CN101893441A

CN101893441A - UAV Track Optimization Method Based on Deviation Maximization and Gray Relational Analysis

Info

Publication number: CN101893441A
Application number: CN 201010200367
Authority: CN
Inventors: 赵敏; 胡中华; 姚敏
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2010-06-13
Filing date: 2010-06-13
Publication date: 2010-11-24

Abstract

The invention discloses an unmanned aerial vehicle track optimization method based on deviation maximization and gray relational analysis, and belongs to the field of unmanned aerial vehicle track planning and uncertain multi-attribute decision-making. According to the different threats to UAVs, the method establishes the optimal decision-making target system of UAV track plan, and constructs the mathematical model of UAV track plan optimization based on evaluation attributes. Specifically, according to the trajectory planning scheme set, the deviation maximization method is used to objectively weight each evaluation attribute, and the gray relational analysis method is used to solve the optimal model, making full use of the gray relational information between each attribute, and finally according to the decision The degree of layer correlation determines the optimal trajectory scheme. The method of the invention has strong objectivity, does not need to estimate according to expert experience, and has strong operability.

Description

UAV Track Optimization Method Based on Deviation Maximization and Gray Relational Analysis

技术领域technical field

本发明涉及一种航迹优选方法，尤其涉及一种基于离差最大化及灰色关联分析的无人机航迹方案优选方法，属于无人机航迹规划及不确定多属性决策领域。The present invention relates to a track optimization method, in particular to an unmanned aerial vehicle track scheme optimization method based on deviation maximization and gray relational analysis, which belongs to the field of unmanned aerial vehicle track planning and uncertain multi-attribute decision-making.

背景技术Background technique

无人机(UAV)自上世纪60年代以来得到了广泛的研究并取得了飞速发展。最初的无人机是作为靶机，而随着研究的深入，其开始逐步扮演各种空战角色，如侦察、监视、火力打击、电子干扰、欺骗牵制、战损评估等。早期的无人机都是按照地面任务规划中心预先计算并设定好的航迹飞行，无人机实时航迹规划是无人机集群配合、集群战术再规划、集群战术目标再制定等高级自主飞行技术的基础，是提高无人机生存概率的一种最有效的手段。Unmanned Aerial Vehicle (UAV) has been extensively researched and developed rapidly since the 1960s. The original UAV was used as a target drone, and with the deepening of research, it began to gradually play various air combat roles, such as reconnaissance, surveillance, fire strikes, electronic jamming, deception containment, and battle damage assessment. Early UAVs flew according to the trajectory pre-calculated and set by the ground mission planning center. The basis of flight technology is one of the most effective means to improve the probability of drone survival.

合理的航迹规划方案使无人机有效地规避威胁，提高生存概率和作战效率。无人机在完成一条航迹方案时，主要考虑5个代价属性，分别是油耗代价、雷达威胁代价、导弹威胁代价、高炮威胁代价及大气威胁代价。该问题属于对于多属性决策问题，由于属性权重信息完全未知，以往一般都根据经验估值法确定权重，因此存在一定的主观性及难以适应战况变化的缺点，一旦情况有变，权重应该根据战况进行不断调整，而专家经验往往难以及时进行判断。A reasonable trajectory planning scheme enables UAVs to effectively avoid threats and improve survival probability and combat efficiency. When the UAV completes a trajectory plan, it mainly considers five cost attributes, namely fuel consumption cost, radar threat cost, missile threat cost, anti-aircraft gun threat cost and atmospheric threat cost. This problem belongs to the multi-attribute decision-making problem. Since the attribute weight information is completely unknown, the weight is generally determined according to the empirical valuation method in the past. Therefore, there is a certain degree of subjectivity and the disadvantage of being difficult to adapt to changes in the battle situation. Once the situation changes, the weight should be based on the battle situation. It is often difficult to make timely judgments based on expert experience.

此外，考虑到导弹、雷达的杀伤距离及有效探测等约束，并且威胁约束之间存在一定的关联，如雷达探测效果对指引导弹进行具体攻击发挥重要的作用。因此，无人机航迹方案优选是个多目标多约束的优化决策系统，且是个有机整体，各属性互相关联共同影响系统特性，且由于影响程度难以确定，故是一种灰色信息系统。这些灰色信息往往包含着各属性间的关联度，因而是具有系统意义的全局性信息，在设计航迹方案优选决策过程中应充分运用这些灰色关联信息，而目前公开发表的相关学术论文均没有讨论各方案之间的灰色关联信息，而是直接进行加权求和，以确定各方案的综合属性值，这样做往往不能反映这些属性的灰色信息。In addition, considering the constraints of missile and radar kill distance and effective detection, and there is a certain relationship between threat constraints, for example, the radar detection effect plays an important role in guiding missiles to carry out specific attacks. Therefore, the UAV track plan is preferably a multi-objective and multi-constraint optimization decision-making system, and it is an organic whole. Each attribute is related to each other and affects the system characteristics, and because the degree of influence is difficult to determine, it is a gray information system. These gray information often contain the degree of correlation between attributes, so they are global information with systematic significance. These gray correlation information should be fully used in the decision-making process of designing trajectory schemes. However, there are no relevant academic papers published so far. Discuss the gray relational information between various schemes, but directly carry out weighted summation to determine the comprehensive attribute value of each scheme, which often cannot reflect the gray information of these attributes.

发明内容Contents of the invention

本发明针对现有无人机航迹方案优选技术存在的不足，而提出一种客观获取各属性权重及充分利用航迹方案内在关系进行航迹方案优选的方法。The present invention aims at the deficiencies in the existing unmanned aerial vehicle track scheme optimization technology, and proposes a method for objectively obtaining the weight of each attribute and making full use of the internal relationship of the track scheme to optimize the track scheme.

本发明方法的主要步骤如下：The main steps of the inventive method are as follows:

(1)建立无人机航迹方案评价属性数据矩阵，采用离差最大化法对各评价属性进行客观赋权；(1) Establish the evaluation attribute data matrix of the UAV track plan, and use the deviation maximization method to objectively weight each evaluation attribute;

(2)采用灰色关联分析法对无人机航迹方案的各评价属性数据进行处理；(2) The gray relational analysis method is used to process the evaluation attribute data of the UAV track scheme;

(3)将步骤(1)中求出的各评价属性的权重进行加权，求出各无人机航迹方案决策层的关联度，根据关联度将各无人机航迹方案排序，最终确定最优航迹方案。(3) Weight the weights of each evaluation attribute obtained in step (1), find out the correlation degree of each UAV track plan decision-making layer, sort the UAV track plans according to the correlation degree, and finally determine Optimal track plan.

本发明方法克服了现有无人机航迹方案优选技术存在的不足，无需通过人工经验设置各属性权重，并且考虑了各方案之间存在的灰色关系，大大提高了无人机航迹方案优选的客观性，避免了传统上设计者凭经验选型的主观性和随机性，此外针对无人机二维和三维航迹规划均可采用本方法进行方案优选。The method of the present invention overcomes the deficiencies in the prior optimization technology of the UAV track scheme, does not need to set the weights of each attribute through manual experience, and considers the gray relationship between the various schemes, greatly improving the optimization of the UAV track scheme. The objectivity of this method avoids the subjectivity and randomness of the traditional designer’s selection based on experience. In addition, this method can be used for program optimization for two-dimensional and three-dimensional UAV trajectory planning.

附图说明Description of drawings

图1为二维航迹节点的网络结构示意图。Figure 1 is a schematic diagram of the network structure of two-dimensional track nodes.

图2为三维航迹节点的网络结构示意图。Figure 2 is a schematic diagram of the network structure of three-dimensional track nodes.

图3为实施例的无人机二维航迹方案示意图。Fig. 3 is a schematic diagram of the two-dimensional track scheme of the unmanned aerial vehicle of the embodiment.

图4为实施例的无人机三维航迹方案示意图。Fig. 4 is a schematic diagram of the three-dimensional track scheme of the unmanned aerial vehicle of the embodiment.

具体实施方式Detailed ways

(一)航迹空间描述(1) Track space description

(Ⅰ)二维航迹空间描述(I) Two-dimensional track space description

无人机在巡航阶段一般保持稳定的速度和高度，且敌方防御区处于平坦地域，因此可以不考虑利用地形属性进行威胁规避，并可将航迹空间简化为一个多目标多约束的二维搜索空间，但仍然需考虑无人机的生存概率和作战效能，所以仍是较为特殊的优化问题。通过对航迹空间进行直角网格划分，由当前节点搜寻下一个相邻节点，直至搜寻到目标节点，形成连接起始节点和目标节点的航迹，采用建立在网格图上的油耗及威胁代价模型，建立航迹优选方案。网格图中的每个节点到达相邻节点需要通过连接相邻节点且带有权重的有向边。算法的数据结构是以当前节点为中心的九宫图，共有8个相邻节点，如图1所示为二维航迹节点α的相邻节点示意图，航迹是由一组节点构成的节点向量，前后节点互为相邻关系，而网格大小需根据实际问题规模及威胁点分布状况进行合理设置，不能过大，亦不能过小。UAVs generally maintain a stable speed and altitude during the cruising phase, and the enemy's defense zone is in a flat area, so the use of terrain attributes for threat avoidance can be ignored, and the track space can be simplified into a multi-objective and multi-constrained two-dimensional However, it still needs to consider the survival probability and combat effectiveness of UAVs, so it is still a relatively special optimization problem. By dividing the track space into a right-angle grid, the current node searches for the next adjacent node until the target node is found, forming a track connecting the starting node and the target node, using the fuel consumption and threat established on the grid map The cost model is used to establish the route optimization scheme. Each node in the grid graph needs to reach the adjacent nodes through directed edges connecting adjacent nodes and carrying weights. The data structure of the algorithm is a nine-square diagram centered on the current node, and there are 8 adjacent nodes in total. Figure 1 shows the schematic diagram of the adjacent nodes of the two-dimensional track node α. The track is a node vector composed of a group of nodes , the front and back nodes are adjacent to each other, and the grid size should be set reasonably according to the actual problem scale and the distribution of threat points, and it should not be too large or too small.

(Ⅱ)三维航迹空间描述(II) Three-dimensional track space description

通过对三维规划空间进行立方体网格划分，将三维空间划分为大小相等、彼此相邻的立方体，搜寻方式为从起始点开始，搜寻下一个相邻节点，搜索前进，直至搜寻到目标节点，最终形成连接起始节点和目标节点的航迹，采用建立在网格图上的代价模型及优化算法求解最优航迹。因此，算法的数据结构是以当前节点为中心的立体结构图，共有26个相邻节点，如图2所示为三维航迹规划节点的网络结构示意图，下一个节点必须从以该节点为中心构成的27个节点中选择，其中X、Y、Z各方向的网格大小分别表示为X_Gird、Y_Gird、Z_Gird。网格大小需根据实际问题规模及威胁点分布状况进行合理设置，设置过大，则空间分辨率过低；设置太小，则数据空间过大，造成计算量过大。By dividing the three-dimensional planning space into cube grids, the three-dimensional space is divided into cubes of equal size and adjacent to each other. The search method is to start from the starting point, search for the next adjacent node, and search forward until the target node is found, and finally Form the track connecting the starting node and the target node, and use the cost model and optimization algorithm established on the grid graph to solve the optimal track. Therefore, the data structure of the algorithm is a three-dimensional structure diagram centered on the current node, and there are 26 adjacent nodes in total. Select from the 27 nodes formed, where the grid sizes in X, Y, and Z directions are denoted as X _Gird , Y _Gird , and Z _Gird , respectively. The grid size needs to be set reasonably according to the actual problem scale and the distribution of threat points. If the setting is too large, the spatial resolution will be too low; if the setting is too small, the data space will be too large, resulting in a large amount of calculation.

(二)威胁模型确定(2) Threat model determination

无人机航迹规划的评价属性主要包含油耗代价和威胁代价，其中威胁代价包括雷达威胁代价、导弹威胁代价、高炮威胁代价和大气威胁代价，航迹规划的目的就是要使整体的代价最小，如式(1)所示。且由于雷达、导弹、高炮及大气的模型存在最大作用距离及有效杀伤距离等约束，因此，该问题属于多目标多约束优化问题。The evaluation attributes of UAV trajectory planning mainly include fuel consumption cost and threat cost. Threat cost includes radar threat cost, missile threat cost, antiaircraft gun threat cost and atmospheric threat cost. The purpose of trajectory planning is to minimize the overall cost , as shown in formula (1). And because the models of radar, missiles, anti-aircraft guns and the atmosphere have constraints such as the maximum range of action and the effective killing distance, this problem is a multi-objective and multi-constrained optimization problem.

Optim[W_R(s)，W_M(s)，W_A(s)，W_C(s)，W_O(s)]＝W_R(s^*)，W_M(s^*)，W_A(s^*)，W_C(s^*)，W_O(s^*)](1)Optim[W _R (s), W _M (s), W _A (s), W _C (s), W _O (s)] = W _R (s ^* ), W _M (s ^* ), W _A ( s ^* ), W _C (s ^* ), W _O (s ^* )] (1)

式(1)中：s为无人机航迹方案；s^*为最优航迹规划方案；W_R(s)为航迹s的雷达威胁代价；W_M(s)为导弹威胁代价；W_A(s)为高炮威胁代价；W_C(s)为大气威胁代价；W_O(s)为油耗代价。油耗代价是航程的函数，其它威胁代价模型与无人机的可探测性以及导弹、高炮等的杀伤半径属性有关。In formula (1): s is the UAV trajectory plan; s ^* is the optimal trajectory planning scheme; W _R (s) is the radar threat cost of track s; W _M (s) is the missile threat cost; W _A (s) is the cost of antiaircraft gun threat; W _C (s) is the cost of atmospheric threat; W _O (s) is the cost of fuel consumption. Fuel consumption cost is a function of range, and other threat cost models are related to the detectability of UAVs and the kill radius attributes of missiles, antiaircraft guns, etc.

威胁模型存在最大作用距离及有效杀伤距离等约束，本发明通过建立合理的目标代价函数，将约束条件引入目标函数内，针对雷达、导弹、高炮及大气威胁模型分别定义如下：The threat model has constraints such as the maximum action distance and the effective killing distance. The present invention introduces the constraints into the objective function by establishing a reasonable target cost function. The threat models for radar, missile, antiaircraft gun and atmosphere are respectively defined as follows:

雷达对无人机的探测概率可近似表示为：The detection probability of radar to UAV can be approximated as:

${P P}_{R R} (({d d}_{R R})) = = \{\begin{matrix} 00 & (({d d}_{R R} > > {d d}_{R R max max})) \\ 11 / / {d d}_{R R}^{44} & (({d d}_{R R min min} \leq \leq {d d}_{R R} \leq \leq {d d}_{R R max max})) \\ 11 & (({d d}_{R R} < < {d d}_{R R min min})) \end{matrix} - - - - - - ((22))$

式(2)中：P_R(d_R)表示雷达威胁概率；d_R表示无人机与雷达之间的距离；d_Rmax表示雷达探测区域的最大半径，超过该距离时，返回信号极其微弱，淹没在噪声中；d_Rmin表示雷达有效探测半径，在该范围内，无人机被探测的概率为1。本发明假设天线在方位上作360°扫描，可形成雷达的全部探测范围，即雷达探测方位角范围0-360°。P_R(d_R)＝1表示无人机被发现的概率为1，则威胁代价可认为是无穷大；P_R(d_R)＝0，表示无人机被发现的概率为0，则无人机受雷达威胁代价为0；当d_M在二者之间时，无人机被发现的概率为

In formula (2): P _R (d _R ) represents the radar threat probability; d _R represents the distance between the UAV and the radar; d _Rmax represents the maximum radius of the radar detection area. When the distance exceeds this distance, the return signal is extremely weak. Submerged in noise; d _Rmin represents the effective detection radius of the radar, within this range, the probability of UAV being detected is 1. The present invention assumes that the antenna scans 360° in azimuth, which can form the entire detection range of the radar, that is, the radar detection azimuth range is 0-360°. P _R (d _R )=1 means that the probability of UAV being discovered is 1, and the threat cost can be regarded as infinite; P _R (d _R )=0, means that the probability of UAV being discovered is 0, and no one The radar threat cost of the drone is 0; when d _M is between the two, the probability of the drone being detected is

导弹对无人机的杀伤概率可近似表示为：The probability of killing a UAV by a missile can be approximated as:

${P P}_{M m} (({d d}_{M m})) = = \{\begin{matrix} 00 & (({d d}_{M m} > > {d d}_{M m max max})) \\ 11 / / {d d}_{M m} & (({d d}_{R R min min} \leq \leq {d d}_{M m} \leq \leq {d d}_{M m max max})) \\ 11 & (({d d}_{M m} < < {d d}_{M m min min})) \end{matrix} - - - - - - ((33))$

式(3)中：P_M(d_M)表示导弹威胁概率；d_M表示无人机与导弹之间的距离。P_M(d_M)＝1表示当无人机在导弹有效杀伤半径d_Mmin内时，无人机被击毁的概率为1，其威胁为无穷大；P_M(d_M)＝0表示当无人机在导弹最大杀伤半径d_Mmax外时，无人机被击中的概率为0，则无人机受导弹威胁代价为0；当d_M在二者之间时，无人机被击中的概率为1/d_M。In formula (3): _PM (d _M ) represents the missile threat probability; d _M represents the distance between the UAV and the missile. P _M (d _M )=1 means that when the UAV is within the effective killing radius d _Mmin of the missile, the probability of the UAV being destroyed is 1, and its threat is infinite; P _M (d _M )=0 means that when no one is When the drone is outside the maximum killing radius d _Mmax of the missile, the probability of the drone being hit is 0, and the cost of the drone being threatened by the missile is 0; when d _M is between the two, the probability of the drone being hit The probability is 1/d _M .

高炮对无人机的杀伤概率可近似表示为：The kill probability of anti-aircraft guns to UAVs can be approximately expressed as:

${P P}_{A A} (({d d}_{A A})) = = \{\begin{matrix} 00 & (({d d}_{A A} > > {d d}_{A A max max})) \\ 11 / / {d d}_{A A} & (({d d}_{A A min min} \leq \leq {d d}_{A A} \leq \leq {d d}_{A A max max})) \\ 11 & (({d d}_{A A} < < {d d}_{A A min min})) \end{matrix} - - - - - - ((44))$

式(4)中：P_A(d_A)表示高炮威胁概率；d_A表示无人机与高炮之间的距离。P_A(d_A)＝1表示当无人机在高炮有效杀伤半径d_Amin内时，无人机被击毁的概率为1，其威胁为无穷大；P_A(d_A)＝0表示当无人机在高炮最大杀伤半径d_Amax外时，无人机被击中的概率为0，则无人机受高炮威胁代价为0；当d_A在二者之间时，无人机被击中的概率为1/d_A。In formula (4): P _A (d _A ) represents the threat probability of the anti-aircraft gun; d _A represents the distance between the UAV and the anti-aircraft gun. P _A (d _A )=1 means that when the UAV is within the effective killing radius d _Amin of the antiaircraft gun, the probability of the UAV being destroyed is 1, and its threat is infinite; P _A (d _A )=0 means that when there is no When the man-machine is outside the maximum killing radius d _Amax of the anti-aircraft gun, the probability of the UAV being hit is 0, and the threat cost of the UAV being threatened by the anti-aircraft gun is 0; when d _A is between the two, the UAV is hit by The probability of hitting is 1/d _A .

大气对无人机的杀伤概率可近似表示为：The probability of killing UAVs by the atmosphere can be approximately expressed as:

${P P}_{C C} (({d d}_{C C})) = = \{\begin{matrix} 00 & (({d d}_{C C} > > {d d}_{C C max max})) \\ 11 / / {d d}_{C C} & (({d d}_{C C min min} \leq \leq {d d}_{C C} \leq \leq {d d}_{C C max max})) \\ 11 & (({d d}_{C C} < < {d d}_{C C min min})) \end{matrix} - - - - - - ((55))$

式(5)中：P_C(d_C)表示大气威胁概率；d_C表示无人机与大气之间的距离。P_C(d_C)＝1表示当无人机在大气有效杀伤半径d_Cmin内时，无人机被击毁的概率为1，其威胁为无穷大；P_C(d_C)＝0表示当无人机在大气最大杀伤半径d_Cmax外时，无人机被击中的概率为0，则无人机受大气威胁代价为0；当d_C在二者之间时，无人机被击中的概率为1/d_C。In formula (5): P _C (d _C ) represents the atmospheric threat probability; d _C represents the distance between the UAV and the atmosphere. P _C (d _C )=1 means that when the UAV is within the effective killing radius d _Cmin of the atmosphere, the probability of the UAV being destroyed is 1, and its threat is infinite; P _C (d _C )=0 means that when no one is When the drone is outside the maximum killing radius d _Cmax of the atmosphere, the probability of the drone being hit is 0, and the cost of the drone being threatened by the atmosphere is 0; when d _C is between the two, the probability of the drone being hit The probability is 1/d _C .

当优化的各属性函数确定后，对于给定的航迹方案可以分别计算出其各属性代价。After the optimized attribute functions are determined, the cost of each attribute can be calculated for a given track scheme.

(三)基于离差最大化的权重计算(3) Weight calculation based on deviation maximization

由n个航迹方案组成航迹规划方案集，每个方案是由m个评价属性构成的属性集，本发明中n可以取50，m取5，5个评价属性分别为雷达、导弹、高炮、大气的威胁代价及油耗代价。The track planning scheme set is composed of n track schemes, and each scheme is an attribute set composed of m evaluation attributes. In the present invention, n can be 50, m is 5, and the five evaluation attributes are radar, missile, altitude The threat cost of guns and atmosphere and the cost of fuel consumption.

设u_j表示第j个属性，x_ij表示第i个方案的u_j的属性值，则第i个方案的m个属性可用向量x_i表示为：Let u _j represent the jth attribute, and x _ij represent the attribute value of u _j in the i-th scheme, then the m attributes of the i-th scheme can be expressed as _:

x_i＝(x_i1，x_i2，…x_ij…，x_im)i＝1，2，…，n j＝1，2，…，m (6)x _i = (x _i1 , x _i2 , ... x _ij ..., x _im ) i = 1, 2, ..., n j = 1, 2, ..., m (6)

则对于所有n个方案的m个属性可用下述矩阵表示：Then the m attributes of all n schemes can be represented by the following matrix:

${X x}_{n no \times \times m m} = = [\begin{matrix} {x x}_{11} \\ {x x}_{22} \\ . . . . . . \\ {x x}_{n no} \end{matrix}] = = [\begin{matrix} {x x}_{1111} & {x x}_{1212} & . . . . . . & {x x}_{11 m m} \\ {x x}_{21 twenty one} & {x x}_{22 twenty two} & . . . . . . & {x x}_{22 m m} \\ . . & . . & . . \\ . . & . . & . . . . . . & . . \\ . . & . . & . . \\ {x x}_{n no 11} & {x x}_{n no 22} & . . . . . . & {x x}_{nm nm} \end{matrix}] - - - - - - ((77))$

为了便于进行基于离差最大化权重分析，不可直接使用初始属性数据X_n×m，这样会导致属性值大的属性权重大，属性值小的属性权重小，而应首先对X_n×m进行无量纲规范化处理，处理方法如下：In order to facilitate the weight analysis based on the maximization of dispersion, the initial attribute data X _n×m cannot be directly used, which will cause the attribute with a large attribute value to have a large weight, and the attribute with a small attribute value to have a small weight. Instead, X _n×m should be first Dimensionless normalization processing, the processing method is as follows:

本发明中航迹规划属性均为代价属性，是成本型的属性，因此，希望总体代价越小越好，故采用以下规范化公式：In the present invention, the trajectory planning attributes are all cost attributes, which are cost-type attributes. Therefore, it is hoped that the smaller the overall cost, the better, so the following standardized formula is adopted:

${r r}_{ij ij} = = \frac{- - {x x}_{ij ij} + + max max (({x x}_{11 j j},, {x x}_{22 j j},, . . . . . .,, {x x}_{nj nj}))}{max max (({x x}_{11 j j},, {x x}_{22 j j},, . . . . . .,, {x x}_{nj nj})) - - min min (({x x}_{11 j j},, {x x}_{22 j j},, . . . . . .,, {x x}_{nj nj}))},, i i = = 1,2 1,2,, . . . . . .,, n no,, j j = = 1,2 1,2,, . . . . . .,, m m - - - - - - ((88))$

式(7)经过规范化处理后为：Formula (7) after normalization processing is:

${R R}_{n no \times \times m m} = = [\begin{matrix} {r r}_{1111} & {r r}_{1212} & . . . . . . & {r r}_{11 m m} \\ {r r}_{21 twenty one} & {r r}_{22 twenty two} & . . . . . . & {r r}_{22 m m} \\ . . & . . & . . \\ . . & . . & . . . . . . & . . \\ . . & . . & . . \\ {r r}_{n no 11} & {r r}_{n no 22} & . . . . . . & {r r}_{nm nm} \end{matrix}] - - - - - - ((99))$

多属性综合评判中，若所有方案在属性u_j下的属性值差异越小，则认为该属性对方案决策与排序所起的作用越小；反之，作用越大。因此，方案属性值偏差越大的属性，应该赋予越大的权重。对于属性u_j，用V_ij(ω)表示方案x_i对其它所有方案之间的离差，则可定义：In multi-attribute comprehensive evaluation, if the attribute value difference of all schemes under attribute u _j is smaller, it is considered that the attribute plays a smaller role in the decision-making and ranking of schemes; otherwise, the effect is greater. Therefore, the attribute with the greater deviation of the attribute value of the scheme should be assigned a greater weight. For the attribute u _j , use V _ij (ω) to represent the dispersion between the scheme x _i and all other schemes, then it can be defined as:

${V V}_{ij ij} ((ω ω)) = = {V V}_{ij ij} ((ω ω)) = = {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} {ω ω}_{j j} - - {r r}_{kj kj} {ω ω}_{j j} | |,, i i = = 1,2 1,2,, . . . . . .,, n no,, j j = = 1,2 1,2,, . . . . . .,, m m - - - - - - ((1010))$

令：make:

${V V}_{j j} ((ω ω)) = = {Σ Σ}_{i i = = 11}^{n no} {V V}_{ij ij} ((ω ω)) = = {Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | | {ω ω}_{j j},, j j = = 1,2 1,2,, . . . . . .,, m m - - - - - - ((1111))$

则V_j(ω)表示对属性u_j而言，所有方案与其它方案的总离差。加权向量ω的选择应使所有属性对所有方案的总离差最大。为此，构造目标函数：Then V _j (ω) represents the total deviation between all schemes and other schemes for attribute u _j . The weighting vector ω should be chosen to maximize the total deviation of all attributes for all schemes. To do this, construct the objective function:

$max max V V ((ω ω)) = = {Σ Σ}_{j j = = 11}^{m m} {V V}_{j j} ((ω ω)) = = {Σ Σ}_{j j = = 11}^{m m} {Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | | {ω ω}_{j j} - - - - - - ((1212))$

则求解加权向量ω等价于求解如下最优化模型：Then solving the weight vector ω is equivalent to solving the following optimization model:

$\{\begin{matrix} max max V V ((ω ω)) = = {Σ Σ}_{j j = = 11}^{m m} {Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | | {ω ω}_{j j} \\ s the s . . t t . . ω ω &GreaterEqual; &Greater Equal; 00,, j j = = 1,2 1,2,, . . . . . .,, m m,, {Σ Σ}_{j j = = 11}^{m m} {ω ω}_{j j}^{22} = = 11 \end{matrix} - - - - - - ((1313))$

解此优化模型，作拉格朗日(Lagrange)函数：Solve this optimization model as a Lagrange function:

$L L ((ω ω,, ζ ζ)) = = {Σ Σ}_{j j = = 11}^{m m} {Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | | {ω ω}_{j j} + + \frac{11}{22} ζ ζ (({Σ Σ}_{j j = = 11}^{m m} {ω ω}_{j j}^{22} - - 11)) - - - - - - ((1414))$

求其偏导数，并令：Find its partial derivative, and let:

$\{\begin{matrix} \frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {ω ω}_{j j}} = = {Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | | + + ζ ζ {ω ω}_{j j} = = 00 \\ \frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; ζ ζ} = = {Σ Σ}_{j j = = 11}^{m m} {ω ω}_{j j}^{22} - - 11 = = 00 \end{matrix} - - - - - - ((1515))$

求得最优解：Find the optimal solution:

${ω ω}_{j j}^{* *} = = \frac{{Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | |}{\sqrt{{Σ Σ}_{j j = = 11}^{m m} {[[{Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | |]]}^{22}}},, j j = = 1,2 1,2,, . . . . . .,, m m$

对其进行归一化处理，满足归一化约束条件：Normalize it to meet the normalization constraints:

${ω ω}_{j j} = = \frac{{ω ω}_{j j}^{* *}}{{Σ Σ}_{j j = = 11}^{m m} {ω ω}_{j j}^{* *}},, j j = = 1,2 1,2,, . . . . . .,, m m$

由此得到：From this we get:

${ω ω}_{j j} = = \frac{{Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | |}{{Σ Σ}_{j j = = 11}^{m m} {[[{Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{k k = = 11}^{n no} | | {r r}_{ij ij} - - {r r}_{kj kj} | |]]}^{22}} - - - - - - ((1616))$

(四)无人机航迹方案集的灰色关联分析(4) Gray relational analysis of UAV trajectory scheme set

如上所述，无人机航迹规划方案集是由n个方案组成灰色系统的方案集，每个方案是由m个属性组成的向量，故灰色系统可用矩阵X_n×m表示，经过规范化处理后为R_n×m。由于无人机航迹规划方案集n个方案的优选具有比较上的相对性，在灰色系统中的优选是相对于该系统中的m个评价属性而言的，故先选一个理想的参考方案，记为：As mentioned above, the UAV track planning scheme set is a gray system scheme set composed of n schemes, and each scheme is a vector composed of m attributes, so the gray system can be represented by a matrix X _n×m , after normalization Then it is R _n×m . Since the optimization of n schemes in the UAV track planning scheme set is relatively relative, the optimization in the gray system is relative to the m evaluation attributes in the system, so an ideal reference scheme is first selected , recorded as:

${F f}^{00} = = {[[{f f}_{11}^{00},, {f f}_{22}^{00},, . . . . . .,, {f f}_{}^{j j},, . . . . . .,, {f f}_{m m}^{00}]]}^{T T} - - - - - - ((1717))$

式(17)中：

j＝1，2，…，m，即F⁰中的m个评价属性是参加优选的全体n个方案中相应评价属性的最大值，将它作为标准的理想方案。把理想方案作为参考序列，n个方案分别作为比较序列。参考序列与比较序列之间的数据关系贴近程度，通常用关联系数的大小来衡量。记ξ_i，j为第i个比较序列与F⁰参考序列中第j个属性的灰色关联系数，由式(18)计算。In formula (17):

j=1, 2,..., m, that is, the m evaluation attributes in F ⁰ are the maximum value of the corresponding evaluation attributes in all the n schemes participating in the optimization, and it is taken as the standard ideal scheme. The ideal scheme is taken as a reference sequence, and the n schemes are respectively used as comparison sequences. The closeness of the data relationship between the reference sequence and the comparison sequence is usually measured by the size of the correlation coefficient. Denote ξi _{, j} as the gray correlation coefficient between the i-th comparison sequence and the j-th attribute in the F ⁰ reference sequence, calculated by formula (18).

${ξ ξ}_{i i,, j j} = = \frac{\underset{j j}{min min} \underset{i i}{min min} | | {f f}_{j j}^{00} - - {r r}_{i i,, j j} | | + + ρ ρ \underset{j j}{max max} \underset{i i}{max max} | | {f f}_{j j}^{00} - - {r r}_{i i,, j j} | |}{| | {f f}_{j j}^{00} - - {r r}_{i i,, j j} | | + + ρ ρ \underset{j j}{max max} \underset{i i}{max max} | | {f f}_{j j}^{00} - - {r r}_{i i,, j j} | |},, i i = = 1,2 1,2,, . . . . . .,, n no,, j j = = 1,2 1,2,, . . . . . .,, m m - - - - - - ((1818))$

式中，ρ∈[0，1]，一般取ρ＝0.5，由此得到无人机航迹规划方案集灰色系统的灰色关联系数矩阵为：In the formula, ρ∈[0, 1], generally take ρ=0.5, thus the gray correlation coefficient matrix of the gray system of the UAV track planning scheme set is obtained as:

${Ξ ξ}_{m m \times \times n no} = = [\begin{matrix} {ξ ξ}_{1111} & {ξ ξ}_{1212} & . . . . . . & {ξ ξ}_{11 m m} \\ {ξ ξ}_{21 twenty one} & {ξ ξ}_{22 twenty two} & . . . . . . & {ξ ξ}_{22 m m} \\ . . & . . & . . \\ . . & . . & . . . . . . & . . \\ . . & . . & . . \\ {ξ ξ}_{n no 11} & {ξ ξ}_{n no 22} & . . . . . . & {ξ ξ}_{nm nm} \end{matrix}] - - - - - - ((1919))$

(五)航迹优选模型的求解方法(5) Solution method of track optimization model

无人机航迹规划方案优选模型的求解过程为：首先，在满足雷达、导弹、高炮及大气等约束条件的前提下，得出可行无人机航迹方案集；然后，根据决策目标体系和优选模型，运用离差最大化法求各属性的权重，即求出雷达、导弹、高炮、大气威胁代价及油耗代价的权重，分别表示为δ_O、δ_R、δ_A、δ_M及δ_C，然后，基于灰色关联分析法对方案集进行决策和评价，并最终确定综合代价最小的无人机航迹方案。其中，灰色关联分析法用于进行各属性数据处理。具体航迹方案选择中，评价体系包括油耗、雷达、导弹、高炮及大气代价5个属性，设共有n条航迹，即n个航迹方案，分别表示为s₁，s₂…s_i…s_n，其中第i条航迹s_i的属性组成可以用向量x_i表示：The solution process of the optimization model of the UAV track planning scheme is as follows: firstly, under the premise of satisfying the constraints of radar, missile, antiaircraft gun and atmosphere, etc., the feasible UAV trajectory scheme set is obtained; then, according to the decision-making target system and optimization model, use the deviation maximization method to find the weight of each attribute, that is to find the weight of radar, missile, anti-aircraft gun, atmospheric threat cost and fuel consumption cost, expressed as δ _O , δ _R , δ _A , δ _M and δ _C , and then, based on the gray relational analysis method, make decisions and evaluate the program set, and finally determine the UAV trajectory program with the smallest comprehensive cost. Among them, the gray relational analysis method is used to process each attribute data. In the selection of specific track schemes, the evaluation system includes five attributes: fuel consumption, radar, missile, anti-aircraft gun and atmospheric cost. Suppose there are n track schemes in total, that is, n track schemes, respectively denoted as s ₁ , s ₂ ...s _i …s _n , where the attribute composition of the i-th track s _i can be represented by a vector _xi :

x_i＝(W_Ri，W_Mi，W_Ai，W_Ci，W_Oi)^T (20)x _i = (W _Ri , W _Mi , W _Ai , W _Ci , W _Oi ) ^T (20)

n条航迹构成备选方案集X(x₁，x₂，…，x_n)。对各属性量化后，可以确定参考属性集，参考属性集是通过选取各无人机航迹规划方案的最佳属性值而构成。参考属性集描述了一种参考无人机航迹设计方案，即理想方案。于是可以进一步求得n个方案相对参考设计方案的灰色关联系数矩阵Ξ。The n trajectories constitute an alternative solution set X(x ₁ , x ₂ ,..., x _n ). After quantifying each attribute, a reference attribute set can be determined, which is formed by selecting the best attribute value of each UAV trajectory planning scheme. The reference attribute set describes a reference UAV trajectory design scheme, that is, the ideal scheme. Therefore, the gray relational coefficient matrix Ξ of the n schemes relative to the reference design scheme can be further obtained.

$Ξ ξ = = [\begin{matrix} {ξ ξ}_{R R 11} & {ξ ξ}_{M m 11} & {ξ ξ}_{A A 11} & {ξ ξ}_{C C 11} & {ξ ξ}_{O o 11} \\ {ξ ξ}_{R R 22} & {ξ ξ}_{M m 22} & {ξ ξ}_{A A 22} & {ξ ξ}_{C C 22} & {ξ ξ}_{O o 22} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {ξ ξ}_{Rn n} & {ξ ξ}_{Mn mn} & {ξ ξ}_{An An} & {ξ ξ}_{Cn Cn} & {ξ ξ}_{On On} \end{matrix}] - - - - - - ((21 twenty one))$

式(20)中的ξ是无人机航迹方案评价属性相对于参考属性集的灰色关联系数。ξ in formula (20) is the gray correlation coefficient of the evaluation attribute of the UAV track plan relative to the reference attribute set.

此外，根据离差最大化法求出的各属性权重，进行加权，求出各方案的决策层的关联度矢量R，计算公式如下：In addition, weighting is carried out according to the weights of each attribute obtained by the method of maximizing the deviation, and the correlation degree vector R of the decision-making layer of each plan is obtained. The calculation formula is as follows:

$R R = = [\begin{matrix} {ξ ξ}_{R R 11} & {ξ ξ}_{M m 11} & {ξ ξ}_{A A 11} & {ξ ξ}_{C C 11} & {ξ ξ}_{O o 11} \\ {ξ ξ}_{R R 22} & {ξ ξ}_{M m 22} & {ξ ξ}_{A A 22} & {ξ ξ}_{C C 22} & {ξ ξ}_{O o 22} \\ . . . . . . & . . . . . . & . . . . . . & . . . . . . & . . . . . . \\ {ξ ξ}_{Rn n} & {ξ ξ}_{Mn mn} & {ξ ξ}_{An An} & {ξ ξ}_{Cn Cn} & {ξ ξ}_{On On} \end{matrix}] {(({δ δ}_{R R},, {δ δ}_{M m},, {δ δ}_{A A},, {δ δ}_{C C},, {δ δ}_{O o}))}^{T T} = = {(({r r}_{11},, {r r}_{22},, . . . . . .,, {r r}_{n no}))}^{T T} - - - - - - ((22 twenty two))$

根据决策层灰色关联度矢量R＝(r₁，r₂，…，r_n)^T的大小对各方案进行优劣排序，确定最佳无人机航迹方案s^*及其对应的属性x^*。According to the decision-making level gray relational degree vector R=(r ₁ , r ₂ ,...,r _n ) ^T , the pros and cons of each program are sorted, and the best UAV track program s ^* and its corresponding attribute x ^* are determined .

(六)航迹规划实例仿真(6) Example simulation of trajectory planning

在保证满足上述5个约束条件的基础上，通过确定区域的随机搜索算法，分别确定50条无人机二维及三维航迹作为备选方案；无人机二维航迹方案如图3所示，无人机三维航迹方案如图4所示，图中正方形为航迹起点，五角星为航迹节点，实心圆为目标点，菱形为雷达威胁点，下三角形为高炮威胁点，六角形为大气威胁点，空心圆圈为导弹威胁点。根据航迹图，计算每条航迹的初始属性数据，分别包括雷达、导弹、高炮、大气威胁代价及油耗代价；然后，按照以上步骤，采用基于离差最大化法求出的各属性权重，采用灰色关联分析法求出航迹方案评价属性相对于参考属性集的灰色关联系数；最后，进行加权求和，求出各方案的决策层的关联度，根据关联度进行排序，并最终确定最优航迹方案。On the basis of ensuring that the above five constraints are met, 50 UAV two-dimensional and three-dimensional tracks are respectively determined as alternatives through the random search algorithm of the determined area; the two-dimensional track scheme of the UAV is shown in Figure 3 The three-dimensional track scheme of UAV is shown in Figure 4. The square in the figure is the starting point of the track, the five-pointed star is the track node, the solid circle is the target point, the rhombus is the radar threat point, and the lower triangle is the antiaircraft gun threat point. Hexagons are atmospheric threat points, and hollow circles are missile threat points. According to the trajectory map, calculate the initial attribute data of each trajectory, including radar, missile, anti-aircraft gun, atmospheric threat cost and fuel consumption cost; then, according to the above steps, use the weight of each attribute based on the deviation maximization method , using the gray relational analysis method to obtain the gray relational coefficient of the evaluation attribute of the track plan relative to the reference attribute set; finally, carry out weighted summation, obtain the relational degree of the decision-making level of each plan, sort according to the relational degree, and finally determine the most Excellent track plan.

Claims

1. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis is characterized in that comprising the steps:

(1) sets up unmanned aerial vehicle flight path evaluate alternatives attribute data matrix, adopt the deviation maximization method that each evaluation attributes is carried out objective tax power;

(2) adopt gray relative analysis method that each evaluation attributes data of unmanned aerial vehicle flight path scheme are handled;

(3) weight with each evaluation attributes of obtaining in the step (1) is weighted, and obtains the degree of association of each unmanned aerial vehicle flight path program decisions layer, with each unmanned aerial vehicle flight path schemes ranking, finally determines the optimal trajectory scheme according to the degree of association.

2. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis according to claim 1 is characterized in that: the theing contents are as follows of described step (1):

At first determine trajectory planning scheme collection by n unmanned aerial vehicle flight path scheme, m evaluation attributes according to each flight path scheme are set up the evaluation attributes data matrix, and carry out the dimensionless standardization processing, calculate each flight path scheme then with respect to the deviation between other each flight path schemes, and calculate total deviation, obtain the weight of each evaluation attributes at last, and carry out normalized, wherein n, m are the natural number greater than 1.

3. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis according to claim 1 is characterized in that: the theing contents are as follows of described step (2):

With the evaluation attributes data matrix set up in the step (1) as the gray system matrix, and carry out the dimensionless standardization processing, in n unmanned aerial vehicle flight path scheme, choose the maximal value of each evaluation attributes then, composition standard ideal scheme, with this ideal scheme as the reference sequence, n unmanned aerial vehicle flight path scheme distinguished sequence as a comparison, calculate the grey incidence coefficient of evaluation attributes between reference sequences and each comparative sequences, be that data relationship between reference sequences and each comparative sequences is pressed close to degree, obtain the grey incidence coefficient matrix of trajectory planning scheme collection gray system thus, wherein n is the natural number greater than 1.

4. the unmanned aerial vehicle flight path optimization method based on deviation maximization and grey correlation analysis according to claim 2, it is characterized in that: the number m of described evaluation attributes gets 5,5 evaluation attributes and is respectively oil consumption cost, threat radar cost, missile threat cost, antiaircraft gun threat cost and atmosphere threat cost.