CN107391891B - Large-aspect-ratio wing optimization design method based on model fusion method - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及一种基于模型融合方法的大展弦比机翼优化设计方法,属于飞行器总体优化设计技术领域。The invention relates to a large aspect ratio wing optimization design method based on a model fusion method, and belongs to the technical field of overall optimization design of aircraft.
背景技术Background technique
大展弦比机翼具有升阻比大、翼内容积大等特点,被广泛应用于高空无人机、太阳能飞机、大型洲际客机等飞行器中。这类飞行器在飞行过程中,大展弦比机翼受到气动载荷的影响,发生结构变形,变形幅度对气动性能的影响十分明显。因此,对大展弦比机翼进行分析设计时需要考虑气动结构耦合问题。针对气动结构耦合问题,可将流体力学和结构力学作为单学科独立求解,并通过软件调度技术实现跨学科数据交互,迭代求解实现耦合分析。为提高耦合分析精度,常采用高精度分析方法如计算流体力学方法(CFD)和有限元分析方法(FEA)分别对两个单学科进行分析求解。然而,高精度分析模型在提高分析精度和可信度的同时也带来了计算耗时的问题,虽然当今计算机软硬件技术已经有了长足的发展,但调用高精度分析模型完成一次迭代求解仍然极其耗时。例如使用CFD模型完成一次气动仿真分析需要数小时甚至数十小时。大展弦比机翼优化设计亦为反复迭代的过程,在优化过程中往往需要上千次调用高精度耦合分析模型,进一步增加设计成本,致使优化设计效率非常低下。Large aspect ratio wings have the characteristics of large lift-to-drag ratio and large in-wing volume, and are widely used in high-altitude UAVs, solar-powered aircraft, large intercontinental passenger aircraft and other aircraft. During the flight of this type of aircraft, the wings with large aspect ratio are affected by aerodynamic loads, resulting in structural deformation, and the deformation amplitude has a significant impact on the aerodynamic performance. Therefore, the aerodynamic-structure coupling problem needs to be considered when analyzing and designing a wing with a large aspect ratio. For the coupling problem of aerodynamic structure, fluid mechanics and structural mechanics can be solved independently as a single discipline, and the interdisciplinary data interaction can be realized through software scheduling technology, and the coupled analysis can be realized by iterative solution. In order to improve the accuracy of coupled analysis, high-precision analysis methods such as computational fluid dynamics (CFD) and finite element analysis (FEA) are often used to analyze and solve the two single disciplines. However, the high-precision analysis model not only improves the analysis accuracy and reliability, but also brings the problem of time-consuming calculation. Although today's computer software and hardware technology has made great progress, it is still difficult to call the high-precision analysis model to complete an iterative solution. Extremely time consuming. For example, it takes hours or even tens of hours to complete a pneumatic simulation analysis using a CFD model. The optimization design of a wing with a large aspect ratio is also an iterative process. In the optimization process, it often needs to call the high-precision coupled analysis model thousands of times, which further increases the design cost and makes the optimization design efficiency very low.
为了更好的说明本发明的技术方案,下面对应用到的气动结构耦合建模技术进行具体介绍。In order to better illustrate the technical solution of the present invention, the applied aerodynamic structure coupling modeling technology is introduced in detail below.
气动结构耦合建模技术:Aerodynamic structure coupling modeling technology:
随着机翼展弦比的增加,机翼的柔性不断增加,其气动性能与结构性能之间的耦合现象也越明显。而气动结构耦合建模技术的关键则是气动与结构学科之间的信息传递。在现有成熟的气动结构耦合建模技术中,常使用三维插值方法来实现气动分析结果向结构学科传递,同时根据变形后机翼的前后缘上控制点的坐标来确定更新机翼的几何外形,重新进行气动学科分析,完成结构学科分析结果向气动学科的传递。另一方面,在气动结构耦合建模中,气动学科网格的疏密程度往往控制着整个耦合分析模型的计算成本与模型精度。加大网格密度,可以提高分析模型精度,但同时也会增加计算成本。相反,降低网格密度则会降低计算精度减少计算成本。As the wing aspect ratio increases, the flexibility of the wing continues to increase, and the coupling phenomenon between its aerodynamic performance and structural performance becomes more obvious. The key to aerodynamic structure coupling modeling technology is the information transfer between aerodynamics and structural disciplines. In the existing mature aero-structure coupled modeling technology, the three-dimensional interpolation method is often used to realize the transfer of aerodynamic analysis results to the structural discipline, and at the same time, the geometric shape of the updated wing is determined according to the coordinates of the control points on the leading and trailing edges of the deformed wing. , re-analyze the aerodynamic discipline, and complete the transfer of the structural discipline analysis results to the aerodynamic discipline. On the other hand, in the coupled modeling of aerodynamic structures, the density of aerodynamic grids often controls the computational cost and model accuracy of the entire coupled analysis model. Increasing the mesh density can improve the accuracy of the analytical model, but it will also increase the computational cost. On the contrary, reducing the mesh density will reduce the calculation accuracy and reduce the calculation cost.
气动结构耦合分析模型的流程图如图1所示,具体方法步骤如下:The flow chart of the aerodynamic structure coupling analysis model is shown in Figure 1, and the specific method steps are as follows:
步骤1.使用基于UG二次开发的模型参数化技术,建立/更新机翼参数化模型。几何模型参数化的参数包括几何设计变量展弦比、根梢比、后掠角、翼型参数以及用于定量表示结构外形变形量的机翼前后缘位置控制点的坐标信息。参数化完成后输出几何外形文件用于后续分析使用,一般为step格式或者igs格式。Step 1. Use the model parameterization technology based on UG secondary development to establish/update the wing parameterization model. The parameterized parameters of the geometric model include geometric design variables aspect ratio, root-to-tip ratio, sweep angle, airfoil parameters, and the coordinate information of the position control points of the leading and trailing edges of the wing used to quantitatively represent the deformation of the structural shape. After the parameterization is completed, the output geometry file is used for subsequent analysis, generally in step format or igs format.
步骤2.使用CFD建立气动分析模型。输入几何外形文件、气动分析工况信息包括马赫数、攻角,输出气动分析结果包括升力、阻力信息以及气动力分布文件。可采用Gambit进行网格绘制,使用Fluent进行气动分析求解。Step 2. Build an aerodynamic analysis model using CFD. Input geometry file, aerodynamic analysis working condition information including Mach number, angle of attack, output aerodynamic analysis results including lift, drag information and aerodynamic distribution file. Gambit can be used for mesh drawing and Fluent for aerodynamic analysis.
步骤3.使用FEA方法建立结构学科分析模型,使用Patran进行前处理,Nastran作为后处理。输入几何外形文件、使用PCL语言进行材料属性、单元属性定义以及气动力加载等相关分析优化设定。Nastran中自带的SQP优化器可实现结构学科优化。最终输出结构分析结构包括最大应力和最大位移以及机翼前后缘控制点的坐标信息。Step 3. Use the FEA method to establish a structural subject analysis model, use Patran for pre-processing, and Nastran for post-processing. Input geometry files, use PCL language for material properties, element property definitions, and aerodynamic loading and other related analysis and optimization settings. The SQP optimizer that comes with Nastran enables structural discipline optimization. The final output structural analysis structure includes maximum stress and maximum displacement and coordinate information for control points on the leading and trailing edges of the wing.
步骤4.若是第一次分析则将变形后的控制点坐标信息输入模型参数化模块,重复步骤2、3、4,若非第一次分析,则计算相对位移量,相对位移量η的计算如式(1)所示。当相对位移量小于0.01,迭代结束,输出此时气动分析结果,包括升阻比、质量、最大应力、最大位移、以及结构学科变量的优化结果;当相对位移量大于0.01,则重复步骤1、2、3、4,直至相对位移量小于0.01,迭代结束。Step 4. If it is the first analysis, input the deformed control point coordinate information into the model parameterization module, and repeat steps 2, 3, and 4. If it is not the first analysis, calculate the relative displacement. The calculation of the relative displacement η is as follows: Formula (1) is shown. When the relative displacement is less than 0.01, the iteration ends, and the aerodynamic analysis results are output at this time, including the lift-drag ratio, mass, maximum stress, maximum displacement, and optimization results of structural variables; when the relative displacement is greater than 0.01, repeat steps 1 and 1. 2, 3, 4, until the relative displacement is less than 0.01, the iteration ends.
式(1)中i表示第i次分析,i-1表示第i次分析的上一次分析。In formula (1), i represents the ith analysis, and i-1 represents the previous analysis of the ith analysis.
发明内容SUMMARY OF THE INVENTION
针对大展弦比机翼优化设计过程中,考虑气动结构耦合时计算成本过高的问题,本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,要解决的技术问题是在保证精度的情况下,考虑气动结构耦合问题实现大展弦比机翼的高效优化设计,具有如下优点:使用模型融合方法对高、低精度分析模型信息进行有效融合,充分利用低精度模型信息保证融合模型的精度,减少高精度分析模型的调用次数,从而降低计算成本,提高大展弦比机翼的优化设计效率。Aiming at the problem that the calculation cost is too high when considering the coupling of aerodynamic structures in the process of optimizing the design of a wing with a large aspect ratio, the invention discloses a method for optimizing the design of a wing with a large aspect ratio based on a model fusion method, and the technical problem to be solved Under the condition of ensuring the accuracy, considering the aerodynamic structure coupling problem to realize the efficient optimization design of the wing with large aspect ratio, it has the following advantages: using the model fusion method to effectively fuse the high- and low-precision analytical model information, making full use of the low-precision model The information ensures the accuracy of the fusion model and reduces the number of calls of the high-precision analysis model, thereby reducing the computational cost and improving the optimization design efficiency of large aspect ratio wings.
本发明的目的是通过下述技术方案实现的。The purpose of the present invention is achieved through the following technical solutions.
本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,根据设计要求选择初始参考翼型以及机翼相关形状参数,确定设计工况;根据需求建立结构学科的优化模型与系统级优化模型,并使用罚函数法处理复杂约束;使用气动结构耦合建模技术建立高、低精度大展弦比机翼气动结构耦合分析模型;使用试验设计方法分别生成高、低精度样本点;分别调用高、低精度大展弦比机翼气动结构耦合分析模型获取高、低精度样本信息并存储;使用模型融合方法,将高精度与低精度模型信息进行融合,建立代理模型实现模型精度与计算成本的综合协调;基于当前代理模型使用优化方法进行优化求解,根据最优解处的真实响应值与基于模型融合方法的代理模型值的差值判定优化结果是否可信,若不可信则返回重新构造融合模型进行优化求解,若可信则输出最优设计结果,即完成考虑气动结构耦合问题实现大展弦比机翼的高效优化设计。The invention discloses a large aspect ratio wing optimization design method based on a model fusion method. The initial reference airfoil and the relevant shape parameters of the wing are selected according to the design requirements, and the design working conditions are determined; the optimization model of the structural discipline is established according to the requirements. System-level optimization model, and use penalty function method to deal with complex constraints; use aero-structure coupled modeling technology to establish high- and low-precision high-aspect-ratio wing aero-structure coupled analysis models; use experimental design method to generate high and low-precision sample points respectively ;Invoke the high- and low-precision high-aspect ratio wing aerodynamic structure coupling analysis models to obtain high- and low-precision sample information and store them; use the model fusion method to fuse the high-precision and low-precision model information, and establish a proxy model to achieve model accuracy Comprehensive coordination with computational cost; use the optimization method to optimize the solution based on the current surrogate model, and determine whether the optimization result is credible based on the difference between the real response value at the optimal solution and the surrogate model value based on the model fusion method, and if not, then Return to reconstruct the fusion model for optimization solution. If it is credible, output the optimal design result, that is, complete the efficient optimization design of the wing with large aspect ratio considering the coupling problem of aerodynamic structure.
本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,包括如下步骤:The invention discloses a large aspect ratio wing optimization design method based on a model fusion method, comprising the following steps:
步骤1:根据设计要求,选择初始参考翼型以及机翼相关形状参数,确定设计工况。Step 1: According to the design requirements, select the initial reference airfoil and relevant shape parameters of the airfoil to determine the design conditions.
所述的设计工况包括马赫数与攻角。The design conditions include Mach number and angle of attack.
步骤2:根据需求建立结构学科的优化模型与系统级优化模型。Step 2: Establish the optimization model and system-level optimization model of structural disciplines according to the requirements.
步骤2.1:根据需求建立结构学科的优化模型。Step 2.1: Establish an optimization model of structural disciplines according to requirements.
为了能够在保证结构强度的同时,最大限度的降低质量,在结构分析过程中对机翼的每个结构组件进行尺寸优化。设计变量包括蒙皮厚度、腹板厚度、凸缘半径、腹板厚度、凸缘半径;优化目标为结构质量最小;约束条件为满足最大应力约束和最大位移变形约束。结构学科的优化在结构学科分析模型中实现。In order to minimize the mass while maintaining the structural strength, the size of each structural component of the wing is optimized during the structural analysis. The design variables include skin thickness, web thickness, flange radius, web thickness, and flange radius; the optimization objective is to minimize the structural mass; the constraints are to satisfy the maximum stress constraint and the maximum displacement deformation constraint. The optimization of the structural discipline is realized in the structural discipline analysis model.
步骤2.2:根据需求建立系统级优化模型。Step 2.2: Build a system-level optimization model based on requirements.
系统级优化中选几何设计参数为设计变量,所述的设计变量包括展弦比、根梢比、后掠角,并根据需求确定其上下限;以升阻比最大,结构质量最小为优化目标,约束条件包括结构最大应力小于许用应力、结构最大位移小于许用位移以及机翼面积不变。The geometric design parameters are selected as design variables in the system-level optimization. The design variables include aspect ratio, root-to-tip ratio, and sweep angle, and the upper and lower limits are determined according to the requirements; the maximum lift-drag ratio and the minimum structural quality are the optimization goals. Constraints include that the maximum structural stress is less than the allowable stress, the maximum structural displacement is less than the allowable displacement, and the wing area remains unchanged.
步骤3:使用气动结构耦合建模技术建立高、低精度大展弦比机翼气动结构耦合分析模型。气动学科网格密度是计算成本与计算精度的主要因素,因此在气动分析模型中使用粗网格建立低精度分析模型,使用细网格建立高精度的分析模型。Step 3: Use the aerodynamic-structure coupled modeling technology to establish a high- and low-precision high-aspect ratio wing aerodynamic-structure coupled analysis model. The grid density of aerodynamics is the main factor of calculation cost and calculation accuracy. Therefore, in the aerodynamic analysis model, coarse grids are used to establish low-precision analysis models, and fine grids are used to establish high-precision analysis models.
步骤3中通过气动学科网格密度的疏密程度实现计算精度与计算成本的协调,建立高、低精度的气动结构耦合分析模型。In step 3, the coordination of calculation accuracy and calculation cost is achieved through the density of aerodynamic grids, and a high- and low-accuracy aerodynamic structure coupling analysis model is established.
步骤4:使用试验设计方法分别生成Nh个高精度样本点和Nl个低精度样本点。样本点数量与系统级优化设计变量维度nv相关。其中低精度样本点中需包含所有的高精度样本点。Step 4: Generate N h high-precision sample points and N l low-precision sample points respectively using the design of experiments method. The number of sample points is related to the system-level optimization design variable dimension nv . The low-precision sample points need to include all high-precision sample points.
为实现考虑气动结构耦合问题的大展弦比机翼优化设计的高效性,步骤4中所述的试验设计方法优选使用拉丁超立方试验设计方法。In order to realize the high efficiency of the high aspect ratio wing optimization design considering the aerodynamic-structure coupling problem, the experimental design method described in step 4 preferably uses the Latin hypercube experimental design method.
样本点数量根据理论分析、实验或经验值而定,优选取Nh=(nv+3)*(nv+2),4Nh≤Nl≤6Nh。The number of sample points is determined according to theoretical analysis, experiments or empirical values, preferably N h =(n v +3)*(n v +2), 4N h ≤N l ≤6N h .
步骤5:调用步骤3中高、低精度大展弦比机翼气动结构耦合分析模型,获得步骤4中的Nh和Nl样本点处的模型响应值,存储高、低精度样本点信息。Step 5: Invoke the high- and low-precision large aspect ratio wing aerodynamic structure coupling analysis model in step 3, obtain the model response values at the N h and N l sample points in step 4, and store the high and low-precision sample point information.
步骤6:使用模型融合方法将高、低精度样本点信息进行融合,建立代理模型。所述的代理模型为由修正模型的代理模型与误差模型的代理模型组成的融合模型ys(x)。Step 6: Use the model fusion method to fuse the high- and low-precision sample point information to establish a proxy model. The surrogate model is a fusion model y s (x) composed of the surrogate model of the correction model and the surrogate model of the error model.
步骤6的具体实现方法如下:The specific implementation method of step 6 is as follows:
步骤6.1:根据高精度样本以及相应的低精度样本信息,使用最小二乘法获得低精度大展弦比机翼气动结构耦合分析样本点的修正因子如式(2)所示:Step 6.1: According to the high-precision samples and the corresponding low-precision sample information, use the least squares method to obtain the correction factor of the low-precision and large-aspect-ratio wing aerodynamic structure coupling analysis sample points, as shown in formula (2):
其中:Nh为高精度大展弦比机翼气动结构耦合分析样本点个数;yh(xi)为高精度气动结构耦合分析模型的响应值,yl(xi)为低精度气动结构耦合分析模型的响应值,所述的响应值包括升阻比、结构质量,结构最大应力,结构最大位移;ρ0、ρ1为低精度气动结构耦合分析模型样本点的修正因子,每一个响应值均有自己对应的修正因子。Among them: N h is the number of sample points for high-precision and large-aspect-ratio wing aerodynamic structure coupling analysis; y h ( xi ) is the response value of the high-precision aerodynamic structure coupling analysis model, and y l ( xi ) is low-precision aerodynamic structure The response value of the structural coupling analysis model, the response value includes the lift-drag ratio, the structural mass, the maximum stress of the structure, and the maximum displacement of the structure; ρ 0 and ρ 1 are the correction factors of the sample points of the low-precision aerodynamic structure coupling analysis model, and each The response values have their own corresponding correction factors.
步骤6.2:使用步骤6.1中的低精度气动结构耦合分析模型样本点的修正因子对所有低精度气动结构耦合分析模型样本点进行修正,基于修正后的低精度气动结构耦合分析模型样本信息使用Kriging方法构造代理模型,低精度气动结构耦合分析模型的修正模型yl s(x)表示为:Step 6.2: Use the correction factor of the sample points of the low-precision aerodynamic structure coupling analysis model in step 6.1 to correct all the sample points of the low-precision aerodynamic structure coupling analysis model, and use the Kriging method based on the corrected sample information of the low-precision aerodynamic structure coupling analysis model To construct a proxy model, the revised model y l s (x) of the low-precision aerodynamic-structure coupled analysis model is expressed as:
yl s(x)=ρ0+ρ1yl(x) (3)y l s (x)=ρ 0 +ρ 1 y l (x) (3)
其中yl(x)为低精度气动结构耦合分析模型样本点的响应值,使用式(3)对所有低精度气动结构耦合分析模型样本点数据进行修正获得低精度气动结构耦合分析模型的修正模型yl s(x)。使用Kriging方法完成低精度气动结构耦合分析模型修正模型yl s(x)的代理模型ys s(x)构造。Among them, y l (x) is the response value of the sample point of the low-precision aerodynamic structure coupling analysis model. Use formula (3) to correct all the sample point data of the low-precision aerodynamic structure coupling analysis model to obtain the corrected model of the low-precision aerodynamic structure coupling analysis model. y l s (x). The surrogate model y s s (x) of the modified model y l s (x) is constructed by using the Kriging method.
步骤6.3:计算步骤5中高精度气动结构耦合分析模型样本点与步骤6.2中低精度气动结构耦合分析模型的修正模型之间的误差值δ(xi),误差值δ(xi)通过式(4)计算获得:Step 6.3: Calculate the error value δ(x i ) between the sample points of the high-precision aerodynamic structure coupling analysis model in step 5 and the corrected model of the low-precision aerodynamic structure coupling analysis model in step 6.2, and the error value δ( xi ) is calculated by the formula ( 4) Calculate to get:
δ(xi)=yh(xi)-yl s(xi)=yh(xi)-[ρ0+ρ1yl(xi)])i=1,2,3…Nh) (4)δ(x i )=y h (x i )-y l s (x i )=y h (x i )-[ρ 0 +ρ 1 y l (x i )])i=1,2,3… N h ) (4)
基于误差信息δ(xi),使用Kriging方法,完成误差模型的代理模型δs(x)的构造。Based on the error information δ(x i ), the Kriging method is used to complete the construction of the surrogate model δ s (x) of the error model.
步骤6.4:构建由步骤6.2中的修正模型的代理模型ys s(x)与步骤6.3中的误差模型的代理模型δs(x)组成的融合模型ys(x),如式(5)所示:Step 6.4: Construct a fusion model y s (x) composed of the surrogate model y s s (x) of the corrected model in step 6.2 and the surrogate model δ s (x) of the error model in step 6.3, as shown in formula (5) shown:
ys(x)=ys s(x)+δs(x) (5)y s (x)=y s s (x)+δ s (x) (5)
所述的融合模型ys(x)为高精度气动结构耦合分析模型的代理模型。The fusion model y s (x) is a proxy model of the high-precision aerodynamic structure coupling analysis model.
步骤7:基于步骤6中所建立的融合模型ys(x),使用罚函数处理问题中的复杂约束,使用优化算法进行系统优化问题求解,得到基于当前融合模型ys(x)的最优解 Step 7: Based on the fusion model y s (x) established in step 6, use the penalty function to deal with the complex constraints in the problem, use the optimization algorithm to solve the system optimization problem, and obtain the optimal solution based on the current fusion model y s (x). untie
所述的罚函数如式(6)所示:The penalty function is shown in formula (6):
F(x)=f(x)+MP(x)M>0F(x)=f(x)+MP(x)M>0
其中:F(x)为处理后的优化目标,f(x)为原始优化目标,M为惩罚因子,P(x)为约束违背度,gi(x)为不等式约束,hi(x)为等式约束,m为不等式约束个数,l为约束总个数。Among them: F(x) is the processed optimization objective, f(x) is the original optimization objective, M is the penalty factor, P(x) is the constraint violation degree, g i (x) is the inequality constraint, h i (x) is the equality constraint, m is the number of inequality constraints, and l is the total number of constraints.
步骤7中使用优化算法进行系统优化问题求解优选遗传算法求解。In step 7, the optimization algorithm is used to solve the system optimization problem, and the optimal genetic algorithm is used to solve it.
步骤8:调用步骤3中的高精度的大展弦比机翼气动结构耦合分析模型,获得步骤7中的代理模型的最优解处的真实响应值。计算最优解的真实响应值与代理模型值的差值,根据差值大小判定该优化结果是否可信。若不可信则返回步骤4,增加低精度大展弦比机翼气动结构耦合分析模型样本点数量,重复步骤5、6、7、8,直至获得可信的优化结果,若可信则输出最优设计结果,即完成考虑气动结构耦合问题的大展弦比机翼的高效优化设计。Step 8: Invoke the high-precision large aspect ratio wing aerodynamic structure coupling analysis model in step 3 to obtain the optimal solution of the surrogate model in step 7 the true response value at . Calculate the difference between the real response value of the optimal solution and the surrogate model value, and determine whether the optimization result is credible according to the difference. If it is not credible, go back to step 4, increase the number of sample points of the low-precision large aspect ratio wing aerodynamic structure coupling analysis model, and repeat steps 5, 6, 7, and 8 until credible optimization results are obtained. If credible, output the most The optimal design result is to complete the high-efficiency optimal design of the wing with a large aspect ratio considering the aerodynamic-structure coupling problem.
有益效果:Beneficial effects:
1、针对大展弦比机翼设计时需要考虑气动结构耦合问题导致优化设计过程计算成本难以承受的问题,本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,通过网格密度控制实现分析模型精度与计算成本的综合协调。1. In view of the problem that the aerodynamic structure coupling problem needs to be considered when designing a large aspect ratio wing, which leads to the unbearable calculation cost of the optimization design process, the present invention discloses a large aspect ratio wing optimization design method based on a model fusion method, through The mesh density control realizes the comprehensive coordination of analytical model accuracy and computational cost.
2、本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,使用模型融合方法将高、低精度模型信息高效融合,在满足设计精度要求的同时,减少高精度分析模型的调用量,降低计算成本,提高大展弦比机翼的设计效率。2. A large aspect ratio wing optimization design method based on the model fusion method disclosed in the present invention uses the model fusion method to efficiently fuse high- and low-precision model information, and reduces the number of high-precision analysis models while meeting the design accuracy requirements. The number of calls is reduced, the computational cost is reduced, and the design efficiency of large aspect ratio wings is improved.
3、本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,使用罚函数的方式对复杂约束问题进行处理,实现了优化设计过程的简洁与便利。3. The present invention discloses a large aspect ratio wing optimization design method based on a model fusion method, which uses a penalty function to deal with complex constraints, thereby realizing the simplicity and convenience of the optimization design process.
4、本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,使用最优解的真实响应值与代理模型值的差值进行最优结果的可靠度判定,完成优化流程的更新与迭代。4. A large aspect ratio wing optimization design method based on a model fusion method disclosed in the present invention uses the difference between the real response value of the optimal solution and the surrogate model value to determine the reliability of the optimal result to complete the optimization process update and iteration.
5、本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,利用Kriging代理模型方法,高效地完成修正模型的代理模型与误差模型的代理模型的构造,进而使高、低精度模型信息更有效地融合。5. A large aspect ratio wing optimization design method based on the model fusion method disclosed in the present invention uses the Kriging surrogate model method to efficiently complete the construction of the surrogate model of the correction model and the surrogate model of the error model. Low-precision model information is fused more efficiently.
6、本发明公开的一种基于模型融合方法的大展弦比机翼优化设计方法,使用遗传算法进行优化求解,能够避免优化求解中出现无解的情况,提高工程优化设计问题的求解可行性。6. A large aspect ratio wing optimization design method based on the model fusion method disclosed in the present invention uses genetic algorithm for optimization solution, which can avoid the situation of no solution in the optimization solution, and improve the solution feasibility of engineering optimization design problems. .
附图说明Description of drawings
图1为大展弦比机翼气动结构耦合分析流程图;Figure 1 is the flow chart of the coupling analysis of the aerodynamic structure of the wing with a large aspect ratio;
图2为考虑气动结构耦合的大展弦比机翼优化设计方法流程图;Fig. 2 is a flow chart of the optimal design method for a wing with a large aspect ratio considering the aerodynamic structure coupling;
图3为气动学科高、低精度网格对比图,Figure 3 is a comparison diagram of high and low precision grids in aerodynamics.
其中图3a为高精度分析模型网格,图3b为低精度分析模型网格;Among them, Figure 3a is a high-precision analysis model grid, and Figure 3b is a low-precision analysis model grid;
图4为模型融合方法流程图;Fig. 4 is the flow chart of model fusion method;
具体实施方式Detailed ways
为了更好地说明本发明的技术方案与优点,下面通过具体的大展弦比机翼优化设计实例,并结合附图与表格对本发明做进一步说明,具体实施方式如下。In order to better illustrate the technical solutions and advantages of the present invention, the present invention is further described below through a specific example of the optimal design of a wing with a large aspect ratio, combined with the accompanying drawings and tables, and the specific embodiments are as follows.
本实施例公开的一种基于模型融合方法的大展弦比机翼优化设计方法,流程图如图2所示,具体实现步骤如下:A method for optimal design of a wing with a large aspect ratio based on a model fusion method disclosed in this embodiment, the flowchart is shown in Figure 2, and the specific implementation steps are as follows:
步骤1:选取层流翼型NACA64A816作为基准初始翼型、设计工况为飞行马赫数Ma=0.64,攻角α=2°机翼形状由系统变量的初始值确定,具体如表2所示。Step 1: Select the laminar airfoil NACA64A816 as the reference initial airfoil, the design condition is the flight Mach number Ma=0.64, the angle of attack α=2° The wing shape is determined by the initial value of the system variable, as shown in Table 2.
步骤2:根据需求建立结构学科的优化模型与系统级优化模型。Step 2: Establish the optimization model and system-level optimization model of structural disciplines according to the requirements.
步骤2.1:根据需求建立结构学科的优化模型。Step 2.1: Establish an optimization model of structural disciplines according to requirements.
在结构学科的优化模型中对机翼的每个结构组件进行尺寸优化。选择每个翼盒的蒙皮厚度(Tskin)、每个翼肋的腹板厚度(Trib)、每个翼肋的凸缘半径(Rrib)、每个翼梁的腹板厚度(Tspar),每个翼梁的上下凸缘半径(Rspar),作为结构学科优化设计变量。约束条件包括结构最大应力σmax小于许用应力100MPa、结构最大位移δmax小于许用位移900mm。结构优化目标为机翼的结构质量W最小。结构学科的优化在结构学科分析模型中实现。结构优化模型如下式(7)所示。Each structural component of the wing is dimensionally optimized in the optimization model of the structural discipline. Select the skin thickness for each wing box (T skin ), the web thickness for each rib (T rib ), the flange radius for each rib (R rib ), the web thickness for each spar (T rib ) spar ), the upper and lower flange radius (R spar ) of each spar, as the structural discipline optimization design variable. Constraints include that the maximum structural stress σ max is less than the allowable stress 100MPa, and the maximum structural displacement δ max is less than the allowable displacement 900mm. The objective of structural optimization is to minimize the structural mass W of the wing. The optimization of the structural discipline is realized in the structural discipline analysis model. The structural optimization model is shown in the following formula (7).
其中,xstruc为结构学科优化设计变量,xstruc lb和xstruc ub分别为结构设计变量的上限与下限,设计变量取值如表1所示。Among them, x struc is the optimization design variable of the structural discipline, x struc lb and x struc ub are the upper and lower limits of the structural design variable, respectively, and the values of the design variables are shown in Table 1.
表1结构设计变量及变化范围Table 1 Structural Design Variables and Variation Scope
步骤2.2:根据需求建立系统级优化模型。Step 2.2: Build a system-level optimization model based on requirements.
系统级优化中选几何设计参数为设计变量,所述的几何设计参数包括展弦比、根梢比、后掠角,并根据需求确定其上下限,如表2所示;以结升阻比D/L最大,结构质量W最小为优化目标,约束条件包括结构最大应力σmax小于许用应力100MPa、结构最大位移δmax小于许用位移900mm以及机翼面积不变恒定为50.17m2。系统级优化模型如式(8)所示。The geometric design parameters are selected as design variables in the system-level optimization. The geometric design parameters include aspect ratio, root-to-tip ratio, and sweep angle, and their upper and lower limits are determined according to requirements, as shown in Table 2; the junction lift-to-drag ratio D /L is the largest, and the structural mass W is the smallest as the optimization objective. The constraints include that the maximum structural stress σ max is less than the allowable stress 100MPa, the maximum structural displacement δ max is less than the allowable displacement 900mm, and the wing area is constant and constant at 50.17m 2 . The system-level optimization model is shown in equation (8).
min F(X)=1/2×Cweight+1/2×CD/L min F(X)=1/2×C weight +1/2×C D/L
s.t.σmax≤100Mpa (8)stσ max ≤100Mpa (8)
δmax≤900mmδmax ≤900mm
Xlb≤X≤Xub X lb ≤X≤X ub
S=50.17m2 S=50.17m 2
F(X)为综合优化目标,由两个优化目标结构质量W与升阻比D/L线性加权所得,在本算例中两个优化目标的权重相同即均取为1/2。由于每个目标的数量级均不相同,使用初始机翼的结构质量Wbaseline和初始机翼的升阻比(D/L)baseline分别对优化目标结构质量与升阻比做归一化处理,获得归一化后的目标函数响应值Cweight和CD/L。X为设计变量,Xlb和Xub分别为设计变量的上下限,具体取值如表2所示。F(X) is the comprehensive optimization objective, which is obtained by the linear weighting of the structural mass W and the lift-drag ratio D/L of the two optimization objectives. Since the order of magnitude of each target is different, the structural mass W baseline of the initial wing and the lift-to-drag ratio (D/L) baseline of the initial wing are used to normalize the structural mass of the optimized target and the lift-to-drag ratio, respectively, to obtain Normalized objective function response values C weight and C D/L . X is the design variable, X lb and X ub are the upper and lower limits of the design variable, respectively, and the specific values are shown in Table 2.
表2系统级设计变量及变化范围Table 2 System-level design variables and their variation ranges
步骤3:使用气动结构耦合建模技术建立高大展弦比机翼气动结构耦合分析模型和低精度大展弦比机翼气动结构耦合分析模型。在该步骤中,通过网格绘制密度调整实现高、低精度分析模型的区分。本实施例中,高精度网格密度为低精度的两倍,如图3所示。在结构学科分析模型中,结构学科的有限元模型单元属性定义如表3所示,使用Nastran自带的SQP优化器完成结构学科的优化,其优化模型为步骤2.1中结构学科的优化模型所述。Step 3: Use the aerodynamic structure coupling modeling technology to establish the aerodynamic structure coupling analysis model of the high aspect ratio wing and the aerodynamic structure coupling analysis model of the low-precision large aspect ratio wing. In this step, the distinction between high and low precision analytical models is achieved by adjusting the density of grid rendering. In this embodiment, the high-precision mesh density is twice that of the low-precision grid, as shown in FIG. 3 . In the structural subject analysis model, the element attributes of the finite element model of the structural subject are defined as shown in Table 3. The SQP optimizer that comes with Nastran is used to complete the optimization of the structural subject. The optimization model is described in the optimization model of the structural subject in step 2.1. .
表3有限元模型单元属性Table 3 Element properties of finite element model
步骤4:使用拉丁超立方试验设计方法生成高精度模型样本点和低精度模型样本点。在本发明中,计算成本以CPU计算时间计算。通过实验统计,每次高精度分析模型需要约20分钟,每次低精度分析模型的计算成本约为3分钟。针对模型融合方法生成30个高精度样本点和130个低精度样本点。为了进行效率对比,同时生成50个高精度样本点(计算成本约为30次高精度分析和130次低精度分析之和)用于构造使用传统方法的代理模型。Step 4: Generate high-precision model sample points and low-precision model sample points using the Latin Hypercube Design of Experiments method. In the present invention, the computation cost is calculated in terms of CPU computation time. According to experimental statistics, it takes about 20 minutes for each high-precision analysis model, and the computational cost for each low-precision analysis model is about 3 minutes. Generate 30 high-precision sample points and 130 low-precision sample points for the model fusion method. For efficiency comparison, 50 high-precision sample points (the computation cost is about the sum of 30 high-precision analyses and 130 low-precision analyses) are simultaneously generated for constructing surrogate models using traditional methods.
上述的使用传统方法构造代理模型在本实施案例中为单独使用Kriging方法直接构造高精度大展弦比机翼气动结构耦合分析模型的代理模型。The above-mentioned use of the traditional method to construct the surrogate model in this example is the surrogate model that directly uses the Kriging method to directly construct a high-accuracy and large aspect ratio wing aerodynamic structure coupled analysis model.
步骤5:调用步骤3中高、低精度大展弦比机翼气动结构耦合分析模型,获得步骤4中的30个高精度样本点和130个低精度样本点处的模型响应值,存储高、低精度大展弦比机翼气动结构耦合分析模型样本点信息。为了进行效率对比,需同时获得50个用于构造基于传统方法的代理模型的高精度样本点处的模型响应值。Step 5: Invoke the high- and low-precision high-aspect ratio wing aerodynamic structure coupling analysis model in Step 3, obtain the model response values at the 30 high-precision sample points and 130 low-precision sample points in Step 4, and store the high and low Accurate large aspect ratio wing aero-structure coupled analysis model sample point information. For efficiency comparison, the model response values at 50 high-precision sample points used to construct the surrogate model based on the traditional method should be obtained at the same time.
步骤6:使用模型融合方法将步骤5中的30个高精度样本点信息与130个低精度样本点信息进行融合,建立基于模型融合方法的高精度大展弦机翼气动结构耦合分析模型的代理模型。其具体流程图如图4所示。同时,使用50个高精度样本点信息基于传统方法直接构造高精度大展弦机翼气动结构耦合分析模型的代理模型。Step 6: Use the model fusion method to fuse the 30 high-precision sample point information and 130 low-precision sample point information in step 5, and establish the proxy of the high-precision large-span chord wing aerodynamic structure coupling analysis model based on the model fusion method Model. Its specific flow chart is shown in Figure 4. At the same time, the surrogate model of the coupled analysis model of the aerodynamic structure of the high-precision large-span chord wing is directly constructed based on the traditional method using the information of 50 high-precision sample points.
步骤7:基于步骤6所建立的利用模型融合方法建立的代理模型与传统方法方法构造的代理模型,使用遗传算法进行优化。对于该优化问题中的复杂约束使用罚函数的方式进行处理,惩罚因子取为1000。分别得到基于模型融合方法的最优解和基于传统方法的最优解。Step 7: Based on the surrogate model established by the model fusion method established in step 6 and the surrogate model constructed by the traditional method, the genetic algorithm is used to optimize. For the complex constraints in the optimization problem, the penalty function is used to deal with it, and the penalty factor is taken as 1000. The optimal solution based on the model fusion method and the optimal solution based on the traditional method are obtained respectively.
步骤8:调用步骤3中的高精度的大展弦比机翼气动结构耦合分析模型,获得步骤7中的代理模型的最优解处的真实响应值。计算最优解的真实响应值与代理模型值的差值,根据差值大小判定该优化结果是否可信。若不可信则返回步骤4,增加低精度大展弦比机翼气动结构耦合分析模型样本点数量,重复步骤5、6、7、8,直至获得可信的优化结果,若可信则输出最优设计结果,即完成考虑气动结构耦合问题的大展弦比机翼的高效优化设计。Step 8: Invoke the high-precision large aspect ratio wing aerodynamic structure coupling analysis model in step 3 to obtain the optimal solution of the surrogate model in step 7 the true response value at . Calculate the difference between the real response value of the optimal solution and the surrogate model value, and determine whether the optimization result is credible according to the difference. If it is not credible, go back to step 4, increase the number of sample points of the low-precision large aspect ratio wing aerodynamic structure coupling analysis model, and repeat steps 5, 6, 7, and 8 until credible optimization results are obtained. If credible, output the most The optimal design result is to complete the high-efficiency optimal design of the wing with a large aspect ratio considering the aerodynamic-structure coupling problem.
统计系统优化结果如表4所示,结构学科优化结果如表5所示。The optimization results of statistical systems are shown in Table 4, and the optimization results of structural disciplines are shown in Table 5.
表4三维机翼系统优化结果Table 4 Optimization results of 3D wing system
观察表4,对比使用两种方法的优化设计结果,可发现升阻比有较小改善,但结构质量变化明显。使用本发明中的优化设计方法,质量降低54%,而传统方法的优化结果中质量仅仅降低4%。使用本发明方法后的归一化后的综合优化目标值为0.7258,远小于相同计算成本下传统方法的优化结果。同时使用本发明优化设计方法时真实目标值与代理模型值的差值较小,说明本发明的的优化设计方法具有更高的精度。通过实验结果对比,得出本发明的方法相较于传统方法,在相同计算成本情况下不仅模型精度更高,且具有更好的优化设计结果。因此,采用本发明提出的一种基于模型融合方法的大展弦比机翼优化设计方法进行大展弦比机翼优化设计可以在保证精度同时,减少高精度分析模型的调用量,从而降低计算成本,提高大展弦比机翼的优化设计效率。Observe Table 4 and compare the results of the optimized design using the two methods. It can be found that the lift-to-drag ratio has been slightly improved, but the structural quality has changed significantly. Using the optimization design method in the present invention, the quality is reduced by 54%, while the quality is only reduced by 4% in the optimization result of the traditional method. The normalized comprehensive optimization target value after using the method of the present invention is 0.7258, which is much smaller than the optimization result of the traditional method under the same computational cost. At the same time, when the optimal design method of the present invention is used, the difference between the real target value and the surrogate model value is small, indicating that the optimal design method of the present invention has higher precision. Through the comparison of experimental results, it is concluded that the method of the present invention not only has higher model accuracy, but also has better optimal design results under the same computational cost as compared with the traditional method. Therefore, using the large aspect ratio wing optimization design method based on the model fusion method proposed by the present invention to carry out the large aspect ratio wing optimization design can ensure the accuracy while reducing the call amount of the high-precision analysis model, thereby reducing the calculation. cost and improve the optimal design efficiency of large aspect ratio wings.
表5三维机翼结构优化结果Table 5 Optimization results of 3D wing structure
根据前述具体的大展弦比机翼优化实例分析可见,本发明能够实现预期的发明目的,相比于传统的大展弦比机翼优化设计方法,本发明有助于提高大展弦比机翼优化设计结果与设计质量;另一方面,涉及大展弦比机翼高精度分析模型的优化问题,本发明还能大大提高的优化效率,降低优化设计成本,缩短优化设计周期。According to the analysis of the above-mentioned specific example of the optimization of a wing with a large aspect ratio, it can be seen that the present invention can achieve the intended purpose of the invention. Wing optimization design results and design quality; on the other hand, in relation to the optimization of high-aspect-ratio wing high-precision analysis models, the present invention can also greatly improve optimization efficiency, reduce optimization design costs, and shorten optimization design cycles.
以上所述的具体描述,对发明的目的、技术方案和有益效果进行了进一步详细说明,所应理解的是,以上所述仅为本发明的具体实施例,用于解释本发明,并不用于限定本发明的保护范围,凡在本发明的精神和原则之内,所做的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。The above-mentioned specific description further describes the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above-mentioned descriptions are only specific embodiments of the present invention, which are used to explain the present invention and are not intended to be used for The protection scope of the present invention is limited, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
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