技术领域Technical Field
本发明属于机场毁伤评估技术领域，具体涉及基于K近邻卷积算法的机场跑道毁伤评估方法及系统。The present invention belongs to the technical field of airport damage assessment, and in particular relates to an airport runway damage assessment method and system based on a K-nearest neighbor convolution algorithm.
背景技术Background technique
机场是空中力量生存和作战的基地，承担着军队航空兵的日常训练、战备、作战等任务，目前机场跑道的主要威胁为子母弹、撒布式覆盖武器等。为研究子母弹对机场跑道的毁伤程度和打击效果，需要对子母弹打击机场跑道开展毁伤评估。毁伤效能评估实现的基础是作战单元和被打击目标的基本技术战术参数。狭义的讲，毁伤效能评估的对象是一组“弹药-目标”体系进攻防对抗的结果。该结果不仅取决于攻击武器的弹目交汇特征、引信作用机制以及战斗部终点效应模式和威力，还取决于目标的结构形式和关键部件固有的安全性、防护装置的效能和结构强度。Airports are the bases for the survival and operation of air forces, and they undertake the daily training, combat readiness, and combat tasks of the military aviation. At present, the main threats to airport runways are cluster bombs and scatter-type covering weapons. In order to study the degree of damage and strike effect of cluster bombs on airport runways, it is necessary to conduct damage assessment on cluster bombs attacking airport runways. The basis for the realization of damage effectiveness assessment is the basic technical and tactical parameters of combat units and targets. In a narrow sense, the object of damage effectiveness assessment is the result of a group of "ammunition-target" system offensive and defensive confrontation. This result depends not only on the missile-target intersection characteristics of the attacking weapon, the fuze action mechanism, and the terminal effect mode and power of the warhead, but also on the structural form of the target and the inherent safety of key components, the effectiveness of the protective device, and the structural strength.
机场跑道毁伤评估是指对机场实施打击后,对机场的毁伤效果进行的综合评估。其评估准则基础的一点为：在布满弹坑的跑道上，若能找到一个矩形区域满足飞机起飞的综合条件，则认为机场跑道毁伤失败；否则认为产生毁伤。Airport runway damage assessment refers to a comprehensive assessment of the damage to an airport after an attack on it. The basis of the assessment criteria is that if a rectangular area can be found on a runway full of craters that meets the comprehensive conditions for an aircraft to take off, the airport runway is considered to have failed to be damaged; otherwise, it is considered to have been damaged.
现有针对机场跑道毁伤评估的研究主要包括：(1)应用四阶龙泽库塔方法求解反跑道子母弹子弹的落点坐标及终点落速；(2)在机场跑道目标易损性分析的基础上，提出一种机场跑道毁伤评估判定方法，基于蒙特卡洛抽样方法建立子母弹对机场目标毁伤效能计算模型；(3)基于计算机仿真技术和蒙特卡罗方法,建立机场跑道目标评估方法，包括跑道的数学模型、飞机的起降模式、子母弹散布的数学模型和遍历算法。综合上述对机场跑道毁伤评估的不同研究可以看出机场跑道毁伤评估相关研究虽然较多，但其评估算法大多运用遍历算法，传统遍历算法运算时间比较缓慢，影响了机场跑道毁伤评估的效率。The existing research on airport runway damage assessment mainly includes: (1) using the fourth-order Longze Kutta method to solve the coordinates of the landing point and the terminal falling speed of the anti-runway submunition bullet; (2) based on the vulnerability analysis of airport runway targets, a method for determining airport runway damage assessment is proposed, and a calculation model for the damage effectiveness of submunitions on airport targets is established based on the Monte Carlo sampling method; (3) based on computer simulation technology and the Monte Carlo method, an airport runway target assessment method is established, including the mathematical model of the runway, the take-off and landing mode of the aircraft, the mathematical model of the submunition dispersion and the traversal algorithm. Based on the above different studies on airport runway damage assessment, it can be seen that although there are many related studies on airport runway damage assessment, most of their assessment algorithms use traversal algorithms. The traditional traversal algorithm has a relatively slow operation time, which affects the efficiency of airport runway damage assessment.
发明内容Summary of the invention
本发明的目的在于克服上述现有技术中的不足，提供一种基于K近邻卷积算法的机场跑道毁伤评估方法及系统，找出炸点稀疏区域并优先在炸点稀疏区域进行遍历搜索机场跑道最小飞行区域，大大提高了机场跑道毁伤评估效率。The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and provide an airport runway damage assessment method and system based on the K nearest neighbor convolution algorithm, so as to find out the sparse bombing point area and preferentially traverse and search for the minimum flight area of the airport runway in the sparse bombing point area, thereby greatly improving the efficiency of airport runway damage assessment.
为实现上述目的，本发明采用的技术方案是提供一种基于K近邻卷积算法的机场跑道毁伤评估方法，包括以下步骤：To achieve the above object, the technical solution adopted by the present invention is to provide an airport runway damage assessment method based on a K-nearest neighbor convolution algorithm, comprising the following steps:
步骤一、建立地面坐标系和弹体坐标系，获取导弹瞄准点坐标、随机弹道方向和拦截点的坐标，构建随机弹道方程，获取母弹开舱点坐标；Step 1: Establish the ground coordinate system and the missile body coordinate system, obtain the coordinates of the missile aiming point, the random ballistic direction and the interception point, construct the random ballistic equation, and obtain the coordinates of the mother missile opening point;
步骤二、假定母弹开舱后，子弹群周向对称抛撒且始终在一个平面上，分布均匀，根据母弹开舱点的坐标，获取子弹落点在地面上的分布区域方程，建立子弹散布区域坐标系，基于蒙特卡洛抽样法获取子弹落点在子弹散布区域坐标系中的坐标，将子弹落点在所述子弹散布区域坐标系中的坐标变换得到子弹在地面坐标系中的坐标；Step 2: Assuming that after the mother bomb is opened, the bullet group is scattered symmetrically in the circumferential direction and is always on a plane with uniform distribution, according to the coordinates of the mother bomb opening point, the distribution area equation of the bullet landing point on the ground is obtained, and a bullet scattering area coordinate system is established. Based on the Monte Carlo sampling method, the coordinates of the bullet landing point in the bullet scattering area coordinate system are obtained, and the coordinates of the bullet landing point in the bullet scattering area coordinate system are transformed to obtain the coordinates of the bullet in the ground coordinate system;
步骤三、假设落在跑道上的子弹100％有效，将矩形机场跑道划分为多个边长为1的矩形块，子弹的炸点坐标对应边长为1的矩形块，利用K近邻判断炸点稀疏程度，构建点密集度打分机制，通过卷积运算获取各个炸点处的点密集度分数，根据分数判断机场跑道内各个炸点处的点密集度，找出炸点稀疏区域；Step 3: Assuming that the bullets dropped on the runway are 100% effective, divide the rectangular airport runway into multiple rectangular blocks with a side length of 1. The coordinates of the bullet's explosion point correspond to the rectangular blocks with a side length of 1. Use K nearest neighbors to determine the sparseness of the explosion point, build a point density scoring mechanism, obtain the point density score at each explosion point through convolution operation, determine the point density at each explosion point in the airport runway based on the score, and find the explosion point sparse area;
步骤四、根据机场跑道毁伤评估准则，运用面积法优先在所述炸点稀疏区域内搜索是否存在满足飞机起飞条件的最小飞行区域。Step 4: Based on the airport runway damage assessment criteria, use the area method to preferentially search within the sparsely populated area of the bomb points to see if there is a minimum flight area that meets the aircraft takeoff conditions.
进一步地，所述步骤一具体包括：Furthermore, the step 1 specifically includes:
步骤11、假设导弹末端弹道为直线，所选地面坐标系为OXYZ，选定导弹瞄准点坐标为(X0,Y0,Z0)，弹体坐标系为oxyz，oy轴为随机弹道，随机弹道的方向为：J＝{cosωcosλ,cosωsinλ,sinω}，其中，ω为导弹发射高低角，λ为导弹发射方位角；Step 11, assuming that the missile terminal trajectory is a straight line, the selected ground coordinate system is OXYZ, the selected missile aiming point coordinates are (X0 , Y0 , Z0 ), the missile body coordinate system is oxyz, the oy axis is a random trajectory, and the direction of the random trajectory is: J = {cosωcosλ, cosωsinλ, sinω}, where ω is the missile launch elevation angle, and λ is the missile launch azimuth;
步骤12、在弹体坐标系oxyz中，oxz平面为制导平面，根据导弹的圆概率偏差CEP，基于蒙特卡洛模拟获取导弹在制导平面上的拦截点坐标，Step 12: In the missile body coordinate system oxyz, the oxz plane is the guidance plane. According to the circular deviation probability CEP of the missile, the interception point coordinates of the missile on the guidance plane are obtained based on Monte Carlo simulation.
x＝x0σxx＝x0 σx
制导平面随机拦截点的坐标表示为：z＝z0σz，式中，x0，z0为μ＝0，σ＝1的正态分布随机数抽样，即其中，r1,r2是一对[0,1]区间的均匀随机数，x0,z0服从二维标准正态分布，其密度函数为：σx和σz为制导误差的横向和纵向标准偏差，σx＝σz＝CEP/1.1774；The coordinates of the random interception point of the guidance plane are expressed as: z = z0 σz , where x0 , z0 are random numbers sampled from a normal distribution with μ = 0 and σ = 1, that is, Among them, r1 ,r2 are a pair of uniform random numbers in the interval [0,1], x0 ,z0 obey the two-dimensional standard normal distribution, and its density function is: σx and σz are the lateral and longitudinal standard deviations of the guidance error, σx =σz =CEP/1.1774;
步骤13、根据所述导弹瞄准点坐标、所述随机弹道方向以及制导误差，获取制导平面随机拦截点在地面坐标系上的坐标：Step 13: According to the missile aiming point coordinates, the random trajectory direction and the guidance error, the coordinates of the random interception point of the guidance plane in the ground coordinate system are obtained:
步骤14、根据所述步骤12和步骤13，得到随机弹道方程为：式中，(X，Y，Z)为母弹开舱点坐标；Step 14: According to step 12 and step 13, the random trajectory equation is obtained as follows: Where, (X, Y, Z) is the coordinates of the mother bomb opening point;
步骤15、根据所述随机弹道方程，选定导弹瞄准点(X0,Y0,Z0)，由攻击高低角ω和方位角λ、拦截点在地面坐标系中的坐标和母弹引信启动规律的抽样得到随机开舱点坐标为(Xb,Yb,Zb)，Zb＝H，H为母弹开舱高度。Step 15: According to the random ballistic equation, the missile aiming point (X0 , Y0 , Z0 ) is selected, and the random opening point coordinates are obtained as (Xb , Yb , Zb ) by sampling the attack elevation angle ω and azimuth angle λ, the coordinates of the interception point in the ground coordinate system and the mother missile fuze activation rule, where Zb =H, and H is the mother missile opening height.
进一步地，所述步骤二中建立子弹散布区域坐标系，基于蒙特卡洛抽样计算子弹落点坐标具体包括：Furthermore, in step 2, the bullet scattering area coordinate system is established, and the bullet landing point coordinates are calculated based on Monte Carlo sampling, which specifically includes:
步骤21、基于子弹群在同一平面上均匀分布的假设，子弹在弹体坐标系上的分布范围近似表示为：式中，a为弹群圆锥形分布的半锥角；子弹在地面上的分布区域为椭圆形区域，所述椭圆形区域的数学方程根据下面的坐标变换关系得到，其中，(Xb,Yb,Zb)为母弹随机开舱点坐标，ω为导弹发射高低角，λ为导弹发射方位角；Step 21: Based on the assumption that the bullet group is evenly distributed on the same plane, the distribution range of the bullets in the projectile coordinate system is approximately expressed as: Where a is the semi-cone angle of the conical distribution of the bullet group; the distribution area of the bullets on the ground is an elliptical area, and the mathematical equation of the elliptical area is obtained according to the following coordinate transformation relationship: Among them, (Xb ,Yb ,Zb ) are the coordinates of the random opening point of the mother missile, ω is the missile launch elevation angle, and λ is the missile launch azimuth angle;
步骤22、以母弹虚拟落点为坐标原点，建立XZOZYZ坐标系作为子弹散布区域坐标系，并基于蒙特卡洛抽样计算子弹落点坐标，即在所述子弹散布区域坐标系的椭圆形区域内选择均匀分布的随机序列来表示子弹的散布位置，通过抽取以椭圆长轴为长、以椭圆短轴为宽的矩形范围内的随机序列，并进行筛选可以得到椭圆范围内均匀分布的随机序列，所述随机序列表示为：其中，s为系数，Lx，Ly分别为椭圆的长轴和短轴，而r1，r2均为(0,1)之间的均匀分布随机数，运用算式判断随机点是否在椭圆范围内，实现矩形范围内随机序列的筛选；Step 22, taking the virtual landing point of the mother bullet as the coordinate origin, establishinganXZOZYZcoordinate system as the bullet dispersion area coordinate system, and calculating the bullet landing point coordinates based on Monte Carlo sampling, that is, selecting a uniformly distributed random sequence in the elliptical area of the bullet dispersion area coordinate system to represent the bullet dispersion position, by extracting a random sequence in a rectangular range with the major axis of the ellipse as the length and the minor axis of the ellipse as the width, and screening, a uniformly distributed random sequence in the elliptical range can be obtained, and the random sequence is expressed as: Among them, s is the coefficient, Lx andLy are the major and minor axes of the ellipse respectively, and r1 and r2 are uniformly distributed random numbers between (0,1). The formula is used to determine whether the random point is within the range of the ellipse to achieve the selection of random sequences within the rectangular range;
步骤23、通过随机抽取所述子弹散布区域坐标系中的子弹落点坐标序列，获得子弹落点在地面坐标系中的坐标：式中，(xd，yd)为子弹落点在地面坐标系中的坐标，(xz，yz)为子弹散布区域坐标系中的子弹落点坐标序列，λ为导弹发射方位角。Step 23, by randomly extracting the bullet landing point coordinate sequence in the bullet scattering area coordinate system, obtain the coordinates of the bullet landing point in the ground coordinate system: Where (xd , yd ) is the coordinate of the bullet landing point in the ground coordinate system, (xz , yz ) is the coordinate sequence of the bullet landing point in the bullet dispersion area coordinate system, and λ is the missile launch azimuth.
进一步地，所述步骤三具体包括：Furthermore, the step three specifically includes:
步骤31、机场跑道是长为M、宽为N的矩形区域，将所述矩形区域分割为M×N个边长为1的矩形块，每个边长为1的矩形块均对应一个炸点的坐标点，将所述矩形区域用M×N的矩阵A表示：AMN＝(aij)M×N，当i＝xi且j＝yi时，aij＝0,否则aij＝1，式中，(xi，yi)为炸点坐标，i＝1,2,3，…M，j＝1,2,3，…N；Step 31, the airport runway is a rectangular area with a length of M and a width of N. The rectangular area is divided into M×N rectangular blocks with a side length of 1. Each rectangular block with a side length of 1 corresponds to a coordinate point of a bombing point. The rectangular area is represented by an M×N matrix A: AMN = (aij )M×N , when i = xi and j = yi , aij = 0, otherwise aij = 1, where (xi , yi ) is the coordinate of the bombing point, i = 1, 2, 3, ... M, j = 1, 2, 3, ... N;
步骤32、利用K近邻算法查找被预测点附近的样本点，基于欧式距离计算出被预测点与所述样本点之间的距离，判断被预测点的点密集度；Step 32: Use the K nearest neighbor algorithm to find sample points near the predicted point, based on the Euclidean distance Calculate the distance between the predicted point and the sample point, and determine the point density of the predicted point;
步骤33、构建打分机制，对所述被预测点与所述被预测点附近的样本点之间的距离打分，距离越近则分数越高，定义点密集度公式为其中，m为被预测点附近样本点的个数，Ki为被预测点与样本点之间对应距离的得分；Step 33: Construct a scoring mechanism to score the distance between the predicted point and the sample points near the predicted point. The closer the distance, the higher the score. The formula for defining the point density is: Where m is the number of sample points near the predicted point, and Kiis the score of the corresponding distance between the predicted point and the sample point;
步骤34、计算所述步骤31中矩形区域内各个炸点的点密集度：根据所述打分机制构建一个m×n的卷积核h，其中，m和n均为奇数，被预测点与样本点之间对应距离的得分作为卷积核的权重，根据所述矩形区域的矩阵A，得到卷积运算公式为：其中，(x，y)为炸点坐标，i为行序号，j为列序号，g(x)为卷积核函数，运算后找出炸点稀疏区域。Step 34, calculate the point density of each explosion point in the rectangular area in step 31: construct an m×n convolution kernel h according to the scoring mechanism, where m and n are both odd numbers, and the score of the corresponding distance between the predicted point and the sample point is used as the weight of the convolution kernel. According to the matrix A of the rectangular area, the convolution operation formula is obtained as follows: Among them, (x, y) is the coordinate of the explosion point, i is the row number, j is the column number, g(x) is the convolution kernel function, and after the operation, the sparse area of the explosion point is found.
进一步地，所述点密集度指的是被预测点附近的样本点数量越多、且距离被预测点距离越近则认为被预测点处点密集度越大。Furthermore, the point density refers to that the more sample points there are near the predicted point and the closer the distance to the predicted point is, the greater the point density at the predicted point is.
进一步地，所述步骤四中的面积法为：优先在炸点稀疏区域内遍历选取最小飞行区域，连接所述炸点稀疏区域中的任一炸点与满足飞机起飞条件的最小飞行区域的顶点，所述最小飞行区域为矩形，所述炸点与所述最小飞行区域的四个边构成四个三角形，根据最小飞行区域的面积与四个三角形的面积之和的大小关系，判断所述炸点是否位于最小飞行区域内。Furthermore, the area method in step 4 is: preferentially traverse and select the minimum flight area in the sparse bombing point area, connect any bombing point in the sparse bombing point area with the vertex of the minimum flight area that meets the aircraft take-off conditions, the minimum flight area is a rectangle, and the bombing point and the four sides of the minimum flight area form four triangles, and judge whether the bombing point is located in the minimum flight area based on the size relationship between the area of the minimum flight area and the sum of the areas of the four triangles.
一种基于K近邻卷积算法的机场跑道毁伤评估系统，包括炸点计算模块和毁伤评估模块，所述炸点计算模块用于依次初始化弹道参数、弹药参数和目标列表参数，并根据所述弹道参数、弹药参数和目标列表参数，基于蒙特卡洛方法计算出拦截点坐标和炸点坐标，并将所述炸点坐标传递至毁伤评估模块；所述毁伤评估模块用于根据接收到的炸点坐标，利用K近邻判断所述炸点稀疏程度，并通过卷积运算对炸点稀疏程度进行打分，运用遍历法搜索最小飞行区域，最终输出评估结果。A damage assessment system for an airport runway based on a K-nearest neighbor convolution algorithm comprises a bombing point calculation module and a damage assessment module. The bombing point calculation module is used to initialize trajectory parameters, ammunition parameters and target list parameters in sequence, and calculate interception point coordinates and bombing point coordinates based on the trajectory parameters, ammunition parameters and target list parameters based on the Monte Carlo method, and transmit the bombing point coordinates to the damage assessment module; the damage assessment module is used to determine the sparsity of the bombing point based on the received bombing point coordinates using the K-nearest neighbor, and score the bombing point sparsity through a convolution operation, use a traversal method to search for a minimum flight area, and finally output an assessment result.
进一步地，所述弹道参数包括导弹入射角、导弹瞄准点坐标、方位角、圆概率偏差以及开舱高度，所述目标列表参数包括机场跑道的长度、宽度和满足飞机起飞条件的最小飞行区域的长度、宽度。Furthermore, the trajectory parameters include the missile incidence angle, missile aiming point coordinates, azimuth, circular deviation probability and cabin opening altitude, and the target list parameters include the length and width of the airport runway and the length and width of the minimum flight area that meets the aircraft take-off conditions.
本发明与现有技术相比具有以下优点：Compared with the prior art, the present invention has the following advantages:
1、本发明运用蒙特卡洛方法结合子母弹炸点分布算法模拟子弹在机场跑道的落点，数学模型简单，计算出的毁伤概率有效。1. The present invention uses the Monte Carlo method combined with the submunition explosion point distribution algorithm to simulate the landing point of bullets on the airport runway. The mathematical model is simple and the calculated damage probability is effective.
2、本发明基于K近邻卷积算法对传统遍历算法进行改进，该算法能够智能选择炸点稀疏区域，优先在炸点稀疏区域进行遍历选取机场跑道最小飞行区域，大大加快了机场跑道最小飞行区域的评估速度。2. The present invention improves the traditional traversal algorithm based on the K nearest neighbor convolution algorithm. The algorithm can intelligently select sparse explosion point areas, and preferentially traverse the sparse explosion point areas to select the minimum flight area of the airport runway, which greatly speeds up the evaluation speed of the minimum flight area of the airport runway.
3、本发明设计的机场跑道毁伤评估系统，能够实际应用于真实打击模式的打击场景时，评估效率高且评估结果准确。3. The airport runway damage assessment system designed by the present invention can be actually applied to strike scenarios in real strike modes, with high assessment efficiency and accurate assessment results.
下面通过附图和实施例，对本发明做进一步的详细描述。The present invention is further described in detail below through the accompanying drawings and examples.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明中机场跑道毁伤失败示意图。FIG. 1 is a schematic diagram of an airport runway damage failure in the present invention.
图2为本发明中机场跑道毁伤成功示意图。FIG. 2 is a schematic diagram showing the successful destruction of an airport runway in the present invention.
图3为本发明中机场跑道毁伤评估系统流程图。FIG3 is a flow chart of the airport runway damage assessment system of the present invention.
图4为本发明中地面坐标系和弹体坐标系示意图。FIG. 4 is a schematic diagram of the ground coordinate system and the projectile coordinate system in the present invention.
图5为本发明中子弹在地面上的分布示意图。FIG. 5 is a schematic diagram showing the distribution of neutron bombs of the present invention on the ground.
图6为本发明中机场跑道中的炸点示意图。FIG. 6 is a schematic diagram of explosion points in an airport runway according to the present invention.
图7为本发明中矩形区域分割示意图。FIG. 7 is a schematic diagram of rectangular region segmentation in the present invention.
图8为本发明实施例1中的矩形区域、炸点以及最小飞行区域示意图。FIG8 is a schematic diagram of a rectangular area, explosion points and minimum flight area in Example 1 of the present invention.
图9为本发明实施例1中的毁伤评估结果示意图。FIG. 9 is a schematic diagram of damage assessment results in Example 1 of the present invention.
图10为本发明实施例2中工况1的机场跑道毁伤示意图。FIG10 is a schematic diagram of airport runway damage in working condition 1 in embodiment 2 of the present invention.
图11为本发明实施例2中工况1的机场跑道毁伤评估结果示意图。FIG11 is a schematic diagram of the airport runway damage assessment results of working condition 1 in Example 2 of the present invention.
图12为本发明实施例2中工况2的机场跑道毁伤示意图。FIG12 is a schematic diagram of airport runway damage in working condition 2 in embodiment 2 of the present invention.
附图标记说明:Description of reference numerals:
1—机场跑道；2—炸点；3—最小飞行区域。1—Airport runway; 2—Bombing point; 3—Minimum flight area.
具体实施方式Detailed ways
下面将参照附图更详细地描述本发明的实施例。虽然附图中显示了本发明的某些实施例，然而应当理解的是，本发明可以通过各种形式来实现，而且不应该被解释为限于这里阐述的实施例，相反提供这些实施例是为了更加透彻和完整地理解本发明。应当理解的是，本发明的附图及实施例仅用于示例性作用，并非用于限制本发明的保护范围。Embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although certain embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as being limited to the embodiments described herein, which are instead provided for a more thorough and complete understanding of the present invention. It should be understood that the drawings and embodiments of the present invention are only for exemplary purposes and are not intended to limit the scope of protection of the present invention.
需要说明的是，在不冲突的情况下，本申请中的实施例及实施例中的特征可以相互组合。下面将参考附图并结合实施例来详细说明本发明。It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.
如图1-12所示，一种基于K近邻卷积算法的机场跑道毁伤评估方法，包括以下步骤：As shown in FIG1-12, a method for airport runway damage assessment based on the K nearest neighbor convolution algorithm includes the following steps:
步骤一、如图4所示，建立地面坐标系和弹体坐标系，获取导弹瞄准点坐标、随机弹道方向和拦截点的坐标，构建随机弹道方程，获取母弹开舱点坐标。具体步骤包括：Step 1: As shown in Figure 4, establish the ground coordinate system and the missile body coordinate system, obtain the coordinates of the missile aiming point, the random ballistic direction and the interception point, construct the random ballistic equation, and obtain the coordinates of the mother missile opening point. The specific steps include:
步骤11、假设导弹末端弹道为直线，所选地面坐标系为OXYZ(O点为目标的几何中心点)，选定导弹瞄准点坐标为(X0,Y0,Z0)，弹体坐标系为oxyz，oy轴为随机弹道，其方向由导弹高低角ω和方位角λ决定，随机弹道的方向为：J＝{cosωcosλ,cosωsinλ,sinω}，其中，ω为导弹发射高低角，λ为导弹发射方位角；Step 11, assuming that the missile terminal trajectory is a straight line, the selected ground coordinate system is OXYZ (point O is the geometric center of the target), the missile aiming point coordinates are selected as (X0 , Y0 , Z0 ), the missile body coordinate system is oxyz, the oy axis is a random trajectory, and its direction is determined by the missile elevation angle ω and azimuth angle λ. The direction of the random trajectory is: J = {cosωcosλ, cosωsinλ, sinω}, where ω is the missile launch elevation angle, and λ is the missile launch azimuth angle;
步骤12、在坐标系oxyz中，oxz平面为制导平面，导弹在制导平面上的拦截点由导弹的圆概率偏差CEP决定，根据导弹的圆概率偏差CEP，基于蒙特卡洛模拟获取导弹在制导平面上的拦截点坐标，制导平面随机拦截点的坐标表示为：式中，x0，z0为μ＝0，σ＝1的正态分布随机数抽样，即/>其中，r1,r2是一对[0,1]区间的均匀随机数，x0,z0服从二维标准正态分布，其密度函数为：σx和σz为制导误差的横向和纵向标准偏差，σx＝σz＝CEP/1.1774；Step 12: In the coordinate system oxyz, the oxz plane is the guidance plane. The interception point of the missile on the guidance plane is determined by the circular error probability CEP of the missile. According to the circular error probability CEP of the missile, the coordinates of the interception point of the missile on the guidance plane are obtained based on the Monte Carlo simulation. The coordinates of the random interception point of the guidance plane are expressed as: In the formula, x0 , z0 are random number samples from a normal distribution with μ = 0 and σ = 1, that is, Among them, r1 ,r2 are a pair of uniform random numbers in the interval [0,1], x0 ,z0 obey the two-dimensional standard normal distribution, and its density function is: σx and σz are the lateral and longitudinal standard deviations of the guidance error, σx =σz =CEP/1.1774;
步骤13、根据所述导弹瞄准点坐标(X0,Y0,Z0)、所述随机弹道方向以及制导误差，获取制导平面随机拦截点在地面坐标系上的坐标：Step 13: According to the missile aiming point coordinates (X0 , Y0 , Z0 ), the random trajectory direction and the guidance error, the coordinates of the random interception point of the guidance plane in the ground coordinate system are obtained:
步骤14、根据所述步骤12和步骤13，得到随机弹道方程为：式中，(X，Y，Z)为母弹开舱点坐标；Step 14: According to step 12 and step 13, the random trajectory equation is obtained as follows: Where, (X, Y, Z) is the coordinates of the mother bomb opening point;
步骤15、根据所述随机弹道方程，选定导弹瞄准点(X0,Y0,Z0)，由攻击高低角ω和方位角λ、拦截点在地面坐标系中的坐标和母弹引信启动规律的抽样得到随机开舱点坐标为(Xb,Yb,Zb)，Zb＝H，H为母弹开舱高度。Step 15: According to the random ballistic equation, the missile aiming point (X0 , Y0 , Z0 ) is selected, and the random opening point coordinates are obtained as (Xb , Yb , Zb ) by sampling the attack elevation angle ω and azimuth angle λ, the coordinates of the interception point in the ground coordinate system and the mother missile fuze activation rule, where Zb =H, and H is the mother missile opening height.
步骤二、假定母弹开舱后，子弹群周向对称抛撒且始终在一个平面上，分布均匀，根据母弹开舱点的坐标，获取子弹落点在地面上的分布区域方程，建立子弹散布区域坐标系，基于蒙特卡洛抽样法获取子弹落点在子弹散布区域坐标系中的坐标，将子弹落点在所述子弹散布区域坐标系中的坐标变换得到子弹在地面坐标系中的坐标；Step 2: Assuming that after the mother bomb is opened, the bullet group is scattered symmetrically in the circumferential direction and is always on a plane with uniform distribution, according to the coordinates of the mother bomb opening point, the distribution area equation of the bullet landing point on the ground is obtained, and a bullet scattering area coordinate system is established. Based on the Monte Carlo sampling method, the coordinates of the bullet landing point in the bullet scattering area coordinate system are obtained, and the coordinates of the bullet landing point in the bullet scattering area coordinate system are transformed to obtain the coordinates of the bullet in the ground coordinate system;
所述步骤二中建立子弹散布区域坐标系，基于蒙特卡洛抽样计算子弹落点坐标具体包括：In the step 2, a bullet scattering area coordinate system is established, and the bullet landing point coordinates are calculated based on Monte Carlo sampling, specifically including:
步骤21、基于子弹群在同一平面上均匀分布的假设，以及导弹的末端弹道为直线的假设，可以得到如图5所示的子弹在地面上的分布示意图。子弹在弹体坐标系上的分布范围近似表示为：式中，a为弹群圆锥形分布的半锥角，弹群圆锥形分布的半锥角a与母弹弹速、子弹的抛撒速度、抛撒高度和气动外形有关，根据试验规律确定；子弹在地面上的分布区域为椭圆形区域，所述椭圆形区域的数学方程根据下面的坐标变换关系得到，/>其中，(Xb,Yb,Zb)为母弹随机开舱点坐标，ω为导弹发射高低角，λ为导弹发射方位角；Step 21: Based on the assumption that the bullet group is evenly distributed on the same plane and the assumption that the terminal trajectory of the missile is a straight line, a distribution diagram of the bullets on the ground as shown in FIG5 can be obtained. The distribution range of the bullets in the missile body coordinate system is approximately expressed as: Wherein, a is the semi-cone angle of the conical distribution of the bullet group, which is related to the mother bullet velocity, bullet scattering velocity, scattering height and aerodynamic shape, and is determined according to the test rules; the distribution area of the bullets on the ground is an elliptical area, and the mathematical equation of the elliptical area is obtained according to the following coordinate transformation relationship,/> Among them, (Xb ,Yb ,Zb ) are the coordinates of the random opening point of the mother missile, ω is the missile launch elevation angle, and λ is the missile launch azimuth angle;
步骤22、以母弹虚拟落点为坐标原点，建立XZOZYZ坐标系作为子弹散布区域坐标系，由于子弹群假定在散布范围内均匀分布，由此可在此坐标系的椭圆范围内选择均匀分布的随机序列来表示子弹的散布位置，即基于蒙特卡洛抽样计算子弹落点坐标，通过抽取以椭圆长轴为长、以椭圆短轴为宽的矩形范围内的随机序列，并进行筛选可以得到椭圆范围内均匀分布的随机序列，所述随机序列表示为：其中，s为系数，Lx，Ly分别为椭圆的长轴和短轴，而r1，r2均为(0,1)之间的均匀分布随机数，运用算式判断随机点是否在椭圆范围内，实现矩形范围内随机序列的筛选，当xz<cosλXb+sinλYb，且yz<-cosωsinλXb-cosωcosλYb时，可得随机系列在椭圆区域范围内；Step 22, taking the virtual landing point of the mother bullet as the coordinate origin, establishtheXZOZYZcoordinate system as the bullet dispersion area coordinate system. Since the bullet group is assumed to be uniformly distributed within the dispersion range, a uniformly distributed random sequence can be selected within the ellipse range of this coordinate system to represent the dispersion position of the bullets, that is, the bullet landing point coordinates are calculated based on Monte Carlo sampling. By extracting a random sequence within a rectangular range with the major axis of the ellipse as the length and the minor axis of the ellipse as the width, and screening, a uniformly distributed random sequence within the ellipse range can be obtained. The random sequence is expressed as: Among them, s is the coefficient, Lx ,Ly are the major axis and minor axis of the ellipse respectively, and r1 , r2 are uniformly distributed random numbers between (0,1). The formula is used to determine whether the random point is within the range of the ellipse to achieve the screening of random sequences within the rectangular range. When xz <cosλXb +sinλYb , and yz <-cosωsinλXb -cosωcosλYb , it can be obtained that the random series is within the range of the ellipse area;
步骤23、通过随机抽取所述子弹散布区域坐标系中的子弹落点坐标序列，获得子弹落点在地面坐标系中的坐标：式中，(xd，yd)为子弹落点在地面坐标系中的坐标，(xz，yz)为子弹散布区域坐标系中的子弹落点坐标序列，λ为导弹发射方位角。Step 23, by randomly extracting the bullet landing point coordinate sequence in the bullet scattering area coordinate system, obtain the coordinates of the bullet landing point in the ground coordinate system: Where (xd , yd ) is the coordinate of the bullet landing point in the ground coordinate system, (xz , yz ) is the coordinate sequence of the bullet landing point in the bullet dispersion area coordinate system, and λ is the missile launch azimuth.
步骤三、假设落在跑道上的子弹100％有效，依据机场功能特性和毁伤概率模型，如果机场跑道1在导弹攻击后仍有一个最小的飞行区域，那么破坏的概率是0；反之，如果没有，破坏的概率就是1，因此将机场跑道1的毁伤判断工作集中在寻找并判断最小飞行区域3上。将矩形机场跑道1划分为多个边长为1的矩形块，子弹的炸点坐标对应边长为1的矩形块，利用K近邻判断炸点2稀疏程度，构建点密集度打分机制，通过卷积运算获取各个炸点2处的点密集度分数，根据分数判断机场跑道1内炸各个炸点2处的点密集度，找出炸点稀疏区域；Step 3: Assuming that the bullets falling on the runway are 100% effective, according to the airport functional characteristics and damage probability model, if the airport runway 1 still has a minimum flight area after the missile attack, then the probability of damage is 0; conversely, if not, the probability of damage is 1. Therefore, the damage judgment work of the airport runway 1 is focused on finding and judging the minimum flight area 3. Divide the rectangular airport runway 1 into multiple rectangular blocks with a side length of 1. The coordinates of the bullet's explosion point correspond to the rectangular blocks with a side length of 1. Use K nearest neighbors to determine the sparsity of the explosion point 2, build a point density scoring mechanism, obtain the point density score of each explosion point 2 through convolution operation, and determine the point density of each explosion point 2 in the airport runway 1 according to the score to find the explosion point sparse area;
所述步骤三具体包括：The step three specifically includes:
步骤31、机场跑道1是长为M、宽为N的矩形区域，如图7所示，将所述矩形区域分割为M×N个边长为1的矩形块，每个边长为1的矩形块均对应一个炸点2的坐标点，将所述矩形区域用M×N的矩阵A表示：AMN＝(aij)M×N，当i＝xi且j＝yi时，aij＝0,否则aij＝1，式中，(xi，yi)为炸点坐标，i＝1,2,3，…M，j＝1,2,3，…N，也即，当存在炸点2时，炸点坐标处的矩阵元素为0，矩形区域内其它点坐标在矩阵中的元素为1；Step 31, the airport runway 1 is a rectangular area with a length of M and a width of N, as shown in FIG7 , the rectangular area is divided into M×N rectangular blocks with a side length of 1, each rectangular block with a side length of 1 corresponds to a coordinate point of a bombing point 2, and the rectangular area is represented by an M×N matrix A: AMN = (aij )M×N , when i = xi and j = yi , aij = 0, otherwise aij = 1, where (xi , yi ) is the bombing point coordinate, i = 1, 2, 3, ... M, j = 1, 2, 3, ... N, that is, when there is a bombing point 2, the matrix element at the bombing point coordinate is 0, and the elements of the matrix coordinates of other points in the rectangular area are 1;
步骤32、利用K近邻算法查找被预测点附近的样本点，基于欧式距离计算被预测点与样本点的相似程度，进而计算出被预测点与所述样本点之间的距离，判断被预测点的点密集度，根据欧式距离和邻近点的思想，定义所述点密集度的含义是被预测点附近的样本点数量越多、且距离被预测点距离越近则认为被预测点处点密集度越大；Step 32: Use the K nearest neighbor algorithm to find sample points near the predicted point, based on the Euclidean distance Calculate the similarity between the predicted point and the sample point, and then calculate the distance between the predicted point and the sample point, and determine the point density of the predicted point. According to the idea of Euclidean distance and neighboring points, the meaning of the point density is defined as the more sample points there are near the predicted point and the closer the distance to the predicted point is, the greater the point density at the predicted point is.
步骤33、构建打分机制，对所述被预测点与所述被预测点附近的样本点之间的距离打分，距离越近则分数越高，定义点密集度公式为其中，m为被预测点附近样本点的个数，i＝1,2,3，…m，Ki为被预测点与样本点之间对应距离的得分；Step 33: Construct a scoring mechanism to score the distance between the predicted point and the sample points near the predicted point. The closer the distance, the higher the score. The formula for defining the point density is: Where m is the number of sample points near the predicted point, i = 1, 2, 3, ... m,Ki is the score of the corresponding distance between the predicted point and the sample point;
步骤34、计算所述步骤31中矩形区域内各个炸点2的点密集度：根据所述打分机制构建一个m×n的卷积核h，其中，m和n均为奇数，被预测点与样本点之间对应距离的得分作为卷积核的权重，根据所述矩形区域的矩阵A，得到卷积运算公式为：其中，i为行序号，j为列序号，g(x)为卷积核函数，运算后找出炸点稀疏区域。Step 34, calculate the point density of each explosion point 2 in the rectangular area in step 31: construct an m×n convolution kernel h according to the scoring mechanism, where m and n are both odd numbers, and the score of the corresponding distance between the predicted point and the sample point is used as the weight of the convolution kernel. According to the matrix A of the rectangular area, the convolution operation formula is obtained as follows: Among them, i is the row number, j is the column number, g(x) is the convolution kernel function, and after the operation, the sparse area of the explosion point is found.
若要从分数较高者开始搜索，卷积核可以设计成由中心向外依次递减，矩形区域的矩阵定义为AMN＝(aij)M×N，当i＝xi且j＝yi时，aij＝0,否则aij＝1，即炸点2处元素为0，空白区域元素为1，实现一种扣分机制，即被预测点附近的样本点越密集，扣分越多，也即被炸点越密集，得分越低。If you want to start searching from the one with a higher score, the convolution kernel can be designed to decrease from the center to the outside. The matrix of the rectangular area is defined as AMN = (aij )M×N . When i = xi and j = yi , aij = 0, otherwise aij = 1, that is, the element at the explosion point 2 is 0, and the element in the blank area is 1, realizing a deduction mechanism, that is, the denser the sample points near the predicted point, the more points will be deducted, that is, the denser the explosion points, the lower the score.
步骤四、根据机场跑道毁伤评估准则，运用面积法优先在所述炸点稀疏区域内搜索是否存在满足飞机起飞条件的最小飞行区域3。Step 4: Based on the airport runway damage assessment criteria, use the area method to preferentially search within the sparsely populated area of the bombing points to see if there is a minimum flight area 3 that meets the aircraft takeoff conditions.
所述步骤四中的面积法为：优先在炸点稀疏区域内遍历选取最小飞行区域3，连接所述炸点稀疏区域中的任一炸点2与满足飞机起飞条件的最小飞行区域3的顶点，所述最小飞行区域3为矩形，所述炸点2与所述最小飞行区域3的四个边构成四个三角形，根据最小飞行区域3的面积与四个三角形的面积之和的大小关系，判断所述炸点2是否位于最小飞行区域3内。当点在矩形区域内部时，所述最小飞行区域3的面积与四个所述三角形的面积之间满足公式：SABCD＝S1+S2+S3+S4时，式中，SABCD为最小飞行区域3的面积，S1、S2、S3和S4分别为炸点2与最小飞行区域3的四条边分别构成的四个三角形的面积；认为子弹落在最小飞行区域3中，计算三角形面积使用海伦公式：其中，a，b，c分别为三角形的三条边长，p为三角形三条边长度和的一半。若在炸点稀疏区域存在最小飞行区域3，则搜索结束；若不存在，则极大概率该待搜索区域内并不存在满足条件的最小飞行区域3，停止搜索，判别为毁伤成功。The area method in step 4 is: preferentially traverse and select the minimum flight area 3 in the sparse bombing point area, connect any bombing point 2 in the sparse bombing point area with the vertex of the minimum flight area 3 that meets the aircraft take-off conditions, the minimum flight area 3 is a rectangle, the bombing point 2 and the four sides of the minimum flight area 3 form four triangles, and judge whether the bombing point 2 is located in the minimum flight area 3 according to the size relationship between the area of the minimum flight area 3 and the sum of the areas of the four triangles. When the point is inside the rectangular area, the area of the minimum flight area 3 and the areas of the four triangles satisfy the formula: SABCD = S1 + S2 + S3 + S4 , in which SABCD is the area of the minimum flight area 3, S1 , S2 , S3 and S4 are the areas of the four triangles formed by the bombing point 2 and the four sides of the minimum flight area 3; it is considered that the bullet falls in the minimum flight area 3, and the triangle area is calculated using Heron's formula: Where a, b, c are the lengths of the three sides of the triangle, and p is half of the sum of the lengths of the three sides of the triangle. If there is a minimum flight area 3 in the sparse bombing area, the search ends; if not, there is a high probability that there is no minimum flight area 3 that meets the conditions in the search area, and the search is stopped, and it is judged that the damage is successful.
一种基于K近邻卷积算法的机场跑道毁伤评估系统，包括炸点计算模块和毁伤评估模块，所述炸点计算模块用于依次初始化弹道参数、弹药参数和目标列表参数，并根据所述弹道参数、弹药参数和目标列表参数，通过蒙特卡洛模拟计算出拦截点坐标后，通过蒙特卡洛抽样计算炸点坐标；所述毁伤评估模块用于根据接收到的炸点坐标，利用K近邻判断所述炸点稀疏程度，并通过卷积运算对炸点稀疏程度进行打分，运用遍历法搜索最小飞行区域3，最终输出评估结果。A damage assessment system for an airport runway based on a K-nearest neighbor convolution algorithm comprises a bombing point calculation module and a damage assessment module. The bombing point calculation module is used to initialize trajectory parameters, ammunition parameters and target list parameters in sequence, and calculate the interception point coordinates through Monte Carlo simulation according to the trajectory parameters, ammunition parameters and target list parameters, and then calculate the bombing point coordinates through Monte Carlo sampling; the damage assessment module is used to determine the sparsity of the bombing point according to the received bombing point coordinates by using K-nearest neighbors, and score the bombing point sparsity through convolution operation, use the traversal method to search for the minimum flight area 3, and finally output the assessment result.
所述弹道参数包括导弹入射角、导弹瞄准点坐标、方位角、圆概率误差以及开舱高度，所述目标列表参数包括机场跑道1的长度、宽度和满足飞机起飞条件的最小飞行区域3的长度、宽度。The ballistic parameters include the missile incidence angle, missile aiming point coordinates, azimuth, circular error probability and cabin opening height, and the target list parameters include the length and width of the airport runway 1 and the length and width of the minimum flight area 3 that meets the aircraft take-off conditions.
实施例1Example 1
如图8所示，假设有四个子弹落在尺寸为8×4的矩形区域的机场跑道内，将矩形区域的机场跑道分割成边长为1的矩形块，矩形区域能够用矩阵表示，四个子弹在矩形区域中的坐标分别是P1(6，3)，P2(6，4)，P2(7，3)，P2(7，4)，将矩阵中四个坐标点处的元素置为0，矩阵其它区域的坐标点处的元素置为1，用矩阵表示为：设计5×5的卷积核：/>其权重分数由中心向周围递减，将原矩形区域周围补0，补0后得到：/>根据卷积运算公式进行卷积运算，得到如下表中数据：As shown in FIG8 , assume that four bullets fall on an airport runway in a rectangular area of 8×4. The airport runway in the rectangular area is divided into rectangular blocks with a side length of 1. The rectangular area can be represented by a matrix. The coordinates of the four bullets in the rectangular area are P1 (6, 3), P2 (6, 4), P2 (7, 3), and P2 (7, 4). Set the elements at the four coordinate points in the matrix to 0, and set the elements at the coordinate points in other areas of the matrix to 1. The matrix is represented as follows: Design a 5×5 convolution kernel:/> The weight score decreases from the center to the periphery. Fill the original rectangular area with 0, and then we get:/> According to the convolution operation formula, the convolution operation is performed to obtain the data in the following table:
表1Table 1
根据表1得出的结果可以看出，最高分为30分，说明在该处点的炸点2最为稀疏，能找到目标矩形的概率最大，与实际情况一致。如图8所示，假设最小飞行区域3的尺寸为4×2，在得分为30处的区域进行搜索，矩形区域中存在如图9所示的最小飞行区域3，毁伤失败。According to the results in Table 1, the highest score is 30, which means that the bomb point 2 at this point is the most sparse, and the probability of finding the target rectangle is the highest, which is consistent with the actual situation. As shown in Figure 8, assuming that the size of the minimum flight area 3 is 4×2, the search is performed in the area with a score of 30. The minimum flight area 3 shown in Figure 9 exists in the rectangular area, and the damage fails.
实施例2Example 2
将本发明提供的机场跑道毁伤评估系统用于真实打击模式的打击场景，设置子母弹对跑道目标进行打击，并针对炸点2分布情况进行飞行区域的评估。The airport runway damage assessment system provided by the present invention is used in a strike scenario of a real strike mode, submunitions are set to strike runway targets, and the flight area is assessed based on the distribution of the bombing point 2.
选用JP233型子母弹进行打击，打击目标为台南机场，机场参数设置长3068m，宽45m，最小飞行区域3为长600m宽20m的矩形区域，设置两个打击工况：JP233 submunitions were selected for the strike, and the target was Tainan Airport. The airport parameters were set to be 3068m long and 45m wide. The minimum flight area 3 was a rectangular area with a length of 600m and a width of 20m. Two strike conditions were set:
工况一：四发子母弹在无偏角，入射角60°条件下对跑道间隔500m均布打击；Working condition 1: Four cluster bombs strike the runway evenly at intervals of 500m with no deflection and an incident angle of 60°;
工况二：五发子母弹在无偏角，入射角60°条件下对跑道间隔500m均布打击；Working condition 2: Five cluster bombs are evenly distributed on the runway at intervals of 500m with no deflection and an incident angle of 60°;
两种工况下的打击结果如下：The striking results under the two working conditions are as follows:
如图10、图11所示的工况一情况下，弹药数量不够，虽然打击范围内宽度方向完全封锁，但是留有长度1000m左右的空白区域，大于最小飞行区域3范围，算法输出代表最小飞行区域3的矩形框，代表存在最小飞行区，机场跑道毁伤失败；In the first working condition as shown in Figures 10 and 11, the number of ammunition is insufficient. Although the width direction of the strike range is completely blocked, there is a blank area of about 1000m in length, which is larger than the minimum flight area 3. The algorithm outputs a rectangular box representing the minimum flight area 3, indicating that there is a minimum flight area and the airport runway damage fails.
如图12所示的工况二情况下，整个跑道系统被分为六块成功实现机场跑道整体封锁，算法无法找到最小飞行区域3，机场跑道毁伤成功。In the second working condition as shown in Figure 12, the entire runway system is divided into six blocks to successfully achieve the overall blockade of the airport runway. The algorithm cannot find the minimum flight area 3, and the airport runway is successfully destroyed.
以上所述，仅是本发明的较佳实施例，并非对本发明作任何限制，凡是根据本发明技术实质对以上实施例所作的任何简单修改、变更以及等效结构变换，均仍属于本发明技术方案的保护范围内。The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural transformation made to the above embodiment based on the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.
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| CN202311276339.XACN118070638A (en) | 2023-09-30 | 2023-09-30 | Airport runway damage assessment method and system based on K-nearest neighbor convolution algorithm |
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