Smoke screen jamming bomb launching optimization method and system based on unmanned aerial vehicle

Abstract

The invention discloses a smoke screen jamming bomb launching optimization method and system based on an unmanned aerial vehicle, and relates to the technical field of jamming bomb launching, and the method comprises the steps: constructing different launching scenes in which the unmanned aerial vehicle carries a smoke screen jamming bomb to interfere with an incoming missile; for different launching scenes, a movement track model of a cloud cluster before and after detonation of an unmanned aerial vehicle, a missile and a smoke screen jamming bomb is constructed, and based on the principle that the missile purchases a target, the target is estimated according to the relationship between the longest distance from a set of all visible light line segments from the missile to the target to the center of the cloud cluster and the radius of the cloud cluster. Establishing an interference judgment basis of the cloud cluster on the missile; taking the time interval meeting the interference judgment basis as the effective interference duration, taking the maximization of the effective interference duration as the target, taking the speed and course angle of the unmanned aerial vehicle as well as the bomb dropping moment and detonation moment of the smoke bomb as decision variables, combining constraint conditions, constructing an unmanned aerial vehicle smoke bomb dropping interference time optimization model, and solving to obtain an optimal dropping strategy.

Description

Technical Field

[0001] This invention belongs to the field of chaff deployment technology, specifically relating to an optimized method and system for deploying smoke chaff based on unmanned aerial vehicles (UAVs). Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Smoke flares can create a smoke screen in a specific airspace, making them a key piece of equipment for jamming incoming enemy missiles and protecting important friendly targets. Traditional smoke flares can be deployed in various ways, but most rely on airborne platforms for manual control, resulting in poor flexibility and slow response times. In recent years, with the rapid development of unmanned aerial vehicle (UAV) technology, their high speed, small size, and operational flexibility have made deploying smoke flares via UAVs a new option for quickly jamming incoming enemy missiles. The design of parameters related to UAV flight and deployment is a crucial factor in determining whether smoke flares can successfully jam incoming enemy missiles and protect high-value friendly targets.

[0004] However, there is currently limited research on systematic jamming smoke grenade deployment strategies. Existing strategies typically deploy smoke grenades in single-UAV mode according to preset fixed parameters (or with simple adjustments based on the general direction of the missile). These strategies have a short effective masking duration and lack quantitative optimization of key indicators such as masking duration, making them difficult to cope with dynamic scenarios. In multi-UAV mode, they rely solely on quantity for coverage, lacking unified scheduling and efficient coordination logic, making it difficult to achieve optimal masking effects. They also lack adaptability to complex scenarios involving multiple UAVs, missiles, and targets, and cannot meet the jamming requirements in complex scenarios. Summary of the Invention

[0005] To address the problems in existing technologies, such as the short duration of fixed-parameter deployment of single UAVs with limited dynamic optimization, and the tendency for overlapping or gaps in the deployment of multiple UAVs without proper coordination to achieve optimal shielding, this invention provides an optimization method and system for UAV-based smoke grenade deployment. By analyzing the shielding effect of smoke clouds on missiles in different scenarios, an optimization model for the UAV smoke grenade deployment interference time is constructed. The optimal deployment strategy is then obtained, enabling the smoke grenade deployment to achieve the maximum effective shielding duration in various combat scenarios and meeting the interference requirements in complex battlefield environments.

[0006] In a first aspect, the present invention provides an optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs).

[0007] An optimized method for the delivery of smoke flares based on unmanned aerial vehicles (UAVs) includes: Construct different deployment scenarios for drones carrying smoke flares to jam incoming missiles; For different deployment scenarios, we construct motion trajectory models of cloud clusters before and after detonation of drones, missiles, and smoke decoys. Based on the missile's target tracking principle, we establish the criteria for judging the interference of cloud clusters on missiles according to the relationship between the longest distance from the collection of all visible light segments from the missile to the target to the center of the cloud cluster and the radius of the cloud cluster. The effective interference duration is defined as the time interval that meets the criteria for interference determination. With the goal of maximizing the effective interference duration, the drone speed and heading angle, the time of smoke grenade dropping and the time of detonation are used as decision variables. Combined with the constraints, a drone smoke grenade dropping interference time optimization model is constructed, and the optimal dropping strategy is obtained by solving the model.

[0008] Secondly, the present invention provides an optimized system for the delivery of smoke flares based on unmanned aerial vehicles (UAVs).

[0009] An optimized system for the delivery of smoke flares based on unmanned aerial vehicles (UAVs) includes: The scenario building module is used to construct different deployment scenarios of drones carrying smoke decoys to interfere with incoming missiles; The motion analysis module is used to construct motion trajectory models of clouds before and after the detonation of drones, missiles, and smoke decoys for different deployment scenarios. Based on the missile's target tracking principle, it establishes the basis for judging the interference of the cloud on the missile by the relationship between the longest distance from the collection of all visible light segments from the missile to the target to the center of the cloud and the radius of the cloud. The deployment optimization module is used to determine the effective interference duration based on the time interval used for interference judgment. With the goal of maximizing the effective interference duration, it uses the drone speed and heading angle, the smoke grenade drop time and detonation time as decision variables, and combines them with constraints to construct an optimization model for drone smoke grenade drop interference time. The optimal deployment strategy is obtained by solving the model.

[0010] The above one or more technical solutions have the following beneficial effects: This invention proposes an optimized method and system for the deployment of smoke and flare grenades based on unmanned aerial vehicles (UAVs). During model building, reasonable assumptions are made to simplify the model solution process. In the basic scenario one, all points on the surface of the target cylinder are selected as the basis for masking judgment, resulting in more accurate full masking determination. When the number of decision variables increases, a hierarchical search is adopted, first a coarse scan and then a fine scan, which speeds up the model solution while avoiding large errors and reducing the computational load. This optimization strategy solves the problems in existing technologies that make it difficult to implement a systematic smoke and flare deployment strategy and ensure maximum effective masking duration in various combat scenarios, thereby maximizing effective masking duration and meeting the jamming requirements in complex battlefield environments. Furthermore, the establishment of this smoke screen interference determination model includes motion trajectory modeling, spatial masking, and collaborative optimization. Its application scenarios can be extended to other smoke screen interference scenarios. In the military field, it can be extended to individual soldier counter-reconnaissance, reducing exposure risk by optimizing personal smoke screen deployment. In the civilian field, such as wildfire prevention and control and forest fire fighting, it can achieve accurate positioning of smoke sources through full masking detection. In the field of environmental emergency response, this model can assist in simulating the masking of vision by natural phenomena such as sandstorms and dense fog. Therefore, this model has strong practical application value.

[0011] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0012] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0013] Figure 1 This is a flowchart of the smoke decoy grenade deployment optimization method proposed in the embodiments of the present invention; Figure 2 This is a spatial relationship diagram of the drone, missile, and target in an embodiment of the present invention; Figure 3 This is a schematic diagram of the location of Scenario 1 in an embodiment of the present invention; Figure 4 This is a schematic diagram of missile target tracking and judgment in an embodiment of the present invention; Figure 5 This is a diagram showing the trajectory of the smoke cloud in an embodiment of the present invention. Figure 6 This is a schematic diagram of the trajectory of the smoke grenade in an embodiment of the present invention; Figure 7 This is a graph showing the variation of the duration of full obstruction with the detonation time of the smoke grenade in an embodiment of the present invention; Figure 8This is a schematic diagram of the drone setting parameters in scenario one of the embodiments of the present invention; Figure 9 This is a schematic diagram of the smoke grenade throwing in scenario two of this embodiment of the invention; Figure 10 This is a simplified missile detection schematic diagram from an embodiment of the present invention; Figure 11 The diagram shows the correlation between the initial velocity and angle of the three smoke grenades and the drone in an embodiment of the present invention; where (a) is the influence of the drone angle on the individual shielding duration of each smoke grenade, and (b) is the influence of the drone velocity on the individual shielding duration of each smoke grenade. Figure 12 This is a schematic diagram of the effective obstruction state under the three-drone cooperative strategy in an embodiment of the present invention; Figure 13 This is a schematic diagram of the velocity sensitivity analysis results for scenario four in an embodiment of the present invention. Detailed Implementation

[0014] It should be noted that the following detailed descriptions are exemplary and are intended only to describe specific embodiments and to provide further explanation of the invention, and are not intended to limit the scope of exemplary embodiments of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0015] Example 1 To achieve optimal concealment effects when UAVs deploy smoke flares (or simply smoke flares or chaff) in different combat scenarios, this embodiment proposes an optimization method for UAV-based smoke flare deployment. By constructing a basic model and optimizing scenario-specific parameters, an optimized deployment strategy that maximizes concealment duration is obtained. For example... Figure 1 As shown, the method specifically includes the following steps: Step S1: Construct different deployment scenarios for drones carrying smoke decoys to interfere with incoming missiles.

[0016] Specifically, in combination Figure 2The simplified spatial relationship diagram of drones, missiles, and the target shows that, in order to fully protect an important target from missile attacks, the defending side deployed five drones carrying smoke flares around the target and set up a decoy target in front of the real target to confuse the enemy's incoming missiles. With the decoy target as the origin, it is known that there are three air-to-ground missiles with known directions, and their flight trajectories are directly pointing to the decoy target set up to cover the real target. The five drones carrying smoke flares deployed around the target can move quickly to the set coordinates at a specified speed, drop smoke flares, form a smoke cloud, and interfere with the incoming missiles.

[0017] Based on the simplified scenario described above, and considering that the specific quantities of drones and missiles can be set according to actual circumstances, this embodiment establishes several different deployment scenarios, including: Scenario 1: A single drone carrying a single smoke grenade jams a single missile; Scenario 2: A single drone carrying multiple smoke flares interferes with a single missile; Scenario 3: Multiple drones, each carrying a single smoke grenade, interfere with a single missile; Scenario 4: Multiple drones, each carrying multiple smoke decoys, interfere with multiple missiles.

[0018] Based on the various delivery scenarios constructed above, the optimal delivery strategy for different delivery scenarios is obtained through the following steps.

[0019] Step S2: For different deployment scenarios, construct motion trajectory models of the cloud clusters before and after detonation of UAVs, missiles, and smoke decoy grenades. Based on the missile's target tracking principle, establish the criteria for judging the interference of the cloud clusters on the missile based on the relationship between the longest distance from the collection of all visible light segments from the missile to the target to the center of the cloud cluster and the radius of the cloud cluster.

[0020] Step S3: The effective interference duration is defined as the time interval that meets the interference judgment criteria. With the goal of maximizing the effective interference duration, the drone speed and heading angle, the smoke grenade drop time and detonation time are used as decision variables. Combined with the constraints, a drone smoke grenade drop interference time optimization model is constructed, and the optimal drop strategy is obtained by solving it.

[0021] Specifically, since Scenario 1, in which a single UAV carries a single smoke grenade to interfere with a single missile, is the most basic scenario, this embodiment first analyzes the optimal deployment strategy under this scenario. Subsequently, based on this scenario, we will analyze and solve the optimal deployment strategies under other more complex scenarios.

[0022] In this embodiment, for scenario one, in order to achieve the optimal deployment of smoke grenades, it is actually necessary to solve the following: under the premise that the incoming missile is M1 and the drone FY1 carries only one smoke grenade, design the drone's flight speed, direction, the timing of smoke grenade deployment and detonation, so that the smoke cloud can cover the incoming missile for as long as possible.

[0023] To address this multi-parameter optimization problem, this embodiment first uses kinematic equations to establish a trajectory model of the UAV, missile, smoke grenade, cloud, and missile at a given time, clarifying position changes and motion states. Then, based on the principle of spatial geometric analysis, a model for determining the interference of the smoke cloud on the missile is established. Using a set of line segments representing the line of sight between the missile and the target point, the line segment with the longest distance to the center of the cloud is selected from the set. The distance between this line segment and the center of the cloud is calculated and compared with the cloud radius. If the distance from this line segment to the center of the cloud is less than the cloud radius, it indicates that the smoke cloud is interfering with the missile. After establishing the smoke interference determination model, the effective interference time interval can be determined. Then, based on this effective interference time interval, an objective function is constructed with the goal of maximizing the full obscuration time of the smoke cloud on the real target, setting decision variables and constraints. Finally, through discrete sampling, grid search, and combined with the optimization model, the smoke grenade throwing parameters are solved to determine the smoke grenade throwing settings and the maximum interference time of the smoke cloud on the incoming missile.

[0024] Specifically, to simplify the calculation, we first assume the gravitational acceleration at that location. It is 9.8 Ignoring the influence of wind above the target point on the smoke screen, ignoring the influence of air resistance on the smoke decoy grenades, the UAV can instantly accelerate to the set speed. Ignoring the influence of weather factors on missile interference judgment, the smoke grenades can still provide shielding for the missile after detonation on the ground. Furthermore, the parameters in the model are defined as shown in Table 1 below.

[0025] Table 1. Meaning of each parameter in the model

[0026] Furthermore, considering the complexity of multi-parameter optimization in this scenario, this embodiment first sets up a simplified problem: Given the UAV's flight speed, direction, bomb release timing, and smoke decoy detonation time in this scenario, determine the incoming missile. Flight speed (e.g.) Under the premise that the flight direction is directly aimed at the false target, kinematic formulas are used to establish the trajectory equations of the UAV, the smoke grenade before and after detonation, and the missile. Then, based on the principles of spatial geometry, a missile target acquisition and judgment model is established. The set parameters are substituted into the model to calculate the effect of the cloud of smoke grenade explosion on the missile. The duration of interference. By analyzing the simplified problem described above, a model for determining the interference of smoke grenades on incoming missiles can be established, laying the foundation for subsequent multi-parameter optimization problems.

[0027] Specifically, such as Figure 3 As shown, in a coordinate system with the false target as the origin, to quantify the effective concealment duration of the smoke flares released by UAV FY1 on incoming missile M1, missile M1 is first processed into a point mass, and a quadrangular pyramid is constructed with missile M1 as the vertex and the circumscribed rectangle of the target cylinder as the base, forming the target detection area. Based on this, a basic motion trajectory model is constructed, including: (1) UAV trajectory model Drone FY1 from point Starting from (17800, 0, 1800), at the same altitude, follow the direction of the false target. For high-speed flight, the unit vector of its heading is: (1) in, It is the horizontal component of the vector pointing from the initial position of the UAV to the origin.

[0028] Since the UAV moves at a constant altitude and uniform speed towards the origin of the coordinate axis, using the initial position, flight speed, and heading angle of the UAV as input and the position coordinates at any given time as output, we can construct the equation for the UAV's uniform motion at a constant altitude, that is, the equation for the UAV's position changing with time, as follows: (2) In the formula, This refers to the horizontal movement speed of the drone.

[0029] (2) Model of the trajectory of a smoke grenade before detonation From the moment a smoke grenade is released / dropped until its detonation, its horizontal direction is affected by inertia, causing it to continue moving at the same constant speed as the drone in the same direction of motion. Vertically, it is affected by gravity and undergoes free fall. For example, when the drone is in flight... Seconds later, the chaff is deployed. Before detonation, its horizontal motion equation is the same as that of the drone, and it undergoes free fall in the vertical direction, with the following equation: (3) In summary, the equations of motion for the UAV are: (4) in, Let be the acceleration due to gravity, taken as 9.8. , The moment the smoke flares detach from the drone is , For the moment the smoke screen decoy grenades detonate, Right now , It is a vertical unit vector with a value of .

[0030] (3) Model of cloud trajectory after smoke grenade detonation exist At a certain moment, the smoke decoy detonates, forming a cloud to interfere with the missile. The cloud descends at a predetermined speed, such as 3 m / s, maintaining its effective position for a predetermined time. The formula for how the position of the sphere's center changes with time is: (5) In the formula, This indicates the initial position at which the smoke decoy grenades form when they detonate.

[0031] (4) Missile trajectory model Missile M1 is detected by radar at point (20000,0,2000) and flies towards the decoy at the origin (0,0,0) at a speed of 300 m / s. The unit vector of the missile's trajectory is... for: (6) In the formula, For missiles The initial position, It is the horizontal component of the vector pointing from the missile's initial position to the origin.

[0032] Using the missile's initial position and flight velocity as input, and its position coordinates at any given time as output, we construct the equation for the missile's uniform motion as it points directly at the decoy target. This equation represents the change in the missile's position with time t: (7) In the formula, missile unit vector of Component vectors on the axis; missile unit vector of Component vectors on the axis; missile unit vector of The component vectors on the axis.

[0033] Secondly, the observation of the missile's target point is determined to establish the basis for judging interference. That is, based on the missile's target tracking principle, the basis for judging the interference of the cloud on the missile is established according to the relationship between the longest distance from the collection of all visible light segments from the missile to the target to the center of the cloud and the radius of the cloud.

[0034] like Figure 4As shown, the target point is a height. ,radius The cylindrical object has its bottom center located at coordinates (0, 200, 0). Therefore, the expression for the target point is: (8) In this embodiment, it is defined that if the missile detects any point of the real target while approaching the decoy target after the cloud formation, it is considered a target detection. Therefore, a visible line segment from the missile to the target point is constructed, and the line segments are aggregated. ,Right now: (9) in, express The collection of all visible light segments as the missile approaches its target point. Let the target point be any point inside the cylinder. It is a description t The positional ratio parameter of the line segment formed by the missile M1 from its own position to point q on the surface of the target cylinder is between 0 and 1, and is determined by the positional characteristics of the line segment.

[0035] Specifically, since the missile is in motion, the above formula uses... To measure in At any moment, the M1 missile is in Point on the surface of the target cylinder The position on the line segment formed, ,when At that time, the missile was at a distance from the missile tip-off point. The ratio is 0, meaning the missile is located at the end of the line segment. Place; when At that time, the missile was at a distance from the missile tip-off point. The ratio is 1, meaning the missile is located at the target point. Place; when At that time, missile M1 was located on the surface of the target cylinder. to In the line segment formed, its distance from the target point distance for: (10) Furthermore, considering that the value range of k from 0 to 1 can completely cover all line segments between the missile and the target, by calculating the distance from each point on the line segment within this range to the center of the smoke cloud, it is possible to accurately determine whether the smoke can block the line of sight between the missile and the target, thus meeting the geometric logic requirements for interference determination. Therefore, based on the missile's target tracking principle, the criteria for determining cloud interference with the missile are established: when the cloud forms between the missile and the target line segment, it interferes with the missile's guidance by blocking the target's light. Whether the cloud can successfully block the target's light depends on... To the center of the cloud Longest distance and cloud radius Since light travels in a straight line, when the shortest distance between the missile's indexer and the target is less than the distance from that line to the center of the sphere, the light is blocked by the smoke cloud. That is, for any given moment... If it exists: (11) Then at this point, it can be assumed that the cloud cluster is at time [time missing]. The missile's line of sight was successfully disrupted, thus achieving missile shielding.

[0036] Furthermore, based on the aforementioned full coverage determination condition, namely, the missile is positioned on the target... Set of line segments of points In the center, to the cloud cluster sphere The longest distance is less than the radius of the cloud. This confirms that the cloud formation successfully interfered with the missile. However, because the smoke screen decoy only forms a cloud to interfere with the missile after its explosion, therefore... During this period of time, The calculation formula is: (12) In the above formula, To the center of the cloud Longest distance There are two scenarios: Firstly, when the missile is far from the cloud (greater than a set distance threshold): the missile's own mass is... The missile reaches its farthest point from the center of the cloud cluster; at this point, the missile's distance from the center of the cloud cluster is... That is .like Larger than the radius of the cloud If the cloud cluster cannot fully cover the detection path of the incoming missile, the jamming will fail. Secondly, when the missile is relatively close to the cloud (less than a set distance threshold): There exists a point on a line segment that is furthest from the center of the smoke sphere. The distance from this point to the center of the smoke sphere is determined by solving for the length of the line segment from that point to the center of the smoke sphere. .

[0037] To simplify calculations, the expression... Through the proportional coefficient on the line segment Map the points on the line segment to the area around the target, then calculate the distance from the mapped point to the target cylinder C, and finally use... Multiplying by this distance restores the length of the line segment, ultimately yielding the set. The maximum distance to the center of the cloud cluster The solution process is as follows: First, we need to determine the maximum distance from the center of the cloud cluster to the missile.

[0038] against The vector magnitude of the three-dimensional vector is: (13) Through calculation Coordinates of the center of the cloud cluster at any given time ( ) and missile mass coordinates ( The spatial distance between two points is used to calculate the vector magnitude of the three-dimensional vector using the spatial distance formula.

[0039] Secondly, calculate the maximum distance from the center of the cloud cluster to a point on the line segment of the line of sight.

[0040] Due to the line segment parameters of each line segment of the cylinder from the missile to the target point Since the line segment is continuous, discrete sampling is used to cover all possible segments. To obtain the maximum distance points as much as possible, the model solution uses non-uniform scanning, with scanning points selected more densely in the edge regions at both ends. 60 scanning points are set in each of the intervals [0,0.02] and [0.98,1], and 360 scanning points are set in the region [0.02,0.98], for a total of 480 scanning points in the entire line segment.

[0041] For each sampling point in the line segment Calculate the origin according to the transformation formula. ,for: (14) Finally, calculate the points on the line segment. To the target cylinder The distance.

[0042] For calculation To the target cylinder To determine the distance, we first need to decompose its spatial distance into radial and axial parts. The axis of cylinder C is a vertical line passing through the center of the base. The distance can be calculated using the formula for the distance from a point in a plane to a line. Distance from the axis in the horizontal direction ,for: (15) set up Points in the horizontal direction The component to cylinder C, The formula is: (16) like Greater than Then point Located outside the target cylinder, horizontal distance component for The difference; if Less than Then point Located within the target cylinder, horizontal distance component Take 0.

[0043] set up Point in the vertical direction To cylinder The amount, The formula is: (17) In the formula, within the vertical range, With the vertical midpoint As a reference, if point of The absolute value of the difference between the coordinates and the midpoint is greater than This explains the point. Outside the vertical range of the cylinder, the vertical distance is taken as... If point of The absolute value of the difference between the coordinates and the midpoint is less than This explains the point. Within the vertical range of the cylinder, the vertical distance component is 0.

[0044] Given the vertical and horizontal components, combine and , using the Pythagorean theorem we can get the point To cylinder The shortest distance is: (18) Point Through the proportional parameter Restored to the true distance from the original missile's line of sight to the center of the cloud. : (19) Based on the above analysis, a model for determining the interference of smoke grenades on incoming missiles was established. Combining the established trajectory equations of the UAV, the smoke grenade before and after detonation, and the missile's trajectory, along with the missile's target acquisition model, the set parameters were substituted into the model to calculate the positions of each entity. Furthermore, by discretely sampling the line-of-sight segments and using a bisection method to search for the effective interference time interval, the impact of the smoke grenade's cloud on the missile after detonation was calculated. The duration of the interference. The solution process is as follows: In time Set the search step size within the interval. The time window length is 20, and the number of discrete points in the coarse scan is... After determining the approximate range of numerical results, the bisection method is used to further improve the accuracy of the model results, and the time... Reset to ,search To the center of the cloud Longest distance and cloud radius The moment the relation sign changes. Substitute the data into the model and utilize... Solving for the problem, we finally obtained the following result: Figure 5 The results show that within the time interval [8.056447, 9.448087], the smoke flares effectively shielded the missile for a duration of [duration missing]. .

[0045] Preferably, the robustness of the established model is tested. The original occlusion duration under strict occlusion conditions is 1.391614 s. Under relaxed occlusion conditions, with four feature points on each of the upper and lower surfaces (a total of eight corner points), the occlusion duration is 1.391981 s. Although this duration does not meet the consistency requirements of the upper and lower bounds of the strict duration, its discrete convergence and symmetry limit test results (0.000% and 0.000000 s respectively) are extremely good, indicating that the model has high rotational symmetry. Although there are some errors in duration consistency, the overall performance of the model is considered reliable due to its strong discrete convergence and rotational invariance.

[0046] After analyzing the effective interference duration of smoke grenade deployment under the given conditions, following the above analytical approach, an optimization model is established with the objective of maximizing the interference time of smoke grenades to solve the multi-parameter optimization problem under the given scenario. This includes the following steps: Step S2.1: For scenario one, construct motion trajectory models of the cloud clusters before and after the detonation of the drone, missile, and smoke decoy.

[0047] To achieve optimal smoke grenade deployment in scenario one, key parameters such as flight speed, direction, and deployment time need to be designed independently, and a system based on full coverage time needs to be established. An optimization model with maximization as the objective. In this embodiment, based on the above modeling method, motion trajectory models of each subject in the scene are constructed, including: (1) UAV trajectory model drone from point Starting from (17800,0,1800), at... At a specified height and constant speed flight, heading angle The value range is [0°, 360°]. Its heading unit vector is: (20) The equation for the change of the UAV's position over time is shown in formula (3). Substituting these equations into the formula, we can finally obtain the final position of the UAV at that time. At time t, the position in this three-dimensional coordinate system.

[0048] (2) Trajectory model of smoke grenade after deployment and before detonation like Figure 6 As shown, after the smoke grenade is deployed, it moves horizontally along the direction of the drone's motion due to inertia, maintaining the same speed as the drone in a uniform linear motion. Vertically, it is subject to gravity and undergoes free fall. Therefore, the trajectory equation of the smoke grenade is: (twenty one) in, It is a vertical unit vector. For the timing of smoke grenade deployment, For the moment the smoke grenade detonates, .

[0049] (3) Model of the trajectory of a smoke grenade after detonation After detonation, the cloud cluster... The cloud falls at a constant speed, with an effective duration of 20 seconds. After detonation, the center of the cloud is located at: (twenty two) (4) Missile trajectory model The missile motion formula in equation (7) above is used to characterize the position coordinates of the missile as its position changes with time t.

[0050] Step S2.2: Determine the missile's observation of the target point and establish the basis for interference determination.

[0051] In this embodiment, the interference determination model given in the above analysis is used, that is, the true target is set as a cylinder, and its mathematical expression is shown in formula (8). Whether the smoke cloud can successfully block the target light depends on... To the center of the cloud Longest distance and cloud radius The distance relationship determines: when To the center of the cloud Longest distance satisfy At that time, it can be considered that the smoke screen successfully blocked the light from the target point towards the missile, and the smoke screen cloud map successfully interfered with the incoming missile; when To the center of the cloud Longest distance satisfy At that time, it can be assumed that the smoke screen did not completely block the light from the target point towards the missile, and the smoke cloud failed to interfere with the incoming missile.

[0052] in, The calculation method is shown in formula (12).

[0053] Based on this, step S3 is executed to construct and solve the optimization model. Specifically, this is to achieve the effective total interference duration. To maximize the result, the interference judgment criteria must be met: Time interval of the condition The goal is to maximize the sum of lengths, i.e., to maximize the effective interference duration, which can be expressed as: (twenty three) Furthermore, when the FY1 drone dropped a single smoke grenade to jam missiles, the drone's speed... , heading angle Release time Detonation Moment Changing the parameters will affect the total effective interference duration. Changes have occurred, therefore, the drone speed has been adjusted. Heading angle Smoke grenade dropping time and the detonation time Using these as decision variables and setting corresponding constraints, an optimization model for the timing of the first UAV smoke grenade dropping interference is constructed. The basic constraints include: (1) Drone speed constraint: The drone's flight speed can be instantly accelerated to a specified speed, but the speed will not change after reaching the specified speed. The drone's speed value is not lower than 70m / s and not higher than 140m / s, that is: (twenty four) (2) UAV heading angle constraint: The UAV starts from point Once launched, it can fly in any direction, meaning: (25) (3) Smoke grenade deployment timing constraints: Smoke grenades can be deployed at any time after the drone departs, regardless of the drone's flight time and distance, i.e.: (26) (4) Smoke grenade detonation time constraint: Smoke grenades should only be detonated after they have been deployed, that is: (27) (5) Effective time constraint of the smoke grenade: After the smoke grenade explodes, the effective time for the cloud to interfere with the missile is 20 seconds, that is: (28) (6) Cloud height constraint: The cloud generated by the smoke grenade should form above the ground, that is: (29) (7) Smoke grenade deployment time constraint: Smoke grenades should be deployed before the missile hits the target, and the time between missile impact and target is... The time it takes for a smoke grenade to form a cloud of smoke after detonation should be less than this time, so as to effectively interfere with incoming missiles. (30) Therefore, the optimization model for the first UAV smoke grenade dropping interference time is as follows: (31) Finally, the optimization model constructed above is solved. In this embodiment, discrete sampling and network search are first used to solve the decision variables. , , , Uniform sampling is performed within the feasible region of the constraints, and the effective interference duration for each sample is calculated. The process involves filtering out local optima, then using a bisection method to further refine the time interval, and finally employing coordinate descent to optimize the decision variables to their limits, thereby improving efficiency. The value is calculated until convergence, yielding the optimal delivery strategy for the current scenario. The specific solution process is as follows: First, discrete sampling and grid search are performed for the decision variables. , , , Uniform sampling is performed within the feasible region to select local optima. (UAV speed) Values m / s, sampling step size is 5 m / s; heading angle The range of values ​​is Sampling step size Release time , The range of values ​​is s, sampling step size is Centered on the decision variable parameters, the system traverses all sampling points in the extended network to calculate the effective interference duration at each point. ,reserve The largest combination of parameters is the local optimum.

[0054] Secondly, the bisection method refines the results. After completing discrete sampling and grid search, in order to further solve for the maximum interference duration, the bisection method is used to accurately solve the results, obtaining the start and end times of the interference. and The effective occlusion time is determined by setting a detection function, namely: (32) when When the number changes from positive to negative, the missile is interfered with by the smoke screen; this moment marks the start of the interference. ;when When the number changes from negative to positive, the missile is no longer affected by the smoke screen; this is the end point. In this embodiment, the binary search method is used to iterate 80 times over each sign change interval, achieving an accuracy of [missing information]. Calculate the sum of all effective interference time intervals to obtain the total interference time.

[0055] Then, the coordinate descent method was used for iterative optimization. This was to determine the impact of parameter adjustments. The influence of this process is gradually applied to approach a better solution. Starting with the initial value obtained from grid search, the one-dimensional golden ratio method is used to optimize the decision variables within their local neighborhood. For each decision variable, the other three terms are fixed, and the search is performed independently on its neighborhood, including: for the UAV heading angle... ,fixed , , Using the golden ratio Search for the optimal angle within the range; for the drone speed ,fixed , , ,exist Search for the optimal speed within the range; for drone bombing time ,fixed , , ,exist Search for the optimal bombing time within the range; for the detonation time of smoke grenades ,fixed , , ,exist Search for the optimal detonation time within the range.

[0056] Repeat the above steps until the iteration is complete. The increase is less than .

[0057] Finally, random perturbation adjustment is performed. (This is for the decision variables.) , , , Randomly added Group random perturbation, generate The optimal data was collected and the effective interference duration for each group was calculated. .

[0058] Substituting the above data, the values ​​are calculated using Python, and the final solution is the time to achieve full occlusion. The maximized UAV flight parameters and smoke grenade dropping parameters are shown in Table 2 below. Under full cover conditions, the maximum interference time of the smoke cloud formed after the smoke grenade explosion on the incoming missile is also shown. = The duration of full coverage varies with the detonation time of the smoke grenade. Figure 7 As shown, the delayed detonation of the smoke grenade is closely related to the time it takes to fully cover the missile. When the delayed detonation time is... At that time, the longest full-coverage time is The value decreases towards both sides, and the duration of full occlusion decreases rapidly after deviating from the peak range, eventually approaching 0.

[0059] Table 2. Smoke grenade throwing settings for the following scenario

[0060] Preferred, such as Figure 8 As shown, this embodiment uses three sampling points—eight-point, twenty-one-point, and dense-point—to test the occlusion duration. It was found that the duration conforms to the range constraints and is consistent. The results converge at different time steps with a relative error of 0. The occlusion duration shows monotonicity as the smoke radius increases. Statistical analysis of 30 sets of LHS random samples shows that the results are relatively stable. The model's consistency, convergence, monotonicity, and robustness all show good performance.

[0061] Similarly, the optimal delivery strategies for scenarios two, three, and four are obtained by following the same steps described above.

[0062] For scenario two, the actual solution is to add drones. The number of smoke grenades carried by the drone Built-in three smoke decoy flares and incoming missiles Under the premise of [specific conditions], design a smoke grenade throwing scheme to achieve [targeting / dealing with] missiles. The maximum interference duration. Since Scenario 2 adds the number of smoke grenades carried by drones compared to Scenario 1, the number of decision variables in the objective function increases. To simplify the calculation, this embodiment simplifies the missile detection mechanism established above, using the selected upper and lower surfaces of the target point... The line segments connecting the key points to the missile replace the set of line segments from the missile to the points on the cylinder in the original judgment model. Based on the constraints of Scenario 2, an additional condition is added: the time between the deployment of adjacent smoke grenades is greater than or equal to... To meet the time requirement, simulated annealing was used to solve the problem, obtaining the maximum interference time of the smoke cloud, determining the UAV flight parameters and smoke grenade dropping parameters, and these parameters are included in the attachment. middle.

[0063] like Figure 9 As shown, in scenario two, UAV FY1 still intercepts missile M1. UAV FY1 carries three smoke decoy flares instead of one, with a one-second interval between drops. Therefore, the motion model for the UAV and missile uses the previously constructed motion model, and a new trajectory model is established for the three smoke decoy flares and the resulting interference cloud. That is, based on the basic trajectory model, an independent trajectory model is first established for each smoke decoy flare, represented as: (1) Model of the trajectory of a smoke decoy before explosion No. The trajectory of a smoke grenade before detonation is as follows: (33) in, For the first The moment the smoke grenade was dropped, The formula for the motion trajectory of the drone. It is the unit vector of the drone's direction of motion. For the first i The vertical height of a smoke grenade at the moment of its release.

[0064] (2) Model of cloud and fog movement trajectory after smoke decoy grenade explosion No. After a smoke grenade detonates, it creates a disruptive smoke screen that descends at a speed of 3 m / s. The equation for the trajectory of the cloud's center is: (34) in, For the first The moment a smoke grenade detonates.

[0065] Secondly, the smoke grenade's ability to conceal the missile still uses the aforementioned interference judgment criteria (or model). However, to simplify calculations, this embodiment employs a discrete sampling method to select eight key points on the cylindrical target and connect them to the missile's mass point, serving as the basis for determining whether the missile can detect the target. For example... Figure 10 As shown, to ensure that the selected points can cover the target cylinder as completely as possible, points with an angle of θ are selected on the edges of the top and bottom surfaces. Based on the four points, the minimum length of the line segment from these eight key points to the missile and then to the center of the cloud cluster is determined. The relationship, when satisfied At this point, it can be assumed that the target's own light is blocked by the smoke cloud, thus successfully interfering with the incoming missile.

[0066] Furthermore, in the multiple smoke grenade jamming model, different smoke grenades may interfere with the incoming missile within the same time interval. Therefore, when calculating the total jamming time interval, it is necessary to take the union of the jamming intervals of the three smoke grenades to prevent the jamming time from being calculated repeatedly.

[0067] set up For the first The effective interference range of a smoke grenade is as follows: (35) Total interference time of multiple smoke screens The set of interference intervals for the three smoke grenades is: (36) Based on this, in a scenario where a single aircraft carries three smoke flares, the total jamming time is calculated by taking the union of the jamming time intervals of the multiple smoke flares, in order to maximize the total effective jamming duration. To make the time interval The sum of lengths satisfies Under the condition of being as long as possible, that is: (37) The final effective jamming duration is obtained by summing all time periods that conform to the jamming model formed by the three smoke flares. .

[0068] Considering the drone's flight speed, flight direction, and the release time of each of the three smoke flares. With detonation time All of these will affect the final total effective interference duration. Therefore, in scenario two, the decision variable includes the drone's flight speed. UAV flight direction and angle , No. Smoke grenade throwing time , No. Detonation time of one smoke grenade .

[0069] The constraints are basically similar to those in Scenario 1, but an additional constraint is added regarding the time interval between the throwing of three smoke grenades. The throwing time of two adjacent smoke grenades should be greater than [missing information]. ,Right now: (38) Based on the above constraints, an optimization model for bombing interference time is established when the UAV is carrying three smoke grenades: (39) Finally, based on the second UAV smoke grenade dropping interference time optimization model, the simulated annealing algorithm is used to solve for the optimal parameters of the decision variables, and the optimal dropping strategy under the current scenario is obtained.

[0070] Specifically, considering that Scenario 2 involves seven decision variables, which is a multi-parameter optimization problem with coupling relationships between variables, the discrete sampling and grid traversal method used in the original solution model has high computational complexity and is time-consuming, making it difficult to solve for the maximum effective total disturbance duration. Therefore, this embodiment simplifies the model and then uses the simulated annealing algorithm to solve it. The specific steps are as follows: First, set the parameters. In this embodiment, the initial temperature is set. Attenuation factor Temperature iteration number To accelerate computation, multiple parallel starting points are set up, and multi-process computation is adopted to calculate the objective function within the range of the decision variables. .

[0071] Secondly, neighborhood perturbation. After the initial scheme is generated through the first simulated annealing, the decision variable parameters are randomly perturbed to generate a new model, and the objective function generated by the new model is calculated. The difference between the two models is obtained. .like If the value is greater than 0, then the value of the new model is taken as the maximum total interference duration. ;like If the value is less than 0, generate a random number from the interval [0,1]. If the value is less than the probability... If the model is correct, update it; otherwise, retain the original model. .

[0072] Then, the temperature decays. At temperature... After repeating step 320 times, and after exploring all possible feasible solutions in the adjacent domains, proceed according to... Cooling is performed to achieve a transition from global to local optimization.

[0073] Finally, convergence is determined. The model has the following two stopping conditions. If these convergence conditions are met, the iteration stops and the optimal solution is output. The stopping conditions are: (1) Minimum temperature Under these conditions, the local search phase begins. (2) If the maximum number of stall steps of 1400 is reached, it means that the optimal solution in this area has been reached, and the search is stopped.

[0074] In this embodiment, by substituting the relevant data and solving the problem using Python, the flight speed of the UAV FY1 is obtained. Flight angle The final effective interference duration The parameters for smoke grenade deployment points are shown in Table 3 below.

[0075] Table 3. Coordinates of Smoke Bomb Drop Points in Scenario 2

[0076] The detonation point and effective interference duration of the smoke grenade are shown in Table 4 below, and the data is stored in result2.xlsx.

[0077] Table 4. Coordinates of Smoke Grenade Detonation Points and Effective Interference Duration

[0078] Depend on Figure 11 It is evident that the first and third smoke grenades have a weak correlation with the drone's initial velocity and initial bearing, while the second smoke grenade has a strong correlation with the initial angle. When the maximum value is reached The initial angle correlation is weak.

[0079] Preferably, for the model constructed under scenario two, a comprehensive test is carried out by combining detailed single-case verification with batch robustness testing, and the test indicators are shown in Table 5.

[0080] Table 5 Key Information Table for Model Validation

[0081] As shown in Table 5 above, the model strictly meets all constraints. The bomb drop interval and the UAV speed and heading angle are all within reasonable ranges, demonstrating reliable performance in terms of numerical stability and physical logic. Single-case testing selected typical parameter combinations for decomposition analysis, while batch testing was conducted based on 20 sets of random samples for statistical verification. The tests showed that the model in scenario two can stably satisfy all constraints.

[0082] For Scenario 3, the actual solution is to design a smoke grenade dropping strategy for the three drones (FY1, FY2, and FY3) to maximize the interference duration against the incoming missile M1, given that the incoming missile is M1 and each drone carries a smoke grenade. This embodiment uses the same trajectory model for the drones, smoke grenades, interference cloud, and missile as in Scenario 2. The interference determination is the same as in Scenario 2, using the relationship between the maximum distance from the line connecting eight key points on the target cylinder to the missile and the center of the cloud, and the radius of the center. Finally, feasible solutions are selected through parameter back-calculation. Then, an exhaustive method is used to iterate through all feasible solutions and combine them, with the combination having the longest total full coverage duration being selected as the optimal solution. The drone configuration parameters are written into the attached result2.xlsx file.

[0083] Specifically, 3 drones Each drone carries one smoke decoy; the parameters of the three drones need to be set independently to intercept incoming missiles together. This achieves continuous masking of friendly targets. First, the motion trajectory model for Scenario 3 is expanded, establishing an independent motion trajectory model for each drone, as follows: drones The unit vector in the heading direction is: (40) in, For drones The unit vector in its heading direction; For drones The heading angle. Known UAV exist Starting from a point, the solution for the UAV's heading direction can be obtained using the unit vector. The formula for the trajectory of motion: (41) Because drones and other aircraft fly at high altitudes, therefore z-coordinate and same.

[0084] In addition, regarding the trajectory of the smoke grenade before the explosion, since each drone carries a single smoke grenade in Scenario 2, and the motion pattern of each smoke grenade before and after the explosion is the same as that of a single smoke grenade in Scenario 2, the formulas for the trajectory of the smoke grenade in free fall before the explosion and the uniform motion of the center of the sphere after the explosion are the same as those in Scenario 2.

[0085] During use, the corresponding drone parameters in the formula were modified to match the parameters of the three drones FY1, FY2, and FY3 in Scenario 3. Scenario 3 uses the effective occlusion determination model of Scenario 2. After setting eight key points on the upper and lower bottom surfaces of the real target cylinder, the full occlusion was determined by using the relationship between the maximum distance between the line segment and the center of the cloud and the radius of the cloud.

[0086] Secondly, in scenario three, the total interference time is the union of the interference time intervals of multiple smoke grenades. The objective is to maximize the total interference duration. Even if the smoke cloud obscures the missile for the maximum interference time, this can be expressed as: (42) The decision variables include the speeds of the three drones in FY1, FY2, and FY3. , , heading angle , , Smoke grenade deployment time , , The moment the smoke grenade detonated , , .

[0087] Ultimately, the drone's flight speed and heading angle are fixed after the settings are completed, the flight altitude remains constant, the smoke grenade detonation time should be greater than the drop time, and the effective time of the smoke grenade should be [missing information]. Then the constraint condition can be expressed as: (43) Finally, based on the above optimization model, the speed, heading angle, and smoke grenade deployment and detonation times of the UAV are inferred from the positional relationship between the missile and the target. Feasible solutions are then selected using constraints. Finally, an exhaustive search method is used to traverse all combinations of feasible solutions for the three UAVs, and the total effective cover time for each combination is calculated. The combination with the largest total shading market is selected as the optimal solution.

[0088] In this embodiment, the data is substituted into the model, and Python is used for calculation to finally obtain the total full cover time of the coordinated interference of the three drones. The drone flight parameters for scenario three are shown in Table 6 below.

[0089] Table 6. Flight parameters of the UAV for Question 4

[0090] The smoke grenade throwing coordinate parameters for Scenario 3 are shown in Table 7 below. Save the drone classification parameters and smoke grenade throwing coordinate parameters to the attached file result2.xlsx.

[0091] Table 7. Coordinate parameters for smoke grenade throwing in Question 4

[0092] like Figure 12 As shown, the horizontal axis represents time, and the vertical axis passes through... and The occlusion state is quantified using a binary variable. At 1:01, drone FY1 dropped the smoke grenade first and detonated it at 1.01 seconds; FY2 dropped it at 6.41 seconds and detonated it at 11.23 seconds; FY3 dropped it at 19.15 seconds and detonated it at 22.35 seconds. Although the aerosol clouds of these three smoke grenades partially overlapped after detonation, by adjusting the detonation time and placement, the three smoke grenades did not overlap within their respective coverage areas, maximizing the continuous coverage time of the smoke on the cylindrical target.

[0093] Preferably, since the decision variables in Scenario 3 include multiple parameters such as the speed, heading angle, bomb drop time, and detonation time of the three drones, the model complexity is high. To ensure the reliability of the solution results for Problem 4, this embodiment establishes multiple checks for Problem 4 to verify the rationality of the model assumptions. The checks select the cooperative interference strategy of the three drones as the test object, and conduct system tests through methods such as criterion consistency verification, numerical convergence analysis, and physical law conformity verification. Finally, the model for Problem 4 shows good reliability in generating the combined optimal strategy.

[0094] For Scenario 4, the solution is to fully utilize the five drones surrounding the target point, each carrying a maximum of three smoke grenades, and, under this premise, formulate a deployment strategy to maximize the interception time of the three incoming missiles. In this embodiment, firstly, the trajectory models of the drones, smoke grenades, and aerosol clouds established in Scenarios 2 and 3 are used, and the interference determination adopts the simplified smoke interference determination model from Scenario 2. Secondly, the decision variables are the speed, heading angle range, bomb deployment time, and detonation time of the five drones. The constraints mainly include the speed range, heading angle range, bomb deployment interval, number of bombs deployed, and the time interval between bomb deployment and detonation. The objective function is to maximize the total time during which the three missiles are simultaneously obscured. Finally, after searching for local optimal solutions, the optimal solution is selected and considered the global optimal solution. The smoke grenade deployment parameters obtained from the solution are written into the attached result3.xlsx file.

[0095] Scenario 4 is a further expansion of Scenarios 2 and 3, increasing the number of drones, drone smoke flares, and incoming missiles. It requires coordinating five drones, each carrying a maximum of three smoke flares, to jam the incoming M1, M2, and M3 missiles. The trajectory model for this scenario is as follows: The drone motion model follows the scenario three setting, i.e., drone From its initial coordinate point Start at a constant speed Heading angle Moving at a constant height with uniform velocity in a straight line, its position changes with time as shown in the formula. Since each of the five drones can drop a maximum of three smoke grenades, a new smoke grenade dropping model needs to be developed for its multi-drone, multi-load configuration. (Drone) The The equation of the trajectory of a smoke grenade before detonation is: (44) in, For drones The The moment a smoke grenade was dropped from the drone , It is a vertical unit vector.

[0096] When by drone The first throw After a smoke grenade is detonated and forms a cloud, the equation for the uniform descent of the cloud's center is: (45) in, For drones The first throw The moment a smoke grenade is detonated and forms a cloud of smoke, after the cloud of smoke forms... The speed decreases at a constant rate, and the effective time of the cloud and fog is... .

[0097] Furthermore, to simplify calculations, the missile interference determination criteria in this scenario still adopt the simplified full-coverage determination model from Scenario 2. That is, based on eight key points on the top and bottom surfaces of the real target cylinder, the smoke screen's coverage performance on the missile is determined, and the determination criteria are as follows: If all eight key points are hidden, the missile is considered successfully jammed; if three missiles are jammed simultaneously, the time interval of this jamming is counted as effective jamming time. Therefore, the... The first drone The effective interference range of a smoke grenade is: (46) in, This is the starting time when the smoke screen interfered with a particular missile. This is the time when the smoke screen stops interfering with a particular missile.

[0098] For missiles M1, M2, and M3, the union of the effective interference zones formed by all smoke grenades within their shielding ranges are as follows: (47) The interval where all three missiles are simultaneously jammed is the intersection of the total shielding intervals, that is: (48) The total jamming time is the union length of the intersection times of the total shielding intervals of the three missiles: (49) Based on this, the maximum total time during which three missiles are simultaneously muted is set as the optimization objective: (50) Furthermore, the speed of each drone With heading angle The timing of the deployment of smoke grenades by each drone At the moment of detonation As decision variables, constraints on the bombing time interval of a single drone and the number of bombs dropped by a single drone are introduced on top of the basic constraints, namely: The bombing interval of a single drone should be no less than one second. (51) Each drone carries fewer than 3 smoke grenades: (52) The smoke grenade should detonate earlier than the time any of the three missiles reaches the target point: (53) Based on this, an optimization model for the drone smoke grenade dropping interference time in this scenario is constructed.

[0099] Finally, the above model is solved. To reduce the computational complexity and computation time under the multi-parameter condition of Scenario 4, this embodiment limits the decision variables to a smaller interval using random numbers. Within each interval, a uniform search is used to find local optima. Then, all local optima are combined, and the solution with the best performance is selected to obtain an optimal solution. Since multiple random samplings have covered the key parameter intervals, the solution is considered to be approximately the global optimum.

[0100] In this embodiment, the data is substituted into the model, and Python is used to calculate and obtain the longest total interference time. The direction of movement and speed of the UAV are set as shown in Table 8 below.

[0101] Table 8. Question 5: UAV Parameter Settings

[0102] The calculation results of smoke grenade deployment point parameters and effective interference duration are shown in Table 9 below.

[0103] Table 9. Parameters of UAV Smoke Grenade Deployment Points and Effective Interference Duration for Question 5

[0104] The calculation results of the detonation point parameters of the smoke decoy and the missile number of the decoy are shown in Table 10 below.

[0105] Table 10. Detonation point parameters of UAV smoke grenades and missile numbering for Question 5.

[0106] like Figure 13 As shown, a speed sensitivity analysis was performed on scenario four. The results show that when the UAV's fixed speed fluctuates within ±10% of the baseline value, the global effective masking duration varies within a range of approximately 4 seconds. This fluctuation characteristic is consistent with the parameter response pattern under actual combat conditions and is a normal phenomenon. The fluctuation range is relatively small, and the masking effect on incoming missiles is still good, which is in line with the model's expectations and demonstrates the model's stability.

[0107] Example 2 This embodiment provides an optimized system for the delivery of smoke flares based on unmanned aerial vehicles (UAVs), specifically including: The scenario building module is used to construct different deployment scenarios of drones carrying smoke decoys to interfere with incoming missiles; The motion analysis module is used to construct motion trajectory models of clouds before and after the detonation of drones, missiles, and smoke decoys for different deployment scenarios. Based on the missile's target tracking principle, it establishes the basis for judging the interference of the cloud on the missile by the relationship between the longest distance from the collection of all visible light segments from the missile to the target to the center of the cloud and the radius of the cloud. The deployment optimization module is used to determine the effective interference duration based on the time interval used for interference judgment. With the goal of maximizing the effective interference duration, it uses the drone speed and heading angle, the smoke grenade drop time and detonation time as decision variables, and combines them with constraints to construct an optimization model for drone smoke grenade drop interference time. The optimal deployment strategy is obtained by solving the model.

[0108] The steps and methods involved in the above embodiment two correspond to those in embodiment one. For specific implementation details, please refer to the relevant description section of embodiment one.

[0109] The above description is only a preferred embodiment of the present invention. Although the specific implementation of the present invention has been described in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative effort are still within the scope of protection of the present invention.

Claims

1. An optimized method for the delivery of smoke flares based on unmanned aerial vehicles (UAVs), characterized in that, include: Construct different deployment scenarios for drones carrying smoke flares to jam incoming missiles; For different deployment scenarios, we construct motion trajectory models of cloud clusters before and after detonation of drones, missiles, and smoke decoys. Based on the missile's target tracking principle, we establish the criteria for judging the interference of cloud clusters on missiles according to the relationship between the longest distance from the collection of all visible light segments from the missile to the target to the center of the cloud cluster and the radius of the cloud cluster. The effective interference duration is defined as the time interval that meets the criteria for interference determination. With the goal of maximizing the effective interference duration, the drone speed and heading angle, the time of smoke grenade dropping and the time of detonation are used as decision variables. Combined with the constraints, a drone smoke grenade dropping interference time optimization model is constructed, and the optimal dropping strategy is obtained by solving the model.

2. The optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 1, characterized in that, The different deployment scenarios include: Scenario 1: A single drone carrying a single smoke grenade jams a single missile; Scenario 2: A single drone carrying multiple smoke flares interferes with a single missile; Scenario 3: Multiple drones, each carrying a single smoke grenade, interfere with a single missile; Scenario 4: Multiple drones, each carrying multiple smoke decoys, interfere with multiple missiles.

3. The optimized method for deploying smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 1, characterized in that, The construction of a basic motion trajectory model includes: Using the initial position, flight speed and heading angle of the UAV as input, and the position coordinates at any time as output, we construct the equation of uniform motion of the UAV at the same altitude. From the time the smoke decoy is deployed until it is detonated, the drone moves at a constant speed in the horizontal direction due to its inertia and undergoes free fall in the vertical direction. The equation of motion of the smoke decoy before it is detonated can be constructed. After the smoke decoy is detonated, the cloud formed by it sinks at a preset speed and maintains a preset effective duration. An equation is established to show the change of the position of the center of the smoke cloud over time. Using the missile's initial position and flight velocity as inputs and the position coordinates at any time as outputs, a uniform motion equation for the missile pointing directly at the decoy target is constructed.

4. The optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 1, characterized in that, Based on the missile's target tracking principle, and according to the set of all visible light segments from the missile to the target... To the center of the cloud Longest distance and cloud radius The relationship between the cloud clusters and the criteria for determining their interference with missiles are established, for any given moment: If it exists That is, the longest distance Smaller than the radius of the cloud At that time, it was determined that the cloud formation had successfully interfered with the missile; Among them, when the missile is farther from the cloud than a set distance threshold, the missile's own mass becomes... Reaching the center of the cloud cluster At its farthest point, the missile is at a distance from the center of the cloud. ; When the missile is less than a set distance threshold from the cloud, There exists a point on a certain line segment that reaches the center of the cloud. The furthest point is determined by finding the length from that point to the center of the cloud. ; Then the longest distance Represented as: ； ； In the above formula, This represents the set of all visible light segments from missile M1 to the target cylinder C. It is a description t The positional ratio parameter of the line segment formed by the missile M1 at its own position and point q on the surface of the target cylinder, with a value between 0 and 1; For the moment the smoke screen decoy grenades detonate, The duration of the cloud cluster.

5. The optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 2, characterized in that, In the first scenario, a basic motion trajectory model is constructed, and the criteria for judging the interference of cloud clusters on missiles are established. With the known parameters of UAV speed, heading angle, bomb release time, and detonation time as input, the position of each subject is calculated. By discretely sampling the line-of-sight segments, combined with the binary search method, the effective interference time interval is searched, and finally the effective interference duration is output.

6. The optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 2, characterized in that, In the first scenario, with the goal of maximizing the effective interference duration, the drone speed, heading angle, smoke grenade drop time and detonation time are used as decision variables, basic constraints are set, and the first drone smoke grenade drop interference time optimization model is constructed. Based on the first UAV smoke grenade dropping interference time optimization model, discrete sampling and network search algorithms are used to uniformly sample decision variables within the feasible region of the constraints, calculate the effective interference time of each sample, screen out the local optimal solution, refine the time interval using the bisection method, and finally use the coordinate descent method to optimize the decision variables to the limit until convergence, so as to obtain the optimal dropping strategy in the current scenario. The basic constraints include: drone speed constraint, drone heading angle constraint, smoke grenade deployment time constraint, smoke grenade detonation time constraint, cloud effective time constraint, cloud altitude constraint, and smoke grenade deployment time constraint.

7. The optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 2, characterized in that, In Scenario 2, based on the basic motion trajectory model, an independent motion trajectory model is established for each smoke chaff. The total interference time is the union of the interference time intervals of multiple smoke grenades. With the goal of maximizing the total interference duration, the drone speed, heading angle, smoke grenade dropping time and detonation time are used as decision variables. Based on the basic constraints, the interval constraint of adjacent smoke grenade dropping is introduced to construct the second drone smoke grenade dropping interference time optimization model. Based on the second UAV smoke grenade dropping interference time optimization model, the simulated annealing algorithm is used to solve for the optimal parameters of the decision variables, and the optimal dropping strategy under the current scenario is obtained.

8. The optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 2, characterized in that, In scenario three, based on the basic motion trajectory model, an independent motion trajectory model is established for each drone. The total interference time is the union of the interference time intervals of multiple smoke grenades. With the goal of maximizing the total interference time, the speed and heading angle of each UAV, the dropping time and detonation time of each smoke grenade are used as decision variables. Combined with the basic constraints, an optimization model for the interference time of the third UAV smoke grenade dropping is constructed. Based on the optimization model of the third UAV smoke grenade dropping interference time, after screening feasible solutions by back-calculation of parameters, the optimal collaborative strategy is solved by exhaustive search and combination to obtain the optimal dropping strategy in the current scenario.

9. The optimized method for the deployment of smoke flares based on unmanned aerial vehicles (UAVs) as described in claim 2, characterized in that, In scenario four, based on the basic motion trajectory model, an independent motion trajectory model is established for each drone, each smoke screen chaff, and each missile. The total interference time is the union of the total shielding intervals of multiple missiles. With the goal of maximizing the total interference duration, the speed and heading angle of each UAV, the drop time and detonation time of each smoke grenade are used as decision variables. Based on the basic constraints, the time interval constraint of single UAV bombing and the number of bombs dropped by single UAV are introduced to construct the fourth UAV smoke grenade bombing interference time optimization model. Based on the fourth UAV smoke grenade dropping interference time optimization model, the optimal dropping strategy under the current scenario is obtained by limiting the parameter range by random numbers and uniformly searching for local optimal solutions, and comprehensively selecting the global approximate optimal solution.

10. An optimized system for the delivery of smoke flares based on unmanned aerial vehicles (UAVs), characterized in that, include: The scenario building module is used to construct different deployment scenarios of drones carrying smoke decoys to interfere with incoming missiles; The motion analysis module is used to construct motion trajectory models of clouds before and after the detonation of drones, missiles, and smoke decoys for different deployment scenarios. Based on the missile's target tracking principle, it establishes the basis for judging the interference of the cloud on the missile by the relationship between the longest distance from the collection of all visible light segments from the missile to the target to the center of the cloud and the radius of the cloud. The deployment optimization module is used to determine the effective interference duration based on the time interval used for interference judgment. With the goal of maximizing the effective interference duration, it uses the drone speed and heading angle, the smoke grenade drop time and detonation time as decision variables, and combines them with constraints to construct an optimization model for drone smoke grenade drop interference time. The optimal deployment strategy is obtained by solving the model.

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