapping relationship between the intelligent behavioral characteristics of goose flocks and their action entropy. During goose migration, individuals in a V-formation position maintain spatially in-phase wing flapping to track the upwash peak of the eddy current ahead. The wing flapping phase difference within the formation... satisfy Inspired by this, we define an action mapping function. In the formula, For action mapping functions, for The action entropy at any given moment, the mapping maps the rhythmic synchronization of goose migration to the action entropy of the drone swarm action phase.

[0056] Step 2: Collect and preprocess the time-series data of the collaborative status of the drone swarm during the mission planning process. S21-S22, Initialization and Data Setup. A heterogeneous group of six UAVs is set up in a two-dimensional simulation environment, including two reconnaissance UAVs (numbered 1 and 2), two relay command UAVs (numbered 3 and 4), and two mission support UAVs (numbered 5 and 6), as well as two dynamic targets. The mission area is a rectangular area of ​​1000m × 1000m. The initial positions of the six UAVs are set as follows: UAV 1 initial position... Initial position of the drone 2 meters Initial position of the drone (3 meters) meter, drone 4 initial position meters, initial position of drone 5 meters, initial position of the drone 6 meters. Initial velocity at Randomly generated within a speed range of meters per second. The initial positions of the two dynamic targets are respectively... Mihe meters, respectively at speed meters per second and It moves at a speed of meters per second and bounces at the boundary of the region.

[0057] The platform capabilities of the six drones are as follows: reconnaissance type Relay command type Mission support type . Communication radius Meters, safe distance meters, maximum flight speed limit is meters per second. Maximum simulation time. seconds, sampling period The total number of simulation steps was 240, and the time was 1 second.

[0058] The entire process of a drone swarm mission is divided into five phases: formation assembly (0-15 seconds), target search (15-40 seconds), target identification (40-55 seconds), task allocation (55-70 seconds), and surveillance coverage (70-120 seconds). In the formation assembly phase, six drones assemble in a V-formation with offsets. In the target search phase, the swarm moves towards the target area while maintaining formation. In the target identification phase, reconnaissance drones advance to approach the target. In the task allocation phase, the swarm contracts its formation and coordinates its strategies. In the surveillance coverage phase, the six drones form a ring-shaped coverage configuration for two dynamic targets. Missing values ​​in the data are imputed using an AR(p) autoregressive model of order [model order missing]. Using Bayesian information criteria Sure.

[0059] Step 3: Construct and calculate the structural entropy model for the observation phase. S31-S32, Construct and calculate five sub-indices of structural entropy. From the structural mapping function. Three types of input variables for drones and Spacing velocity vector and communication topology diagram Starting from this point, it is decomposed into five sub-indices. Based on velocity vector... Compute neighborhood speed consistency:

[0060] In this embodiment, the initial moment of the formation assembly phase Because the group's velocity direction is highly consistent during this stage.

[0061] Calculate the order parameter:

[0062] Initial time This indicates that the group as a whole is in a highly polarized and ordered state.

[0063] Based on communication topology graph Construct the Laplace matrix Calculate algebraic connectivity Initially, since all six drones were within the communication radius, The communication graph is fully connected. The task region is discretized into... Calculate the cover distribution entropy using equal-area grid cells: The convergence time of the structure is defined as: .

[0064] S33. Calculate structural entropy to characterize the degree of order in group spatial organization and communication topology. Let... ( Let represent the original values ​​of five structural entropy sub-indices: neighborhood velocity consistency, polarization order parameter, algebraic connectivity, cover distribution entropy, and structural convergence time. To eliminate the influence of different sub-indices' dimensions and values, each sub-indice is uniformly converted into a normalized entropy penalty term. For the large-scale index, where a larger value indicates a more ordered structural state, the following normalization method is adopted:

[0065] For smaller-valued indices, which indicate a more ordered structural state, the following normalization method is adopted:

[0066] In the formula, and The first The minimum and maximum values ​​of each structural entropy sub-index within the evaluation window or the preset range of the task scenario. The preset minimum positive number is used. Neighborhood velocity consistency, polarization order parameter, algebraic connectivity, and cover distribution entropy are indicators of tendency towards larger values, while structural convergence time is an indicator of tendency towards smaller values. Let the weights of each sub-indicator of structural entropy be... Then the structural entropy is expressed as , For the first The normalized entropy penalty term corresponds to each structural entropy sub-index. Simulation results in this embodiment show that the average structural entropy during the formation assembly phase is 0.1456, while during the task allocation phase, the structural entropy increases to an average of 0.4795 due to formation reorganization. After entering the monitoring coverage phase, the structural entropy drops back to an average of 0.1900.

[0067] Step 4: Construct and calculate the information flow entropy model for the judgment phase. S41-S42, Construct and calculate four types of sub-indices of information flow entropy. From the information flow mapping function. Two types of input heading angle time series and communication link set Starting from this point, we break it down into four sub-indicators. Let the time window length be... Step (i.e., 10 seconds), embedding dimension parameters For each pair of drones with a communication link Calculate the transit entropy:

[0068] The probability distribution is estimated using the histogram method, and the transit entropy is assumed to be zero for non-connected UAV pairs.

[0069] Constructing an information flow matrix And calculate its spectral entropy Information flow directionality index Group cognitive convergence The convergence of group cognition is approximated using the cosine similarity of the heading angle.

[0070] Initial cognitive convergence in this embodiment This indicates that the group's initial situational awareness was not yet unified; as information transmission continued, the convergence of the final state awareness increased to [a certain level]. .

[0071] S43. Calculate the information flow entropy to characterize the efficiency and consistency of information organization within the group. Let... ( The numbers () represent the original values ​​of four types of information flow entropy sub-indices: spectral entropy of the transfer entropy matrix, information flow directionality index, group cognitive convergence, and information convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, the spectral entropy of the transfer entropy matrix and the information convergence time are indicators of tending towards smaller values, while the information flow directionality index and the group cognitive convergence degree are indicators of tending towards larger values. Let the weights of each sub-indicator of information flow entropy be... Then the information flow entropy is expressed as , For the first The normalized entropy penalty term corresponds to each information flow entropy sub-index. Simulation results show that the average information flow entropy is 0.4591 during the formation assembly phase (when the time window data is still insufficient), drops to 0.3652 during the target search phase, and further decreases to 0.3408 after entering the surveillance coverage phase, indicating that the efficiency of group information organization gradually improves.

[0072] Step 5: Construct and calculate the decision entropy model for the decision-making stage. S51-S52, Construct and calculate five sub-indices of decision entropy. From the decision mapping function. Four types of input policy selection vectors Task load Platform capability value Collaborative Decision Diagram Starting from this point, it is broken down into five sub-indicators. Strategy selection vector. Defined as drone The inverse distance weight vector for each target. Task load. Taken as drone Divide the distance to the nearest target by the normalized value of 100 meters. Calculate group policy consistency:

[0073] Initial policy consistency in this embodiment Final state This indicates that group strategies tend to be highly consistent during the surveillance coverage phase. Computational task assignment fairness:

[0074] Initial fairness Final state This directly corresponds to the reciprocal fairness constraint in claim 2 regarding the zeroing of the Gini coefficient in the goose piloting time distribution.

[0075] S53. Calculate the decision entropy to characterize the convergence degree of the group's strategy consensus. Let... ( The numbers () represent the original values ​​of five decision entropy sub-indices: policy consistency, policy polarization order parameter, task assignment fairness, collaborative decision graph connectivity, and decision convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, policy consistency, policy polarization order parameter, task assignment fairness, and collaborative decision graph connectivity are indicators of tendency towards larger scales, while decision convergence time is an indicator of tendency towards smaller scales. Let the weights of each sub-indicator of decision entropy be... Then the decision entropy is expressed as , For the first The normalized entropy penalty term corresponds to each decision entropy sub-index. Simulation results show that the average decision entropy during the formation assembly phase is only 0.0373, rising to 0.1114 during the target search phase (at which point the group is still in the search process and there are significant strategy differences), and the decision entropy during the surveillance coverage phase rises back to 0.1740 (at which point the distributed coverage surveillance strategy is clear but the division of labor and coordination are still being dynamically adjusted).

[0076] Step Six: Construct and calculate the action entropy model for the action phase. S61-S62, Construct and calculate six sub-indices of action entropy. From the action mapping function. The three types of input Actual flight sequence of the drone Actual speed sequence and expected track sequence The process is broken down into six sub-indicators. An action evaluation window is established. Step (i.e., 5 seconds), permutation entropy embedding dimension Time delay Calculate the tracking deviation. Group speed and attitude consistency Permutation entropy Task space coverage effectiveness And the distribution of collision risks:

[0077] Initial velocity and attitude consistency in this embodiment Final state This is because during the surveillance coverage phase, each drone approaches the target from different directions to conduct surveillance, and their speed and direction naturally disperse.

[0078] S63. Calculate the action entropy to characterize the rhythmic stability and coordination of task execution. The collision risk remains zero throughout the entire process, indicating that the group collision avoidance mechanism is effective. Let... ( The numbers () represent the original values ​​of six types of action entropy sub-indicators: track tracking deviation, velocity and attitude consistency, arrangement entropy, mission space coverage effectiveness, collision risk distribution, and action convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, velocity and attitude consistency and mission space coverage effectiveness are considered large-scale indicators, while trajectory tracking deviation, arrangement entropy, collision risk distribution, and action convergence time are considered small-scale indicators. Let the weights of each sub-indicator of action entropy be... Then the action entropy is expressed as , For the first The normalized entropy penalty term corresponds to each action entropy sub-index. Simulation results show that the average action entropy is 0.3382 during the formation assembly phase, drops to 0.2734 during the target search phase, rises to 0.3950 during the task allocation phase due to formation reorganization, and falls back to 0.2794 after entering the surveillance coverage phase.

[0079] Step 7: Combine and fuse the structural entropy, information flow entropy, decision entropy, and action entropy obtained in steps 3 to 6 to obtain the total cluster entropy. S71. Construct a composite function of total cluster entropy, which fuses a weighted aggregation function and a nonlinear modulation function. Define the composite function of cluster entropy.

[0080] The weighted aggregation function is:

[0081] In the formula, the first-order weights The cross-coupling coefficient is taken as , , , , , Among them, the coupling coefficients of the three adjacent stages—structure-information flow, information flow-decision, and decision-action—are relatively large, reflecting the cascading effect of the OODA loop. The nonlinear modulation function is:

[0082] In the formula, The covariance matrix is ​​a 2×2 matrix representing the positions of the 6 drones.

[0083] S72. The weights of each dimension are determined using a combined weighting method, and the total cluster entropy is obtained. The weights... The subjective weights are determined using a combined weighting method, specifically by employing the analytic hierarchy process (AHP). The entropy of each dimension was calculated using the entropy weight method on 240 steps of sampled data. To obtain objective weights Construct a relative entropy optimization model for subjective and objective weights to solve for the aggregate weights:

[0084] Solving the above relative entropy fusion model, the final comprehensive weight is obtained as follows:

[0085] In this embodiment, the weights of decision entropy and action entropy (0.30, 0.28) are higher than the weights of structural entropy and information flow entropy (0.20, 0.22) in the close-range continuous surveillance mission scenario, highlighting the dominant role of target assignment clarity and coverage coordination in surveillance effectiveness.

[0086] Step 8: Convert the total cluster entropy into a group performance evaluation result and output the confidence level of the evaluation result. S81-S82: Map the total cluster entropy to a group performance index, and output the sub-performance indices for each dimension. Define the group performance index as a negative exponential mapping of the total cluster entropy. ,in, Simultaneously output the sub-efficiency indices for each dimension. , .

[0087] The initial performance index obtained from the simulation in this embodiment is: The final state efficiency index is The average efficiency index for each stage is as follows: Formation assembly stage Target search phase Target identification stage Task allocation phase Surveillance Coverage Phase The efficiency index is lowest during the task allocation phase, which corresponds to the physical process of group formation reorganization leading to a significant increase in structural entropy during this phase.

[0088] The combined weighting performance evaluation scheme proposed in this method is compared with two comparative schemes. The performance index comparison results of the three schemes in the steady-state phase of the monitoring coverage stage are as follows: Scheme (1) This method (combined weighting), weight Efficiency Index ; Scheme (2) Equal Weight Method, weights Efficiency Index ; Option (3) Partial Dimensional Approach (Focusing Only on Structure and Action), Weights Efficiency Index .

[0089] Scheme (3) neglects the contributions of information flow entropy and decision entropy, resulting in an evaluation score 0.0294 lower than Scheme (1). This indicates that considering only the structure and action dimensions in close-range continuous surveillance scenarios cannot fully reflect the group's collaborative effectiveness. Scheme (2) uses equal weighting, failing to highlight the dominant role of decision and action dimensions in close-range continuous surveillance scenarios, and its evaluation result falls between Scheme (1) and Scheme (3). The combined weighting scheme using this method can take into account both subjective and objective information, making the evaluation results more reasonable.

[0090] Therefore, under the parameter conditions of this embodiment, the designed goose-based intelligent swarm entropy measurement method can realize continuous time-series evaluation of four dimensions—structural orderliness, information transmission efficiency, decision-making consensus, and action coordination—throughout the entire process of a swarm of 6 UAVs performing collaborative reconnaissance and close-range surveillance of dynamic targets. The time series of total swarm entropy and efficiency index accurately reflect the state evolution characteristics of the five task stages.

[0091] Output simulation results, and the performance evaluation results of the drone swarm are as follows: Figures 3 to 9 As shown. Figure 3 A schematic diagram of a mission scenario involving six drones and two dynamic targets is shown. Figure 4 It demonstrates structural entropy The time series curves of its three key sub-indicators. Figure 5 It shows the entropy of information flow The time series curves of its two key sub-indicators. Figure 6 Demonstrates decision entropy The time series curves of its three key sub-indicators. Figure 7 Demonstrates action entropy The time series curves of its three key sub-indicators. Figure 8 Shows total cluster entropy Group effectiveness index The time series curve. Figure 9 The paper presents a comparison of the effectiveness indices of three evaluation schemes during the steady-state phase of the monitoring coverage stage.

Claims

1. A method for evaluating the effectiveness of unmanned aerial vehicle (UAV) swarms based on the entropy metric of goose flocks, characterized in that: The steps include the following: Step 1: Construct a goose flock biomimetic mapping model to form a cross-domain mapping framework of four stages from goose flock intelligence to UAV swarm OODA loop, including: S11. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and structural entropy; S12. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and the entropy of information flow; S13. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and decision entropy; S14. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and the action entropy; Step 2: Collect and preprocess the collaborative status time-series data of the drone swarm during the task planning process, including: S21. Collect time-series data on the collaborative status of drone groups; S22. Perform missing data repair and time synchronization alignment on the collaborative state time series data collected in step S21. Step 3: Construct and calculate the structural entropy model for the observation phase, including: S31. Construct a structural entropy modeling index system to extract structural features related to group spatial organization and communication topology; S32. Five sub-indices of structural entropy based on structural features; S33. Calculate structural entropy to characterize the degree of order in the spatial organization and communication topology of a group; Step 4: Construct and calculate the information flow entropy model for the judgment phase, including: S41. Construct an information flow entropy modeling index system to extract group heading information and communication link information; S42. Construct four sub-indicators of information flow entropy based on judgment information; S43. Calculate the information flow entropy to characterize the efficiency and consistency of information organization within a group; Step 5: Construct and calculate the decision entropy model for the decision-making stage, including: S51. Construct a decision entropy modeling index system and extract strategy selection, task load, platform capability value and collaborative decision graph; S52. Five sub-indicators for constructing decision entropy based on decision information; S53. Calculate the decision entropy to characterize the convergence of the group's strategy consensus; Step Six: Construct and calculate the action entropy model for the action phase, including: S61. Construct an action entropy modeling index system to extract action state information of actual trajectory, velocity vector and expected trajectory; S62. Constructing six sub-indicators of action entropy based on action status information; S63. Calculate action entropy to characterize the rhythmic stability and coordination of task execution; Step 7: Combine and fuse the structural entropy, information flow entropy, decision entropy, and action entropy obtained in steps 3 to 6 to obtain the total cluster entropy, including: S71. Construct a composite function of total cluster entropy that fuses a weighted aggregation function and a nonlinear modulation function; S72. The weights of each dimension are determined by the combined weighting method and the total cluster entropy is obtained. Step 8: Convert the total cluster entropy into a cluster performance evaluation result, and output the confidence level of the evaluation result, including: S81. Map the total cluster entropy to the group efficiency index and output the sub-efficiency indices for each dimension. S82. Generate a normal cloud model from the sampled cluster entropy values ​​and output the confidence level of the evaluation results.

2. The method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks according to claim 1, characterized in that: Step 1 involves constructing a goose flock biomimetic mapping model, forming a cross-domain mapping framework encompassing four stages from goose flock intelligence to UAV swarm OODA loop. The specific process is as follows: S11. Establishing a mapping relationship between intelligent behavioral characteristics of goose flocks and structural entropy: Geese spontaneously form a V-formation during migration. Following geese gain additional lift by positioning their wingtips in the upwash region generated by the wingtip vortex of the goose in front. The first goose in the formation... Optimal wingtip spacing of an individual relative to the individual in front satisfy ,in, For wingspan, formation size With the reduction rate of group-induced resistance Between satisfy ,in, Let be the wingtip overlap coefficient, and let the relationship exhibit a logarithmic decreasing characteristic; define the structural mapping function. In the formula, For structure mapping functions, for Structural entropy at time step For drones and The spacing, For the first The velocity vector of the drone The communication topology diagram maps the spatial order constraint of the goose V-formation to the structural entropy during the observation phase of the UAV swarm. S12. Establish the mapping relationship between the intelligent behavioral characteristics of goose flocks and the entropy of information flow: During flight, the heading adjustment signal of the lead goose propagates directionally from the front of the V-formation to the follower birds, and the individual... For individuals The intensity of information influence is measured by transmission entropy and is defined as: (1) In the formula, Given the conditional Shannon entropy, For individuals exist The heading angle at any moment, For individuals The length is The heading history vector, For individuals The length is The heading history vector, and The embedded dimension parameter is a preset integer ranging from 1 to 5. The propagation entropy exhibits asymmetry. Distinguish the causal direction of information between the lead goose and the follower goose; define the information flow mapping function. In the formula, For information flow mapping functions, for Information flow entropy at any given moment For time window Sampling time within, For the first Time series of heading angle of a drone For a set of communication links, The time window length is used to map the directionality and causality of goose information transmission to the information flow entropy of the drone swarm judgment stage; S13. Establishing a mapping relationship between intelligent behavioral characteristics of goose flocks and decision entropy: Leader rotation in goose formations follows a direct reciprocity mechanism, assuming individual... In time period The cumulative time spent in the lead position is The cumulative time spent in the follower position to obtain the benefits of the wash is Then the two satisfy the positive correlation constraint. And the Gini coefficient for the group navigation time distribution is: (2) A value approaching zero indicates fair rotation; define the decision mapping function. In the formula, For decision mapping function, for Decision entropy at any given moment Choose a vector for the strategy. For task load, For platform capability values, For collaborative decision-making graphs, the reciprocal fairness of goose leader rotation is mapped to the decision entropy of the drone swarm decision-making stage; S14. Establishing a mapping relationship between intelligent behavioral characteristics of goose flocks and action entropy: During goose migration, individuals in V-formation positions maintain spatially in-phase wing flapping to track the upwash peak of the eddy ahead, with wing flapping phase differences within the formation. satisfy ,in, The longitudinal spacing along the flight direction. Using the wingbeat wavelength, phase matching ensures the rhythmic synchronization of migration movements; a movement mapping function is defined. In the formula, For action mapping functions, for Action entropy at any moment For time window Sampling time within, For the first The actual flight path sequence of the drone. For the first The actual flight speed sequence of the drone. For the first The expected flight path sequence of the drone. To assess the window length, the mapping synchronizes the rhythm of goose migration with the action entropy of the drone swarm action phase.

3. The method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks according to claim 1, characterized in that: Step two involves collecting and preprocessing the collaborative status time-series data of the drone swarm during the task planning process. The specific process is as follows: S21. Collect drone group status time-series data: Assume the group consists of... Composed of drones, the system uses a drone telemetry link to perform sampling at a preset period. For group number The drone's status is collected at various times; the collected status data includes the first... A drone in Position vector at time velocity vector Heading angle Remaining energy Sensor operating status indicator and communication link quality parameters ; S22. Preprocess the group status time series data collected in step S21: Use an AR(p) autoregressive model to interpolate and repair missing data. The autoregressive model is defined as... ,in, For a moment Status data, For the autoregressive parameter vector, White noise, model order Using Bayesian information criteria It is confirmed that, among them, The length of the sampled data. Least squares estimation of residual variance.

4. The method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks according to claim 1, characterized in that: Step 3 involves constructing and calculating the structural entropy model for the observation phase. The specific process is as follows: S31. Construct a structural entropy modeling index system to extract structural features related to group spatial organization and communication topology: In the V-formation of geese, adjacent individuals maintain an optimal wingtip spacing of 0.78 times the wingspan to maximize upwash airflow utilization; the velocity directions among individuals are highly consistent, and the overall formation exhibits a polarized ordered state; from the mapping function... Three types of input variables for drones and Spacing velocity vector and communication topology diagram Starting from this point, it is decomposed into five sub-indicators: neighborhood velocity consistency, polarization order parameter, algebraic connectivity, cover distribution entropy, and structural convergence time. S32. Five sub-indices of structural entropy are constructed based on the structural features of S31: based on the first... drones and their neighbors exist velocity vector at time t and Calculate neighborhood speed consistency Let the first The neighborhood set of the drone is ,in, For communication radius, Given the number of drones in the neighborhood set, the neighborhood speed consistency is... : (3) The closer the value is to 1, the more consistent the local velocity directions become, corresponding to the neighborhood velocity coupling characteristics in goose formation; based on the first A drone in velocity vector at time t Calculate polarization order parameters : (4) The values ​​from 0 to 1 correspond to completely disordered to completely ordered, respectively, which correspond to the homogeneity of the global movement direction of the goose formation. Based on communication topology input Construct the Laplace matrix Calculate the second smallest eigenvalue, i.e., the algebraic connectivity. A value greater than 0 indicates that the communication graph is connected, and the larger the value, the more stable the topology, corresponding to the stability of the visual perception link in the goose formation. Based on spacing input and UAV position vector Discretize the task region into A uniform area grid cell, and at time... Select a length of for the endpoint Structural evaluation window; set To evaluate the set of sampling times within the evaluation window, The number of sampling times. To evaluate whether all drone trajectory sampling points within the evaluation window fall into the first... The number of times the th grid cell is defined. The coverage percentage of each grid cell is Calculate the entropy of the coverage distribution: (5) The closer the values ​​are The more uniform the trajectory coverage, the more uniform the spatial deployment of the V-formation of geese; considering the temporal evolution of the above three types of inputs, the structural convergence time is defined as follows: (6) In the formula, , , The preset threshold is the structure convergence time. This corresponds to the time required for geese to achieve a stable V-formation after taking off from a dispersed position; S33. Calculate structural entropy to characterize the degree of order in group spatial organization and communication topology: Let... These represent the original values ​​of five structural entropy sub-indices: neighborhood velocity consistency, polarization order parameter, algebraic connectivity, cover distribution entropy, and structural convergence time. To eliminate the influence of different sub-indices' dimensions and values, each sub-indice is uniformly converted into a normalized entropy penalty term. For the large-scale index, where a larger value indicates a more ordered structural state, the following normalization method is adopted: (7) For smaller-valued indices, which indicate a more ordered structural state, the following normalization method is adopted: (8) In the formula, and The first The minimum and maximum values ​​of each structural entropy sub-index within the evaluation window or the preset range of the task scenario. The preset minimum positive number is used; neighborhood velocity consistency, polarization order parameter, algebraic connectivity, and cover distribution entropy are indices for tending towards larger values, while structural convergence time is an index for tending towards smaller values; let the weight of the structural entropy sub-index be . ,and , Then the structural entropy is expressed as , For the first The normalized entropy penalty term corresponds to each structural entropy sub-index; the decrease in structural entropy indicates that the group structure converges from loose randomness to ordered compactness, corresponding to the entropy reduction process of geese gradually forming a stable V-formation from dispersed take-off.

5. The method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks according to claim 1, characterized in that: Step four involves constructing and calculating the information flow entropy model for the judgment phase. The specific process is as follows: S41. Construct an information flow entropy modeling index system and extract group heading information and communication link information: During the migratory flight of geese, formation information is propagated directionally along the leader-follower link. Changes in the heading of the leader bird have a causal impact on the following birds, and this impact is asymmetric. Using transfer entropy as the core tool, from the mapping function Two types of input heading angle time series and communication link set Starting from this point, it is decomposed into four sub-indicators: the spectral entropy of the transfer entropy matrix, the information flow directionality index, the convergence degree of group cognition, and the information convergence time. S42. Based on the information judged in S41, construct four types of sub-indicators for information flow entropy: based on the heading angle time series input. and communication link input For each pair of drones with a communication link Calculation from individual To individuals Transitive entropy: (9) In the formula, For individuals exist The heading angle at any moment, For individuals The length is The heading history vector, For individuals The length is The heading history vector, and The probability distribution is defined as follows: The embedding dimension parameter is a preset integer ranging from 1 to 5. Obtained by kernel density estimation method; for non-connected UAV pairs set up Asymmetry of transfer entropy Used to distinguish between information drivers and responders, corresponding to the causal direction of information between leaders and followers in a goose formation; Construct a group information flow matrix For disconnected UAVs, assume the transit entropy is zero; perform singular value decomposition on the matrix to obtain singular values. ,in, To find the rank of the matrix, normalize the singular values ​​as follows: Calculate the spectral entropy of the transfer entropy matrix: (10) In the formula, Information flow matrix The A singular value, The proportion of singular values ​​after normalization; a lower spectral entropy indicates that the information flow is concentrated in a few dominant causal links, corresponding to a clear hierarchical transmission structure in goose formations; the directionality index is calculated based on the information flow matrix as follows: (11) In the formula, For individuals For individuals The propagation entropy, For individuals For individuals The propagation entropy, The total number of communication links. Preset minimum positive number to prevent division by zero; The closer the value is to 1, the stronger the directionality of the information flow, corresponding to the unidirectional dominant transmission characteristic from the lead goose to the follower geese in a goose formation; calculating the convergence degree of group cognition. : (12) In the formula, and For the first drones and their neighbors The situation estimation vector; Define information convergence time for First time reaching the preset threshold The minimum moment; S43. Calculate the information flow entropy to characterize the efficiency and consistency of information organization within a group: Let... These represent the original values ​​of four types of information flow entropy sub-indices: spectral entropy of the transfer entropy matrix, information flow directionality index, group cognitive convergence, and information convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, the spectral entropy of the transfer entropy matrix and the information convergence time are indicators of minimization, while the information flow directionality index and the group cognitive convergence degree are indicators of large-scale convergence; let the weight of the information flow entropy sub-indicator be... ,and , Then the information flow entropy is expressed as , For the first The normalized entropy penalty term corresponding to each information flow entropy sub-index; the decrease in information flow entropy indicates that the information causal link converges from scattered and fuzzy to directional and clear, corresponding to the entropy reduction process in the goose formation from disordered diffusion to effective convergence along the hierarchical chain.

6. The method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks according to claim 1, characterized in that: Step 5 involves constructing and calculating the decision entropy model for the decision-making stage. The specific process is as follows: S51. Construct a decision entropy modeling index system to extract strategy selection, task load, platform capability values, and collaborative decision-making graphs: In migratory goose formations, leader rotation is frequent and follows direct reciprocity; the group automatically adjusts the leader role based on individual energy depletion while maintaining overall directional stability; from the mapping function... Four types of input policy selection vectors Task load Platform capability value Collaborative Decision Diagram Starting from this point, it is decomposed into five sub-indicators: policy consistency, policy polarization order parameter, task assignment fairness, collaborative decision graph connectivity, and decision convergence time. S52. Five sub-indices of decision entropy are constructed based on the decision information in S51: These are used to map the local consensus among adjacent individuals in a goose formation regarding directional decisions, and to obtain... Each drone and its neighbors Strategy selection vector and Calculate the consistency of group policies: (13) Based on policy selection vector input Calculate the strategy polarization order parameter: (14) Approaching 1 indicates that all individual strategies are concentrated in a few patterns, corresponding to the majority decision-making mechanism of the goose flock; let the first... The mission payload of the drone is Platform capability value Calculate the fairness index of task assignment: (15) In the formula, The average load capacity ratio of the flock; the fairness index directly corresponds to the Gini coefficient of the goose piloting time distribution. The reciprocal fairness constraint approaching zero The closer the value is to 1, the more balanced the task allocation. Constructing a collaborative decision graph And calculate the connectivity of the collaborative decision graph. This corresponds to the accessibility of decision-making information within a goose formation; Define decision convergence time for First time reaching the preset threshold The minimum moment; S53. Calculate the decision entropy to characterize the convergence of the group's strategy consensus: Let... These represent the original values ​​of five decision entropy sub-indices: policy consistency, policy polarization order parameter, task assignment fairness, collaborative decision graph connectivity, and decision convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, policy consistency, policy polarization order parameter, task assignment fairness, and collaborative decision graph connectivity are indicators of tending towards larger scales, while decision convergence time is an indicator of tending towards smaller scales; let the weight of the decision entropy sub-indicator be . ,and , Then the decision entropy is expressed as , For the first The normalized entropy penalty term corresponds to each decision entropy sub-indicator; the decrease in decision entropy indicates that the group strategy is converging from divergent fluctuations to consensus, corresponding to the entropy reduction process of the goose group forming a unified migration decision through a reciprocal rotation mechanism.

7. The method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks according to claim 1, characterized in that: Step six involves constructing and calculating the action entropy model for the action phase. The specific process is as follows: S61. Construct an action entropy modeling index system to extract action state information from actual trajectories, velocity vectors, and desired trajectories: During goose migration, individual geese in formation maintain wingbeat frequency synchronization and spatial phase matching, ensuring rhythmic consistency and efficient energy utilization of group actions; from the mapping function The three types of input Actual flight sequence of the drone Actual speed sequence and expected track sequence The starting point is decomposed into six sub-indicators: trajectory tracking deviation, velocity and attitude consistency, arrangement entropy, mission space coverage effectiveness, collision risk distribution, and action convergence time. S62. Constructing six sub-indicators of action entropy based on S61 action status information: based on each UAV within the evaluation window. Actual flight path within With expected trajectory Calculate the tracking deviation: (16) This corresponds to the degree to which an individual goose deviates from the ideal V-shaped position in the formation; based on the first... drones and their neighbors Actual speed sequence and Calculate the group's velocity and attitude consistency: (17) This corresponds to the synchronization of the flight speed direction of adjacent individuals in a goose formation; based on actual flight track input. The time series of each drone's action mode are used to construct the first... The sequence of motion changes of the drone Used to characterize the The amplitude of the change in the motion state of the UAV between adjacent sampling times is obtained by velocity vector difference or trajectory difference; with embedding dimension and time delay Constructing action embedding vectors And map the components in the vector to a permutation pattern according to their magnitude. ,remember For all A set of permutation patterns; let... For the first Drones in the action assessment window Arrangement pattern appears inside Calculate the entropy of the drone swarm based on the relative frequencies: (18) The lower the permutation entropy, the more regular the movement rhythm, corresponding to the rhythmic order of wing beat phase synchronization during long-distance goose migration; Based on actual flight path input Calculate the spatial coverage effectiveness of the task This is the ratio of the target area actually covered by the group to the total task area. Based on the drones and their neighbors Actual track input and Calculate the collision risk distribution based on the instantaneous position in the data: (19) In the formula, To pre-set a safe distance, the spatial constraints are mapped to ensure that individuals in a goose formation maintain the optimal wingtip spacing to avoid collisions; Define the action convergence time for First time below the preset threshold The minimum moment; S63. Calculate action entropy to characterize the rhythmic stability and coordination of task execution: Let... These represent the original values ​​of six types of action entropy sub-indicators: track tracking deviation, velocity and attitude consistency, arrangement entropy, mission space coverage effectiveness, collision risk distribution, and action convergence time. Following the normalization rules in step S33, each sub-indicator is converted into a normalized entropy penalty term. Among them, velocity and attitude consistency and mission space coverage effectiveness are large-scale indices, while trajectory tracking deviation, arrangement entropy, collision risk distribution, and action convergence time are small-scale indices; let the weight of the action entropy sub-indicator be... ,and , Then the action entropy is expressed as , For the first The normalized entropy penalty term corresponds to each action entropy sub-index; the decrease in action entropy indicates that the group's execution is converging from jittery chaos to rhythmic coordination, corresponding to the entropy reduction process of individual wingbeats from desynchronization to precise phase matching during goose migration.

8. The method for evaluating the effectiveness of UAV swarms based on the intelligent swarm entropy measurement of geese, as described in claim 1, is characterized in that: Step seven involves combining and fusing the structural entropy, information flow entropy, decision entropy, and action entropy obtained in steps three through six to obtain the total cluster entropy. The specific process is as follows: S71. Constructing a composite function of total cluster entropy, which combines a weighted aggregation function and a nonlinear modulation function: Define cluster entropy as a composite function of individual entropy and cooperative entropy. (20) In the formula, For weighted aggregation functions, The nonlinear modulation function is defined as follows: The weighted aggregation function is defined as follows: (21) In the formula, For the first The entropy component of a dimension, Corresponding structural entropy , Corresponding information flow entropy , Corresponding decision entropy , Corresponding action entropy , For the first First-order weights of the dimension For the first With the Cross-coupling coefficients between dimensions are used to characterize the cascading effects between adjacent stages of the OODA loop; The nonlinear modulation function is defined as: (22) In the formula, for A drone at all times The joint state covariance matrix, for The identity matrix of order 1, and the covariance term capture the overall statistical coupling strength of the system; S72. Determine the weights of each dimension and obtain the total cluster entropy using a combined weighting method: weights The subjective weights are determined using a combined weighting method, specifically by employing the analytic hierarchy process (AHP). Determining objective weights using the entropy weight method The final comprehensive weight is obtained through relative entropy fusion. Corresponding to structural entropy Information flow entropy Decision entropy and action entropy ; for the evaluation window The sampling calculation is recorded as the nth... The dimension in the first The entropy component at the next sampling time is... The corresponding normalized percentage is In the formula, A minimum positive number is preset to avoid denominators of zero or undefined logarithmic terms; the first term is calculated based on the time percentage. Normalized information entropy of each dimension indicator ,and ,but In the formula, For normalized summation index, Indicates the first The normalized information entropy of each dimension indicator, when At that time, take Subjective weight Determined by the analytic hierarchy process, satisfying and Objective weighting satisfy and Construct a relative entropy optimization model for subjective and objective weights to solve for the aggregate weights: (23) In the formula, For the first The final comprehensive weight of each dimension The subjective and objective weighting balance coefficient; when When the value is large, the final overall weighting places more emphasis on subjective factors. ,when When the weight is relatively small, the final overall weighting places more emphasis on objective weights. Solving the relative entropy fusion model, the final comprehensive weight is obtained as follows: (24) In the formula, For normalized summation index, Indicates the first Subjective weights of each dimension indicator, Indicates the first Objective weights of each dimension indicator.

9. The method for evaluating the effectiveness of UAV swarms based on the entropy measurement of goose flocks according to claim 1, characterized in that: Step eight transforms the total cluster entropy into a cluster performance evaluation result and outputs the confidence level of the evaluation result. The specific process is as follows: S81. Map the total cluster entropy to the group performance index and output the sub-performance indices for each dimension: Define the group performance index as a negative exponential mapping of the total cluster entropy. ,in, , This corresponds to the ideal state of complete order where the total cluster entropy is zero. Approaching zero corresponds to a highly disordered degenerate state; output sub-efficiency indices for each dimension. , These correspond to the multi-dimensional efficacy values ​​of the four stages: observation, judgment, decision-making, and action. S82. Generate a normal cloud model from the cluster entropy sample values ​​and output the confidence level of the evaluation results: Cluster entropy sampled values ​​obtained from sub-Monte Carlo simulation Generate a normal cloud model In the formula, the expectation is... Entropy is used to characterize the center level of cluster entropy sample values. Hyperentropy is used to characterize the degree of dispersion of cluster entropy sample values ​​relative to the expectation. Used to characterize the uncertainty of the degree of discreteness itself; Specifically, the expectation In the formula, For the first The cluster entropy sample value obtained from the Monte Carlo simulation, entropy hyperentropy In the formula, The sample variance of the cluster entropy sample values ​​and Calculate confidence using a cloud model: (25) In the formula, The entropy value of the cluster to be evaluated. For entropy For the expected value, the squared value of hyperentropy is a normally distributed random number with variance.

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