[0053] The present invention will be described in detail below in conjunction with specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, several changes and improvements can be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.
[0054] Such as figure 1 As shown, the coordinated air defense mission planning method for multi-type air defense weapons provided by the present invention includes:
[0055] Estimation steps: Based on the performance indicators of each weapon and the trajectory of each target, estimate the start time, end time and number of interceptions of each weapon against each target;
[0056] Constraint determination steps: determine the number of targets that each weapon can intercept at the same time, the number of weapons that can be intercepted at the same time for each target, the number of interceptions for each target, and the degree to which each weapon can intercept each target;
[0057] Matrix establishment step: According to the results of the estimation step and the constraint determination step, establish the interception start time matrix, interception end time matrix and interception advantage degree matrix of each weapon against each target;
[0058] Transformation steps: According to the established matrix, the problem of coordinated air defense mission planning for multi-type air defense weapons is transformed into a constrained optimization problem. The optimization index is the total interception advantage, and the constraints include no time conflict constraint and interception frequency constraint;
[0059] Solution steps: Use numerical optimization algorithms to solve constrained optimization problems, and obtain a cooperative air defense mission planning scheme for multi-type air defense weapons.
[0060] Among them, in the constraint determination step, the degree of advantage of each weapon's interception of each target is determined by the probability of killing each weapon q ij Decision based on weapon W i To target T j Number of interceptions n ij And the kill probability q calculated for each interception, namely:
[0061]
[0062] In the matrix establishment step, the number of weapons W is n, the number of targets T is m, and the interception start time matrix T of each weapon against each target 0 , Interception end time matrix T f The interception advantage degree matrix Q has the following form:
[0063]
[0064] Where t ij0 Representative weapon W i To target T j The interception start moment, t ijf Representative weapon W i To target T j When the interception ends, q ij Representative weapon W i To target T j Favorable degree of interception.
[0065] In the solving step, a numerical optimization algorithm is used to solve the constrained optimization problem, and the optimal solution D obtained has the following form:
[0066]
[0067] Where d ij =0 or 1, d ij =1 means in [t ij0 ,t ijf ] Within the time period by weapon W i Intercept target T j , D ij =0 means in [t ij0 ,t ijf ] Weapon W in time period i Do not intercept target T j.
[0068] In the conversion step, the no time conflict constraint is expressed as:
[0069] C(T 0 *D,T f *D)-N W ≤0 and C((T 0 *D) T ,(T f *D) T )-N T ≤0
[0070] In the formula, the operator * means to multiply the elements with the same row and column in two matrices of the same dimension;
[0071] Function C(T 0 *D,T f *D) means that T 0 *D and T f *For each row of D, calculate the non-zero element t ij0 And t ijf Several time periods represented by [t ij0 ,t ijf ] The number of overlaps g i , Using all g i Compose column vector [g 1 g 2 …G n ] T;
[0072] Column vector N W =[n W1 n W2 …N Wn ] T , Whose element n Wi By weapon W i At the same time, the number of intercepted targets is restricted;
[0073] Function C((T 0 *D) T ,(T f *D) T ) Means that T 0 *D and T f *For each column of D, calculate the non-zero element t ij0 And t ijf Represents several time periods [t ij0 ,t ijf ] The number of overlaps k i , Using all k i Compose column vector [k 1 k 2 …K m ] T;
[0074] Column vector N T =[n T1 n T2 …N Tm ] T , Whose element n Tj By the target T j The number of simultaneous interception weapons is determined by the restriction.
[0075] The number of interception constraints is expressed as:
[0076] I 1×n ×(N I *D)-R≥0
[0077] Where I 1×n Is an n-dimensional row vector whose elements are all 1; N I Is an n×m dimensional matrix with n elements ij By weapon W i To target T j Is determined by the number of interceptions; R is the m-dimensional row vector, the element r j By the target T j The number of interceptions is determined by the constraint.
[0078] The total interception advantage is expressed as:
[0079] I 1×n ×(Q*D)×I m×1
[0080] Where I m×1 Is an m-dimensional column vector whose elements are all 1.
[0081] The constrained optimization problem is expressed as:
[0082]
[0083]
[0084] That is to find a matrix D with an element of 0 or 1, satisfying the constraint of no time conflict and the number of interceptions, so as to maximize the benefit of the total interception. The triple (T 0 , T f , D) represents the coordinated air defense mission planning scheme of multi-type air defense weapons, that is, the corresponding relationship of "time period-weapon-target".
[0085] On the basis of the above-mentioned coordinated air defense mission planning method for multi-type air defense weapons, the present invention also provides a multi-type air defense weapon coordinated air defense mission planning system, including:
[0086] Estimation module: According to the performance indicators of each weapon and the trajectory of each target, estimate the start time, end time and number of interceptions of each weapon against each target;
[0087] Constraint determination module: determine the number of targets that can be intercepted simultaneously by each weapon, the number of weapons that can be intercepted at the same time for each target, the number of interceptions for each target, and the degree of advantage of each weapon in intercepting each target;
[0088] Matrix building module: According to the estimated result and the result of constraint determination, establish the interception start time matrix, interception end time matrix and interception advantage degree matrix of each weapon against each target;
[0089] Conversion module: According to the established matrix, the problem of coordinated air defense mission planning for multi-type air defense weapons is transformed into a constrained optimization problem. The optimization index is the total interception advantage. The constraints include the time-free conflict constraint and the number of interceptions;
[0090] Solving module: Use numerical optimization algorithms to solve constrained optimization problems, and obtain a cooperative air defense mission planning scheme for multi-type air defense weapons.
[0091] This embodiment is suitable for processing application scenarios where 3 air defense missile weapons intercept 5 aerial targets, and the scope of protection of this patent is not limited by the specific implementation of this embodiment.
[0092] This embodiment relates to a coordinated air defense mission planning of two types and three air defense missile weapons. The application scenarios are as figure 2 Shown; 3 air defense missile weapons are W 1 , W 2 , W 3 , Weapon W 2 And W 3 Be the same model, have the same performance, weapon W 1 It is another model, its performance and weapon W 2 And W 3 different, figure 2 The solid-line sector area marks W 1 , W 2 , W 3 The interception range; the targets are respectively T 1 , T 2 , T 3 , T 4 , T 5 , Its track is like figure 2 Shown by the dotted line with arrow in the middle.
[0093] Combine figure 1 The specific description of the embodiments of the present invention is as follows:
[0094] Step 1: According to the performance indicators of each weapon and the trajectory of each target, estimate the interception start time, interception end time, and intercept times of each weapon against each target. According to target T 1 , T 2 , T 3 , T 4 , T 5 Speed and its track through weapon W 1 , W 2 , W 3 Length of interception range, estimated weapon W 1 , W 2 , W 3 To target T 1 , T 2 , T 3 , T 4 , T 5 The interception start time and interception end time are shown in the following table:
[0095] Table 1 Interception start time (unit: s)
[0096]
[0097] Table 2 Interception end time (unit: s)
[0098]
[0099] According to the above interception start time and interception end time, and the target T 1 , T 2 , T 3 , T 4 , T 5 Speed and weapon W 1 , W 2 , W 3 The speed of the interceptor fired, estimated weapon W 1 , W 2 , W 3 To target T 1 , T 2 , T 3 , T 4 , T 5 The number of interceptions is shown in the following table:
[0100] Table 3 Number of interceptions
[0101]
[0102] Step 2: Determine the restriction on the number of simultaneous interception targets for each weapon, the restriction on the number of weapons intercepted at the same time for each target, the restriction on the number of interceptions for each target, and the degree to which each weapon intercepts each target. Under weapon W 1 , W 2 , W 3 The performance of simultaneously intercepting targets is restricted to n W1 = 3, n W2 = 2, n W3 =2; according to W 1 , W 2 , W 3 For air defense missile weapons, in order to avoid mutual interference between weapons, the target T 1 , T 2 , T 3 , T 4 , T 5 The number of weapons intercepted at the same time is restricted to n T1 =1, n T2 =1, n T3 =1, n T4 =1, n T5 =1; Assuming target T 2 , T 3 Is greater than target T 5 Threat level, target T 5 Is greater than target T 1 , T 4 Targets with higher threat levels should be intercepted more times. According to target T 1 , T 2 , T 3 , T 4 , T 5 The threat level of the target T 1 , T 2 , T 3 , T 4 , T 5 The interception times constraints are r 1 = 2, r 2 =4, r 3 =4, r 4 = 2, r 5 =3; assuming that the probability of a weapon's interception against the target is 0.6, according to the number of interceptions, the calculation of the weapon's interception advantage to the target is shown in the following table:
[0103] Table 4 Advantages of interception
[0104]
[0105] Step 3: Establish the interception start time matrix, interception end time matrix, and interception advantage degree matrix of each weapon to each target. According to the calculation results of the interception start time, the interception end time and the interception advantage degree in the foregoing steps, the interception start time matrix T 0 , Interception end time matrix T f , Interception advantage degree matrix Q is as follows:
[0106]
[0107]
[0108] Step 4: Transform the coordinated air defense mission planning problem into a constrained optimization problem. The optimization index is the total interception advantage. The constraints include the time-free conflict constraint and the number of interceptions. According to the calculation of the foregoing steps, the constrained optimization problem is expressed as:
[0109]
[0110]
[0111] Where: D is a 3×5 dimensional matrix, and its element d ij =0 or 1, its value needs to be optimized; T 0 , T f , Q is 3×5 dimensional matrix as described in step 3; N W Is a 3-dimensional column vector, N T Is a 5-dimensional column vector, N I Is a 3×5 dimensional matrix, R is a 5-dimensional row vector, and its value is as follows:
[0112]
[0113] I 1×n Is a 3-dimensional row vector, I m×1 It is a 5-dimensional column vector, and its value is as follows:
[0114]
[0115] Step 5: Use a numerical optimization algorithm to solve the constrained optimization problem, and obtain a cooperative air defense mission planning scheme for multi-type air defense weapons. In this embodiment, a genetic algorithm is used to solve the constrained optimization problem, and the optimal solution is:
[0116]
[0117] The triple (T 0 , T f , D) represents the cooperative air defense mission plan of multi-type air defense weapons, specifically:
[0118] To W 1 , Assign it to intercept T in 3s~9s 2 、Intercept T in 3s~11s 3 、Intercept T in 5s~15s 5;
[0119] To W 2 , Assign it to intercept T in 10s~15s 1 、Intercept T in 9s~15s 2;
[0120] To W 3 , Assign it to intercept T in 12s~18s 3 、Intercept T in 12s~18s 4;
[0121] In the above mission plan, W 1 The number of intercepted targets at the same time does not exceed 3, W 2 And W 3 The number of intercepted targets at the same time does not exceed 2; 1 , T 2 , T 3 , T 4 , T 5 For each target, the number of weapons intercepted at the same time does not exceed one; for T 1 , T 2 , T 3 , T 4 , T 5 The number of interceptions is 2 times, 6 times, 6 times, 2 times, and 4 times respectively; the above situation satisfies the time-free conflict constraint and the number of interception constraints, and the total interception advantage is 6.41, which achieves its maximum optimization goal.
[0122] Those skilled in the art know that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code manner, it is entirely possible to make the system and its various devices provided by the present invention by logically programming method steps. , Modules and units realize the same functions in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by the present invention can be regarded as a hardware component, and the devices, modules, and units included in the system for realizing various functions can also be regarded as hardware components. The structure; the devices, modules, and units used to implement various functions can also be regarded as both software modules for implementing methods and structures within hardware components.
[0123] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the case of no conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.
