技术领域technical field
本发明属于天线罩设计技术领域，具体涉及一种天线罩系统结构一体化优化算法。The invention belongs to the technical field of radome design, and in particular relates to an integrated optimization algorithm of a radome system structure.
背景技术Background technique
天线罩作为机载雷达系统的重要组成部分，能够保护天线免受外界严酷环境的影响。因天线罩的安装位置接近天线，会导致天线辐射电波的折射与反射，进而影响到天线的性能。天线罩对天线性能影响的主要参数包括：瞄准误差(Boresight error，BSE)与透波率(transmission coefficient，TC)，前者体现的是天线罩对天线指向精度的影响程度，后者反映的是天线罩对天线作用距离的削弱程度。As an important part of the airborne radar system, the radome can protect the antenna from the harsh external environment. Because the installation position of the radome is close to the antenna, it will cause the refraction and reflection of the radio waves radiated by the antenna, thereby affecting the performance of the antenna. The main parameters affecting the antenna performance by the radome include: Boresight error (BSE) and transmission coefficient (TC). The former reflects the influence of the radome on the antenna pointing accuracy, and the latter reflects the antenna. The extent to which the cover reduces the working distance of the antenna.
在天线罩优化设计中，基于变厚度罩体的设计方法得到了广泛的使用，特别是对于结构特殊的机载或弹载罩而言，这种设计方法有助于实现罩体各个空间位置的最佳透波特性。最基本的变厚度设计方法通过计算天线罩壁局部的射线入射角，根据平板介质透射特性求解该位置的局部厚度。但这种方法没有考虑带罩天线的远场特性，计算精度有限。基于进化算法的天线罩设计方法更精确，如Hsu采用模拟退火方法优化了单层天线罩的瞄准误差，Carlin研究了基于替代模型的粒子群算法，提高了瞄准误差优化的的计算效率。Meng与Cheng分别用遗传算法和免疫克隆算法优化了天线罩的瞄准误差与透波率。Xu借助多目标粒子群算法，优化了天线罩的瞄准误差、传输损耗，并进一步优化了罩厚度的方差。文献依靠对阵列单元激励的调节，实现了天线罩瞄准误差的优化。以上研究仅对天线罩体或者仅对天线阵列单元进行单独优化，分别实现瞄准误差与透波率的优化。实际中，天线与罩作为一个整体的系统，不应将二者割裂开来，应考虑天线与罩的一体化优化设计。In the optimization design of the radome, the design method based on the variable thickness cover has been widely used, especially for the airborne or bomb-borne cover with special structure, this design method is helpful to realize the different spatial positions of the cover. Best penetrating properties. The most basic variable thickness design method calculates the local ray incident angle of the radome wall, and solves the local thickness of the position according to the transmission characteristics of the plate medium. However, this method does not consider the far-field characteristics of the shielded antenna, and the calculation accuracy is limited. The radome design method based on the evolutionary algorithm is more accurate. For example, Hsu uses the simulated annealing method to optimize the aiming error of the single-layer radome. Carlin studies the particle swarm algorithm based on the surrogate model, which improves the calculation efficiency of aiming error optimization. Meng and Cheng optimized the aiming error and wave transmittance of the radome by using genetic algorithm and immune cloning algorithm respectively. With the help of multi-target particle swarm optimization, Xu optimized the aiming error and transmission loss of the radome, and further optimized the variance of the thickness of the radome. The literature relies on the adjustment of the excitation of the array element to realize the optimization of the aiming error of the radome. The above research only optimizes the radome or only the antenna array unit to achieve the optimization of aiming error and wave transmittance respectively. In practice, the antenna and the cover as a whole system should not be separated, and the integrated optimization design of the antenna and the cover should be considered.
因此，对天线罩壁结构优化是天线罩电性能设计的有效方法，因传统的变厚度天线罩优化算法仅对天线罩进行优化，无法实现对天线与罩的一体化优化。针对相控阵天线-罩系统，本申请提出一种天线罩系统结构一体化优化算法，实现瞄准误差与透波率的联合优化。Therefore, optimizing the structure of the radome wall is an effective method to design the electrical performance of the radome, because the traditional optimization algorithm of the radome with variable thickness only optimizes the radome, and cannot realize the integrated optimization of the antenna and the cover. For the phased array antenna-cover system, the present application proposes an integrated optimization algorithm for the structure of the antenna cover system, which realizes the joint optimization of aiming error and wave transmittance.
发明内容SUMMARY OF THE INVENTION
为了克服上述现有技术存在的不足，本发明提供了一种天线罩系统结构一体化优化算法。In order to overcome the above-mentioned deficiencies in the prior art, the present invention provides an integrated optimization algorithm for the structure of a radome system.
为了实现上述目的，本发明提供如下技术方案：In order to achieve the above object, the present invention provides the following technical solutions:
天线罩系统结构一体化优化算法，包括以下步骤：The integrated optimization algorithm of the radome system structure includes the following steps:
利用天线罩的瞄准误差和透波率评价所设计天线罩的性能，这两个参数的获取均以天线-罩系统的远场计算为前提；根据设计指标确定天线罩与天线的基本参数，所述参数包括罩体形状、罩外部轮廓尺寸、罩壁结构、阵列单元数，建立相控阵天线-罩系统模型，具体包括以下步骤：The aiming error and wave transmittance of the radome are used to evaluate the performance of the designed radome. The acquisition of these two parameters is based on the far-field calculation of the radome system; the basic parameters of the radome and the antenna are determined according to the design indicators. The above parameters include the shape of the cover body, the outer contour size of the cover, the structure of the cover wall, and the number of array elements, and the phased array antenna-cover system model is established, which includes the following steps:
步骤1、通过远场计算，获取天线罩与天线参数，得到天线罩阵列单元，计算天线罩阵列单元的激励电流；Step 1. Obtain the radome and antenna parameters through far-field calculation, obtain the radome array unit, and calculate the excitation current of the radome array unit;
用一组无限长电流源代表罩内的阵列天线，每个阵元天线罩阵列单元的电流为：A set of infinite current sources is used to represent the array antenna inside the cover, and the current of each element radome array element is:
其中，m为阵元序号，A与φ分别代表电流的幅度与相位，M为阵列单元数，e为自然常数，j为虚数单位；Among them, m is the array element serial number, A and φ represent the amplitude and phase of the current respectively, M is the number of array elements, e is a natural constant, and j is an imaginary unit;
步骤2、辐射场计算Step 2. Radiation field calculation
步骤2.1、罩内辐射场Step 2.1. Radiation field inside the cover
天线阵的辐射电场仅有z向分量，天线罩内表面第p个剖分单元处的入射电场为：The radiated electric field of the antenna array has only the z-direction component, and the incident electric field at the p-th subdivision element on the inner surface of the radome is:
其中，d是罩内总的剖分单元数，ω是电磁波角频率，μ0是自由空间导磁率，H0(2)为第二类零阶汉克尔函数，k是自由空间波数，ρpn为源点n与场点p的距离；罩内表面入射磁场的x分量为：where d is the total number of subdivision elements in the enclosure, ω is the angular frequency of the electromagnetic wave, μ0 is the free-space permeability, H0(2) is the second kind of zero-order Hankel function, k is the free-space wave number, ρpn is the distance between the source point n and the field point p; the x component of the incident magnetic field on the inner surface of the cover is:
其中，yn和yp分别是源点n与场点p的y坐标，为第一类零阶汉克尔函数，j为虚数单位；where yn and yp are the y-coordinates of the source point n and the field point p, respectively, is the zero-order Hankel function of the first kind, and j is an imaginary unit;
罩内表面入射磁场的y分量为：The y-component of the incident magnetic field on the inner surface of the cover is:
其中，xn和xp分别是源点n与场点d的x坐标；where xn andxp are the x-coordinates of source pointn and field point d, respectively;
将电流激励源、罩内表面入射电场、入射磁场的x分量和y分量分别用矩阵表示，即The current excitation source, the incident electric field on the inner surface of the cover, the x component and the y component of the incident magnetic field are respectively represented by a matrix, namely
针对全部d个罩内离散点，罩内表面入射电场、入射磁场表示为矩阵形式：For all d discrete points in the hood, the incident electric field and incident magnetic field on the inner surface of the hood are expressed in matrix form:
E＝W1I (9)E=W1 I (9)
Hx＝W2I (10)Hx =W2 I (10)
Hy＝W3I (11)Hy =W3 I (11)
其中，in,
在进行天线罩内辐射场计算时，预先计算矩阵W1、W2和W3并存储；When calculating the radiation field in the radome, the matrices W1 , W2 and W3 are pre-calculated and stored;
步骤2.2、罩外辐射场Step 2.2. Radiation field outside the cover
天线罩外表面上的切向电场Et与切向磁场Ht分别为：The tangential electric field Et and tangential magnetic field Ht on the outer surface of the radome are respectively:
Et＝[(b·Ei)b]T⊥+[(t·Ei)t]T// (15)Et =[(b·Ei )b]T⊥ +[(t·Ei )t]T// (15)
Ht＝[(b·Hi)b]T//+[(t·Hi)t]T⊥ (16)Ht =[(b·Hi )b]T// +[(t·Hi )t]T⊥ (16)
其中，Ei为天线罩内表面上的入射电场，Hi为天线罩内表面上的入射磁场，T//为平行极化传输系数，T⊥为垂直极化传输系数，b为入射面的垂直极化方向单位矢量，t为平行极化方向单位矢量；基于局部平板近似原理，根据入射角、罩厚、罩介电常数ε，借助传输线矩阵法求得T//与T⊥；Among them, Ei is the incident electric field on the inner surface of the radome, Hi is the incident magnetic field on the inner surface of the radome, T// is the transmission coefficient of parallel polarization, T⊥ is the transmission coefficient of vertical polarization, and b is the incident surface Unit vector in the vertical polarization direction, t is the unit vector in the parallel polarization direction; T// and T⊥ are obtained by means of the transmission line matrix method based on the local flat plate approximation principle, according to the incident angle, the thickness of the cover, and the dielectric constant ε of the cover;
罩外表面上的等效电磁流可表示为：The equivalent electromagnetic current on the outer surface of the cover can be expressed as:
J＝a×Ht (17)J=a×Ht (17)
M'＝Et×a (18)M'=Et ×a (18)
其中，J为等效电流，M'为等效磁流，a为该等效面的单位外法向矢量；Among them, J is the equivalent current, M' is the equivalent magnetic current, and a is the unit outer normal vector of the equivalent surface;
二维空间中的等效电磁流的辐射场为：The radiation field of the equivalent electromagnetic current in two-dimensional space is:
其中，ρ为罩外表面点与远场点之间的距离矢量，l为罩的外表面轮廓；当ρ→∞时，利用汉克尔函数对公式(19)进行渐进展开简化，并将其表示为标量形式：Among them, ρ is the distance vector between the outer surface point of the cover and the far-field point, and l is the outer surface contour of the cover; when ρ→∞, the Hankel function is used to progressively expand and simplify the formula (19), and it is Represented in scalar form:
其中，π为圆周率，e为自然常数，为远场单位方向矢量，ρ′为罩外表面点的位置矢量，n′为罩外表面点的外法向方向矢量，η为无耗媒质本质阻抗；Among them, π is pi, e is a natural constant, is the unit direction vector of the far field, ρ' is the position vector of the point on the outer surface of the cover, n' is the outer normal direction vector of the point on the outer surface of the cover, η is the intrinsic impedance of the lossless medium;
将公式(20)转换为数值积分，得到罩外第q个表面点处的远场：Converting Equation (20) to a numerical integration yields the far field at the qth surface point outside the hood:
其中，d为罩外表面剖分单元的编号，为第d单元的远场单位方向矢量，np为第d单元的外法向方向矢量，Mp为第d单元的等效磁流，Jp为第d单元的等效电流，ρp为第d单元的位置矢量，lp为罩外表面第d单元的剖分区间长度；Among them, d is the number of the division unit of the outer surface of the cover, is the far-field unit direction vector of the d-th unit, np is the outer normal direction vector of the d-th unit, Mp is the equivalent magnetic current of the d-th unit, Jp is the equivalent current of the d-th unit, and ρp is The position vector of the d-th unit, and lp is the length of the division interval of the d-th unit on the outer surface of the cover;
假定罩外共有Q个远场点，将远场辐射场用矩阵形式表示：Assuming that there are Q far-field points outside the cover, the far-field radiation field is represented in matrix form:
则罩外辐射远场表示为矩阵形式：Then the radiated far field outside the hood is expressed in matrix form:
Efar＝wW4M-wW5J (23)Efar = wW4 M-wW5 J (23)
且and
当天线和天线罩确定后，天线罩外形与位置并不发生变化，系数w与矩阵W4、W5可预先计算并存储；After the antenna and the radome are determined, the shape and position of the radome do not change, and the coefficient w and the matrices W4 and W5 can be pre-calculated and stored;
步骤3、天线罩系统结构一体化优化算法Step 3. Radome system structure integration optimization algorithm
步骤3.1、天线罩系统结构一体化优化模型Step 3.1, the integrated optimization model of the radome system structure
设定天线罩的结构参数用Xr表示，代表天线罩上有限个站位点处的可变厚度芯层的厚度，天线罩其他站位点处的芯层厚度通过对Xr样条插值得到；设定天线辐射参数用Xa表示，代表天线各个天线罩阵列单元上的激励变化，包括相位的补偿与幅值的调整，其维数由天线罩阵列单元数目决定；设定G代表带罩天线阵列的指标参数，包括瞄准误差G1与透波率G2；The structural parameters of the radome are denoted by Xr , which represents the thickness of the variable-thickness core layer at a limited number of sites on the radome. The thickness of the core layer at other sites of the radome is obtained by interpolating the Xr spline. ; Set the antenna radiation parameter to be represented by Xa , which represents the excitation change on each radome array unit of the antenna, including the compensation of the phase and the adjustment of the amplitude, and its dimension is determined by the number of radome array elements; set G to represent the band cover The index parameters of the antenna array, including the aiming error G1 and the wave transmittance G2 ;
根据天线罩结构参数Xr和天线辐射参数Xa，计算带罩天线在空间各个方向上的远场辐射强度，画出差方向图，然后找到差方向图的零深方向，该方向与天线期望指向的偏差称为瞄准误差，用G1＝B(Xr，Xa，θ)表示，其中θ表示天线扫描角，也即天线的期望指向角；透波率是指加罩前后，最大辐射方向上的远场强度比值，用G2＝P(Xr，Xa，θ)表示；According to the radome structure parameter Xr and the antenna radiation parameter Xa , calculate the far-field radiation intensity of the antenna with the cover in all directions in space, draw the difference pattern, and then find the zero-depth direction of the difference pattern, which is the same as the antenna's desired direction. The deviation is called aiming error, which is expressed by G1 =B(Xr , Xa , θ), where θ represents the scanning angle of the antenna, that is, the desired pointing angle of the antenna; the wave transmittance refers to the maximum radiation direction before and after the cover is applied. The far-field intensity ratio on , expressed by G2 =P(Xr , Xa , θ);
将所有扫描角下的瞄准误差与透波率作为整体目标进行优化，建立的天线罩系统结构一体化优化模型为：The aiming error and wave transmittance under all scanning angles are optimized as the overall goal, and the integrated optimization model of the radome system structure is established as follows:
其中，F为对带罩天线系统的总体评价，S为扫描角的总数，s为扫描角的编号，U为带罩天线阵列的指标参数总数，u为指标参数的编号，v(θs)是对应于扫描角θs的权重函数，wu代表指标参数Gu的权重因子，Dr与Da是Xr与Xa的取值空间；Among them, F is the overall evaluation of the antenna system with cover, S is the total number of scan angles,s is the number of scan angles,U is the total number of index parameters of the antenna array with cover,u is the number of index parameters, v(θs ) is the weight function corresponding to the scanning angle θs ,wu represents the weight factor of the index parameterGu , Dr and Da are the value spaces of Xr and Xa ;
在公式(27)代表的一体化优化模型中，调节罩参数Xr与天线参数Xa，以使多个扫描角下的瞄准误差G1与透波率G2达到最优；In the integrated optimization model represented by formula (27), adjust the cover parameter Xr and the antenna parameter Xa , so as to optimize the aiming error G1 and the wave transmittance G2 under multiple scanning angles;
步骤3.2、一体化优化算法的实现过程Step 3.2, the implementation process of the integrated optimization algorithm
利用算子分离思想对优化模型进行求解，采用两步优化策略；The optimization model is solved by using the operator separation idea, and a two-step optimization strategy is adopted;
首先，保持天线辐射参数Xa不变，利用传统的变厚度天线罩优化方法对天线罩结构参数Xr进行优化；然后，保持天线罩结构参数Xr不变，利用粒子群算法对天线辐射参数Xa进行优化；First, keep the antenna radiation parameter Xa constant, and use the traditional variable thickness radome optimization method to optimize the radome structure parameter Xr ; then, keep the radome structure parameter Xr unchanged, use particle swarm algorithm to optimize the antenna radiation parameter Xa is optimized;
利用粒子群算法对天线辐射参数进行优化的实现过程如下；The realization process of using particle swarm algorithm to optimize the antenna radiation parameters is as follows;
每个粒子都代表优化问题的一个潜在最优解，用位置、速度和适应度值三项指标表示该粒子特征；Each particle represents a potential optimal solution of the optimization problem, and the particle characteristics are represented by three indicators of position, velocity and fitness value;
假设搜索空间的维数是L，M个粒子组成种群Z＝(Z1,Z2,...,Zi,...,ZM)，其中第i个粒子的位置表示为向量Zi＝(zi1,zi2,...,zil,...,ziL)，速度表示为Vi＝(vi1,vi2,...,vil,...,viL)，l＝1,2,...,L；根据适应度函数即可计算出粒子Zi对应的适应度值，其个体极值为Pbesti＝(Pi1,Pi2,...,Pil,...,PiL)，种群的群体极值为Gbest＝(G1,G2,...,Gl,...,GL)；粒子通过跟踪个体极值Pbest和群体极值Gbest更新自身的速度和位置，即：Assuming that the dimension of the search space is L, M particles form a population Z = (Z1 , Z2 ,...,Zi ,...,ZM ), where the position of the i-th particle is represented as a vector Zi =(zi1 ,zi2 ,...,zil ,...,ziL ), the velocity is expressed as Vi =(vi1 ,vi2 ,...,vil ,...,viL ) , l=1,2,...,L; the fitness value corresponding to particle Zi can be calculated according to the fitness function, and its individual extreme value is Pbesti =(Pi1 ,Pi2 ,...,Pil ,...,PiL ), the groupextreme value of the population is Gbest =(G1 ,G2 ,...,Gl ,...,GL ); The group extremum Gbest updates its own speed and position, namely:
其中，c为惯性权重，iter为迭代次数；c1和c2是非负的常数，称为加速度因子；r1和r2是分布于[0,1]区间的随机数；Among them, c is the inertia weight, iter is the number of iterations; c1 and c2 are non-negative constants called acceleration factors; r1 and r2 are random numbers distributed in the [0,1] interval;
利用粒子群算法实现天线辐射参数优化的实现过程包括三个方面：粒子位置和适应度、粒子初始化及粒子更新；The realization process of using particle swarm optimization algorithm to realize the optimization of antenna radiation parameters includes three aspects: particle position and fitness, particle initialization and particle update;
(1)粒子位置和适应度(1) Particle position and fitness
当天线罩阵列单元个数为M'时，搜索空间为L＝2M'，前M'维是天线罩阵列单元电流的相位，后M'维是天线罩阵列单元电流的幅度；定义粒子为一个2M'维的向量，向量元素的取值范围是Da；为同时优化瞄准误差与透波率，将适应度函数定义为：When the number of radome array elements is M', the search space is L=2M', the first M' dimension is the phase of the radome array element current, and the latter M' dimension is the amplitude of the radome array element current; the definition particle is a2M' -dimensional vector, the value range of the vector element is Da; in order to optimize the aiming error and the wave transmittance at the same time, the fitness function is defined as:
其中，w1与w2是瞄准误差B(Xr，Xa，θs)与透波率P(Xr，Xa，θs)的权重系数，决定了两个优化目标的优先程度；v(θs)是对应于扫描角θs的权重函数；Bmax是优化之前，各扫描角的最大瞄准误差，Pmax与Pmin是优化之前的最大与最小透波率；Among them, w1 and w2 are the weight coefficients of aiming error B (Xr , Xa , θs ) and wave transmittance P (Xr , Xa , θs ), which determine the priority of the two optimization goals; v(θs ) is the weight function corresponding to the scanning angle θs ; Bmax is the maximum aiming error of each scanning angle before optimization, Pmax and Pmin are the maximum and minimum wave transmittances before optimization;
(2)粒子初始化(2) Particle initialization
第i个粒子的初始位置为初始群体为计算每个粒子的适应度，设置第i个粒子的最优位置为初始群体极值设置为同时设置每个粒子的初始速度，其每个变量的速度范围是对应位置范围的一半；The initial position of the i-th particle is The initial group is Calculate the fitness of each particle, and set the optimal position of the i-th particle as The initial population extrema is set to At the same time, the initial speed of each particle is set, and the speed range of each variable is half of the corresponding position range;
(3)粒子更新(3) Particle update
在迭代过程中，根据公式(28)更新每个粒子的速度，更新后需要检查粒子速度是否在速度范围内，如果否，则用边界值替代.然后根据公式(29)更新每个粒子的位置；计算更新后粒子的适应度，如果粒子适应度小于它的个体极值，即则更新个体极值位置否则保持不变；同时根据更新后的个体极值，更新群体极值位置Gbest；In the iterative process, the velocity of each particle is updated according to formula (28). After the update, it is necessary to check whether the particle velocity is within the velocity range. If not, replace it with the boundary value. Then update the position of each particle according to formula (29). ; Calculate the fitness of the updated particle, if the fitness of the particle is less than its individual extreme value, that is Then update the individual extreme value position Otherwise, it remains unchanged; at the same time, according to the updated individual extreme value, the group extreme value position Gbest is updated;
通过不断的迭代，则可搜索到具有最小适应度值的天线辐射参数Xa，并对天线罩阵列单元电流的相位和幅度进行调整，能够保证瞄准误差最小、透波率最高，实现带罩天线系统的一体化优化设计。Through continuous iteration, the antenna radiation parameter Xa with the smallest fitness value can be searched, and the phase and amplitude of the current of the radome array unit can be adjusted, which can ensure the smallest aiming error and the highest wave transmittance, and realize the antenna with cover Integrated optimization design of the system.
本发明提供的天线罩系统结构一体化优化算法通过分析天线罩结构参数与天线辐射参数对瞄准误差与透波率的影响，建立天线罩系统结构设计的优化模型；借助算子分离的思想，对天线罩结构参数和天线辐射参数采用不同的优化策略；利用变厚度天线罩优化方法对天线罩结构参数进行优化，并采用粒子群算法对天线辐射参数进行优化，实现天线罩系统结构的一体化优化。实验结果表明，与传统的变厚度天线罩优化算法相比，本实施例提供的算法的瞄准误差更低，透波率更高，充分表明本实施例提供的算法的有效性。The integrated optimization algorithm of the radome system structure provided by the present invention establishes an optimization model for the structure design of the radome system by analyzing the influence of the radome structure parameters and antenna radiation parameters on the aiming error and wave transmittance; Different optimization strategies are used for radome structural parameters and antenna radiation parameters; the radome structural parameters are optimized by the variable thickness radome optimization method, and the antenna radiation parameters are optimized by particle swarm algorithm to realize the integrated optimization of the radome system structure. . Experimental results show that, compared with the traditional variable thickness radome optimization algorithm, the algorithm provided by this embodiment has lower aiming error and higher wave transmittance, which fully demonstrates the effectiveness of the algorithm provided by this embodiment.
附图说明Description of drawings
图1为本实施例提供的天线罩系统结构一体化优化算法的相控阵天线-罩系统模型；FIG. 1 is a phased array antenna-cover system model of the integrated optimization algorithm of the radome system structure provided by the present embodiment;
图2为瞄准误差随扫描角的变化曲线；Fig. 2 is the change curve of aiming error with scanning angle;
图3为透波率随扫描角的变化曲线；Fig. 3 is the change curve of wave transmittance with the scanning angle;
图4为A夹层天线罩优化后的芯层厚度分布曲线；Figure 4 is the core layer thickness distribution curve after optimization of the A sandwich radome;
图5为IO-RPA优化得到的补偿相位与电流幅度曲线。Figure 5 shows the compensation phase and current amplitude curves obtained by IO-RPA optimization.
具体实施方式Detailed ways
下面结合附图，对本发明的具体实施方式作进一步描述。以下实施例仅用于更加清楚地说明本发明的技术方案，而不能以此来限制本发明的保护范围。The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. The following examples are only used to illustrate the technical solutions of the present invention more clearly, and cannot be used to limit the protection scope of the present invention.
实施例1Example 1
本发明提供了一种天线罩系统结构一体化优化算法，利用天线罩的瞄准误差和透波率评价所设计天线罩的性能，这两个参数的获取均以天线-罩系统的远场计算为前提；首先给出相控阵天线-罩系统模型，然后采用AI-SI方法计算远场辐射场，为瞄准误差和透波率的计算提供依据，具体包括以下步骤：The invention provides an integrated optimization algorithm for the structure of a radome system. The aiming error and wave transmittance of the radome are used to evaluate the performance of the designed radome. The acquisition of these two parameters is based on the far-field calculation of the radome system The premise; firstly, the phased array antenna-cover system model is given, and then the AI-SI method is used to calculate the far-field radiation field, which provides a basis for the calculation of aiming error and wave transmittance, which includes the following steps:
步骤1、通过远场计算，获取天线罩与天线参数，得到天线罩阵列单元，计算天线罩阵列单元的激励电流；Step 1. Obtain the radome and antenna parameters through far-field calculation, obtain the radome array unit, and calculate the excitation current of the radome array unit;
用一组无限长电流源代表罩内的阵列天线，每个阵元天线罩阵列单元的电流为：A set of infinite current sources is used to represent the array antenna inside the cover, and the current of each element radome array element is:
相控阵天线-罩系统模型如图1所示，其中，n为阵元序号，A与φ分别代表电流的幅度与相位，N为阵列单元数，e为自然常数，j为虚数单位；The phased array antenna-cover system model is shown in Figure 1, where n is the array element serial number, A and φ represent the amplitude and phase of the current respectively, N is the number of array elements, e is a natural constant, and j is an imaginary unit;
步骤2、辐射场计算Step 2. Radiation field calculation
步骤2.1、罩内辐射场Step 2.1. Radiation field inside the cover
天线阵的辐射电场仅有z向分量，天线罩内表面第p个剖分单元处的入射电场为：The radiated electric field of the antenna array has only the z-direction component, and the incident electric field at the p-th subdivision element on the inner surface of the radome is:
其中，d是罩内总的剖分单元数，ω是电磁波角频率，μ0是自由空间导磁率，为第二类零阶汉克尔函数，k是自由空间波数，ρpn为源点n与场点p的距离；罩内表面入射磁场的x分量为：where d is the total number of subdivision elements in the enclosure, ω is the electromagnetic wave angular frequency, μ0 is the free space permeability, is the second type of zero-order Hankel function, k is the free space wave number, ρpn is the distance between the source point n and the field point p; the x component of the incident magnetic field on the inner surface of the cover is:
其中，yn和yp分别是源点n与场点p的y坐标，为第一类零阶汉克尔函数，j为虚数单位；where yn and yp are the y-coordinates of the source point n and the field point p, respectively, is the zero-order Hankel function of the first kind, and j is an imaginary unit;
罩内表面入射磁场的y分量为：The y-component of the incident magnetic field on the inner surface of the cover is:
其中，xn和xp分别是源点n与场点d的x坐标；where xn andxp are the x-coordinates of source pointn and field point d, respectively;
将电流激励源、罩内表面入射电场、入射磁场的x分量和y分量分别用矩阵表示，即The current excitation source, the incident electric field on the inner surface of the cover, the x component and the y component of the incident magnetic field are respectively represented by a matrix, namely
针对全部d个罩内离散点，罩内表面入射电场、入射磁场表示为矩阵形式：For all d discrete points in the hood, the incident electric field and incident magnetic field on the inner surface of the hood are expressed in matrix form:
E＝W1I (9)E=W1 I (9)
Hx＝W2I (10)Hx =W2 I (10)
Hy＝W3I (11)Hy =W3 I (11)
其中，in,
分析矩阵W1、W2和W3，发现它们的每个元素代表的是辐射场与源点之间的空间位置关系，与源电流特性无关；在进行天线罩内辐射场计算时，可预先计算矩阵W1、W2和W3并存储，以提高辐射场的求解速度；Analyzing the matrices W1 , W2 and W3 , it is found that each element of them represents the spatial position relationship between the radiation field and the source point, and has nothing to do with the source current characteristics; when calculating the radiation field in the radome, it can be pre- Calculate and store the matrices W1 , W2 and W3 to improve the speed of solving the radiation field;
步骤2.2、罩外辐射场Step 2.2. Radiation field outside the cover
天线罩外表面上的切向电场Et与切向磁场Ht分别为：The tangential electric field Et and tangential magnetic field Ht on the outer surface of the radome are respectively:
Et＝[(b·Ei)b]T⊥+[(t·Ei)t]T// (15)Et=[(b·Ei )b]T⊥ +[(t·Ei )t]T// (15)
Ht＝[(b·Hi)b]T//+[(t·Hi)t]T⊥ (16)Ht =[(b·Hi )b]T// +[(t·Hi )t]T⊥ (16)
其中，Ei为天线罩内表面上的入射电场，Hi为天线罩内表面上的入射磁场，T//为平行极化传输系数，T⊥为垂直极化传输系数，b为入射面的垂直极化方向单位矢量，t为平行极化方向单位矢量；基于局部平板近似原理，根据入射角、罩厚、罩介电常数ε，借助传输线矩阵法求得T//与T⊥；Among them, Ei is the incident electric field on the inner surface of the radome, Hi is the incident magnetic field on the inner surface of the radome, T// is the transmission coefficient of parallel polarization, T⊥ is the transmission coefficient of vertical polarization, and b is the incident surface Unit vector in the vertical polarization direction, t is the unit vector in the parallel polarization direction; T// and T⊥ are obtained by means of the transmission line matrix method based on the local flat plate approximation principle, according to the incident angle, the thickness of the cover, and the dielectric constant ε of the cover;
罩外表面上的等效电磁流可表示为：The equivalent electromagnetic current on the outer surface of the cover can be expressed as:
J＝a×Ht (17)J=a×Ht (17)
M'＝Et×a (18)M'=Et ×a (18)
其中，J为等效电流，M'为等效磁流，a为该等效面的单位外法向矢量；Among them, J is the equivalent current, M' is the equivalent magnetic current, and a is the unit outer normal vector of the equivalent surface;
二维空间中的等效电磁流的辐射场为：The radiation field of the equivalent electromagnetic current in two-dimensional space is:
其中，ρ为罩外表面点与远场点之间的距离矢量，l为罩的外表面轮廓；当ρ→∞时，利用汉克尔函数对公式(19)进行渐进展开简化，并将其表示为标量形式：Among them, ρ is the distance vector between the outer surface point of the cover and the far-field point, and l is the outer surface contour of the cover; when ρ→∞, the Hankel function is used to progressively expand and simplify the formula (19), and it is Represented in scalar form:
其中，π为圆周率，e为自然常数，为远场单位方向矢量，ρ′为罩外表面点的位置矢量，n′为罩外表面点的外法向方向矢量，η为无耗媒质本质阻抗；Among them, π is pi, e is a natural constant, is the unit direction vector of the far field, ρ' is the position vector of the point on the outer surface of the cover, n' is the outer normal direction vector of the point on the outer surface of the cover, η is the intrinsic impedance of the lossless medium;
将公式(20)转换为数值积分，得到罩外第q个表面点处的远场：Converting Equation (20) to a numerical integration yields the far field at the qth surface point outside the hood:
其中，d为罩外表面剖分单元的编号，为第d单元的远场单位方向矢量，Among them, d is the number of the division unit of the outer surface of the cover, is the far-field unit direction vector of the d-th unit,
np为第d单元的外法向方向矢量，Mp为第d单元的等效磁流，Jp为第d单元的等效电流，ρp为第d单元的位置矢量，lp为罩外表面第d单元的剖分区间长度；np is the outer normal direction vector of the d-th unit, Mp is the equivalent magnetic current of the d-th unit, Jp is the equivalent current of the d-th unit, ρp is the position vector of the d-th unit, and lp is the cover The length of the division interval of the dth element on the outer surface;
假定罩外共有Q个远场点，将远场辐射场用矩阵形式表示：Assuming that there are Q far-field points outside the cover, the far-field radiation field is represented in matrix form:
则罩外辐射远场表示为矩阵形式：Then the radiated far field outside the hood is expressed in matrix form:
Efar＝wW4M-wW5J (23)Efar = wW4 M-wW5 J (23)
且and
当天线和天线罩确定后，天线罩外形与位置并不发生变化，系数w与矩阵W4、W5可预先计算并存储，以提高罩外辐射远场计算的效率；After the antenna and the radome are determined, the shape and position of the radome do not change, and the coefficient w and the matrices W4 and W5 can be pre-calculated and stored to improve the calculation efficiency of the far-field radiation outside the hood;
步骤3、天线罩系统结构一体化优化算法Step 3. Radome system structure integration optimization algorithm
分析瞄准误差和透波率与天线罩结构参数及天线辐射参数的关系，建立天线罩系统结构设计的优化模型；在算子分离思想的基础上，以瞄准误差和透波率为优化目标，设计两步优化策略，采用传统的变厚度优化方法对天线罩结构参数进行优化，并利用粒子群算法对天线辐射参数进行优化，给出一体化优化算法的实现过程；The relationship between aiming error and wave transmittance and radome structural parameters and antenna radiation parameters is analyzed, and an optimization model for radome system structure design is established. The two-step optimization strategy adopts the traditional variable thickness optimization method to optimize the radome structural parameters, and uses the particle swarm algorithm to optimize the antenna radiation parameters, and gives the realization process of the integrated optimization algorithm;
步骤3.1、天线罩系统结构一体化优化模型Step 3.1, the integrated optimization model of the radome system structure
设定天线罩的结构参数用Xr表示，代表天线罩上有限个站位点处的可变厚度芯层的厚度，天线罩其他站位点处的芯层厚度通过对Xr样条插值得到；设定天线辐射参数用Xa表示，代表天线各个天线罩阵列单元上的激励变化，包括相位的补偿与幅值的调整，其维数由天线罩阵列单元数目决定；设定G代表带罩天线阵列的指标参数，包括瞄准误差G1与透波率G2；The structural parameters of the radome are denoted by Xr , which represents the thickness of the variable-thickness core layer at a limited number of sites on the radome. The thickness of the core layer at other sites of the radome is obtained by interpolating the Xr spline. ; Set the antenna radiation parameter to be represented by Xa , which represents the excitation change on each radome array unit of the antenna, including the compensation of the phase and the adjustment of the amplitude, and its dimension is determined by the number of radome array elements; set G to represent the band cover The index parameters of the antenna array, including the aiming error G1 and the wave transmittance G2 ;
根据天线罩结构参数Xr和天线辐射参数Xa，计算带罩天线在空间各个方向上的远场辐射强度，画出差方向图，然后找到差方向图的零深方向，该方向与天线期望指向的偏差称为瞄准误差，用G1＝B(Xr，Xa，θ)表示，其中θ表示天线扫描角，也即天线的期望指向角；透波率是指加罩前后，最大辐射方向上的远场强度比值，用G2＝P(Xr，Xa，θ)表示；According to the radome structure parameter Xr and the antenna radiation parameter Xa , calculate the far-field radiation intensity of the antenna with the cover in all directions in space, draw the difference pattern, and then find the zero-depth direction of the difference pattern, which is the same as the antenna's desired direction. The deviation is called aiming error, which is expressed by G1 =B(Xr , Xa , θ), where θ represents the scanning angle of the antenna, that is, the desired pointing angle of the antenna; the wave transmittance refers to the maximum radiation direction before and after the cover is applied. The far-field intensity ratio on , expressed by G2 =P(Xr , Xa , θ);
将所有扫描角下的瞄准误差与透波率作为整体目标进行优化，建立的天线罩系统结构一体化优化模型为：The aiming error and wave transmittance under all scanning angles are optimized as the overall goal, and the integrated optimization model of the radome system structure is established as follows:
其中，F为对带罩天线系统的总体评价，S为扫描角的总数，s为扫描角的编号，U为带罩天线阵列的指标参数总数，u为指标参数的编号，v(θs)是对应于扫描角θs的权重函数，wu代表指标参数Gu的权重因子，Dr与Da是Xr与Xa的取值空间；Among them, F is the overall evaluation of the antenna system with cover, S is the total number of scan angles,s is the number of scan angles,U is the total number of index parameters of the antenna array with cover,u is the number of index parameters, v(θs ) is the weight function corresponding to the scanning angle θs ,wu represents the weight factor of the index parameterGu , Dr and Da are the value spaces of Xr and Xa ;
在公式(27)代表的一体化优化模型中，调节罩参数Xr与天线参数Xa，以使多个扫描角下的瞄准误差G1与透波率G2达到最优；这是一个多变量多目标优化的问题，如何保证优化的精度和效率是实现天线罩结构一体化优化的关键；In the integrated optimization model represented by formula (27), the hood parameter Xr and the antenna parameter Xa are adjusted to optimize the aiming error G1 and the wave transmittance G2 under multiple scanning angles; For the problem of variable multi-objective optimization, how to ensure the accuracy and efficiency of the optimization is the key to realize the integrated optimization of the radome structure;
步骤3.2、一体化优化算法的实现过程Step 3.2, the implementation process of the integrated optimization algorithm
一体化优化模型是典型的多目标优化问题，可采用进化算法进行求解；但因模型中的可变参数过多，计算负担沉重，以致难以求出最优解；考虑到罩体厚度不存在剧烈波动，可以认为罩内任意位置上的辐射来波入射角不会因罩体厚度与天线罩阵列单元激励的调节而变化，Xr与Xa没有耦合关系；因此利用算子分离思想对优化模型进行求解，采用两步优化策略；The integrated optimization model is a typical multi-objective optimization problem, which can be solved by an evolutionary algorithm; however, due to too many variable parameters in the model, the computational burden is heavy, so that it is difficult to find the optimal solution; considering that the thickness of the cover does not have severe fluctuation, it can be considered that the incident angle of incoming radiation at any position in the cover will not change due to the thickness of the cover and the adjustment of the excitation of the radome array unit, and Xr and Xa have no coupling relationship; therefore, the optimization model is optimized by using the operator separation idea. To solve, adopt a two-step optimization strategy;
首先，保持天线辐射参数Xa不变，利用传统的变厚度天线罩优化方法对天线罩结构参数Xr进行优化；然后，保持天线罩结构参数Xr不变，利用粒子群算法对天线辐射参数Xa进行优化；传统的变厚度天线罩优化方法此处不再赘述，下面分析利用粒子群算法对天线辐射参数进行优化的实现过程；First, keep the antenna radiation parameter Xa constant, and use the traditional variable thickness radome optimization method to optimize the radome structure parameter Xr ; then, keep the radome structure parameter Xr unchanged, use particle swarm algorithm to optimize the antenna radiation parameter Xa is optimized; the traditional variable thickness radome optimization method will not be repeated here, and the implementation process of optimizing the antenna radiation parameters by using the particle swarm algorithm is analyzed below;
每个粒子都代表优化问题的一个潜在最优解，用位置、速度和适应度值三项指标表示该粒子特征；Each particle represents a potential optimal solution of the optimization problem, and the particle characteristics are represented by three indicators of position, velocity and fitness value;
假设搜索空间的维数是L，M'个粒子组成种群Z＝(Z1,Z2,...,Zi,...,ZM)，其中第i个粒子的位置表示为向量Zi＝(zi1,zi2,...,zil,...,ziL)，速度表示为Vi＝(vi1,vi2,...,vil,...,viL)，l＝1,2,...,L；根据适应度函数即可计算出粒子Zi对应的适应度值，其个体极值为Pbesti＝(Pi1,Pi2,...,Pil,...,PiL)，种群的群体极值为Gbest＝(G1,G2,...,Gl,...,GL)；粒子通过跟踪个体极值Pbest和群体极值Gbest更新自身的速度和位置，即：Assuming that the dimension of the search space is L, M' particles form a population Z=(Z1 , Z2 ,...,Zi ,...,ZM ), where the position of the i-th particle is represented by the vector Zi =(zi1 ,zi2 ,...,zil ,...,ziL ), the velocity is expressed as Vi =(vi1 ,vi2 ,...,vil ,...,viL ), l=1,2,...,L; the fitness value corresponding to particle Zi can be calculated according to the fitness function, and its individual extreme value is Pbesti =(Pi1 ,Pi2 ,..., Pil ,...,PiL ), the groupextreme value of the population is Gbest =(G1 ,G2 ,...,Gl ,...,GL ); and the group extremum Gbest to update its own speed and position, namely:
其中，c为惯性权重，iter为迭代次数；c1和c2是非负的常数，称为加速度因子；r1和r2是分布于[0,1]区间的随机数；Among them, c is the inertia weight, iter is the number of iterations; c1 and c2 are non-negative constants called acceleration factors; r1 and r2 are random numbers distributed in the [0,1] interval;
优化模型需要兼顾瞄准误差与透波率两个参数，若利用传统的多目标粒子群算法实现优化，则计算效率较低；通过设计合理的适应度函数，可以利用单目标粒子群算法实现上述优化过程，优化效率将能大大提高；利用粒子群算法实现天线辐射参数优化的实现过程包括三个方面：粒子位置和适应度、粒子初始化及粒子更新；The optimization model needs to take into account the two parameters of aiming error and wave transmittance. If the traditional multi-objective particle swarm algorithm is used to achieve optimization, the calculation efficiency will be low; by designing a reasonable fitness function, the single-objective particle swarm algorithm can be used to achieve the above optimization. process, the optimization efficiency will be greatly improved; the realization process of using particle swarm algorithm to realize the optimization of antenna radiation parameters includes three aspects: particle position and fitness, particle initialization and particle update;
(1)粒子位置和适应度(1) Particle position and fitness
当天线罩阵列单元个数为M'时，搜索空间为L＝2M'，前M'维是天线罩阵列单元电流的相位，后M'维是天线罩阵列单元电流的幅度；定义粒子为一个2M'维的向量，向量元素的取值范围是Da；为同时优化瞄准误差与透波率，将适应度函数定义为：When the number of radome array elements is M', the search space is L=2M', the first M' dimension is the phase of the radome array element current, and the latter M' dimension is the amplitude of the radome array element current; the definition particle is a2M' -dimensional vector, the value range of the vector element is Da; in order to optimize the aiming error and the wave transmittance at the same time, the fitness function is defined as:
其中，w1与w2是瞄准误差B(Xr，Xa，θs)与透波率P(Xr，Xa，θs)的权重系数，决定了两个优化目标的优先程度；v(θs)是对应于扫描角θs的权重函数；Bmax是优化之前，各扫描角的最大瞄准误差，Pmax与Pmin是优化之前的最大与最小透波率；Among them, w1 and w2 are the weight coefficients of aiming error B (Xr , Xa , θs ) and wave transmittance P (Xr , Xa , θs ), which determine the priority of the two optimization goals; v(θs ) is the weight function corresponding to the scanning angle θs ; Bmax is the maximum aiming error of each scanning angle before optimization, Pmax and Pmin are the maximum and minimum wave transmittances before optimization;
(2)粒子初始化(2) Particle initialization
第i个粒子的初始位置为初始群体为计算每个粒子的适应度，设置第i个粒子的最优位置为初始群体极值设置为同时设置每个粒子的初始速度，其每个变量的速度范围是对应位置范围的一半；The initial position of the i-th particle is The initial group is Calculate the fitness of each particle, and set the optimal position of the i-th particle as The initial population extrema is set to At the same time, the initial speed of each particle is set, and the speed range of each variable is half of the corresponding position range;
(3)粒子更新(3) Particle update
在迭代过程中，根据公式(28)更新每个粒子的速度，更新后需要检查粒子速度是否在速度范围内，如果否，则用边界值替代.然后根据公式(29)更新每个粒子的位置；计算更新后粒子的适应度，如果粒子适应度小于它的个体极值，即则更新个体极值位置否则保持不变；同时根据更新后的个体极值，更新群体极值位置Gbest；In the iterative process, the velocity of each particle is updated according to formula (28). After the update, it is necessary to check whether the particle velocity is within the velocity range. If not, replace it with the boundary value. Then update the position of each particle according to formula (29). ; Calculate the fitness of the updated particle, if the fitness of the particle is less than its individual extreme value, that is Then update the individual extreme value position Otherwise, it remains unchanged; at the same time, according to the updated individual extreme value, the group extreme value position Gbest is updated;
通过不断的迭代，则可搜索到具有最小适应度值的天线辐射参数Xa，并对天线罩阵列单元电流的相位和幅度进行调整，能够保证瞄准误差最小、透波率最高，实现带罩天线系统的一体化优化设计。Through continuous iteration, the antenna radiation parameter Xa with the smallest fitness value can be searched, and the phase and amplitude of the radome array unit current can be adjusted, which can ensure the smallest aiming error and the highest wave transmittance, and realize the antenna with cover Integrated optimization design of the system.
下面，通过实验对本实施例提供的天线罩系统结构一体化优化算法进行验证和分析：Next, verify and analyze the integrated optimization algorithm of the radome system structure provided by the present embodiment through experiments:
建立一个包含有25元线性阵列的正切卵形A夹层结构天线罩系统，对其系统结构进行优化。天线罩的参数为：罩长40λ，底部直径20λ，λ为自由空间波长。A夹层罩的两表层介电常数εr＝3.0，损耗正切tanδ＝0.005。芯层材料εr＝1.1，tanδ＝0.001。优化过程中，表层材料的厚度保持为0.8mm不变，芯层材料的厚度在5个选定的站位点处的变化范围是7mm到12mm。A tangential oval A sandwich radome system with a 25-element linear array is established, and its system structure is optimized. The parameters of the radome are: the cover length is 40λ, the bottom diameter is 20λ, and λ is the free space wavelength. The dielectric constant of the two surface layers of the A sandwich cover is εr =3.0, and the loss tangent tanδ = 0.005. Core layer material εr =1.1, tanδ = 0.001. During the optimization process, the thickness of the skin material was kept constant at 0.8 mm, and the thickness of the core material varied from 7 mm to 12 mm at the 5 selected stations.
当芯层材料的厚度保持为10mm不变时，得到的瞄准误差和透波率为未优化时的结果。采用变厚度天线罩优化方法和本实施例提供的算法对该天线罩系统结构进行优化。变厚度天线罩优化方法(Radome Optimization，RO)仅对天线罩的结构参数进行优化。本实施例提供的算法采用两步优化策略，先对天线罩的结构参数进行优化，然后对天线辐射参数进行优化。本实施例提供的算法同时调节天线罩阵列单元电流的相位与幅度，补偿相位的变化范围是-5°～5°，电流幅度变化范围是4～6mA，本实施例提供的算法记为IO-RPA(Integrated Optimization ofRadome Phase andAmplitude)。When the thickness of the core material is kept constant at 10mm, the aiming error and wave transmittance obtained are unoptimized results. The radome system structure is optimized by using the variable thickness radome optimization method and the algorithm provided in this embodiment. The variable thickness radome optimization method (Radome Optimization, RO) only optimizes the structural parameters of the radome. The algorithm provided in this embodiment adopts a two-step optimization strategy. First, the structural parameters of the radome are optimized, and then the antenna radiation parameters are optimized. The algorithm provided in this embodiment adjusts the phase and amplitude of the current of the radome array element at the same time. The variation range of the compensation phase is -5° to 5°, and the variation range of the current amplitude is 4 to 6 mA. The algorithm provided by this embodiment is denoted as IO- RPA (Integrated Optimization of Radome Phase and Amplitude).
利用两种算法对天线罩进行优化后的瞄准误差和透波率如图2和图3所示，其中扫描角θ的变化范围是0～50°，间隔为5°。与均匀厚度天线罩相比较，变厚度优化使最大BSE从0.332°减至0.306°。本实施例提供的算法同时对电流幅值与相位进行优化，最大BSE进一步降低至0.118°。与均匀厚度天线罩相比较，变厚度优化使最小透波率从86.5％上升到92.0％。本实施例提供的算法联合优化电流幅值与补偿相位，透波率接近于97.5％。Figures 2 and 3 show the aiming error and wave transmittance of the radome optimized by the two algorithms, where the scanning angleθ varies from 0 to 50° with an interval of 5°. Compared to the uniform thickness radome, the variable thickness optimization reduces the maximum BSE from 0.332° to 0.306°. The algorithm provided in this embodiment simultaneously optimizes the current amplitude and phase, and the maximum BSE is further reduced to 0.118°. Compared to the uniform thickness radome, the variable thickness optimization increases the minimum transmittance from 86.5% to 92.0%. The algorithm provided in this embodiment jointly optimizes the current amplitude and the compensation phase, and the wave transmittance is close to 97.5%.
利用不同算法对天线罩系统进行优化后，得到的瞄准误差与透波率的平均值见表1。从表1中可以看到，RO方法的平均瞄准误差要高于未优化时的瞄准误差，这是因为，RO方法仅能够令某些扫描角下的瞄准误差低于优化前的瞄准误差，而本实施例提供的算法IO-RPA能够使所有扫描角下的瞄准误差均得到优化，平均瞄准误差仅为0.0196°，比未优化的瞄准误差要降低一个数量级。分析透波率的结果可以发现，在扫描角小于20°时，RO方法能够提高透波率，但扫描角大于20°后，RO方法的透波率要低于未优化的结果，因此平均透波率低于未优化结果。本实施例提供的算法将所有扫描角下的透波率作为整体目标进行优化，整体性能得到提升，平均透波率高达97.5150％。因此，与未优化相比，本实施例提供的算法能够在降低瞄准误差的同时，提高透波率。After optimizing the radome system with different algorithms, the average values of aiming error and wave transmittance obtained are shown in Table 1. It can be seen from Table 1 that the average aiming error of the RO method is higher than that of the unoptimized aiming error, because the RO method can only make the aiming error at some scanning angles lower than the aiming error before optimization, while The algorithm IO-RPA provided in this embodiment can optimize the aiming error at all scanning angles, and the average aiming error is only 0.0196°, which is an order of magnitude lower than the unoptimized aiming error. From the analysis of the transmittance, it can be found that when the scan angle is less than 20°, the RO method can improve the transmittance, but when the scan angle is greater than 20°, the transmittance of the RO method is lower than that of the unoptimized result. The baud rate is lower than the unoptimized result. The algorithm provided in this embodiment optimizes the wave transmittance at all scanning angles as an overall target, and the overall performance is improved, and the average wave transmittance is as high as 97.5150%. Therefore, compared with the unoptimized algorithm, the algorithm provided in this embodiment can improve the wave transmittance while reducing the aiming error.
表1不同算法的平均瞄准误差和平均透波率Table 1 Average aiming error and average transmittance of different algorithms
图4给出了利用变厚度天线罩优化方法得到的芯层厚度沿着天线罩轴向站位的分布。从图中可以看出，因为仅选择了有限的点进行优化，再依据样条插值确定罩体的具体厚度，厚度变化比较和缓，有利于罩体的工艺实现。Figure 4 shows the distribution of the core thickness along the radome's axial position using the variable-thickness radome optimization method. It can be seen from the figure that because only limited points are selected for optimization, and the specific thickness of the cover is determined based on spline interpolation, the thickness change is relatively gentle, which is beneficial to the process realization of the cover.
在一体化优化中需要给出每个扫描角对应的最佳天线罩阵列单元激励方案，当扫描角为30°时，图5给出了利用IO-RPA优化得到的电流幅值与补偿相位。利用图中给出的补偿相位和电流幅度对天线罩阵列单元天线进行调整，系统的瞄准误差仅为0.019°，透波率达到97.5133％。In the integrated optimization, the optimal radome array unit excitation scheme corresponding to each scan angle needs to be given. When the scan angle is 30°, Figure 5 shows the current amplitude and compensation phase optimized by IO-RPA. Using the compensation phase and current amplitude given in the figure to adjust the antenna of the radome array element, the aiming error of the system is only 0.019°, and the wave transmittance reaches 97.5133%.
针对相控阵天线罩系统，提出了一种系统结构一体化优化算法。通过分析天线罩结构参数和天线辐射参数对瞄准误差和透波率的影响，建立天线罩系统结构的一体化优化模型。采用算子分离思想，制定两步优化策略，采用变厚度方法和粒子群方法分别对天线罩结构参数和天线辐射参数进行优化，实现了天线罩系统结构的一体化优化设计。实验结果表明，与仅优化天线罩的变厚度天线罩优化方法相比，本实施例提供的算法具备瞄准误差小、透波率高的优势，有助于降低天线罩的总体设计难度。For the phased array radome system, an integrated optimization algorithm of system structure is proposed. By analyzing the influence of radome structure parameters and antenna radiation parameters on aiming error and wave transmittance, an integrated optimization model of radome system structure is established. Using the operator separation idea, a two-step optimization strategy was formulated, and the radome structural parameters and antenna radiation parameters were optimized by the variable thickness method and the particle swarm method, respectively, and the integrated optimization design of the radome system structure was realized. The experimental results show that, compared with the variable-thickness radome optimization method that only optimizes the radome, the algorithm provided in this embodiment has the advantages of small aiming error and high wave transmittance, which helps to reduce the overall design difficulty of the radome.
以上所述实施例仅为本发明较佳的具体实施方式，本发明的保护范围不限于此，任何熟悉本领域的技术人员在本发明披露的技术范围内，可显而易见地得到的技术方案的简单变化或等效替换，均属于本发明的保护范围。The above-mentioned embodiments are only preferred specific embodiments of the present invention, and the protection scope of the present invention is not limited thereto. Any person skilled in the art can obviously obtain the simplicity of the technical solution within the technical scope disclosed in the present invention. Changes or equivalent replacements all belong to the protection scope of the present invention.
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