CN117910140A - Aerodynamic and electromagnetic coupling optimization design method for aircraft based on hybrid conditional generative adversarial network - Google Patents
Aerodynamic and electromagnetic coupling optimization design method for aircraft based on hybrid conditional generative adversarial network Download PDFInfo
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Abstract
本发明属于飞行器设计优化技术领域,具体为基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法,包括如下步骤:步骤S1:确定优化状态、优化目标和约束;步骤S2:选择基准外形,对基准飞行器外形进行参数化,确定设计变量、设计空间,并抽取样本;步骤S3:对样本点开展气动隐身性能计算,获得样本气动隐身数据集;步骤S4:基于样本气动隐身数据集构建MCGAN模型并验证;步骤S5:确定具体的优化数学模型,采用粒子群算法基于步骤S4获得的MCGAN模型进行寻优求解,获得优化后的飞行器外形。本发明的MCGAN模型能够在小样本下具备高精度预测能力,对样本数量需求小可降低计算成本,进而能够直接对飞行器三维外形开展气动电磁耦合优化设计。
The present invention belongs to the technical field of aircraft design optimization, specifically, an aircraft aerodynamic electromagnetic coupling optimization design method based on a hybrid conditional generative adversarial network, comprising the following steps: step S1: determining the optimization state, optimization target and constraint; step S2: selecting a reference shape, parameterizing the reference aircraft shape, determining the design variables, design space, and extracting samples; step S3: performing aerodynamic stealth performance calculations on sample points to obtain a sample aerodynamic stealth data set; step S4: constructing and verifying an MCGAN model based on the sample aerodynamic stealth data set; step S5: determining a specific optimization mathematical model, using a particle swarm algorithm to perform optimization and solution based on the MCGAN model obtained in step S4, and obtaining an optimized aircraft shape. The MCGAN model of the present invention can have high-precision prediction capabilities under small samples, and the small sample quantity requirement can reduce the calculation cost, thereby being able to directly perform aerodynamic electromagnetic coupling optimization design on the three-dimensional shape of the aircraft.
Description
技术领域Technical Field
本发明涉及飞行器设计优化技术领域,具体的为一种基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法。The present invention relates to the technical field of aircraft design optimization, and specifically to an aircraft aerodynamic electromagnetic coupling optimization design method based on a mixed condition generative adversarial network.
背景技术Background technique
随着航空技术的飞速发展,对飞行器隐身性能要求越来越高,飞行器的设计需要在气动、隐身多学科要求下进行。为了解决高气动性能和高隐身性能之间的矛盾点,设计人员广泛采用各种方法对飞行器进行气动隐身一体化设计,以实现更高的性能水平。With the rapid development of aviation technology, the requirements for aircraft stealth performance are getting higher and higher. The design of aircraft needs to be carried out under the requirements of aerodynamics and stealth. In order to solve the contradiction between high aerodynamic performance and high stealth performance, designers widely use various methods to integrate aerodynamic stealth design of aircraft to achieve a higher performance level.
目前,主要采用基于智能优化算法(如遗传算法、粒子群算法等)和代理模型的气动隐身优化设计方法对飞行器气动进行气动电磁耦合设计,取得了相应的效果,但是仍然存在一些不足,主要体现在:1,只局限于二维翼型的优化,而在真实的飞行过程中,飞行器作为一个三维实体,其性能的表现与二维翼型性能的表现仍会存在着差异,例如机翼表面的横流效应,因此二维翼型优化的结果不能代表飞行器最终的性能;2,常用的代理模型,比如插值型代理模型(Kriging代理模型、RBF代理模型)和回归型代理模型(LS-SVR代理模型),存在设计维数低、泛化能力差、训练计算量大的问题,一旦考虑直接三维外形优化设计,设计变量数量较大,上述常用代理模型的预测精度将会显著下降,从而使得设计精度低;此外,由于设计变量数量大,构建代理模型所需样本点数量也相应增大,若采用高精度的气动求解器和隐身求解器,构建上述代理模型的计算代价非常高,从而使得设计效率低。At present, the aerodynamic stealth optimization design method based on intelligent optimization algorithm (such as genetic algorithm, particle swarm algorithm, etc.) and proxy model is mainly used to perform aerodynamic electromagnetic coupling design on aircraft aerodynamics, and corresponding effects have been achieved. However, there are still some shortcomings, mainly reflected in: 1. It is limited to the optimization of two-dimensional airfoils. In the actual flight process, the performance of the aircraft as a three-dimensional entity will still be different from that of the two-dimensional airfoil, such as the cross-flow effect on the wing surface. Therefore, the result of two-dimensional airfoil optimization cannot represent the final performance of the aircraft; 2. Commonly used proxy models, such as interpolation proxy models (Kriging proxy model, RBF proxy model) and regression proxy models (LS-SVR proxy model), have the problems of low design dimension, poor generalization ability and large training calculation amount. Once the direct three-dimensional shape optimization design is considered, the number of design variables is large, and the prediction accuracy of the above commonly used proxy models will be significantly reduced, resulting in low design accuracy; in addition, due to the large number of design variables, the number of sample points required to construct the proxy model is also increased accordingly. If a high-precision aerodynamic solver and stealth solver are used, the computational cost of constructing the above proxy model is very high, resulting in low design efficiency.
发明内容Summary of the invention
为了解决现有技术中存在的上述问题,本发明提出一种基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法,通过探究样本数量、学习率、批尺寸对神经网络模型的影响,构建了一种混合条件生成对抗网络(Mixed Conditional GenerativeAdversarial Network,MCGAN)模型,能够直接针对三维飞行器外形高效地进行气动电磁耦合优化设计,并能获得良好的设计结果。In order to solve the above problems existing in the prior art, the present invention proposes an aircraft aerodynamic electromagnetic coupling optimization design method based on a mixed conditional generative adversarial network. By exploring the influence of sample number, learning rate and batch size on the neural network model, a mixed conditional generative adversarial network (MCGAN) model is constructed. The MCGAN model can directly and efficiently perform aerodynamic electromagnetic coupling optimization design for the three-dimensional aircraft shape and obtain good design results.
本发明通过以下技术方案来实现:The present invention is achieved through the following technical solutions:
一种基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法,包括以下步骤:A method for optimizing the aerodynamic and electromagnetic coupling of an aircraft based on a hybrid conditional generative adversarial network comprises the following steps:
步骤S1:根据翼型气动隐身优化具体问题,确定优化状态、优化目标和约束;Step S1: Determine the optimization state, optimization target and constraints according to the specific problem of airfoil aerodynamic stealth optimization;
步骤S2:选择基准飞行器外形,围绕基准飞行器外形生成网格,对基准飞行器外形进行参数化,确定设计变量、设计空间,并在设计空间中抽样,获得样本;Step S2: selecting a reference aircraft shape, generating a grid around the reference aircraft shape, parameterizing the reference aircraft shape, determining design variables and a design space, and sampling in the design space to obtain a sample;
步骤S3:对步骤S2中获得的飞行器外形样本,开展气动隐身性能计算,获得样本的气动隐身数据集;Step S3: performing aerodynamic stealth performance calculation on the aircraft shape sample obtained in step S2 to obtain an aerodynamic stealth data set of the sample;
步骤S4:基于步骤S3中获得的样本气动隐身数据集,通过探究样本数量、学习率、批尺寸对神经网络模型的影响,构建MCGAN模型,并验证其可靠性;Step S4: Based on the sample aerodynamic stealth dataset obtained in step S3, the MCGAN model is constructed by exploring the influence of sample number, learning rate, and batch size on the neural network model, and its reliability is verified;
步骤S5:根据步骤S1中确定的优化目标和约束,确定具体的优化数学模型,采用智能优化算法基于步骤S4获得的MCGAN模型在设计空间中进行寻优求解,获得优化后的飞行器外形。Step S5: According to the optimization objectives and constraints determined in step S1, a specific optimization mathematical model is determined, and an intelligent optimization algorithm is used to search for an optimal solution in the design space based on the MCGAN model obtained in step S4 to obtain the optimized aircraft shape.
进一步的,所述步骤S1中的优化目标包括:升力目标、阻力目标、俯仰力矩目标、雷达散射截面面积目标。Furthermore, the optimization targets in step S1 include: lift target, drag target, pitch moment target, and radar cross-sectional area target.
进一步的,所述步骤S3包含以下子步骤:Furthermore, step S3 includes the following sub-steps:
步骤S31:基于RANS方法,对样本内的飞行器外形进行气动特性数值计算,存储设计变量及计算所得的气动数据,获得样本点的气动数据集;Step S31: Based on the RANS method, numerically calculate the aerodynamic characteristics of the aircraft shape in the sample, store the design variables and the calculated aerodynamic data, and obtain the aerodynamic data set of the sample point;
步骤S32:基于物理光学法,对样本内的飞行器外形进行隐身计算,将计算所得的隐身数据添加到步骤S31获得的飞行器外形的气动数据集,获得飞行器外形的气动隐身数据集。Step S32: Based on the physical optics method, perform stealth calculation on the aircraft shape in the sample, add the calculated stealth data to the aerodynamic data set of the aircraft shape obtained in step S31, and obtain the aerodynamic stealth data set of the aircraft shape.
进一步的,所述步骤S31中气动数据包含升力系数、阻力系数、俯仰力矩系数;所述步骤S32中的隐身数据为雷达散射截面面积。Furthermore, the aerodynamic data in step S31 includes lift coefficient, drag coefficient, and pitch moment coefficient; and the stealth data in step S32 is radar cross-sectional area.
进一步的,所述步骤S4中的构建的MCGAN模型包括:一个生成器和一个判别器;所述生成器用于生成气动隐身目标参数,所述判别器用于判别生成器生成的气动隐身目标参数的真实性;具体构建过程如下:Furthermore, the MCGAN model constructed in step S4 includes: a generator and a discriminator; the generator is used to generate aerodynamic stealth target parameters, and the discriminator is used to discriminate the authenticity of the aerodynamic stealth target parameters generated by the generator; the specific construction process is as follows:
模型的训练遵守博弈理论,公式表达为:The training of the model follows the game theory, and the formula is expressed as:
其中D是判别器,G是生成器,x是通过生成器生成的气动和隐身目标参数,y和z是生成器的输入参数,y是设计变量即物理约束,z是噪声,Pdata是原始数据分布,Pz是噪声分布,对于一个给定的生成器,需要最大化判别器即数学期望V(D,G)最大,将V(D,G)进行积分:Where D is the discriminator, G is the generator, x is the aerodynamic and stealth target parameters generated by the generator, y and z are the input parameters of the generator, y is the design variable, i.e., the physical constraint, z is the noise, P data is the original data distribution, P z is the noise distribution. For a given generator, it is necessary to maximize the discriminator, i.e., the mathematical expectation V(D,G), and integrate V(D,G):
为了简化表达式,令a=Pdata(x|y),b=PG(x|y),D=D(x|y),最大化判别器即最大化函数f(D)=alog(D)+blog(1-D),因此得:To simplify the expression, let a = P data (x|y), b = P G (x|y), D = D (x|y), and maximize the discriminator, that is, maximize the function f (D) = alog (D) + blog (1-D), so we get:
解得Solutions have to
当且仅当Pdata(x|y)=PG(x|y)时,判别器D取得最优解,此时的生成器G就是二元极小极大博弈的最优解,此时的对应的x即为根据物理约束y预测获得的目标参数值。When and only when P data (x|y) = P G (x|y), the discriminator D obtains the optimal solution. At this time, the generator G is the optimal solution of the binary minimax game. At this time, the corresponding x is the target parameter value predicted according to the physical constraint y.
进一步的,所述步骤S4中验证MCGAN模型的可靠性评估指标为平均绝对误差(MAE)、平均绝对百分比误差(MAPE)、均方根误差(RMSE)、相关系数(R^2);具体定义如下:Furthermore, the reliability evaluation indicators for verifying the MCGAN model in step S4 are mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and correlation coefficient (R ^2 ); the specific definitions are as follows:
平均绝对误差(MAE)的定义为:The mean absolute error (MAE) is defined as:
平均绝对百分比误差(MAPE)的定义为:The mean absolute percentage error (MAPE) is defined as:
均方根误差(RMSE)的定义为:The root mean square error (RMSE) is defined as:
相关系数(R^2)的定义为:The correlation coefficient (R ^2 ) is defined as:
其中,N为数据点数量,yi和分别为真实值和模型预测值;SSR和SST分别为回归平方和和总平方和;评估标准为MAE、MAPE、RMSE越接近于0,R^2越接近于1,说明模型的预测能力越好。Where N is the number of data points, yi and are the true value and the model predicted value respectively; SSR and SST are the regression sum of squares and the total sum of squares respectively; the evaluation criteria are MAE, MAPE, and RMSE. The closer they are to 0 and R ^2 is to 1, the better the predictive ability of the model.
进一步的,所述步骤S5中采用的智能优化算法为粒子群算法;Furthermore, the intelligent optimization algorithm used in step S5 is a particle swarm algorithm;
进一步的,本发明还提供一种计算机设备,包括:处理器、存储介质和总线,所述存储介质存储有所述处理器可执行的程序指令,当所述计算机设备运行时,所述处理器与所述存储介质之间通过总线通信,所述处理器执行所述程序指令时用于实现所述基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法。Furthermore, the present invention also provides a computer device, comprising: a processor, a storage medium and a bus, wherein the storage medium stores program instructions executable by the processor, and when the computer device is running, the processor and the storage medium communicate through the bus, and when the processor executes the program instructions, it is used to implement the aircraft aerodynamic electromagnetic coupling optimization design method based on the mixed condition generation adversarial network.
进一步的,本发明还提供一种计算机可读存储介质,所述存储介质上存储有计算机程序,所述计算机程序被计算机运行时用于实现所述基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法。Furthermore, the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a computer, it is used to implement the aircraft aerodynamic electromagnetic coupling optimization design method based on the mixed condition generative adversarial network.
有益效果Beneficial Effects
本发明提供一种基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法,本发明通过探究样本数量、学习率、批尺寸对神经网络模型的影响,构建一种混合条件生成对抗网络(MCGAN)模型,该模型基于二元极小极大博弈理论,通过生成器和判别器动态博弈获得生成器最优解,能够在小样本条件下预测高维、多目标的气动隐身性能参数,从而可以解决高维约束、多目标优化问题,且相比传统代理模型,能够在小样本下具备高精度的预测能力,对样本数量需求的减少能够降低优化设计的计算成本,从而在保证设计精度的同时极大提高设计效率,缩短设计周期,进而能够直接针对三维飞行器外形高效地进行气动电磁耦合优化设计。The present invention provides an aircraft aerodynamic electromagnetic coupling optimization design method based on a mixed conditional generative adversarial network. The present invention constructs a mixed conditional generative adversarial network (MCGAN) model by exploring the influence of sample quantity, learning rate and batch size on the neural network model. The model is based on binary minimax game theory, and obtains the optimal solution of the generator through dynamic game between a generator and a discriminator. The model can predict high-dimensional and multi-objective aerodynamic stealth performance parameters under small sample conditions, thereby solving high-dimensional constraints and multi-objective optimization problems. Compared with traditional proxy models, the model can have high-precision prediction capabilities under small samples. The reduction in the number of samples required can reduce the computational cost of the optimization design, thereby greatly improving the design efficiency while ensuring the design accuracy, shortening the design cycle, and then being able to directly and efficiently perform aerodynamic electromagnetic coupling optimization design for the three-dimensional aircraft shape.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明实施例飞行器外形气动电磁耦合优化设计方法的流程图;FIG1 is a flow chart of a method for optimizing aerodynamic and electromagnetic coupling design of an aircraft shape according to an embodiment of the present invention;
图2为本发明实施例的FFD框及设计变量示意图;FIG2 is a schematic diagram of an FFD frame and design variables according to an embodiment of the present invention;
图3为本发明实施例飞行器气动隐身性能计算流程示意图;FIG3 is a schematic diagram of a calculation flow of aerodynamic stealth performance of an aircraft according to an embodiment of the present invention;
图4为本发明实施例的MCGAN模型的建立流程图;FIG4 is a flow chart of establishing an MCGAN model according to an embodiment of the present invention;
图5为本发明实施例的MCGAN模型的组成示意图;FIG5 is a schematic diagram of the composition of the MCGAN model according to an embodiment of the present invention;
图6为本发明实施例提供的样本数量size对模型的损失影响示意图;FIG6 is a schematic diagram showing the effect of sample size on model loss provided by an embodiment of the present invention;
图7为本发明实施例提供的样本数量size对模型的均方根误差影响示意图;FIG7 is a schematic diagram showing the effect of sample size on the root mean square error of a model provided by an embodiment of the present invention;
图8为本发明实施例提供的学习率lr对模型的损失影响示意图;FIG8 is a schematic diagram showing the effect of the learning rate lr on the loss of the model provided by an embodiment of the present invention;
图9为本发明实施例提供的学习率lr对模型的均方根误差影响示意图;FIG9 is a schematic diagram showing the effect of the learning rate lr on the root mean square error of the model provided by an embodiment of the present invention;
图10为本发明实施例提供的批尺寸bs对模型的损失影响示意图;FIG10 is a schematic diagram showing the effect of batch size bs on the loss of a model provided by an embodiment of the present invention;
图11为本发明实施例提供的批尺寸bs对模型的均方根误差影响示意图;FIG11 is a schematic diagram showing the effect of batch size bs on the root mean square error of a model provided by an embodiment of the present invention;
图12为本发明实施例提供的第一种优化情况下的优化结果;FIG12 is an optimization result of the first optimization case provided by an embodiment of the present invention;
其中,图12(a)为飞行器整体压力系数云图;图12(b)为翼根压力系数分布曲线;图12(c)为飞行器上表面压力系数等值线图;图12(d)为翼中压力系数分布曲线;图12(e)为RCS示意图;图12(f)为翼尖压力系数分布曲线;Among them, Figure 12(a) is a cloud diagram of the overall pressure coefficient of the aircraft; Figure 12(b) is a distribution curve of the wing root pressure coefficient; Figure 12(c) is a contour diagram of the pressure coefficient on the upper surface of the aircraft; Figure 12(d) is a distribution curve of the mid-wing pressure coefficient; Figure 12(e) is a schematic diagram of RCS; Figure 12(f) is a distribution curve of the wing tip pressure coefficient;
图13为本发明实施例提供的第二种优化情况下的优化结果;FIG13 is an optimization result of the second optimization case provided by an embodiment of the present invention;
其中,图13(a)为飞行器整体压力系数云图;图13(b)为翼根压力系数分布曲线;图13(c)为飞行器上表面压力系数等值线图;图13(d)为翼中压力系数分布曲线;图13(e)为RCS示意图;图13(f)为翼尖压力系数分布曲线;Among them, Figure 13 (a) is a cloud diagram of the overall pressure coefficient of the aircraft; Figure 13 (b) is a distribution curve of the wing root pressure coefficient; Figure 13 (c) is a contour diagram of the pressure coefficient on the upper surface of the aircraft; Figure 13 (d) is a distribution curve of the mid-wing pressure coefficient; Figure 13 (e) is a schematic diagram of RCS; Figure 13 (f) is a distribution curve of the wing tip pressure coefficient;
具体实施方式Detailed ways
为了使本发明所解决的技术问题、技术方案和有益效果更加清楚明白,使本技术领域的人员更好地理解本发明方案,以下结合附图和实施例,对本发明进一步详细说明和完整描述。应当理解,此处所述的具体实施例仅用于解释本发明,并不用于限定本发明。In order to make the technical problems, technical solutions and beneficial effects solved by the present invention clearer and more understandable, and to enable those skilled in the art to better understand the solutions of the present invention, the present invention is further described and fully described in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
如图1所示,本实施例利用本发明提出的基于混合条件生成对抗网络的飞行器气动电磁耦合优化设计方法,针对某飞行器外形直接开展三维外形气动电磁耦合优化设计,包括如下步骤:As shown in FIG1 , this embodiment uses the aircraft aerodynamic electromagnetic coupling optimization design method based on the hybrid conditional generative adversarial network proposed in the present invention to directly carry out a three-dimensional shape aerodynamic electromagnetic coupling optimization design for a certain aircraft shape, including the following steps:
步骤S1:根据翼型气动隐身优化具体问题,确定优化状态、优化目标和约束;Step S1: Determine the optimization state, optimization target and constraints according to the specific problem of airfoil aerodynamic stealth optimization;
本实施例中,优化状态为Ma=0.8,AOA=2°,优化目标为升力系数,阻力系数,俯仰力矩系数以及雷达散射面积;In this embodiment, the optimization state is Ma=0.8, AOA=2°, and the optimization targets are lift coefficient, drag coefficient, pitch moment coefficient and radar scattering area;
步骤S2:选择基准飞行器外形,围绕基准飞行器外形生成网格,对基准飞行器外形进行参数化,确定设计变量、设计空间,并在设计空间中抽样,获得样本;Step S2: selecting a reference aircraft shape, generating a grid around the reference aircraft shape, parameterizing the reference aircraft shape, determining design variables and a design space, and sampling in the design space to obtain a sample;
在本实施例中,具体为,选择某飞翼布局的飞行器作为基准飞行器外形,由于所选择基准飞行器左右对称,取半模,采用FFD参数化方法沿飞行器展向选择5个剖面作为特征剖面对三维外形进行参数化,特征剖面和控制点如图2所示,将5个剖面处的FFD控制框的节点的Z向坐标zi,i=1…n的改变量Δzi,i=1…n作为设计变量,建立起表面网格和设计变量之间的映射,其中下标i表示第i个控制节点,n为全部FFD框控制节点的数量;坐标轴的定义为:X轴对称面机翼弦线指向流向,Y轴垂直于对称面指向右翼,Z轴在对称面内,垂直于X轴指向上方,满足右手系;其中,每个剖面的上下表面各5个设计变量,共计50个设计变量,即本实施例的优化问题为50维,是典型的高维设计变量问题;设计变量范围取:±0.04,形成设计空间;然后在设计空间内采用拉丁超立方抽样,获得5000不同的飞行器外形样本;In this embodiment, a certain flying wing layout aircraft is selected as the reference aircraft shape. Since the selected reference aircraft is bilaterally symmetrical, a half mold is taken, and five sections are selected as characteristic sections along the span direction of the aircraft using the FFD parameterization method to parameterize the three-dimensional shape. The characteristic sections and control points are shown in FIG2 . The Z-coordinates z i , i=1…n of the nodes of the FFD control frame at the five sections are changed by Δz i , i=1…n as design variables, and establish a mapping between the surface grid and the design variables, where the subscript i represents the i-th control node, and n is the number of all FFD box control nodes; the coordinate axis is defined as: the chord line of the wing of the X-axis symmetry plane points to the flow direction, the Y-axis is perpendicular to the symmetry plane and points to the right wing, and the Z-axis is in the symmetry plane, perpendicular to the X-axis and points upward, satisfying the right-hand system; wherein, each section has 5 design variables on the upper and lower surfaces, a total of 50 design variables, that is, the optimization problem of this embodiment is 50-dimensional, which is a typical high-dimensional design variable problem; the design variable range is: ±0.04, forming a design space; then Latin hypercube sampling is used in the design space to obtain 5000 different aircraft shape samples;
通过改变设计变量对表面网格施加变形扰动,从而实现变形得到新外形的表面网格,继而采用径向基函数(Radial Basis Function,RBF)-无限插值(Trans-finiteInterpolation,TFI)网格变形方法,基于新外形的表面网格对空间网格进行插值变形,得到新外形的CFD计算网格;By changing the design variables, the surface mesh is subjected to deformation disturbance, so that the surface mesh of the new shape is deformed. Then, the radial basis function (RBF)-infinite interpolation (TFI) mesh deformation method is used to interpolate and deform the space mesh based on the surface mesh of the new shape to obtain the CFD calculation mesh of the new shape.
步骤S3:对步骤S2中获得的飞行器外形样本,开展气动隐身性能计算,获得样本的气动隐身数据集;如图3所示,具体又包括如下子步骤:Step S3: Carry out aerodynamic stealth performance calculation on the aircraft shape sample obtained in step S2 to obtain an aerodynamic stealth data set of the sample; as shown in FIG3 , it specifically includes the following sub-steps:
步骤S31:基于RANS方法,对样本内的飞行器外形进行气动特性数值计算,存储设计变量及计算所得的气动数据,获得样本点的气动数据集;所述气动数据包含升力系数、阻力系数、俯仰力矩系数;Step S31: Based on the RANS method, numerically calculate the aerodynamic characteristics of the aircraft shape in the sample, store the design variables and the calculated aerodynamic data, and obtain the aerodynamic data set of the sample point; the aerodynamic data includes the lift coefficient, the drag coefficient, and the pitch moment coefficient;
在本实施例中,采用有限体积方法求解三维NS方程,三维NS方程为:In this embodiment, the finite volume method is used to solve the three-dimensional NS equation, and the three-dimensional NS equation is:
其中ξ,η,ζ为广义坐标,为解向量,/>为无粘通量矢量,/>为粘性通量矢量;Among them, ξ,η,ζ are generalized coordinates, is the solution vector, /> is the inviscid flux vector, /> is the viscous flux vector;
在本实施例中,RANS方程对流项和压强项采用三阶迎风偏置,时间推进格式选用隐式近似因式分解方法,湍流模型采用SA(Spalart-Allmaras),为加速收敛,计算采用多重网格加速技术;In this embodiment, the convection term and pressure term of the RANS equation adopt the third-order upwind bias, the time-marching format adopts the implicit approximate factorization method, the turbulence model adopts SA (Spalart-Allmaras), and the calculation adopts the multi-grid acceleration technology to accelerate convergence;
步骤S32:基于物理光学法,对样本内的飞行器外形进行隐身计算,将计算所得的隐身数据添加到步骤S31获得的飞行器外形的气动数据集,获得飞行器外形的气动隐身数据集;所述隐身数据为雷达散射截面面积;Step S32: Based on the physical optics method, a stealth calculation is performed on the aircraft shape in the sample, and the calculated stealth data is added to the aerodynamic data set of the aircraft shape obtained in step S31 to obtain an aerodynamic stealth data set of the aircraft shape; the stealth data is a radar cross-sectional area;
在本实施例中,RCS计算表达式为:In this embodiment, the RCS calculation expression is:
其中k=2π/λ为波数,λ为波长,为物面S处的单位外方向矢量,/>接受装置电极化方向的单位矢量,/>为磁场极化方向,/>入射方向单位矢量,/>散射方向的单位矢量;Where k = 2π/λ is the wave number, λ is the wavelength, is the unit outward direction vector at the object surface S,/> The unit vector of the receiving device's electric polarization direction, /> is the magnetic field polarization direction, /> The incident direction unit vector, /> The unit vector of the scattering direction;
RCS具有面积的量纲,为表述方便,通常以对数形式给出,表达式为:RCS has the dimension of area. For convenience, it is usually given in logarithmic form. The expression is:
RCSdBsm=10log10RCSm2 RCS dBsm = 10log 10 RCS m2
在本实施例中,取飞行器偏航角±60°即[0°,60°]和[300°,360°],作为主要威胁区域进行隐身性能优化;In this embodiment, the aircraft yaw angle ±60°, i.e., [0°, 60°] and [300°, 360°], is taken as the main threat area for stealth performance optimization;
步骤S4:基于步骤S3中获得的样本气动隐身数据集,通过探究样本数量、学习率、批尺寸对神经网络模型的影响,构建MCGAN模型,并验证其可靠性;Step S4: Based on the sample aerodynamic stealth dataset obtained in step S3, the MCGAN model is constructed by exploring the influence of sample number, learning rate, and batch size on the neural network model, and its reliability is verified;
在本实施例中,如图4和图5所示,所述MCGAN模型包括一个生成器和一个判别器;所述生成器用于生成气动隐身目标参数,所述判别器用于判别生成器生成的气动隐身目标参数的真实性;具体构建过程如下:In this embodiment, as shown in FIG. 4 and FIG. 5 , the MCGAN model includes a generator and a discriminator; the generator is used to generate aerodynamic stealth target parameters, and the discriminator is used to discriminate the authenticity of the aerodynamic stealth target parameters generated by the generator; the specific construction process is as follows:
模型的训练遵守博弈理论,公式表达为:The training of the model follows the game theory, and the formula is expressed as:
其中D是判别器,G是生成器,x是通过生成器生成的气动和隐身目标参数,y和z是生成器的输入参数,y是设计变量即物理约束,z是噪声,Pdata是原始数据分布,Pz是噪声分布,对于一个给定的生成器,需要最大化判别器即数学期望V(D,G)最大,将V(D,G)进行积分:Where D is the discriminator, G is the generator, x is the aerodynamic and stealth target parameters generated by the generator, y and z are the input parameters of the generator, y is the design variable, i.e., the physical constraint, z is the noise, P data is the original data distribution, P z is the noise distribution. For a given generator, it is necessary to maximize the discriminator, i.e., the mathematical expectation V(D,G), and integrate V(D,G):
为了简化表达式,令a=Pdata(x|y),b=PG(x|y),D=D(x|y),最大化判别器即最大化函数f(D)=alog(D)+blog(1-D),因此得:To simplify the expression, let a = P data (x|y), b = P G (x|y), D = D (x|y), and maximize the discriminator, that is, maximize the function f (D) = alog (D) + blog (1-D), so we get:
解得Solutions have to
当且仅当Pdata(x|y)=PG(x|y)时,判别器D取得最优解,此时的生成器G就是二元极小极大博弈的最优解,此时的对应的x即为根据物理约束y预测获得的目标参数值;If and only if P data (x|y) = P G (x|y), the discriminator D obtains the optimal solution. At this time, the generator G is the optimal solution of the binary minimax game. At this time, the corresponding x is the target parameter value predicted according to the physical constraint y.
在本实施例中,所述MCGAN模型采用的网络结构详细配置如表1和表2所示。生成器采用卷积池化层和全连接层结构,判别器采用全连接层结构;除输出层外,均采用LeakyRelu函数作为生成器和判别器的非线性激活函数,LeakyRelu函数使得在输入小于零时允许一个小的非零梯度,从而在模型训练中缓解梯度消失问题;损失函数均采用均方误差MSE(Mean Squared Error),作为一个凸函数它只有一个全局最小值,这使得训练过程更加稳定,减少了陷入局部最小值的风险,同时对于大误差的惩罚相对较大;模型的权重计算基于梯度下降思想,即:In this embodiment, the detailed configuration of the network structure adopted by the MCGAN model is shown in Table 1 and Table 2. The generator adopts a convolutional pooling layer and a fully connected layer structure, and the discriminator adopts a fully connected layer structure; except for the output layer, the LeakyRelu function is used as the nonlinear activation function of the generator and the discriminator. The LeakyRelu function allows a small non-zero gradient when the input is less than zero, thereby alleviating the gradient vanishing problem in model training; the loss function adopts the mean square error MSE (Mean Squared Error), which, as a convex function, has only one global minimum, which makes the training process more stable and reduces the risk of falling into a local minimum. At the same time, the penalty for large errors is relatively large; the weight calculation of the model is based on the idea of gradient descent, that is:
其中ω为权重,α为学习率,loss为损失函数。Where ω is the weight, α is the learning rate, and loss is the loss function.
在优化器选择方面,采用结合RMSProp和Momentum两种优化算法的思想的Adam优化器,同时调整初始学习率为0.0001。相比传统的随机梯度下降方法,Adam优化器可以根据历史梯度信息来自适应地调节学习率,使得在训练初期使用较大的学习率,能够快速收敛,在训练后期使用较小的学习率,能够更加准确地找到损失函数的最小值。In terms of optimizer selection, the Adam optimizer, which combines the ideas of the RMSProp and Momentum optimization algorithms, is used, and the initial learning rate is adjusted to 0.0001. Compared with the traditional stochastic gradient descent method, the Adam optimizer can adaptively adjust the learning rate based on historical gradient information, so that a larger learning rate can be used in the early stage of training to converge quickly, and a smaller learning rate can be used in the later stage of training to more accurately find the minimum value of the loss function.
表1生成器超参数选取Table 1 Generator hyperparameter selection
表2判别器超参数选取Table 2 Discriminator hyperparameter selection
样本数量(size)对MCGAN模型的损失(loss)和均方根误差(RMSE)的影响如图6和图7所示,所述样本数量(size)获取的规则为,从步骤S2获得的5000个样本点里面随机抽取100个、500个、1500个、2500个、3500个和4500个;从图中结果可以得出,在样本量为100时,模型的损失loss表现出明显的锯齿状振荡,同时模型的RMSE也有相似的表现。相比于样本量为500时,模型的损失loss收敛速度略慢,可以看到降到平稳RMSE值时,样本量为100的模型迭代周期更长;总体来看,增加样本的数量有利于模型损失loss更早达到平衡状态、缩小损失loss的振荡幅值,RMSE振荡幅值在减小的同时其达到稳定状态迭代的次数减少;增大样本数量有利于加快模型的收敛速度、稳定模型的训练。The influence of sample size on the loss and root mean square error (RMSE) of the MCGAN model is shown in Figures 6 and 7. The rule for obtaining the sample size is to randomly select 100, 500, 1500, 2500, 3500 and 4500 sample points from the 5000 sample points obtained in step S2. From the results in the figure, it can be concluded that when the sample size is 100, the loss of the model shows obvious sawtooth oscillation, and the RMSE of the model also has similar performance. Compared with the sample size of 500, the loss of the model converges slightly slower. It can be seen that when the RMSE value drops to a stable value, the iteration cycle of the model with a sample size of 100 is longer. In general, increasing the number of samples is conducive to the model loss reaching a balanced state earlier and reducing the oscillation amplitude of the loss. The RMSE oscillation amplitude is reduced while the number of iterations to reach a stable state is reduced. Increasing the number of samples is conducive to accelerating the convergence speed of the model and stabilizing the training of the model.
学习率(lr)对模型的损失(loss)和均方根误差(RMSE)的影响如图8和图9所示,从图中结果可以得出,在学习率为1e-3时,参数更新的幅值过大,造成模型不能收敛,同时RMSE呈现出突然的大幅度增加;在学习率为1e-3时,参数更新的幅值过小,模型训练稳定、但收敛过慢,在迭代1000步后模型损失loss仍未收敛;在学习率为1e-4时,模型损失loss收敛稳定、收敛速度适中,RMSE收敛速度很快;总体来看,过大过小的学习率均不利于模型的训练,在实际模型的训练中,需要针对特定的数据样本调节学习率,使得模型具有较快的收敛速度和较好的稳定性。The influence of learning rate (lr) on the loss and root mean square error (RMSE) of the model is shown in Figures 8 and 9. From the results in the figures, it can be concluded that when the learning rate is 1e-3, the amplitude of parameter update is too large, causing the model to fail to converge, and the RMSE shows a sudden and substantial increase; when the learning rate is 1e-3, the amplitude of parameter update is too small, the model training is stable, but the convergence is too slow, and the model loss has not converged after 1000 iterations; when the learning rate is 1e-4, the model loss converges stably, the convergence speed is moderate, and the RMSE converges very quickly; Overall, too large or too small learning rates are not conducive to model training. In the actual model training, the learning rate needs to be adjusted for specific data samples so that the model has a faster convergence speed and better stability.
批尺寸(bs)对模型的损失(loss)和均方根误差(RMSE)的影响如图10和图11所示,从图中结果可以得出,在bs为50时,模型的损失loss和RMSE均表现出较快的收敛速度、较小的振荡的特点;在bs为100时,模型的损失loss在1000步之内仍能收敛,但是收敛速度比bs为50时减缓,RMSE在初始几个epoch内振荡加强;在bs为500时,模型的损失loss未收敛,RMSE表现出更为剧烈的振荡且达到收敛的epoch数量增加。The influence of batch size (bs) on the loss and root mean square error (RMSE) of the model is shown in Figures 10 and 11. From the results in the figures, it can be concluded that when bs is 50, the loss and RMSE of the model both show faster convergence speed and smaller oscillation; when bs is 100, the loss of the model can still converge within 1000 steps, but the convergence speed is slower than when bs is 50, and the RMSE oscillates more strongly in the initial few epochs; when bs is 500, the loss of the model does not converge, the RMSE shows more violent oscillations and the number of epochs to converge increases.
在本实施例中,验证MCGAN模型的可靠性评估指标为平均绝对误差(MAE)、平均绝对百分比误差(MAPE)、均方根误差(RMSE)、相关系数(R^2);具体定义如下:In this embodiment, the reliability evaluation indicators for verifying the MCGAN model are mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and correlation coefficient (R ^2 ); the specific definitions are as follows:
平均绝对误差(MAE)的定义为:The mean absolute error (MAE) is defined as:
平均绝对百分比误差(MAPE)的定义为:The mean absolute percentage error (MAPE) is defined as:
均方根误差(RMSE)的定义为:The root mean square error (RMSE) is defined as:
相关系数(R^2)的定义为:The correlation coefficient (R ^2 ) is defined as:
其中,N为数据点数量,yi和分别为真实值和模型预测值;SSR和SST分别为回归平方和和总平方和;评估标准为MAE、MAPE、RMSE越接近于0,R^2越接近于1,说明模型的预测能力越好。Where N is the number of data points, yi and are the true value and the model predicted value respectively; SSR and SST are the regression sum of squares and the total sum of squares respectively; the evaluation criteria are MAE, MAPE, and RMSE. The closer they are to 0 and R ^2 is to 1, the better the predictive ability of the model.
在本实施例中,将5000个样本的数据随机分为90%的训练集、10%的测试集,学习率确定为1e-4,批尺寸确定为50;模型的预测性能如表3所示,从表中可见,四个性能指标平均绝对百分比误差均小于2.2%、相关系数均大于0.999,对阻力系数的平均绝对误差仅有2.95counts、均方根误差仅有0.47×10-4,对于飞行器外形优化问题来说,其代理精度非常高。In this embodiment, the data of 5000 samples are randomly divided into 90% training set and 10% test set, the learning rate is determined to be 1e-4, and the batch size is determined to be 50; the prediction performance of the model is shown in Table 3. It can be seen from the table that the average absolute percentage errors of the four performance indicators are all less than 2.2%, and the correlation coefficients are all greater than 0.999. The average absolute error of the drag coefficient is only 2.95 counts, and the root mean square error is only 0.47× 10-4 . For the problem of aircraft shape optimization, its proxy accuracy is very high.
表3模型预测性能Table 3 Model prediction performance
步骤S5:根据步骤S1中确定的优化目标和约束,确定具体的优化数学模型,采用智能优化算法基于步骤S4获得的MCGAN模型在设计空间中进行寻优求解,获得优化后的飞行器外形。Step S5: According to the optimization objectives and constraints determined in step S1, a specific optimization mathematical model is determined, and an intelligent optimization algorithm is used to search for an optimal solution in the design space based on the MCGAN model obtained in step S4 to obtain the optimized aircraft shape.
在本实施例中,确定2个具体的优化数学模型分别是case1和case2,如表4所示,其中case1为最小化雷达散射面积的同时约束气动性能,而case2为提升升力系数的同时约束其隐身性能;采用粒子群优化算法基于步骤S4获得的气动隐身代理模型对上述2个具体优化数学模型在设计空间中进行寻优求解,获得优化后的飞行器外形;In this embodiment, two specific optimization mathematical models are determined to be case 1 and case 2, as shown in Table 4, where case 1 is to minimize the radar scattering area while constraining the aerodynamic performance, and case 2 is to improve the lift coefficient while constraining its stealth performance; the particle swarm optimization algorithm is used to optimize and solve the above two specific optimization mathematical models in the design space based on the aerodynamic stealth proxy model obtained in step S4 to obtain the optimized aircraft shape;
表4具体的优化数学模型Table 4 Specific optimization mathematical model
case1的优化结果如图12所示,从图中结果可以得出,飞行器经由MCGAN代理优化后,在主要威胁区域即偏航角为±60°内的RCS最大峰值降低,但带来的代价是飞行器尾部的电磁散射特性整体提升,除了在RCS的谷值处,其谷值得到了进一步降低;压力分布的差异在翼中处比较明显,优化后的翼型前缘吸力峰降低,空气流速降低、不易产生分离涡,激波位置后移,使得飞行器更容易保持平衡和稳定。压力区域围成的面积增大,升力系数增加。case1优化前后气动隐身性能对比如表5所示,可见,雷达散射面积降低0.021dBsm,升力系数增大了0.0107,阻力系数增大了7counts,俯仰力矩系数降低0.0007,改善了力矩特性。The optimization results of case 1 are shown in Figure 12. From the results in the figure, it can be concluded that after the aircraft is optimized by the MCGAN agent, the maximum peak value of RCS in the main threat area, that is, within the yaw angle of ±60°, is reduced, but the cost is that the electromagnetic scattering characteristics of the tail of the aircraft are improved as a whole, except at the valley value of RCS, the valley value is further reduced; the difference in pressure distribution is more obvious in the middle of the wing. The suction peak of the leading edge of the optimized airfoil is reduced, the air flow rate is reduced, it is not easy to generate separation vortex, and the shock wave position is moved backward, making it easier for the aircraft to maintain balance and stability. The area enclosed by the pressure area is increased, and the lift coefficient is increased. The comparison of the aerodynamic stealth performance of case 1 before and after optimization is shown in Table 5. It can be seen that the radar scattering area is reduced by 0.021dBsm, the lift coefficient is increased by 0.0107, the drag coefficient is increased by 7counts, the pitch moment coefficient is reduced by 0.0007, and the moment characteristics are improved.
表5case1的优化结果对比Table 5 Comparison of optimization results of case 1
case2的优化结果如图13所示,从图中结果可以得出,优化前后的翼型剖面相差不大,在主要威胁区域RCS值基本不变,但飞行器尾部的电磁散射特性整体提升。相对于case1,激波强度基本不变,翼根、翼中、翼尖三个压力围成的面积略有增加;case2优化前后气动隐身性能对比如表6所示,雷达散射面积增加0.0009dBsm,升力系数增大了0.0043,阻力系数增大了2counts,俯仰力矩系数降低0.0001。The optimization results of case 2 are shown in Figure 13. From the results in the figure, it can be concluded that the airfoil profiles before and after optimization are not much different, and the RCS value in the main threat area is basically unchanged, but the electromagnetic scattering characteristics of the tail of the aircraft are improved overall. Compared with case 1, the shock wave intensity is basically unchanged, and the area surrounded by the three pressures of the wing root, wing center, and wing tip is slightly increased; the aerodynamic stealth performance comparison of case 2 before and after optimization is shown in Table 6. The radar scattering area increases by 0.0009dBsm, the lift coefficient increases by 0.0043, the drag coefficient increases by 2counts, and the pitch moment coefficient decreases by 0.0001.
表6case2的优化结果对比Table 6 Comparison of optimization results of case 2
尽管上面已经示出和描述了本发明的实施例,可以理解的是,上述实施例是示例性的,不能理解为对本发明的限制,本领域的普通技术人员在不脱离本发明的原理和宗旨的情况下在本发明的范围内可以对上述实施例进行变化、修改、替换和变型。Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, substitute and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.
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