A radar equipment system deployment point optimization method based on Seagull optimization algorithm

Abstract

A method for optimizing the deployment points of a radar equipment system based on a Seagull optimization algorithm relates to the field of radar equipment deployment. The present invention is to solve the problem that the optimization target of the existing radar deployment point optimization method lacks pertinence, which leads to the problem that the comprehensive combat effectiveness of the current radar system is not high. The present invention includes: obtaining the effectiveness evaluation index of the anti-missile early warning radar system, and using the effectiveness evaluation index to obtain the radar comprehensive effectiveness evaluation value; deploying the radar to be deployed in a given deployable area, and using the Seagull optimization algorithm to obtain the optimal deployment plan using the radar comprehensive effectiveness evaluation value; decoding the Seagull position in the optimal deployment plan, thereby obtaining the optimized deployment position information of the radar to be deployed. The present invention is used to optimize the radar deployment points.

Description

Technical Field

[0001] The present invention relates to the field of radar equipment deployment, and in particular to a radar equipment system deployment point optimization method based on a Seagull optimization algorithm. Background Art

[0002] As an important part of the anti-missile early warning system, the anti-missile early warning radar system is the key to the success of anti-missile operations. The main task of the anti-missile early warning radar system is to detect and track incoming ballistic missiles and provide information support for interception weapon systems.

[0003] At present, the research on radar deployment optimization problem generally only focuses on the situation where the attack scenario is unknown. The main optimization goal is to improve the airspace coverage of the radar system. However, the track of the defense target of the anti-missile early warning radar system is relatively fixed. Without considering the attack scenario, optimizing the deployment of the anti-missile early warning radar based on a single principle such as maximum airspace coverage does not conform to the actual characteristics of anti-missile operations. Therefore, the current radar deployment optimization goals lack specificity, resulting in the current radar system's comprehensive combat effectiveness is not high. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the optimization objectives of the existing radar deployment point optimization methods lack pertinence, thus leading to the low comprehensive combat effectiveness of the current radar system, and propose a radar equipment system deployment point optimization method based on the Seagull optimization algorithm.

[0005] A radar equipment system deployment point optimization method based on the Seagull optimization algorithm. The specific process is as follows:

[0006] Step 1: Obtain the effectiveness evaluation index of the anti-missile early warning radar system, and use the effectiveness evaluation index to obtain the effectiveness value E of the radar system for the i-th trajectory i ;

[0007] Step 2: Deploy the radar to be deployed in the given deployable area, and use the Seagull optimization algorithm to use the E obtained in step 1 i Get the optimal deployment solution;

[0008] Step 3: Decode the seagull position in the optimal deployment solution output in step 2 to obtain the optimized deployment position information of the radar to be deployed.

[0009] Furthermore, the step 1 of obtaining the effectiveness evaluation index of the anti-missile early warning radar system and obtaining the radar comprehensive effectiveness evaluation value by using the effectiveness evaluation index comprises the following steps:

[0010] Step 1: Obtain the performance evaluation index of the anti-missile early warning radar system and normalize each performance evaluation index:

[0011] Step 111: Obtain the i-th trajectory warning time, and normalize the i-th trajectory warning time to obtain the normalized i-th trajectory warning time, as shown in the following formula:

[0012]

[0013] T Ai =T4-T2

[0014] Among them, T s is the requirement value of the system combat technical index for the warning time, T4 is the moment when the missile lands, T2 is the first moment when the radar detects the incoming target for the first time, and T Ai is the warning time of the ith trajectory;

[0015] Step 112: Obtain the life cycle tracking ratio of the ith trajectory, and normalize the life cycle tracking ratio of the ith trajectory to obtain the normalized life cycle tracking ratio of the ith trajectory, as shown in the following formula:

[0016]

[0017] P ci =(T4-T2) / (T4-T0)

[0018] Among them, T0 is the launch time of the missile, P ci is the life cycle tracking ratio of the ith trajectory;

[0019] Step 113: Obtain the fire control support time of the ith trajectory, and normalize the fire control support time of the ith trajectory to obtain the normalized fire control support time of the ith trajectory, as shown in the following formula:

[0020]

[0021] T wi =T4-T2

[0022] Among them, T wi is the fire control support time of the ith trajectory, T s1 It is the required value of the system combat technical index for the fire control information support time;

[0023] Step 1 and 2: Establish a weighted coefficient for the normalized performance evaluation index to obtain the performance value E of the radar system for the i-th trajectory. i .

[0024] Furthermore, the effectiveness value E of the radar system in steps 1 and 2 for the i-th trajectory is i , obtained by the following formula:

[0025] E i =Tai *w a +T ci *w c +T fi *w f

[0026] Among them, T ai is the normalized warning time of the ith trajectory, w a is the normalized warning time weight, T ci is the normalized tracking ratio of the life cycle of the ith trajectory, w c is the normalized lifecycle tracking ratio weight, T fi is the normalized fire control support time value of the ith trajectory, w f is the normalized fire control support time weight.

[0027] Furthermore, in step 2, the radar to be deployed is deployed in a given deployable area, and the Seagull optimization algorithm is used to utilize the E obtained in step 1 i Obtaining the optimal deployment solution includes the following steps:

[0028] Step 21: deploy the radar to be deployed in a given deployable area, obtain an initial radar deployment plan, and encode the initial radar deployment plan;

[0029] Step 22: using the encoded initial radar deployment plan obtained in step 21, establish an initial seagull population;

[0030] Step 2: Use the E obtained in step 1 i Obtain the fitness value of each radar deployment scheme in the initial population, and take the radar deployment scheme with the smallest fitness value as the optimal individual;

[0031] Step 24: Conduct seagull migration behavior to obtain the position where seagulls do not collide with each other and the direction of the best individual in the seagull population, thereby obtaining the distance between the seagull and the best individual;

[0032] Step 25: Based on the distance between the seagull and the optimal individual obtained in step 24, the seagull attacks and updates the position of the seagull:

[0033] Step 26: Repeat steps 23 to 25 until the preset maximum number of iterations is reached, output the position of the seagull, and thus obtain the optimal deployment plan.

[0034] Furthermore, the encoding of the initial radar deployment plan in step 21 is specifically as follows:

[0035] The latitude and longitude coordinates (R lon ,R lat) is converted into polar coordinates (r,θ) with the center point of the deployable area as the pole, and the encoded initial radar deployment plan is obtained.

[0036] Furthermore, in step 22, the encoded initial radar deployment scheme obtained in step 21 is used to establish an initial seagull population, as shown in the following formula:

[0037]

[0038] Among them, P i' =[P i',1 P i',2 … P i',M' ] represents the position vector of the i'th seagull in the M'-dimensional space, i.e., the first deployment scheme, P i',j' It represents the position component of the i'th seagull in the j'th dimension, M'=2N, N is the total number of radars to be deployed, i'∈[1,N'], j'∈[1,M'].

[0039] Furthermore, the E obtained in step 1 is used in step 2 or 3. i Get the fitness value of each radar deployment scheme in the initial population as follows:

[0040]

[0041] Among them, i∈[1,n], n is the total number of incoming ballistics, m i is the threat weight of each trajectory.

[0042] Furthermore, the seagull migration behavior in step 24 is performed to obtain a position where no collision occurs between the seagulls and the direction of the best individual in the seagull population, thereby obtaining the distance between the seagull and the best individual, including the following steps:

[0043] Step 241: Perform seagull migration behavior to obtain positions where seagulls do not collide with each other:

[0044] C(k)=A×P(k)

[0045]

[0046] Among them, P(k) is the position of the seagull before the migration behavior occurs, A is the control factor, k is the current generation, and k max is the maximum number of iterations, f c is a constant;

[0047] Step 242: Use the positions of the seagulls obtained in step 241 where no collision occurs to obtain the direction of the best individual in the seagull population:

[0048] M(k)=B×[P best(k)-P(k)]

[0049] B = 2 × A 2 ×R d

[0050] Among them, B is the balance factor, P best (k) is the optimal individual position vector after the kth iteration, P(k) is the position vector of the current seagull after the kth iteration, R d is a random number between 0 and 1 that follows a uniform distribution;

[0051] Step 243: Using the non-collision positions between the seagulls obtained in step 241 and the direction of the best individual in the seagull population obtained in step 242, the distance between the seagull and the best individual is obtained, as follows:

[0052] D(k)=|C(k)+M(k)|.

[0053] Furthermore, in step 25, based on the distance between the seagull and the optimal individual obtained in step 24, the seagull attack behavior is performed, thereby updating the position of the seagull, as shown in the following formula:

[0054] P(k+1)=D(K)×x×y×z+P best (k)

[0055] r=u×e θv

[0056] x=r×cosθ

[0057] y=r×sinθ

[0058] z=r×θ

[0059] Among them, x, y, z are the spiral motion of the seagull in the x, y, and z directions in the three-dimensional coordinates, r is the radius of the seagull's spiral motion, u and v are the spiral coefficients, and θ is a random number between 0 and 2π that follows a uniform distribution.

[0060] Furthermore, in step 25, based on the distance between the seagull and the optimal individual obtained in step 24, the seagull attack behavior is performed, thereby updating the position of the seagull, as shown in the following formula:

[0061] P(k+1)=D(K)×x×y×z+P best (k)

[0062] r=u×e θv

[0063] x=r×cosθ

[0064] y=r×sinθ

[0065] z=r×θ

[0066] Among them, x, y, z are the spiral motion of the seagull in the x, y, and z directions in the three-dimensional coordinates, r is the radius of the seagull's spiral motion, u and v are the spiral coefficients, and θ is a random number between 0 and 2π that follows a uniform distribution.

[0067] The beneficial effects of the present invention are:

[0068] The present invention proposes a radar deployment optimization method based on the best comprehensive combat effectiveness, and obtains indicators that are greatly affected by changes in radar deployment positions as performance evaluation indicators (warning time, life cycle tracking ratio, and fire control support time). The present invention quantifies the performance evaluation indicators according to the actual anti-missile early warning radar system, obtains the corresponding relationship between the radar position to be optimally deployed and the evaluation indicators, and optimizes the deployment points of mobile radars based on the improved Seagull Optimization Algorithm (SOA). The present invention takes the best comprehensive combat effectiveness as the criterion, makes the optimization target more targeted, optimizes the deployment position of radar equipment in the anti-missile early warning radar system, enables the radar system to reasonably configure limited radar equipment, and optimizes the comprehensive combat effectiveness of the anti-missile early warning radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Functional diagram of key indicators for optimal deployment evaluation;

[0070] Figure 2 This is a schematic diagram showing the impact of radar deployment parameters on indicators;

[0071] Figure 3 is a coding diagram;

[0072] Figure 4 To optimize the deployment algorithm process. DETAILED DESCRIPTION

[0073] Specific implementation method 1: This implementation method is a radar equipment system deployment point optimization method based on the Seagull optimization algorithm. The specific process is as follows:

[0074] Step 1: Obtain the effectiveness evaluation index of the anti-missile early warning radar system, and use the effectiveness evaluation index to obtain the radar's comprehensive effectiveness evaluation value:

[0075] Step 1: Obtain the performance evaluation index of the anti-missile early warning radar system and normalize the performance evaluation index:

[0076] The main tasks of the anti-missile early warning radar system are early detection, stable tracking and effective support for operations. Therefore, the selection of its evaluation indicators should be able to reflect this task requirement. Through analysis, the three most critical indicators of warning time, life cycle tracking ratio and fire control support time are selected to evaluate the anti-missile early warning radar system. Among them, the warning time reflects the system's timely detection capability, the life cycle tracking ratio reflects the system's stable tracking capability, and the fire control support time reflects the system's guidance and interception capability.

[0077] The two indicators of early warning time and life cycle tracking ratio selected at the same time also better meet the functional requirements of the system, achieving the comprehensive optimization of the detection time and tracking time of the early warning radar. The target recognition capability indicator in the functional requirements of the anti-missile early warning radar system is not used as an evaluation indicator here because the target recognition capability of the anti-missile early warning radar system is not sensitive to changes in the deployment position of the radar. A simplified performance evaluation indicator system, such as Figure 1 As shown. To conduct a comprehensive evaluation of the performance indicators, we must first quantify the indicators. After all indicators are quantified, they are still not comparable due to their different dimensions and functional relationships, and they need to be normalized. Therefore, it is necessary to normalize the indicators according to the actual situation of the anti-missile early warning radar system.

[0078] Radar deployment optimization mainly optimizes the combination of two parameters: longitude and latitude. Changes in these two parameters will have a greater impact on the selected indicators. For example, the detection indicators of a single radar for a single trajectory. Figure 1 As shown; Assume that the threatening ballistic incoming missile is launched from point L, the attack target is point D, and the flight trajectory is as follows Figure 2 As shown. In this attack scenario, assume that the radar is deployed at position P. At this time, the incoming target is within the radar detection range from time T2 until it lands. The radar's early warning effectiveness index for the incoming trajectory is as follows:

[0079] (1) Warning time

[0080] The warning time is defined as the total time from the first time the target enters the detection range of the radar system to the time the target lands. The larger the warning time index value, the earlier the radar system can detect the incoming target. The system's warning time for the i-th ballistic incoming target is as follows:

[0081] T Ai =T4-T2

[0082] Among them, T2 is the first moment when the radar detects the incoming target, and T4 is the moment when the missile lands;

[0083] The normalized warning time of the ith trajectory is as follows:

[0084]

[0085] Among them, T s It is the requirement value of the system's combat technical indicators for the warning time.

[0086] (2) Lifecycle tracking ratio

[0087] The life cycle tracking ratio is defined as the ratio of the total time the radar system tracks the threat target to the total time the missile takes to land. The larger the value of this indicator, the greater the proportion of the target being monitored by the radar during its entire life cycle, that is, the radar can better achieve stable tracking of the target. The main factors affecting the life cycle tracking ratio are equipment detection probability, equipment tracking threshold, clutter density, detection and tracking error (process noise and measurement noise), fusion algorithm, etc.

[0088] The life cycle tracking ratio P of the i-th trajectory ci , as follows:

[0089] P ci =(T4-T2) / (T4-T0)

[0090] Among them, T0 is the launch time of the missile;

[0091] Then the normalized value T ci for:

[0092]

[0093] (3) Fire control information support time

[0094] After determining the detailed information of the incoming target, it is necessary to intercept the incoming target through the fire control radar guided interception weapon with precise tracking. The key fire control information support time index that affects the anti-missile early warning radar system's guidance and interception capability is calculated as follows:

[0095] T wi =T4-T2

[0096] Normalized fire control support time T for the ith trajectory fi , as follows:

[0097]

[0098] Among them, T s1 The required value of the system combat technical indicator for the fire control information support time;

[0099] At this time, if the deployment position of the radar changes, such as Figure 2As shown in the figure, when the radar deployment state changes to P′, the radar effectiveness evaluation index value will change significantly. The incoming target enters the radar detection range from time T1, and the radar's early warning effectiveness index for the incoming target changes as follows:

[0100] Warning time: T A =T4-T1;

[0101] Life cycle tracking ratio P c For: P c =(T3-T1) / (T4-T0);

[0102] Assuming the radar has guidance function, the fire control support time is: T w =T4-T1.

[0103] Among them, T3 is the moment when the missile leaves the radar detection range;

[0104] The impact of changes in the deployment optimization parameters of multiple radars on the system effectiveness index value is more complex and nonlinear, but the principle is similar to the relationship between a single radar and a single trajectory. It can be seen that the selected radar system effectiveness evaluation index value is greatly affected by the radar optimization parameters, so the warning time, life cycle tracking ratio and fire control support time as functions of performance indicators can still be used as the objective function of the optimized deployment of multiple radars.

[0105] Step 1 and 2: Establish weighted coefficients for the normalized performance evaluation index to obtain the radar comprehensive performance evaluation function, which is as follows:

[0106] First, based on different combat scenarios and combat missions, and considering the different importance of various performance indicators, it is necessary to reasonably select various indicators and establish weighting coefficients to obtain the effectiveness value E of the radar system for a certain trajectory. i , as follows:

[0107] E i =T ai *w a +T ci *w c +T fi *w f

[0108] Among them, T ai is the normalized warning time value of the radar system for a certain trajectory, w a is the normalized warning time weight, T ci is the normalized tracking ratio of the life cycle of the ith trajectory, w c is the normalized lifecycle tracking ratio weight, T fi is the normalized fire control support time value of the ith trajectory, w fis the normalized fire control support time weight;

[0109] Then, in a combat scenario, when multiple attack trajectories appear within the detectable range of a single deployed radar, the comprehensive effectiveness evaluation value of the radar is obtained as follows:

[0110]

[0111] Where n is the number of incoming projectiles, is the performance evaluation value of n trajectories corresponding to a single radar, and the weight of each trajectory is w i , the early warning detection efficiency of a certain trajectory is E i .

[0112] Finally, the total ballistic effectiveness value of M radar systems for n incoming trajectories is obtained as follows:

[0113]

[0114] in, is the performance evaluation value of n ballistic trajectories corresponding to a single radar, and the weight of the performance evaluation value of n ballistic trajectories corresponding to each radar is

[0115] Step 2: Figure 4 As shown in the figure, the radar to be deployed is deployed in a given deployable area, and the Seagull optimization algorithm is used to use the E obtained in step 1 i Get the optimal deployment solution:

[0116] Step 21: Set the radar deployment constraints of the anti-missile early warning radar system:

[0117] (1) To facilitate the use of polar coordinates for encoding, it is assumed that the deployable location of each radar is limited to a circular area;

[0118] (2) The performance parameters and quantity of radars to be deployed are known;

[0119] (3) Assume that the attack scenario is known, that is, the parameters such as the launch point and impact point of the incoming missile and the threat weight are known;

[0120] (4) It is assumed that the various equipment in the radar system can be well connected.

[0121] Step 22: According to the constraints of radar deployment, the radar to be deployed is deployed in a given deployable area, an initial radar deployment plan is obtained, and the initial radar deployment plan is encoded, specifically:

[0122] According to the radar deployment constraints, the radar to be deployed is deployed in a given circular deployable area, that is, at a certain point (P lon ,P lat) is the center of the circle and R is the radius. lon ,R lat ) is converted into polar coordinates (r,θ) with the center of the deployable area as the pole. The value range of the polar axis r should be [0,R] (unit: km), and the value range of the polar angle θ should be [0,360] (unit: degree).

[0123] Assuming that the number of radars to be deployed is N, a deployment plan consisting of N radars can be encoded using the polar angle and polar axis of each radar relative to the center of the deployable circular area as the quantity to be optimized. A set of coding combinations consisting of N radars represents a candidate radar deployment plan. The specific encoding method of the polar coordinates (r, θ) of each radar deployment point is as follows: Figure 3 As shown, Figure 3 Each cell in represents a radar deployment optimization parameter.

[0124] Step 23: Use the encoded initial radar deployment plan obtained in step 22 to establish an initial seagull population, specifically:

[0125] The number of individuals in the seagull population N', the number of all radars in the radar system is half the searchable space dimension The position vector of each seagull represents a set of deployment plans for all radars to be deployed. For example, the position vector P of the i'th seagull in the M'-dimensional space is i' =[P i',1 P i',2 … P i',M' ] represents the position information combination of M' radars to be deployed in the i'th group deployment scheme. Then the position component P of the i'th seagull in the j'th dimension i',j' The coded coordinates representing the deployment position of the j'th radar in the i'th group deployment scheme, i.e., the corresponding polar coordinates, the number of seagull individuals in the population is set to N', and N' groups of position information are randomly generated, thus obtaining the first generation population consisting of N' individuals.

[0126] The position vector of each seagull in the initial population is as follows:

[0127]

[0128] Among them, P i' =[P i',1 P i',2 …P i',M' ] represents the position vector of the i'th seagull in the M'-dimensional space, which is the first deployment scheme, P i',j'It represents the position component of the i'th seagull in the j'th dimension. The initial position of each seagull in the population in the M'-dimensional space is randomly determined by uniform distribution, M'=2N, i'∈[1,N'], j'∈[1,M'].

[0129] Step 24: Use the E obtained in step 1 i Calculate the fitness value of each row vector in the initial population, and obtain the row vector with the smallest fitness value as the optimal individual;

[0130] The fitness value is the value obtained by calculating the fitness function. Its size is the basis for updating individual extreme values ​​and overall extreme values ​​in the optimization algorithm. The fitness function is designed according to the specific problem. Usually, when the objective function is not special, the objective function can be directly selected as the fitness function. In the process of radar network deployment optimization, the fitness function is the decision condition for optimization search.

[0131] The position vector of each seagull individual corresponds to a set of mobile radar deployment schemes. The present invention takes the fitness function as a function related to the comprehensive combat effectiveness value of the radar to be deployed for the attack and defense scene.

[0132] Assume that the number of incoming ballistics is n, and determine the threat weight of each ballistic as m i , the early warning detection efficiency value of a certain trajectory is E i , then the fitness function can be defined as:

[0133]

[0134] Step 25: Perform seagull migration behavior to obtain the position where seagulls do not collide with each other and the direction of the best individual in the seagull population, so as to obtain the distance between the seagull and the best individual obtained in step 24:

[0135] Step 251: Conduct seagull migration behavior and obtain positions where seagulls do not collide with each other:

[0136] The global search in the SOA optimization algorithm is simulated by the migration behavior of seagulls. In the natural world, seagulls will generally look for a location that does not collide with other seagulls during migration. In the SOA optimization algorithm, this behavior is implemented through the following formula:

[0137] C(k)=A×P(k)

[0138] Among them, P(k) is the position before the migration behavior occurs, C(k) represents the position after migration without collision with other seagulls; A is the control factor used to adjust the position of the seagull, and its calculation method is as follows:

[0139]

[0140] In the formula, f c It is usually taken as 2, k is the current algebra, k max is the maximum number of iterations. From the above formula, we can find that during the migration of seagulls, the new position will expand to a larger space, and as the algorithm iterates, the expansion range is shrinking.

[0141] Step 252: Using the positions of the seagulls obtained in step 251 where no collision occurs, obtain the direction of the best individual in the seagull population:

[0142] During migration, after searching for a position to avoid collision, the seagulls will move towards the direction of the best individual seagull in the population. The direction of the best individual in the seagull group is calculated as follows:

[0143] M(k)=B×[P best (k)-P(k)]

[0144] Where M(k) is the direction of the best seagull in the group, P best (k) and P(k) represent the position vectors of the optimal seagull individual and the seagull after the kth iteration, respectively. B is the balance factor, which can appropriately adjust the balance between global search and local search. Its calculation expression is as follows:

[0145] B = 2 × A 2 ×R d

[0146] Where A is the control factor mentioned above, which is used to adjust the position of the seagull, and R d is a random number between 0 and 1 that follows a uniform distribution.

[0147] Step 253: After each seagull obtains a new position and direction during migration, the distance D(k) between the seagull and the optimal individual can be calculated. The calculation expression is as follows:

[0148] D(k)=|C(k)+M(k)|

[0149] Step 26: Based on the distance D(k) between the seagull and the optimal individual obtained in step 25, the seagull attacks and updates the position of the seagull:

[0150] When attacking prey, seagulls often approach their prey in spiral motions, and generally change the angle and speed of their attacks to catch their prey off guard. The SOA optimization algorithm uses the attacking behavior of seagulls to simulate the local search capability of the algorithm, which shows a good optimization effect.

[0151] The spiral motion of the seagull in the xyz three-dimensional coordinates is as follows:

[0152] r=u×eθv

[0153] x=r×cosθ

[0154] y=r×sinθ

[0155] z=r×θ

[0156] Where r is the radius of the seagull's spiral motion; u and v are the spiral coefficients, which are taken as a constant 1 here; θ is a random number between 0 and 2π that follows a uniform distribution.

[0157] Through the above series of calculations, the position update calculation method of the seagull after each iteration is as follows:

[0158] P(k+1)=D(K)×x×y×z+P best (k)

[0159] Among them, P best (k) is the position of the seagull before updating, and P(k+1) is the position of the seagull after updating.

[0160] Step 27: Repeat steps 24 to 26 until the preset maximum number of iterations is reached, and the position of the seagull is output to obtain the optimal deployment plan.

[0161] Step 3: Decode the seagull position in the optimal deployment solution output in step 2 to obtain the optimized deployment position information of the radar to be deployed:

[0162] By (P lon ,P lat ) and (r',θ') can determine the longitude and latitude of the radar deployment location, the formula is as follows:

[0163]

[0164]

[0165] Among them, (P lon ,P lat ) is the center coordinate of the given deployable area, (r',θ') is the polar coordinate of the seagull position output in step 2, (R' lon ,R' lat ) is the decoded seagull position.

[0166] Embodiment 1:

[0167] In order to verify the beneficial effects of the present invention, the present invention optimizes the points to be deployed under different anti-missile interception situations, as follows:

[0168] 1. Based on different combat scenarios and combat tasks, and taking into account the different levels of importance when establishing evaluation indicators, the weights of the three indicators, namely, warning time, life cycle tracking ratio and fire control support time, are redistributed under different anti-missile interception situations, and different weights are assigned under different interception situations.

[0169] ①SM-3II interception and anti-missile interception situation

[0170] This interception situation focuses on describing the SM-3II interception problem, with an emphasis on the fire control support time of the fire control radar for the SM-3II. Therefore, when establishing the optimization index here, the normalized fire control support time value is used as the main optimization index. Considering that the SM-3II is deployed on the Aegis ship, SBX is selected as the fire control support radar.

[0171] That is, the comprehensive performance expression is:

[0172]

[0173] Among them, w' a 、w' c 、w' f is the indicator weight, is the normalized SBX supported fire control time;

[0174] ②SM-3II and GBI joint interception anti-missile interception situation

[0175] This interception situation focuses on the joint interception problem, but the trajectory of the attacking missile is relatively fixed, so the same early warning radar is basically used in the early warning phase. However, in the interception phase, because the SM-3II interceptor missile and the GBI interceptor missile are deployed in different positions, different fire control radars are required for guidance and interception. Therefore, when establishing the optimization index here, considering the above factors, the normalized fire control support time value is used as the main optimization index.

[0176] That is, the comprehensive performance expression is:

[0177] E=T a *w a ′+T c *w c ′+T f *w f '

[0178] The normalized fire control support time value T f It is calculated by the SBX radar responsible for fire control time support for SM-3II and other radars that support fire control time for GBI: such as UEWR, LRDR and Danish Cobra radar deployed in Alaska, and UEWR at Beale Air Force Base in California.

[0179]

[0180] in, is the support fire control time of SM-3II, It is the GBI support fire control time.

[0181] ③Single / multiple early warning radars are interfered with

[0182] The interference to the early warning radar is mainly suppressive interference, which will compress the detection distance and detection range of the early warning radar. In this situation, the front-line mobile deployment radar will delay the detection time and reduce the tracking time when detecting and tracking the target. Therefore, in this situation, the deployment position of the front-line mobile radar is optimized, and the three indicators of early warning time, life cycle tracking ratio and fire control support time are still selected for optimization calculation, but the weight of early warning time and life cycle tracking ratio should be increased compared with the normal situation when the early warning radar is not interfered with, to indicate the importance of this situation to the ballistic effectiveness value.

[0183] That is, the comprehensive performance expression is:

[0184]

[0185] in, is the normalized warning time value of single / multiple early warning radars, is the normalized life cycle tracking ratio value of single / multiple early warning radars, It is the supporting fire control time of single / multiple early warning radars;

[0186] ④Guidance radar is interfered with

[0187] The interference to the guidance radar is mainly deceptive interference. When the ballistic missile target is flying in the middle stage outside the atmosphere, it will throw out light and heavy decoys and use this penetration measure to penetrate. The guidance radar needs to track and identify the target flying in the middle stage of the ballistic missile, but because of the long distance, it is difficult to distinguish between true and false targets in time, and it is possible to lose the real target, resulting in continuous tracking of the false target. In addition, in the reentry phase of the ballistic missile target, the light decoy will burn in the atmosphere, leaving the heavy decoy and the real warhead flying. The guidance radar needs to continue to track and identify the target in the terminal phase to continuously provide the interception unit with tracking and time information for fire control support. Therefore, as long as the guidance radar is interfered with, the tracking is inaccurate, which will lead to a reduction in the fire control support time, and the interception weapon's ability to intercept the incoming target will decrease. Here, the three indicators of warning time, life cycle tracking ratio and fire control support time are still selected for optimization calculation, but the weight of the fire control support time should be increased compared to the case where the guidance radar is not interfered with, to indicate the importance of the interference situation of this guidance radar to the ballistic effectiveness value.

[0188] That is, the comprehensive performance expression is:

[0189]

[0190] in, is the normalized warning time value of the guidance radar, is the normalized lifetime tracking ratio value of the guidance radar, It is the time it takes for the guidance radar to support fire control;

[0191] 2. Implementation Method of Anti-missile Early Warning Radar Deployment Optimization Software

[0192] According to the principle of SOA optimization algorithm, the anti-missile early warning radar deployment optimization method will be designed according to the actual situation of anti-missile early warning radar system deployment, and the steps of the mobile radar deployment point optimization algorithm on the software development platform will be given.

[0193] Here, we consider that the final optimized position of the forward mobile radar will be near the initial optimized position, so the radar deployment area is set to be in a circular area centered on a certain point:

[0194] a. Input

[0195] Before optimizing the deployment of anti-missile early warning equipment, it is necessary to construct the attack and defense scenarios and set the necessary input parameters. The input parameters include:

[0196] (1) Performance parameters and deployment locations of existing early warning equipment;

[0197] (2) Missile attack scenario parameters and trajectory weights;

[0198] (3) Performance parameters and deployment locations of interception weapons and equipment;

[0199] (4) Parameters of the deployable circular area of ​​the radar to be deployed;

[0200] (5) The number of equipment to be deployed, its performance parameters, and the areas where it can be deployed;

[0201] (6) The weight of each indicator in the indicator system;

[0202] (7) The maximum number of iterations of the optimization algorithm.

[0203] b. Output

[0204] After optimizing the deployment of anti-missile early warning equipment through optimization algorithms based on all input parameters, the output data includes: the longitude and latitude of the deployment location of the radar to be deployed.

[0205] The algorithm flow for optimizing radar deployment in a circular area is as follows:

[0206] (1) Read all input parameters;

[0207] (2) Set the number of seagull populations N';

[0208] (3) Set the maximum number of iterations G;

[0209] (4) Randomly generate an initial population based on the input parameters and initialize the generation number i1=1;

[0210] (5) Combined with the constructed attack and defense scenarios, calculate the fitness values ​​of all individuals in the initial population;

[0211] (6) Based on the fitness of individuals, select the individuals with the best contemporary fitness;

[0212] (7) Calculate the new position and direction based on the seagull migration behavior and the individual with the best fitness;

[0213] (8) Simulate seagull attack behavior and update attack position;

[0214] (9) Calculate the fitness values ​​of all individuals in the new population respectively;

[0215] (10) Let i1′=i1+1. If i1<G, go to (6); otherwise, output the deployment plan data of the individual with the best fitness.

[0216] Embodiment 2: The present invention carries out the following simulation test to verify the beneficial effects of the present invention:

[0217] 1. SM3 interception scenario simulation analysis

[0218] 1.1SM3 interception scenario design

[0219] Table 1

[0220]

[0221] The threat weight of each trajectory should be a normalized value that comprehensively considers factors such as the threat level of the incoming missile and the probability of an attack. It can generally be obtained through expert scoring. Here, for simplicity, the threat weight of each trajectory is set to the same value. The parameters are shown in the following table.

[0222] Table 2

[0223]

[0224]

[0225] In order to deal with the above attack scenarios, there are two types of radars deployed in this simulation optimization, namely the ground-based early warning radar AN / TPY-2 and the sea-based early warning radar SBX. The ground-based early warning radar AN / TPY-2 is set to be responsible for early warning detection, and the sea-based early warning radar SBX is responsible for guiding interception. The parameters of the two types of radars are shown in the following table.

[0226] Table 3

[0227] Radar model Maximum detection distance Deployable areas Radar function AN / TPY-2 2900Km 60Km Early warning detection SBX 5000Km 60Km Guided Interception

[0228] The weights of various performance evaluation indicators can be given by the hierarchical analysis method combined with expert scoring. The weight parameters of the warning time, life cycle tracking ratio and fire control support time set in the simulation are shown in the following table.

[0229] Table 4 Evaluation index weight parameters

[0230] Indicator name Weight value Warning time 0.4 Fire control support time 0.4 Lifecycle tracking ratio 0.2

[0231] 1.2 SM3 interception scenario radar optimization deployment

[0232] Mobile radar deployment optimization generally requires fewer radars to be deployed. This scenario simulation uses two AN / TPY-2 radars and two SBX radars for optimized deployment. Among them, one AN / TPY-2 radar is placed in the deployment range near the Chelifentun base in Japan for optimization, another AN / TPY-2 radar is placed near the Seongju County deployment base in South Korea for optimization, one SBX radar is placed near the Pearl Harbor Naval Base in the Hawaiian Islands for optimization, and another SBX radar is placed near the Adak home port in Alaska for optimization.

[0233] Table 5 Radar deployment information

[0234]

[0235]

[0236] 2. GBI and SM3 joint interception scenario simulation analysis

[0237] 2.1GBI and SM3 Joint Interception Scenario Design

[0238] Table 6 GBI and SM3 joint interception scenarios

[0239]

[0240] The threat weight of each trajectory should be a normalized value that takes into account factors such as the threat level of the incoming missile and the probability of an attack. It can generally be obtained through expert scoring. Here, for simplicity, the threat weight of each trajectory is set to the same value, as shown in the following table.

[0241] Table 7 Ballistic weights for GBI and SM3 joint interception scenarios

[0242]

[0243]

[0244] In order to deal with the above attack scenarios, there are two types of radars deployed in this simulation optimization, namely the ground-based early warning radar AN / TPY-2 and the sea-based early warning radar SBX. The ground-based early warning radar AN / TPY-2 is set to be responsible for early warning detection, and the sea-based early warning radar SBX is responsible for guiding interception. The parameters of the two types of radars are shown in the following table.

[0245] Table 8 Optimized deployment radar parameters

[0246] Radar model Maximum detection distance Deployable areas Radar function AN / TPY-2 2900Km 60Km Early warning detection SBX 5000Km 60Km Guided Interception

[0247] The weights of various performance evaluation indicators can be given by the hierarchical analysis method combined with expert scoring. The weight parameters of the warning time, life cycle tracking ratio and fire control support time set in the simulation are shown in the following table.

[0248] Table 9 Evaluation index weight parameters

[0249] Indicator name Weight value Warning time 0.4 Fire control support time 0.4 Lifecycle tracking ratio 0.2

[0250] 2.2 Radar Optimization Deployment for GBI and SM3 Joint Interception Scenario

[0251] Mobile radar deployment optimization generally requires fewer radars to be deployed. This scenario simulation uses two AN / TPY-2 radars and two SBX radars for optimized deployment. Among them, one AN / TPY-2 radar is placed in the deployment range near the Chelifentun base in Japan for optimization, another AN / TPY-2 radar is placed near the Seongju County deployment base in South Korea for optimization, one SBX radar is placed near the Pearl Harbor Naval Base in the Hawaiian Islands for optimization, and another SBX radar is placed near the Ventura Naval Base in California for optimization, as shown in Table 10.

[0252] Table 10 Radar deployment information

[0253]

[0254] 2.3 Optimizing deployment when early warning radar is interfered with

[0255] The interference to the early warning radar is mainly suppressive interference, which will compress the detection distance and detection range of the early warning radar. In this situation, the front-line mobile deployment radar will delay the detection time and reduce the tracking time when detecting and tracking the target. Therefore, in this situation, the deployment position of the front-line mobile radar is optimized, and the three indicators of early warning time, life cycle tracking ratio and fire control support time are still selected for optimization calculation, but the weight of early warning time and life cycle tracking ratio should be increased compared with the normal situation when the early warning radar is not interfered with, to indicate the importance of this situation to the ballistic effectiveness value.

[0256] Therefore, in this comprehensive attack scenario, the radar parameter changes of the two models of AN / TPY-2 radar and SBX radar are shown in the following table.

[0257] Table 11 Optimized deployment radar parameters

[0258] Radar model Maximum detection distance Deployable areas Radar function AN / TPY-2 1900Km 60Km Early warning detection SBX 5000Km 60Km Guided Interception

[0259] And the weight parameters of the warning time, life cycle tracking ratio and fire control support time set in the simulation in this scenario are shown in the following table.

[0260] Table 12 Evaluation index weight parameters

[0261] Indicator name Weight value Warning time 0.5 Fire control support time 0.25 Lifecycle tracking ratio 0.25

[0262] Mobile radar deployment optimization generally requires fewer radars to be deployed. This scenario simulation uses two AN / TPY-2 radars and two SBX radars for optimized deployment. Among them, one AN / TPY-2 radar is placed in the deployment range near the Chelifentun base in Japan for optimization, another AN / TPY-2 radar is placed near the Seongju County deployment base in South Korea for optimization, one SBX radar is placed near the Pearl Harbor Naval Base in the Hawaiian Islands for optimization, and another SBX radar is placed near the Ventura Naval Base in California for optimization, as shown in Table 13.

[0263] Table 13 Radar deployment information

[0264]

[0265] 2.4 Optimizing deployment when the guidance radar is interfered with

[0266] The interference to the guidance radar is mainly deceptive interference. When the ballistic missile target is flying in the mid-stage outside the atmosphere, it will throw out light and heavy decoys and use this penetration measure to penetrate. The guidance radar needs to track and identify the target flying in the mid-stage of the ballistic missile, but because of the long distance, it is difficult to distinguish between real and fake targets in time, and it is possible to lose the real target, resulting in continuous tracking of the fake target. In addition, during the reentry phase of the ballistic missile target, the light decoy will burn in the atmosphere, leaving the heavy decoy and the real warhead flying. The guidance radar needs to continue to track and identify the target in the terminal phase, and continue to provide the interception unit with tracking and time information for fire control support. Therefore, as long as the guidance radar is interfered with and the tracking is inaccurate, the fire control support time will be reduced, and the ability of the interception weapon to intercept the incoming target will be reduced. Here, the three indicators of warning time, life cycle tracking ratio and fire control support time are still selected for optimization calculation. However, the weight of fire control support time should be increased compared with the normal situation where the guidance radar is not interfered with, so as to show the importance of the interference situation of this guidance radar to the ballistic effectiveness value.

[0267] Therefore, in this comprehensive attack scenario, the radar parameter changes of the two models of AN / TPY-2 radar and SBX radar are shown in the following table.

[0268] Table 14 Optimized deployment radar parameters

[0269] Radar model Maximum detection distance Deployable areas Radar function AN / TPY-2 2900Km 60Km Early warning detection SBX 4000Km 60Km Guided Interception

[0270] And the weight parameters of the warning time, life cycle tracking ratio and fire control support time set in the simulation in this scenario are shown in the following table.

[0271] Table 15 Evaluation index weight parameters

[0272] Indicator name Weight value Warning time 0.35 Fire control support time 0.5 Lifecycle tracking ratio 0.15

[0273] Mobile radar deployment optimization generally requires fewer radars to be deployed. This scenario simulation uses two AN / TPY-2 radars and two SBX radars for optimized deployment. Among them, one AN / TPY-2 radar is placed in the deployment range near the Chelifentun base in Japan for optimization, another AN / TPY-2 radar is placed near the Seongju County deployment base in South Korea for optimization, one SBX radar is placed near the Pearl Harbor Naval Base in the Hawaiian Islands for optimization, and another SBX radar is placed near the Ventura Naval Base in California for optimization, as shown in Table 16.

[0274] Table 16 Radar deployment information

[0275]

[0276]

[0277] The present invention is based on the deployment optimization problem of the mobile radar equipment system with the best comprehensive performance. The indicators that are greatly affected by the change of radar deployment position are selected as performance evaluation indicators, including radar warning time, life cycle tracking ratio and fire control support time, and the deployment position of the mobile radar is optimized based on the Seagull optimization algorithm. Taking into account the actual possible offensive and defensive confrontation scenarios, the present invention optimizes the deployment design of the mobile radar under different anti-missile interception situations, and selects the corresponding offensive ballistic scenario for simulation analysis to obtain the longitude and latitude of the mobile radar deployment after the point deployment is optimized.

Claims

1. A radar equipment system deployment point optimization method based on the Seagull optimization algorithm, characterized in that The method comprises the following steps: Step 1: Obtain the effectiveness evaluation index of the anti-missile early warning radar system, and use the effectiveness evaluation index to obtain the effectiveness value E of the radar system for the i-th trajectory i ; Step 2: Deploy the radar to be deployed in the given deployable area, and use the Seagull optimization algorithm to use the E obtained in step 1 i Get the optimal deployment solution; Step 3: Decode the seagull position in the optimal deployment solution output in step 2 to obtain the optimized deployment position information of the radar to be deployed.

2. According to claim 1, a radar equipment system deployment point optimization method based on the Seagull optimization algorithm is characterized by: The step 1 of obtaining the effectiveness evaluation index of the anti-missile early warning radar system and obtaining the radar comprehensive effectiveness evaluation value by using the effectiveness evaluation index comprises the following steps: Step 1: Obtain the performance evaluation index of the anti-missile early warning radar system and normalize each performance evaluation index: Step 111: Obtain the i-th trajectory warning time, and normalize the i-th trajectory warning time to obtain the normalized i-th trajectory warning time, as shown in the following formula: T Ai =T4-T2 Among them, T s is the requirement value of the system combat technical index for the warning time, T4 is the moment when the missile lands, T2 is the first moment when the radar first detects the incoming target, and T Ai is the warning time of the ith trajectory; Step 112: Obtain the life cycle tracking ratio of the ith trajectory, and normalize the life cycle tracking ratio of the ith trajectory to obtain the normalized life cycle tracking ratio of the ith trajectory, as shown in the following formula: P ci =(T4-T2) / (T4-T0) Among them, T0 is the launch time of the missile, P ci is the life cycle tracking ratio of the ith trajectory; Step 113: Obtain the fire control support time of the ith trajectory, and normalize the fire control support time of the ith trajectory to obtain the normalized fire control support time of the ith trajectory, as shown in the following formula: T wi =T4-T2 Among them, T wi is the fire control support time of the ith trajectory, T s1 It is the required value of the system combat technical index for the fire control information support time; Step 1 and 2: Establish a weighted coefficient for the normalized performance evaluation index to obtain the performance value E of the radar system for the i-th trajectory. i .

3. The radar equipment system deployment point optimization method based on the Seagull optimization algorithm according to claim 2 is characterized by: The effectiveness value E of the radar system in steps 1 and 2 for the i-th trajectory i , obtained by the following formula: E i =T ai *w a +T ci *w c +T fi *w f Among them, T ai is the normalized warning time of the ith trajectory, w a is the normalized warning time weight, T ci is the normalized tracking ratio of the life cycle of the ith trajectory, w c is the normalized lifecycle tracking ratio weight, T fi is the normalized fire control support time value of the ith trajectory, w f is the normalized fire control support time weight.

4. According to claim 3, a radar equipment system deployment point optimization method based on the Seagull optimization algorithm is characterized in that: In the step 2, the radar to be deployed is deployed in a given deployable area, and the Seagull optimization algorithm is used to utilize the E obtained in the step 1 i Obtaining the optimal deployment solution includes the following steps: Step 21: deploy the radar to be deployed in a given deployable area, obtain an initial radar deployment plan, and encode the initial radar deployment plan; Step 22: using the encoded initial radar deployment plan obtained in step 21, establish an initial seagull population; Step 2: Use the E obtained in step 1 i Obtain the fitness value of each radar deployment scheme in the initial population, and take the radar deployment scheme with the smallest fitness value as the optimal individual; Step 24: Conduct seagull migration behavior to obtain the position where seagulls do not collide with each other and the direction of the best individual in the seagull population, thereby obtaining the distance between the seagull and the best individual; Step 25: Based on the distance between the seagull and the optimal individual obtained in step 24, the seagull attacks and updates the position of the seagull: Step 26: Repeat steps 23 to 25 until the preset maximum number of iterations is reached, output the position of the seagull, and thus obtain the optimal deployment plan.

5. The radar equipment system deployment point optimization method based on the Seagull optimization algorithm according to claim 4 is characterized in that: The encoding of the initial radar deployment plan in step 21 is specifically as follows: The latitude and longitude coordinates (R lon ,R lat ) is converted into polar coordinates (r,θ) with the center point of the deployable area as the pole, and the encoded initial radar deployment plan is obtained.

6. The radar equipment system deployment point optimization method based on the Seagull optimization algorithm according to claim 5 is characterized in that: In step 22, the encoded initial radar deployment scheme obtained in step 21 is used to establish an initial seagull population, as shown in the following formula: Among them, P i' =[P i',1 P i',2 … P i',M' ] represents the position vector of the i'th seagull in the M'-dimensional space, i.e., the first deployment scheme, P i',j' It represents the position component of the i'th seagull in the j'th dimension, M'=2N, N is the total number of radars to be deployed, i'∈[1,N'], j'∈[1,M'].

7. The radar equipment system deployment point optimization method based on the Seagull optimization algorithm according to claim 6 is characterized by: The E obtained in step 1 is used in step 2 and step 3 i Get the fitness value of each radar deployment scheme in the initial population as follows: Among them, i∈[1,n], n is the total number of incoming ballistics, m i is the threat weight of each trajectory.

8. The radar equipment system deployment point optimization method based on the Seagull optimization algorithm according to claim 7 is characterized by: The step 24 of performing seagull migration to obtain a position where no collision occurs between seagulls and the direction of the best individual in the seagull population, thereby obtaining the distance between the seagull and the best individual, includes the following steps: Step 241: Perform seagull migration behavior to obtain positions where seagulls do not collide with each other: C(k)=A×P(k) Among them, P(k) is the position of the seagull before the migration behavior occurs, A is the control factor, k is the current generation, and k max is the maximum number of iterations, f c is a constant; Step 242: Use the positions of the seagulls obtained in step 241 where no collision occurs to obtain the direction of the best individual in the seagull population: M(k)=B×[P best (k)-P(k)] B=2×A 2 ×R d Among them, B is the balance factor, P best (k) is the optimal individual position vector after the kth iteration, P(k) is the position vector of the current seagull after the kth iteration, R d is a random number between 0 and 1 that follows a uniform distribution; Step 243: Using the non-collision positions between the seagulls obtained in step 241 and the direction of the best individual in the seagull population obtained in step 242, the distance between the seagull and the best individual is obtained, as follows: D(k)=|C(k)+M(k)|.

9. The radar equipment system deployment point optimization method based on the Seagull optimization algorithm according to claim 8 is characterized in that: In step 25, based on the distance between the seagull and the optimal individual obtained in step 24, the seagull attack behavior is performed, thereby updating the position of the seagull, as shown in the following formula: P(k+1)=D(K)×x×y×z+P best (k) r=u×e θv x=r×cosθ y=r×sinθ z=r×θ Among them, x, y, z are the spiral motion of the seagull in the x, y, and z directions in the three-dimensional coordinates, r is the radius of the seagull's spiral motion, u and v are the spiral coefficients, and θ is a random number between 0 and 2π that follows a uniform distribution.

10. The radar equipment system deployment point optimization method based on the Seagull optimization algorithm according to claim 9, characterized in that: In the step 3, the seagull position in the optimal deployment solution output in the step 2 is decoded to obtain the optimized deployment position information of the radar to be deployed, as shown in the following formula: Among them, (P lon ,P lat ) is the center coordinate of the given deployable area, (r',θ') is the polar coordinate of the seagull position in the optimal deployment solution, (R' lon ,R' lat ) is the decoded seagull position.

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