Analysis Method of Armed Helicopter Fire-Fly Cooperation Mechanism Based on Multi-Target Wolf Pack Algorithm

Abstract

This invention discloses an analysis method for the air-to-ground coordination mechanism of armed helicopters based on a multi-target wolf pack algorithm. This method studies the air-to-ground target aiming and attack problem of rotating turret weapons such as armed helicopter cannons. It mainly establishes the air-to-ground aiming and attack mechanism of rotating turret weapons by improving the CCIP fire control solution method and a multi-target optimization method. First, based on the aiming method and characteristics of rotating turret weapons of armed helicopters, the original CCIP fire control solution method is analyzed and improved, and a novel IFFC coupler is proposed to solve the coordinated attack problem between the armed helicopter and the weapon's servo system. Second, a multi-objective function optimization model for aiming of rotating turret weapons of armed helicopters is established through angle error analysis and dynamic coupling analysis. Finally, the optimization problem is solved using an improved multi-target adaptive wolf pack method, and the feasibility and effectiveness of the method are verified through simulation.

Description

Technical Field

[0001] This invention belongs to the field of target aiming technology for armed helicopters, specifically an analysis method for the fire-flying cooperative mechanism of armed helicopters based on a multi-target wolf pack algorithm. Background Technology

[0002] Due to the rapid development of flight control and airborne weapon technologies, highly maneuverable attack helicopters are playing an increasingly important role in the ever-changing modern battlefield, especially in low-altitude ground attack missions. In ground attack operations, compared to rack-mounted weapons, controlling the weapon servo system to drive the weapon line is more advantageous, as its ability to rotate rapidly in both lateral and longitudinal directions greatly enhances the attack and survivability of attack helicopters in complex low-altitude environments. For high-altitude combat aircraft such as fighter jets and bombers, controlling the weapon servo system to drive the weapon line is primarily a close-range defense measure; however, for attack helicopters operating at extremely low altitudes, it is a primary attack method. Therefore, researching high-precision, high-efficiency weapon servo systems is crucial for improving the accuracy of rotating turret-mounted weapons such as helicopter cannons.

[0003] Based on the IFFC system, most attack helicopters employ the GG-type aiming principle for fire control calculations in air-to-ground targeting of weapon servo systems. Its advantage lies in the fact that aiming does not require adjusting the helicopter's flight attitude; target aiming is achieved solely through rotating the turret, aligning with the original design intent of rotating turret weapons. Its strengths include high flight freedom and strong pilot control over the attack process. However, with advancements in computer technology, airborne weapon systems are evolving towards systematization, intelligence, and automation. The traditional GG-type rotating turret aiming principle for attack helicopters fails to account for the impact of helicopter attitude adjustments on the rotation of the weapon servo system. Its aiming efficiency largely depends on the pilot's skill in piloting and target aiming, which contradicts the trend towards intelligent and automated weapon systems.

[0004] Therefore, we no longer consider the attack helicopter and the weapon servo system as two independent systems. Instead, we consider the influence of the attack helicopter's attitude on the elevation and azimuth angles of the weapon line controlled by the weapon servo system. To this end, we improve the original CCIP aiming principle, considering the mutual coupling relationship and adjustment mechanism of the two systems during the aiming process, in order to establish a more realistic air-to-ground aiming mechanism for attack helicopter rotating turret-type weapons.

[0005] In conclusion, to ensure the accuracy and speed of air-to-ground attacks by armed helicopters using cannons, further research should be conducted on the aiming and attacking of air-to-ground targets by rotating turret weapons such as helicopter cannons. Summary of the Invention

[0006] To address the air-to-ground attack problem of armed helicopters in actual battlefield scenarios, the Integrated Fire / Flight Control (IFFC) system aims to integrate the fire control system and flight control system into a single system through a fire / flight coupler. However, when armed helicopters use weapon servo systems to attack targets, traditional IFFC systems cannot achieve high-precision aiming. First, based on the analysis of the CCIP aiming principle of armed helicopters, a novel IFFC coupler is proposed to solve the problem of coordinated attack between the armed helicopter and the weapon servo system. Second, in the novel IFFC coupler, the aiming problem is transformed into a multi-target optimization problem using angle error analysis and dynamic coupling analysis. Finally, to solve this problem, an improved Adaptive Multi-Target Wolf Pack Method (AMOWA) is designed, and its effectiveness is demonstrated through simulation examples.

[0007] To solve its technical problem, the present invention adopts the following technical solution:

[0008] The analysis method of the armed helicopter fire-fly cooperation mechanism based on the multi-target wolf pack algorithm includes the following steps:

[0009] Step 1) Establish the CCIP fire control solution vector relationship for weapons with rotating turrets of armed helicopters, and obtain the projectile pitch angle, azimuth angle and flight time information of the projectile impact point of the weapons with rotating turrets of armed helicopters.

[0010] Step 2) Transform the target angle aiming problem into a multi-objective optimization problem using target aiming angle error analysis and dynamic coupling analysis;

[0011] Step 3) Design a multi-objective wolf pack algorithm to solve the multi-objective optimization problem in Step 2).

[0012] Preferably, in step 1): the CCIP fire control solution vector relationship for armed helicopter rotating turret-type weapons is:

[0013]

[0014] in, For the target velocity vector, For wind speed vectors, For the composite wind speed vector; T d For the projectile's flight time, Install position difference vectors for rotating turret-type weapons; The distance vector from the point of projectile launch to the point of projectile impact. The projectile's ray vector. Reduce the projectile trajectory vector;

[0015] Projecting the vector equation in equation (1) onto the three axes of the body coordinate system, we get:

[0016]

[0017] Among them, [A] x A y A z [ is the distance vector] The components of the three-axis projection onto the body coordinate system, [U zx U zy U zz [This refers to the combined wind speed vector] The components projected onto the three axes of the aircraft coordinate system, where V1 is the absolute velocity of the projectile, V0 is the airspeed of the attack helicopter, and V... 01 Let v be the relative velocity of the projectile. w For the weapon line azimuth, μ w φ is the weapon line elevation angle, α is the lateral approach angle of the attack helicopter, β is the longitudinal approach angle of the attack helicopter; φ is the yaw angle of the attack helicopter, θ is the pitch angle of the attack helicopter, and ψ is the roll angle of the attack helicopter.

[0018] According to equation (2), the pitch angle μ at the point of impact of the projectile is... c , Azimuth of the hit point ν c and bullet flight time T d The expressions are:

[0019]

[0020]

[0021]

[0022] Among them, V pj The average velocity of the projectile.

[0023] Preferably, the implementation process of step 2) is as follows:

[0024] Step 2.1) Target aiming angle error analysis:

[0025] From equations (2)-(5), we know that the pitch angle μ of the hit point is... c , Azimuth of the hit point ν c Projectile flight time T d The yaw angle φ, pitch angle θ, roll angle ψ, and weapon line elevation angle μ of the attack helicopter w Weapon line azimuth ν w There exists a functional relationship:

[0026]

[0027] Let the elevation angle of the target line be μ. c c The azimuth of the target line is ν cc Then the target aiming angle error equation for the IFFC firepower and flight system of the armed helicopter is:

[0028]

[0029] Where N μ N represents the difference between the elevation angle of the weapon line and the elevation angle of the target line. ν This represents the error between the weapon line azimuth and the target line azimuth.

[0030] In order to achieve air-to-ground targeting, N μ and N ν Satisfying equation (8):

[0031]

[0032] Solving equation (8) yields the attitude command φ of the armed helicopter in the IFFC fire and flight system. c ,θ c , ψ c and weapon servo system commands μ w c ν w c ;

[0033] Let Φ = [φ θ ψ μ w ν w ] T As a parameter vector, define the target aiming angle error optimization function:

[0034] F1(Φ)=N μ 2 (Φ)+N ν 2 (Φ) (9)

[0035] Step 2.2) Dynamic Coupling Analysis of Target Aiming Angle Error

[0036] The IFFC fire and flight systems are divided into two directly coupled channels: {μ c ,μ w ,θ} and {ν c ,ν w ,φ}, the remaining channels are indirect coupling channels;

[0037] Through the elevation angle of the target line and target line azimuth pitch angle μ at the point of impact c , Azimuth of the hit point ν c Differentiating, we get:

[0038]

[0039] Based on equation (10), the dynamic coupling matrix G is defined as follows:

[0040]

[0041] To determine the impact of indirect coupling channels on direct coupling channels, the dynamic coupling function is defined as follows:

[0042]

[0043] Based on equation (12), a coupling influence optimization function is established:

[0044] F2(Φ)=K1(Φ)+K2(Φ) (13)

[0045] Step 2.3) Define a multi-objective function optimization model

[0046] The optimization model for air-to-ground multi-target targeting of attack helicopter rotating turret-type weapons is defined as follows:

[0047]

[0048] Where, φ max For the maximum yaw angle, θ max For the maximum pitch angle, ψ max For the maximum roll angle, μ wmax1 and μ wmax2 For the maximum weapon line elevation angle, ν wmax This is the azimuth angle of the maximum weapon line.

[0049] Preferably, the implementation process of step 3) is as follows:

[0050] Step 3.1) Using the Pareto principle, the quality of the solutions in the air-to-ground multi-target optimization model for air-to-ground targeting of attack helicopter rotating turret-type weapons is evaluated;

[0051] Establish feasible domain:

[0052]

[0053] Based on the concept of Pareto optimal solutions, the Pareto optimal solution set for a multi-target optimization model of air-to-ground targeting of attack helicopter rotating turret-type weapons is as follows:

[0054]

[0055] Among them, the individual solution Φ a and Φ b They are:

[0056] Φ a =[φ a ,θ a ,ψa ,μ wa ,ν wa ] T ∈Ω (17)

[0057] Φ b =[φ b ,θ b ,ψ b ,μ wb ,ν wb ] T ∈Ω (18)

[0058] Where a and b are parameters;

[0059] Step 3.2) Design adaptive crowding degree wolf pack individual selection criteria;

[0060] The definition of congestion is as shown in equation (19):

[0061]

[0062] Among them, the individual solution Φ i =[φ i ,θ i ,ψ i ,μ wi ,ν wi ] T ∈ρ, i is a parameter, D c (Φ i ) is the individual solution Φ i The degree of congestion, Φ i-1 and Φ i+1 To be with Φ i Two adjacent individual solutions, F m (Φ i+1 ) and F m (Φ i-1 ) is the individual solution Φ i+1 and Φ i+1 The corresponding function value of the m-th objective function; F m (Φ max ) and F m (Φ min () represents the maximum and minimum values ​​of the m-th objective function in the Pareto optimal solution set;

[0063] Design adaptive congestion level V(Φ) i,t As shown in equation (20):

[0064]

[0065] Where e is an exponential function, t is the number of iterations, and D c (Φ i,t) represents the crowding degree of the i-th individual in the t-th iteration, and k1 and k2 are adaptive scaling coefficients;

[0066] Selection criteria for designing the Fierce Wolf and the Probing Wolf:

[0067] Individual solution Φ i Defined as:

[0068]

[0069] Among them, N w The number of individuals in the wolf pack;

[0070] The number of wolves is determined by using the Pareto optimal solution set. After determining the number of wolves, a roulette wheel method is used to select the wolves. The probability that an individual in the Pareto optimal solution set is selected as a wolf is expressed as:

[0071]

[0072] Where j is a parameter;

[0073] The adaptive search direction and step size for the wolf are designed as follows:

[0074]

[0075] in, Let i be the position of the i-th wolf in dimension d during the t-th iteration. Let be the position of the alpha wolf in dimension d during the t-th iteration. This represents the wolf and the alpha wolf at the current iteration number. The distance between them, e is the exponential function, λ is the logarithmic spiral constant, l1 is a uniformly distributed random number in the interval [-1,1], k3 and k4 are adaptive scaling coefficients, and a and b are parameters;

[0076] Apart from the alpha wolf and the main wolf, the remaining individual solutions are determined to be scout wolves, and the number of scout wolves is S. _num The iteration step size and direction for detecting wolves are designed as follows:

[0077]

[0078] in, Let j be the position of the j-th scout wolf in dimension d during the t-th iteration. It is the direction of iteration. It is the iteration step size, h d It refers to the number of directions, parameter p. d The value is from 1 to h d l2 is a random number uniformly distributed within the interval [0.5, 1.5].

[0079] The implementation process of the multi-objective wolf pack algorithm is as follows:

[0080] Step 1: Solve for individual Φ i and the number of wolf pack members N w Perform initialization and set the maximum number of iterations t. max ;

[0081] Step 2: Calculate the objective function value for all wolf individuals and determine the Pareto solution set using Pareto dominance relationships;

[0082] Step 3: Select the first generation alpha wolf individual based on the Pareto optimal solution set established by equation (16) and the definition of adaptive crowding degree in equation (20), whose position is Φ. lead The remaining individuals in the Pareto optimal solution set select the wolf individuals by formula (22), and they perform a raiding behavior by formula (23); at the same time, the scout wolf individuals are determined outside the Pareto optimal solution set, and they roam by formula (24); when an individual superior to the alpha wolf is generated among the wolf individuals and scout wolf individuals, the next step is carried out.

[0083] Step 4: Update the Pareto optimal solution set and check whether the Pareto solution set in Step 2 has reached the upper limit. If it has reached the upper limit, remove individuals with high crowding and proceed to the next step; otherwise, proceed directly to the next step.

[0084] Step 5: Determine if the maximum number of iterations t has been reached. max If the condition is met, output all non-dominated solutions in the Pareto solution set in step 2; otherwise, proceed to step 2.

[0085] The beneficial effects of the present invention are as follows:

[0086] 1. The fire-fly coupler is designed based on the angle error, which facilitates the analysis of the coupling and coordination relationship between the attitude angle of the armed helicopter and the rotation angle of the weapon servo system, thereby obtaining an efficient coordination mechanism.

[0087] 2. Establish a multi-target optimization model for ground attack by armed helicopters and solve it using the adaptive multi-target wolf pack method. This model can take more flight aiming factors into account during ground attack, which is more in line with the actual aiming and attack of armed helicopters. Attached Figure Description

[0088] Figure 1 This is a basic structural block diagram of the IFFC armed helicopter of the present invention;

[0089] Figure 2 This is a vector diagram of the CCIP fire control solution for the rotating turret-type weapon of the armed helicopter of this invention;

[0090] Figure 3This is a flowchart of the adaptive multi-objective wolf pack method of the present invention;

[0091] Figure 4 This is a simulation diagram of the optimal solution set for the aiming optimization function of the armed helicopter of this invention. Detailed Implementation

[0092] 1. IFFC Fire Control Solution for Rotating Turret Weapons

[0093] Unlike pylon-mounted weapons, which directly adjust the weapon line of fire by adjusting the attitude angle of the attack helicopter, rotating turret weapons require coordination between the attack helicopter and the weapon servo system to achieve aiming. Therefore, in addition to the existing subsystems such as the attack helicopter system, target motion state, and fire control system, the weapon servo system and its controller also need to be considered. In the IFFC system for rotating turret weapons, the basic aiming and attack process is as follows: Figure 1 As shown.

[0094] Based on the air-to-ground CCIP principle of armed helicopters, a CCIP fire control solution vector diagram for armed helicopter rotating turret weapons is established as follows: Figure 2 As shown.

[0095] Where O-XYZ is the geographic coordinate system, O is the firing point of the armed helicopter, and O′ is the projection of O onto the ground. Here, H represents the airspeed vector of the attack helicopter, and H represents the flight altitude. For wind speed vectors, For the target velocity vector, This is the combined wind speed vector. The absolute velocity vector of the weapon projectile. T is the relative velocity vector of the weapon projectile. d For the flight time of weapon projectiles, Install position difference vectors for the weapon. Let O be the distance vector from the firing point O of the attack helicopter to the impact point C of the weapon projectile. For the ray vector of the weapon projectile, Reduce the projectile trajectory vector of the weapon. Figure 2 We can obtain:

[0096]

[0097] Projecting the vector equation in equation (1) onto the three axes of the body coordinate system, we can obtain:

[0098]

[0099] Among them, [A] x A y A z]for The components of the three-axis projection onto the body coordinate system, [U zx U zy U zz ]for The components projected onto the three axes of the aircraft coordinate system, where V1 is the absolute velocity of the weapon projectile, V0 is the airspeed of the attack helicopter, and V... 01 v is the relative velocity of the weapon projectile. w For the weapon line azimuth, μ w Let α be the weapon line elevation angle, β be the lateral approach angle of the attack helicopter, and β be the longitudinal approach angle of the attack helicopter. After projection, all vectors in equation (1) are transformed into their corresponding scalars.

[0100] According to equation (2), the pitch angle μ of the turret-type weapon impact point of the armed helicopter can be obtained. c , Azimuth of the hit point ν c and bullet flight time T d The expression is:

[0101]

[0102]

[0103]

[0104] Among them, V pj This represents the average velocity of the weapon projectile.

[0105] 2. Optimization Model for Ground Attack Targets of Rotating Turret Weapons Based on Angle Error Analysis and Coupling Error Analysis

[0106] 1) Target aiming angle analysis

[0107] In a two-dimensional plane, the air combat target x i air combat target x j Based on five features, their similarity distance is defined as follows:

[0108] From equations (2)-(5), we can see that the pitch angle μ of the hit point is... c , Azimuth of the hit point ν c Projectile flight time T d The yaw angle φ, pitch angle θ, roll angle ψ, and weapon line elevation angle μ of the attack helicopter w Weapon line azimuth ν w The following functional relationship exists:

[0109]

[0110] Let the elevation angle of the target line be μ. c c The azimuth of the target line is ν cc The aiming error equation of the IFFC system for armed helicopters can then be expressed as:

[0111]

[0112] Where N μ N represents the difference between the elevation angle of the weapon line and the elevation angle of the target line. ν This represents the error between the weapon line azimuth and the target line azimuth.

[0113] In order to achieve air-to-ground targeting, N μ and N ν Should meet:

[0114]

[0115] The attitude command φ of the armed helicopter in the IFFC system can be obtained by solving equation (8). c ,θ c , ψ c and weapon servo system command signal μ w c ν w c From equations (2)-(7), it can be seen that equation (8) is a complex nonlinear system of equations, therefore its analytical solution cannot be directly calculated. A numerical optimization method is used to find its numerical solution. Let Φ=[φθψμ w ν w ] T Define the angle error optimization function as a parameter vector:

[0116] F1(Φ)=N μ 2 (Φ)+N ν 2 (Φ) (9)

[0117] 2) Target aiming dynamic coupling analysis

[0118] As can be seen from equation (9), the IFFC system of the attack helicopter and its weapon servo system is a complex nonlinear system. When aiming at a target through the attitude adjustment of the attack helicopter and the rotation of the weapon servo system, the change in the attitude of the attack helicopter will affect the rotation of the weapon servo system, and the rotation of the weapon servo system will also affect the attitude adjustment of the attack helicopter. The interaction between the two systems will lead to a decrease in aiming accuracy.

[0119] During aiming, the pitch angle of the attack helicopter and the elevation angle of the weapon line of the weapon servo system directly affect the elevation angle of the hit point. Similarly, the yaw angle of the attack helicopter and the azimuth angle of the weapon line of the weapon servo system directly affect the azimuth angle of the hit point. Therefore, the IFFC system can be divided into the following two directly coupled channels: {μc ,μ w ,θ} and {ν c ,ν w ,φ}。 The remaining channels are indirect coupling channels.

[0120] Based on the dynamic coupling analysis mechanism, through and Differentiating the attitude angles of the attack helicopter and the weapon line angle of the weapon servo system, we get:

[0121]

[0122] Based on equation (10), the dynamic coupling matrix G can be described as:

[0123]

[0124] To determine the impact of indirect coupling channels on direct coupling channels, the dynamic coupling function is defined as follows:

[0125]

[0126] Based on equation (12), a coupling influence optimization function is established:

[0127] F2(Φ)=K1(Φ)+K2(Φ) (13)

[0128] 3) Multi-objective function optimization model

[0129] The optimized model for air-to-ground multi-target targeting of attack helicopter rotating turret-type weapons is as follows:

[0130]

[0131] Where, φ max For the maximum yaw angle, θ max For the maximum pitch angle, ψ max For the maximum roll angle, μ wmax1 and μ wmax2 For the maximum weapon line elevation angle, ν wmax This is the azimuth angle of the maximum weapon line.

[0132] 3. Optimized solution for air-to-ground target aiming based on the improved wolf pack method

[0133] For multi-constraint, multi-objective optimization problems, to ensure that the obtained solution is optimal for multiple objective functions, we need to establish an optimal solution set to balance the various objective functions. Using the Pareto principle, we evaluate the quality of solutions in an optimization model for target aiming of mobile turret-type weapons like armed helicopters. Establish the feasible region:

[0134]

[0135] Secondly, determine the Pareto dominance relationship. If Φ a =[φ a ,θ a ,ψ a ,μ wa ,ν wa ] T ∈Ω and Φ b =[φ b ,θ b ,ψ b ,μ wb ,ν wb ] T ∈Ω satisfies the following equation:

[0136]

[0137] Then Φ a Pareto dominates Φ b denoted as Φ a <Φ b If the two do not form a Pareto relation, then they are called non-dominated relations. In the feasible region, if Φ does not exist... b Make Φ b <Φ a Φ is then called a This represents the Pareto optimal solution. Based on the concept of Pareto optimal solution, the set of Pareto optimal solutions for a multi-objective optimization problem is:

[0138]

[0139] The introduction of the Pareto optimal solution set solves the problem of judging the merits of objective functions in multi-objective optimization problems. However, during the iteration process, how to select a solution as the alpha wolf from all the non-dominated solutions in the Pareto optimal solution set becomes an important problem that needs to be solved. Based on the traditional concept of crowding, this chapter designs an adaptive crowding wolf selection criterion according to the actual method.

[0140] The definition of congestion is as follows:

[0141]

[0142] Where, Φ i =[φ i ,θ i ,ψ i ,μ wi ,ν wi ] T ∈ρ,D c (Φ i ) is Φ i The degree of congestion, D cThe larger the value, the less crowded it is. Φ i-1 and Φ i+1 To be with Φ i Two adjacent solutions, F m (Φ i+1 ) and F m (Φ i-1 F is the function value of its corresponding m-th objective function. m (Φ max ) and F m (Φ min ) represents the maximum and minimum values ​​of the m-th objective function in the Pareto optimal solution set.

[0143] When selecting the alpha wolf based on crowding density, individuals with high crowding density are typically chosen as the alpha wolf, which improves the convergence of the entire method. However, this selection method can easily lead to the method getting trapped in local optima. Conversely, choosing individuals with low crowding density severely impacts the speed and convergence of the method. Therefore, based on the original definition of crowding density, an adaptive crowding density concept is designed:

[0144]

[0145] Where t is the number of iterations of the method, and D c (Φ i,t ) represents the crowding degree of the i-th individual in the t-th iteration, and k1 and k2 are adaptive scaling coefficients.

[0146] After determining the selection criteria for the alpha wolf, the selection criteria for the predatory wolves and the scout wolves, as well as their search step size and direction, are analyzed. For ease of analysis and description, the individual solution Φ is... i Defined as:

[0147]

[0148] Among them, N w The number of individuals in the wolf pack.

[0149] First, wolves are selected. Individual wolves are determined using the Pareto optimal solution set. After determining the number of individuals, a roulette wheel method is used to select the wolves. The probability that an individual in the Pareto optimal solution set is selected as a wolf can be expressed as...

[0150]

[0151] To improve optimization quality, the adaptive search direction and step size of the wolf algorithm were designed with reference to the whale optimization method, which can be expressed as:

[0152]

[0153] in, Let i be the position of the i-th wolf in dimension d during the t-th iteration. Let be the position of the alpha wolf in dimension d during the t-th iteration. This represents the individual wolf and the alpha wolf at the current iteration number. The distance between them, e is an exponential function, λ is the logarithmic spiral constant, l1 is a uniformly distributed random number in the interval [-1,1], and k3 and k4 are adaptive scaling coefficients.

[0154] Apart from the alpha wolf and the main wolf, the remaining solutions are determined to be scout wolves, and the number of scout wolves is S. _num The iteration step size and direction for detecting wolves are designed as follows:

[0155]

[0156] in, Let j be the position of the j-th scout wolf in dimension d during the t-th iteration. It is the direction of iteration. It is the iteration step size. h d It is the number of directions, p d The value is from 1 to h d l2 is a random number uniformly distributed in the interval [0.5, 1.5].

[0157] The basic steps of the improved adaptive multi-objective wolf pack method are as follows:

[0158] Step 1: Locate the individual wolf pack members. i and the number of wolf pack members N w Perform initialization and set the maximum number of iterations t. max .

[0159] Step 2: Calculate the objective function values ​​for all individual wolves in the pack and determine the Pareto solution set based on the Pareto dominance relationship;

[0160] Step 3: Using the Pareto optimal solution set established by equation (17) and the definition of adaptive crowding degree in equation (19), select the first generation alpha wolf individual, whose position is Φ. lead The remaining individuals in the Pareto optimal solution set select the alpha wolf using equation (21) and perform a raiding behavior using equation (22). Simultaneously, scout wolves are identified outside the Pareto optimal solution set and roam using equation (23). When an individual superior to the alpha wolf is found among the alpha wolves and scout wolves, the next step is performed.

[0161] Step 4: Update the Pareto optimal solution set and determine whether the solution set has reached the upper limit. If it has reached the upper limit, remove individuals with high crowding based on crowding and proceed to the next step; otherwise, proceed directly to the next step.

[0162] Step 5: Determine if the maximum number of iterations t has been reached. max If the condition is met, output all non-dominated solutions in the Pareto solution set; otherwise, proceed to step 2.

[0163] Optimize the solution process as follows Figure 3 As shown.

[0164] To verify the rationality of the theory and the effectiveness of the method, simulation analysis was conducted using the MATLAB platform. The initial velocity of the armed helicopter was set to 40 m / s, and the velocity of the tank target was set to V. x =20m / s, V y =10m / s, V z =5m / s, the initial velocity of the weapon projectile is 500m / s, the weapon installation position difference is 0.1m, and the wind speed V x =3m / s, V y =3m / s, V z =3m / s, α=β=0°, The method uses an initial population size of 300, a maximum non-dominated solution set size of 20, and a maximum number of iterations of 200. The Pareto optimal solution set obtained in this scenario is as follows: Figure 4 As shown:

[0165] pass Figure 4 It can be seen that, under the conditions of the target line elevation and azimuth angles, all the resulting non-dominated solutions exhibit linearity and low overall congestion, with both the angle error function and coupling function values ​​falling within a very small range. Therefore, the method achieves reasonable adjustment of the hit point elevation and target line azimuth angles under these conditions, completing the aiming attack task while minimizing the coupling effects between channels.

[0166] exist Figure 4 The objective function values ​​for angle error and coupling degree error of each optimal solution, along with their corresponding signals from the armed helicopter and weapon servo systems, are shown in the table below:

[0167] Table 1 Optimal Solution Set Function and Command Signal Variables

[0168]

[0169] Table 1 shows the attitude command signals of the armed helicopter and the weapon servo system corresponding to different non-dominated solutions. Analysis reveals that in each adjustment scheme, the three attitude command signals of the armed helicopter are within a reasonable range. Reasonable attitude command signals are crucial for the flight safety of armed helicopters in actual battlefield operations, thus proving the rationality of the method design.

Claims

1. An analysis method for the fire-fly cooperation mechanism of armed helicopters based on a multi-target wolf pack algorithm, characterized in that, Includes the following steps: Step 1) Establish the CCIP fire control solution vector relationship for weapons with rotating turrets of armed helicopters, and obtain the projectile pitch angle, azimuth angle and flight time information of the projectile impact point of the weapons with rotating turrets of armed helicopters. Step 2) Transform the target angle aiming problem into a multi-objective optimization problem using target aiming angle error analysis and dynamic coupling analysis; Step 3) Design a multi-objective wolf pack algorithm to solve the multi-objective optimization problem in Step 2); In step 1): The CCIP fire control solution vector relationship for armed helicopter rotating turret-type weapons is: in, For the target velocity vector, For wind speed vectors, For the composite wind speed vector; T d For the projectile's flight time, Install position difference vectors for rotating turret-type weapons; The distance vector from the point of projectile launch to the point of projectile impact. The projectile's ray vector. Reduce the projectile trajectory vector; Projecting the vector equation in equation (1) onto the three axes of the body coordinate system, we get: Among them, [A] x A y A z [ is the distance vector] The components of the three-axis projection onto the body coordinate system, [U zx U zy U zz [This refers to the combined wind speed vector] The components projected onto the three axes of the aircraft coordinate system, where V1 is the absolute velocity of the projectile, V0 is the airspeed of the attack helicopter, and V... 01 Let v be the relative velocity of the projectile. w For the weapon line azimuth, μ w φ is the weapon line elevation angle, α is the lateral approach angle of the attack helicopter, β is the longitudinal approach angle of the attack helicopter; φ is the yaw angle of the attack helicopter, θ is the pitch angle of the attack helicopter, and ψ is the roll angle of the attack helicopter. According to equation (2), the pitch angle μ at the point of impact of the projectile is... c , Azimuth of the hit point ν c and bullet flight time T d The expressions are: Among them, V pj The average velocity of the projectile.

2. The method for analyzing the fire-fly cooperation mechanism of armed helicopters based on the multi-target wolf pack algorithm as described in claim 1, characterized in that, The implementation process of step 2) is as follows: Step 2.1) Target aiming angle error analysis: From equations (2)-(5), we know that the pitch angle μ of the hit point is... c , Azimuth of the hit point ν c Projectile flight time T d The yaw angle φ, pitch angle θ, roll angle ψ, and weapon line elevation angle μ of the attack helicopter w Weapon line azimuth ν w There exists a functional relationship: Let the elevation angle of the target line be μ. c c The azimuth of the target line is ν c c Then the target aiming angle error equation for the IFFC firepower and flight system of the armed helicopter is: Where N μ N represents the difference between the elevation angle of the weapon line and the elevation angle of the target line. ν This represents the error between the weapon line azimuth and the target line azimuth. In order to achieve air-to-ground targeting, N μ and N ν Satisfying equation (8): Solving equation (8) yields the attitude command φ of the armed helicopter in the IFFC fire and flight system. c ,θ c , ψ c and weapon servo system commands μ w c ν w c ; Let Φ = [φ θ ψ μ w ν w ] T As a parameter vector, define the target aiming angle error optimization function: F1(Φ)=N μ 2 (F)+N ν 2 (F) (9) Step 2.2) Dynamic Coupling Analysis of Target Aiming Angle Error The IFFC fire and flight systems are divided into two directly coupled channels: {μ c ,μ w ,θ} and {ν c ,ν w ,φ}, the remaining channels are indirect coupling channels; Through the elevation angle of the target line and target line azimuth pitch angle μ at the point of impact c , Azimuth of the hit point ν c Differentiating, we get: Based on equation (10), the dynamic coupling matrix G is defined as follows: To determine the impact of indirect coupling channels on direct coupling channels, the dynamic coupling function is defined as follows: Based on equation (12), a coupling influence optimization function is established: F2(Φ)=K1(Φ)+K2(Φ) (13) Step 2.3) Define a multi-objective function optimization model The optimization model for air-to-ground multi-target targeting of attack helicopter rotating turret-type weapons is defined as follows: Where, φ max For the maximum yaw angle, θ max For the maximum pitch angle, ψ max For the maximum roll angle, μ wmax1 and μ wmax2 For the maximum weapon line elevation angle, ν wmax This is the azimuth angle of the maximum weapon line.

3. The method for analyzing the fire-fly cooperation mechanism of armed helicopters based on the multi-target wolf pack algorithm as described in claim 2, characterized in that, The implementation process of step 3) is as follows: Step 3.1) Using the Pareto principle, the quality of the solutions in the air-to-ground multi-target optimization model for air-to-ground targeting of attack helicopter rotating turret-type weapons is evaluated; Establish feasible domain: Based on the concept of Pareto optimal solutions, the Pareto optimal solution set for a multi-target optimization model of air-to-ground targeting of attack helicopter rotating turret-type weapons is as follows: Among them, the individual solution Φ a and Φ b They are: F a =[φ a ,i a ,ψ a ,m wa ,n wa ] T ∈Ω (17) F b =[φ b ,i b ,ψ b ,m wb ,n wb ] T ∈Ω (18) Where a and b are parameters; Step 3.2) Design adaptive crowding degree wolf pack individual selection criteria; The definition of congestion is as shown in equation (19): Among them, the individual solution Φ i =[φ i ,θ i ,ψ i ,μ wi ,ν wi ] T ∈ρ, i is a parameter, D c (Φ i ) is the individual solution Φ i The degree of congestion, Φ i-1 and Φ i+1 To be with Φ i Two adjacent individual solutions, F m (Φ i+1 ) and F m (Φ i-1 ) is the individual solution Φ i+1 and Φ i+1 The corresponding function value of the m-th objective function; F m (Φ max ) and F m (Φ min () represents the maximum and minimum values ​​of the m-th objective function in the Pareto optimal solution set; Design adaptive congestion level V(Φ) i,t As shown in equation (20): Where e is an exponential function, t is the number of iterations, and D c (Φ i,t ) represents the crowding degree of the i-th individual in the t-th iteration, and k1 and k2 are adaptive scaling coefficients; Selection criteria for designing the Fierce Wolf and the Probing Wolf: Individual solution Φ i Defined as: Among them, N w The number of individuals in the wolf pack; The number of wolves is determined by using the Pareto optimal solution set. After determining the number of wolves, a roulette wheel method is used to select the wolves. The probability that an individual in the Pareto optimal solution set is selected as a wolf is expressed as: Where j is a parameter; The adaptive search direction and step size for the wolf are designed as follows: in, Let i be the position of the i-th wolf in dimension d during the t-th iteration. Let be the position of the alpha wolf in dimension d during the t-th iteration. This represents the wolf and the alpha wolf at the current iteration number. The distance between them, e is the exponential function, λ is the logarithmic spiral constant, l1 is a uniformly distributed random number in the interval [-1,1], k3 and k4 are adaptive scaling coefficients, and a and b are parameters; Apart from the alpha wolf and the main wolf, the remaining individual solutions are determined to be scout wolves, and the number of scout wolves is S. _num The iteration step size and direction for detecting wolves are designed as follows: in, Let j be the position of the j-th scout wolf in dimension d during the t-th iteration. It is the direction of iteration. It is the iteration step size, h d It refers to the number of directions, parameter p. d The value is from 1 to h d l2 is a random number uniformly distributed within the interval [0.5, 1.5]. The implementation process of the multi-objective wolf pack algorithm is as follows: Step 1: Solve for individual Φ i and the number of wolf pack members N w Perform initialization and set the maximum number of iterations t. max ; Step 2: Calculate the objective function value for all wolf individuals and determine the Pareto solution set using Pareto dominance relationships; Step 3: Select the first generation alpha wolf individual based on the Pareto optimal solution set established by equation (16) and the definition of adaptive crowding degree in equation (20), whose position is Φ. lead The remaining individuals in the Pareto optimal solution set select the wolf individuals by formula (22), and they perform a raiding behavior by formula (23); at the same time, the scout wolf individuals are determined outside the Pareto optimal solution set, and they roam by formula (24); when an individual superior to the alpha wolf is generated among the wolf individuals and scout wolf individuals, the next step is carried out. Step 4: Update the Pareto optimal solution set and check whether the Pareto solution set in Step 2 has reached the upper limit. If it has reached the upper limit, remove individuals with high crowding and proceed to the next step; otherwise, proceed directly to the next step. Step 5: Determine if the maximum number of iterations t has been reached. max If the condition is met, output all non-dominated solutions in the Pareto solution set in step 2; otherwise, proceed to step 2.

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