CN107391891B - Large-aspect-ratio wing optimization design method based on model fusion method - Google Patents

Large-aspect-ratio wing optimization design method based on model fusion method Download PDF

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CN107391891B
CN107391891B CN201710790069.2A CN201710790069A CN107391891B CN 107391891 B CN107391891 B CN 107391891B CN 201710790069 A CN201710790069 A CN 201710790069A CN 107391891 B CN107391891 B CN 107391891B
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龙腾
汪艳
刘莉
李鑫
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a high aspect ratio wing optimization design method based on a model fusion method, and belongs to the field of overall optimization design of aircrafts. According to the optimization method, optimization is divided into an optimization model and a system-level optimization model of a structural subject according to requirements, and complex constraints are processed by using a penalty function method; establishing a high-precision pneumatic structure coupling analysis model and a low-precision pneumatic structure coupling analysis model by using a pneumatic structure coupling modeling technology; respectively generating high-precision sample points and low-precision sample points by using a test design method; respectively calling a high-precision structure coupling analysis model and a low-precision structure coupling analysis model to obtain high-precision sample information and low-precision sample information and storing the high-precision sample information and the low-precision sample information; fusing high-precision model information and low-precision model information by using a model fusion method to establish a proxy model; and performing optimization solution by using an optimization method based on the current agent model, judging whether the optimization result is credible according to the difference value between the real response value at the optimal solution and the agent model value based on the model fusion method, returning to the reconstructed fusion model for optimization solution if the optimization result is not credible, and outputting the optimal design result if the optimization result is credible to complete the optimization design.

Description

Large-aspect-ratio wing optimization design method based on model fusion method
Technical Field
The invention relates to a high aspect ratio wing optimization design method based on a model fusion method, and belongs to the technical field of overall optimization design of aircrafts.
Background
The high-aspect-ratio wing has the characteristics of large lift-drag ratio, large wing internal volume and the like, and is widely applied to aircrafts such as high-altitude unmanned planes, solar aircrafts, large intercontinental airliners and the like. In the flying process of the aircraft, the high-aspect-ratio wing is influenced by aerodynamic load to generate structural deformation, and the influence of the deformation amplitude on the aerodynamic performance is very obvious. Therefore, the aerodynamic structure coupling problem needs to be considered when analyzing and designing the high aspect ratio wing. Aiming at the coupling problem of the pneumatic structure, the fluid mechanics and the structural mechanics can be independently solved as a single subject, cross-subject data interaction is realized through a software scheduling technology, and coupling analysis is realized through iterative solution. To improve the precision of the coupling analysis, high precision analysis methods such as Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) are often used to analyze and solve two single subjects separately. However, the high-precision analysis model also brings a problem of time consumption in calculation while improving the analysis precision and the reliability, and although the computer software and hardware technology has been developed sufficiently at present, it is still extremely time-consuming to call the high-precision analysis model to complete one iteration solution. For example, several hours or even tens of hours are required to complete a pneumatic simulation analysis using a CFD model. The optimization design of the high-aspect-ratio wing is also a repeated iteration process, and a high-precision coupling analysis model is often called for thousands of times in the optimization process, so that the design cost is further increased, and the optimization design efficiency is very low.
In order to better explain the technical scheme of the invention, the applied pneumatic structure coupling modeling technology is specifically described below.
The pneumatic structure coupling modeling technology comprises the following steps:
with the increase of the aspect ratio of the wing, the flexibility of the wing is continuously increased, and the coupling phenomenon between the aerodynamic performance and the structural performance of the wing is more obvious. The key of the pneumatic structure coupling modeling technology is the information transfer between pneumatic and structural disciplines. In the existing mature pneumatic structure coupling modeling technology, a three-dimensional interpolation method is often used for transmitting a pneumatic analysis result to a structural subject, meanwhile, the geometric shape of the wing is determined and updated according to the coordinates of control points on the front edge and the rear edge of the deformed wing, the pneumatic subject analysis is carried out again, and the transmission of the structural subject analysis result to the pneumatic subject is completed. On the other hand, in the pneumatic structure coupling modeling, the density degree of the pneumatic subject grid often controls the calculation cost and the model precision of the whole coupling analysis model. Increasing the grid density can improve the accuracy of the analytical model, but also increases the computational cost. Conversely, reducing the grid density reduces the computational accuracy and reduces the computational cost.
The flow chart of the pneumatic structure coupling analysis model is shown in fig. 1, and the specific method comprises the following steps:
step 1, establishing/updating a wing parameterized model by using a model parameterized technology based on UG secondary development. The parameters parameterized by the geometric model comprise geometric design variable aspect ratio, root-tip ratio, sweep angle, airfoil parameters and coordinate information of wing leading and trailing edge position control points for quantitatively representing structural shape deformation. After the parameterization is completed, the geometry file is output for subsequent analysis, and the geometry file is generally in a step format or an igs format.
And 2, establishing a pneumatic analysis model by using CFD. The method comprises the steps of inputting a geometric shape file and aerodynamic analysis working condition information including Mach number and attack angle, and outputting an aerodynamic analysis result including lift force and resistance information and an aerodynamic force distribution file. Gambit can be adopted for grid drawing, and Fluent is used for pneumatic analysis and solution.
And 3, establishing a structural subject analysis model by using an FEA method, carrying out pretreatment by using Patran, and using Nastran as post-treatment. Inputting a geometric shape file, and performing related analysis optimization settings such as material attribute, unit attribute definition and aerodynamic loading by using a PCL language. The self-contained SQP optimizer in Nastran can realize structural subject optimization. And the final output structural analysis structure comprises the maximum stress and the maximum displacement and the coordinate information of the control points of the front edge and the rear edge of the wing.
And 4, if the first analysis is carried out, inputting the coordinate information of the deformed control point into a model parameterization module, repeating the steps 2, 3 and 4, if the first analysis is not carried out, calculating the relative displacement η, wherein the calculation of the relative displacement is shown as the formula (1), when the relative displacement is less than 0.01, outputting the pneumatic analysis result at the moment, including the optimization results of lift-drag ratio, mass, maximum stress, maximum displacement and structural subject variables, and when the relative displacement is more than 0.01, repeating the steps 1, 2, 3 and 4 until the relative displacement is less than 0.01, and finishing the iteration.
Figure BDA0001398872930000021
In the formula (1), i represents the i-th analysis, and i-1 represents the last analysis of the i-th analysis.
Disclosure of Invention
Aiming at the problem of overhigh calculation cost when a pneumatic structure is coupled in the optimization design process of the high-aspect-ratio wing, the invention discloses a high-aspect-ratio wing optimization design method based on a model fusion method, aiming at solving the technical problem that the high-efficiency optimization design of the high-aspect-ratio wing is realized by considering the pneumatic structure coupling problem under the condition of ensuring the precision, and the method has the following advantages: the model fusion method is used for effectively fusing the high-precision analysis model information and the low-precision analysis model information, the low-precision model information is fully utilized to ensure the precision of the fusion model, and the calling times of the high-precision analysis model are reduced, so that the calculation cost is reduced, and the optimization design efficiency of the high-aspect-ratio wing is improved.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a high aspect ratio wing optimization design method based on a model fusion method, which comprises the steps of selecting an initial reference wing section and relevant shape parameters of a wing according to design requirements, and determining design working conditions; establishing an optimization model and a system-level optimization model of the structural discipline according to requirements, and processing complex constraints by using a penalty function method; establishing a high-precision high-aspect-ratio wing aerodynamic structure coupling analysis model by using an aerodynamic structure coupling modeling technology; respectively generating high-precision sample points and low-precision sample points by using a test design method; respectively calling high-precision and low-precision high-aspect-ratio wing pneumatic structure coupling analysis models to obtain and store high-precision and low-precision sample information; fusing high-precision model information and low-precision model information by using a model fusion method, and establishing a proxy model to realize the comprehensive coordination of model precision and calculation cost; and performing optimization solution by using an optimization method based on the current agent model, judging whether the optimization result is credible according to the difference value between the real response value at the optimal solution and the agent model value based on the model fusion method, returning to the reconstructed fusion model for performing optimization solution if the optimization result is not credible, and outputting the optimal design result if the optimization result is credible, namely finishing the high-efficiency optimization design of the wing with the high aspect ratio by considering the coupling problem of the pneumatic structure.
The invention discloses a high aspect ratio wing optimization design method based on a model fusion method, which comprises the following steps:
step 1: according to design requirements, selecting initial reference wing profiles and relevant shape parameters of wings, and determining design conditions.
The design working condition comprises Mach number and attack angle.
Step 2: and establishing an optimization model and a system level optimization model of the structural discipline according to the requirements.
Step 2.1: and establishing an optimization model of the structural discipline according to the requirement.
In order to be able to reduce the mass to the maximum extent while ensuring the structural strength, each structural component of the wing is optimized dimensionally during the structural analysis. Design variables include skin thickness, web thickness, flange radius; the optimization goal is that the structure quality is minimum; the constraint conditions are that the maximum stress constraint and the maximum displacement deformation constraint are satisfied. The optimization of the structural disciplines is implemented in a structural discipline analysis model.
Step 2.2: and establishing a system-level optimization model according to the requirements.
Selecting geometric design parameters as design variables in system level optimization, wherein the design variables comprise an aspect ratio, a root-tip ratio and a sweep angle, and determining upper and lower limits according to requirements; the maximum lift-drag ratio and the minimum structure mass are taken as optimization targets, and the constraint conditions comprise that the maximum structure stress is smaller than the allowable stress, the maximum structure displacement is smaller than the allowable displacement and the wing area is unchanged.
And step 3: and establishing a high-precision high-aspect-ratio wing aerodynamic structure coupling analysis model by using an aerodynamic structure coupling modeling technology. The grid density of the pneumatic discipline is a main factor of the calculation cost and the calculation precision, so that a low-precision analysis model is established by using a coarse grid in a pneumatic analysis model, and a high-precision analysis model is established by using a fine grid.
And 3, realizing coordination of calculation precision and calculation cost through the density degree of the grid density of the pneumatic discipline, and establishing a high-precision and low-precision pneumatic structure coupling analysis model.
And 4, step 4: separately generating N Using a design of experiments approachhA high precision sample point and NlA low precision sample point. Number of sample points and system-level optimization design variable dimension nvAnd (4) correlating. Wherein all high-precision sample points need to be included in the low-precision sample points.
In order to realize the high efficiency of the optimized design of the high-aspect-ratio wing considering the coupling problem of the aerodynamic structure, the Latin hypercube test design method is preferably used in the test design method in the step 4.
The number of sample points is determined by theoretical analysis, experiment or empirical value, and N is preferredh＝(nv+3)*(nv+2)，4Nh≤Nl≤6Nh。
And 5: calling the high-precision and low-precision high-aspect-ratio wing aerodynamic structure coupling analysis model in the step 3 to obtain N in the step 4hAnd NlAnd storing the high-precision sample point information and the low-precision sample point information according to the model response value at the sample point.
And 6, fusing the high-precision sample point information and the low-precision sample point information by using a model fusion method to establish a proxy model. The proxy model is a fusion model y consisting of a proxy model of a correction model and a proxy model of an error models(x)。
The specific implementation method of the step 6 is as follows:
step 6.1: according to the high-precision sample and the corresponding low-precision sample information, a least square method is used for obtaining correction factors of low-precision and high-aspect-ratio wing aerodynamic structure coupling analysis sample points, wherein the correction factors are as shown in formula (2):
Figure BDA0001398872930000041
wherein: n is a radical ofhAnalyzing the number of sample points for the coupling of the high-precision high-aspect-ratio wing aerodynamic structure; y ish(xi) Response value, y, for a high-precision pneumatic structure coupling analysis modell(xi) Response values of the coupling analysis model of the low-precision pneumatic structure comprise lift-drag ratio, structure mass, structure maximum stress and structure maximum displacement; rho0、ρ1Each response value has a corresponding correction factor for the correction factor of the low-precision pneumatic structure coupling analysis model sample point.
Step 6.2: correcting all low-precision pneumatic structure coupling analysis model sample points by using correction factors of the low-precision pneumatic structure coupling analysis model sample points in the step 6.1, constructing an agent model by using a Kriging method based on the corrected low-precision pneumatic structure coupling analysis model sample information, and correcting the model y of the low-precision pneumatic structure coupling analysis modell s(x) Expressed as:
yl s(x)＝ρ0+ρ1yl(x) (3)
wherein y isl(x) For the response value of the sample point of the low-precision pneumatic structure coupling analysis model, correcting all sample point data of the low-precision pneumatic structure coupling analysis model by using the formula (3) to obtain a corrected model y of the low-precision pneumatic structure coupling analysis modell s(x) In that respect Method for finishing correction model y of low-precision pneumatic structure coupling analysis model by using Kriging methodl s(x) Agent model y ofs s(x) And (5) constructing.
Step 6.3: calculating sample points and steps of high-precision pneumatic structure coupling analysis model in step 5Step 6.2 error value delta (x) between correction models of low-precision pneumatic structure coupling analysis modeli) Error value delta (x)i) Obtained by calculation of equation (4):
δ(xi)＝yh(xi)-yl s(xi)＝yh(xi)-[ρ0+ρ1yl(xi)])i＝1,2,3…Nh) (4)
based on error information delta (x)i) Using Kriging method to complete the proxy model delta of error models(x) The structure of (1).
Step 6.4: constructing a proxy model y from the modified model in step 6.2s s(x) Surrogate model delta to the error model in step 6.3s(x) Composed fusion model ys(x) As shown in formula (5):
ys(x)＝ys s(x)+δs(x) (5)
the fusion model ys(x) The method is a proxy model of a high-precision pneumatic structure coupling analysis model.
And 7: based on the fusion model y established in step 6s(x) Using complex constraint in penalty function processing problem, using optimization algorithm to solve system optimization problem to obtain current fusion model ys(x) Of (2) an optimal solution
Figure BDA0001398872930000051
The penalty function is shown in equation (6):
F(x)＝f(x)+MP(x)M＞0
Figure BDA0001398872930000052
wherein: f (x) is the processed optimization target, f (x) is the original optimization target, M is the penalty factor, P (x) is the constraint violation degree, gi(x) Is inequality constraint, hi(x) For equality constraint, m is the number of inequality constraints, and l is the total number of constraints.
And 7, carrying out system optimization problem solution by using an optimization algorithm, and preferably solving a genetic algorithm.
Step 8, calling the high-precision high-aspect-ratio wing aerodynamic structure coupling analysis model in the step 3 to obtain the optimal solution of the proxy model in the step 7
Figure BDA0001398872930000053
The true response value of (c). And calculating the difference value between the real response value of the optimal solution and the proxy model value, and judging whether the optimization result is credible according to the difference value. And if the model is not credible, returning to the step 4, increasing the number of sample points of the aerodynamic structure coupling analysis model of the low-precision high-aspect-ratio wing, repeating the steps 5, 6, 7 and 8 until a credible optimization result is obtained, and if the model is credible, outputting an optimal design result, namely completing the high-efficiency optimization design of the high-aspect-ratio wing considering the aerodynamic structure coupling problem.
Has the advantages that:
1. aiming at the problem that the calculation cost in the optimization design process is hard to bear because the pneumatic structure coupling problem needs to be considered when designing the high-aspect-ratio wing, the invention discloses the high-aspect-ratio wing optimization design method based on the model fusion method, and the comprehensive coordination of the analysis model precision and the calculation cost is realized through grid density control.
2. The invention discloses a high-aspect-ratio wing optimization design method based on a model fusion method, which is used for efficiently fusing high-precision model information and low-precision model information, reducing the calling amount of a high-precision analysis model while meeting the design precision requirement, reducing the calculation cost and improving the design efficiency of a high-aspect-ratio wing.
3. The invention discloses a high-aspect-ratio wing optimization design method based on a model fusion method, which uses a penalty function mode to process a complex constraint problem, and realizes the conciseness and convenience of an optimization design process.
4. The invention discloses a high-aspect-ratio wing optimization design method based on a model fusion method, which is characterized in that the reliability of an optimal result is judged by using the difference value between the real response value of an optimal solution and a proxy model value, and the updating and iteration of an optimization process are completed.
5. The invention discloses a high-aspect-ratio wing optimization design method based on a model fusion method, which utilizes a Kriging proxy model method to efficiently complete the construction of a proxy model of a correction model and a proxy model of an error model, thereby enabling high-precision model information and low-precision model information to be more effectively fused.
6. The invention discloses a high-aspect-ratio wing optimization design method based on a model fusion method, which is characterized in that a genetic algorithm is used for carrying out optimization solution, so that the situation of no solution in the optimization solution can be avoided, and the solution feasibility of the engineering optimization design problem is improved.
Drawings
FIG. 1 is a flow chart of a high aspect ratio wing aerodynamic structure coupling analysis;
FIG. 2 is a flow chart of a method for optimally designing a high aspect ratio wing in view of aerodynamic structure coupling;
FIG. 3 is a comparison graph of high and low precision grids of the pneumatic discipline,
wherein FIG. 3a is a high-precision analysis model grid and FIG. 3b is a low-precision analysis model grid;
FIG. 4 is a flow chart of a model fusion method;
Detailed Description
In order to better illustrate the technical solutions and advantages of the present invention, the present invention is further described below by using specific high aspect ratio wing optimization design examples, and with reference to the accompanying drawings and tables, and the following specific embodiments are described below.
The flow chart of the method for optimally designing the high aspect ratio wing based on the model fusion method disclosed by the embodiment is shown in fig. 2, and the method specifically comprises the following implementation steps:
step 1, selecting a laminar flow airfoil NACA64A816 as a reference initial airfoil, wherein the design working condition is that the flight Mach number Ma is 0.64, and the airfoil shape with the attack angle α being 2 degrees is determined by the initial value of a system variable, and is specifically shown in Table 2.
Step 2: and establishing an optimization model and a system level optimization model of the structural discipline according to the requirements.
Step 2.1: and establishing an optimization model of the structural discipline according to the requirement.
Each structural component of the wing is dimensionally optimized in an optimization model of the structural discipline. Selecting a skin thickness (T) for each wing boxskin) Web thickness (T) of each ribrib) Flange radius of each rib (R)rib) Web thickness (T) of each sparspar) Upper and lower flange radii (R) of each sparspar) As a structural discipline optimization design variable. The constraints including the structural maximum stress σmaxLess than allowable stress 100MPa and maximum structure displacement deltamaxLess than 900mm of allowable displacement. The structural optimization objective is to minimize the structural mass W of the wing. The optimization of the structural disciplines is implemented in a structural discipline analysis model. The structure optimization model is shown in the following formula (7).
Figure BDA0001398872930000071
Wherein x isstrucOptimization of design variables, x, for structural disciplinesstruc lbAnd xstruc ubThe upper and lower limits are the structural design variables, respectively, whose values are shown in table 1.
TABLE 1 structural design variables and ranges of variation
Figure BDA0001398872930000072
Step 2.2: and establishing a system-level optimization model according to the requirements.
Selecting geometric design parameters as design variables in system level optimization, wherein the geometric design parameters comprise an aspect ratio, a root-tip ratio and a sweep angle, and determining upper and lower limits according to requirements, as shown in table 2; the method takes the maximum D/L of the junction lift-drag ratio and the minimum W of the structure mass as optimization targets, and the constraint conditions comprise the maximum stress sigma of the structuremaxLess than allowable stress 100MPa and maximum structure displacement deltamaxLess than 900mm of allowable displacement and 50.17m of unchanged and constant wing area2. The system level optimization model is shown in formula (8).
min F(X)＝1/2×Cweight+1/2×CD/L
Figure BDA0001398872930000081
Figure BDA0001398872930000082
s.t.σmax≤100Mpa (8)
δmax≤900mm
Xlb≤X≤Xub
S＝50.17m2
F (x) is a comprehensive optimization objective obtained by linearly weighting the structural mass W and the lift-drag ratio D/L of the two optimization objectives, and the weights of the two optimization objectives in this example are equal to each other, i.e., 1/2. Since the order of magnitude of each target is different, the structural mass W of the original airfoil is usedbaselineAnd lift-to-drag ratio (D/L) of the original airfoilbaselineRespectively normalizing the optimized target structure mass and the lift-drag ratio to obtain a normalized target function response value CweightAnd CD/L. X is a design variable, XlbAnd XubThe upper and lower limits of the design variables are shown in table 2.
TABLE 2 System level design variables and variation Range
Figure BDA0001398872930000083
And step 3: and establishing a high-aspect-ratio wing aerodynamic structure coupling analysis model and a low-precision high-aspect-ratio wing aerodynamic structure coupling analysis model by using an aerodynamic structure coupling modeling technology. In the step, the high-precision analysis model and the low-precision analysis model are distinguished by adjusting the grid drawing density. In this embodiment, the high-precision grid density is twice the low precision, as shown in fig. 3. In the structural discipline analysis model, the finite element model element attribute definition of the structural discipline is shown in table 3, and the optimization of the structural discipline is completed by using the Nastran own SQP optimizer, and the optimization model of the structural discipline is described in step 2.1.
TABLE 3 finite element model element Properties
Figure BDA0001398872930000084
Figure BDA0001398872930000091
And 4, step 4: and generating high-precision model sample points and low-precision model sample points by using a Latin hypercube test design method. In the present invention, the calculation cost is calculated in terms of CPU calculation time. Through experimental statistics, each high-precision analysis model needs about 20 minutes, and each low-precision analysis model has the calculation cost of about 3 minutes. 30 high precision sample points and 130 low precision sample points are generated for the model fusion method. For efficiency comparison, 50 high-precision sample points (calculated at a cost of approximately the sum of 30 high-precision analyses and 130 low-precision analyses) were generated simultaneously for constructing a proxy model using the conventional method.
In the embodiment, the conventional method is used for constructing the proxy model, and the proxy model of the high-precision high-aspect-ratio wing aerodynamic structure coupling analysis model is directly constructed by using the Kriging method alone.
And 5: and (3) calling the high-precision and low-precision high-aspect-ratio wing aerodynamic structure coupling analysis model in the step (4), obtaining model response values at 30 high-precision sample points and 130 low-precision sample points in the step (4), and storing sample point information of the high-precision and low-precision high-aspect-ratio wing aerodynamic structure coupling analysis model. For efficiency comparison, 50 model response values at high-precision sample points for constructing a proxy model based on the conventional method are obtained at the same time.
And 6, fusing the 30 pieces of high-precision sample point information and the 130 pieces of low-precision sample point information in the step 5 by using a model fusion method, and establishing a proxy model of the high-precision large-span chord wing pneumatic structure coupling analysis model based on the model fusion method. The specific flow chart is shown in fig. 4. Meanwhile, 50 pieces of high-precision sample point information are used for directly constructing an agent model of the high-precision large-span-chord wing aerodynamic structure coupling analysis model based on the traditional method.
And 7: and (6) optimizing by using a genetic algorithm based on the agent model established by the model fusion method and the agent model constructed by the traditional method established in the step 6. For complex constraints in the optimization problem, a penalty function is used for processing, and a penalty factor is 1000. And respectively obtaining an optimal solution based on a model fusion method and an optimal solution based on a traditional method.
Step 8, calling the high-precision high-aspect-ratio wing aerodynamic structure coupling analysis model in the step 3 to obtain the optimal solution of the proxy model in the step 7
Figure BDA0001398872930000092
The true response value of (c). And calculating the difference value between the real response value of the optimal solution and the proxy model value, and judging whether the optimization result is credible according to the difference value. And if the model is not credible, returning to the step 4, increasing the number of sample points of the aerodynamic structure coupling analysis model of the low-precision high-aspect-ratio wing, repeating the steps 5, 6, 7 and 8 until a credible optimization result is obtained, and if the model is credible, outputting an optimal design result, namely completing the high-efficiency optimization design of the high-aspect-ratio wing considering the aerodynamic structure coupling problem.
The statistical system optimization results are shown in table 4, and the structural discipline optimization results are shown in table 5.
TABLE 4 three-dimensional wing system optimization results
Figure BDA0001398872930000101
Observing table 4, comparing the optimized design results using the two methods, it can be found that the lift-drag ratio is slightly improved, but the structural quality changes significantly. With the optimized design method of the present invention, the mass is reduced by 54%, while the mass is reduced by only 4% in the optimized result of the conventional method. The normalized comprehensive optimization target value after the method is used is 0.7258 which is far smaller than the optimization result of the traditional method under the same calculation cost. Meanwhile, when the optimal design method is used, the difference value between the real target value and the proxy model value is small, and the optimal design method has higher precision. Compared with the traditional method, the method has the advantages that the model precision is higher and the optimal design result is better under the condition of the same calculation cost. Therefore, when the optimization design method of the high-aspect-ratio wing based on the model fusion method is adopted to carry out the optimization design of the high-aspect-ratio wing, the precision can be ensured, and the calling amount of a high-precision analysis model can be reduced, so that the calculation cost is reduced, and the optimization design efficiency of the high-aspect-ratio wing is improved.
TABLE 5 three-dimensional wing structural optimization results
Figure BDA0001398872930000111
According to the analysis of the specific optimization example of the high-aspect-ratio wing, the expected invention purpose can be realized, and compared with the traditional optimization design method of the high-aspect-ratio wing, the optimization design method of the high-aspect-ratio wing is beneficial to improving the optimization design result and the design quality of the high-aspect-ratio wing; on the other hand, the invention relates to the optimization problem of the high-precision analysis model of the high-aspect-ratio wing, and the invention can also greatly improve the optimization efficiency, reduce the optimization design cost and shorten the optimization design period.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention, and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A high aspect ratio wing optimization design method based on a model fusion method is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
step 1: according to design requirements, selecting initial reference wing profiles and relevant shape parameters of wings, and determining design working conditions;
step 2: establishing an optimization model and a system level optimization model of the structural discipline according to requirements;
and step 3: establishing a high-precision high-aspect-ratio wing aerodynamic structure coupling analysis model by using an aerodynamic structure coupling modeling technology; the density of the grid of the pneumatic discipline is a main factor of the calculation cost and the calculation precision, so that a low-precision analysis model is established by using a coarse grid in a pneumatic analysis model, and a high-precision analysis model is established by using a fine grid;
and 4, step 4: separately generating N Using a design of experiments approachhA high precision sample point and NlA low precision sample point; number of sample points and system-level optimization design variable dimension nvCorrelation; wherein all the high-precision sample points need to be contained in the low-precision sample points;
and 5: calling the high-precision and low-precision high-aspect-ratio wing aerodynamic structure coupling analysis model in the step 3 to obtain N in the step 4hAnd NlStoring the high-precision sample point information and the low-precision sample point information according to the model response value at each sample point;
step 6, fusing the high-precision sample point information and the low-precision sample point information by using a model fusion method to establish a proxy model; the proxy model is a fusion model y consisting of a proxy model of a correction model and a proxy model of an error models(x)；
The specific implementation method of the step 6 is as follows:
step 6.1: according to the high-precision sample and the corresponding low-precision sample information, a least square method is used for obtaining correction factors of low-precision and high-aspect-ratio wing aerodynamic structure coupling analysis sample points, wherein the correction factors are as shown in formula (1):
Figure FDA0002444997820000011
wherein: n is a radical ofhAnalyzing the number of sample points for the coupling of the high-precision high-aspect-ratio wing aerodynamic structure; y ish(xi) Response value, y, for a high-precision pneumatic structure coupling analysis modell(xi) Response values of the coupling analysis model of the low-precision pneumatic structure comprise lift-drag ratio, structure mass, structure maximum stress and structure maximum displacement; rho0、ρ1Each response value has a corresponding correction factor for the correction factor of the low-precision pneumatic structure coupling analysis model sample point;
step 6.2: correcting all low-precision pneumatic structure coupling analysis model sample points by using correction factors of the low-precision pneumatic structure coupling analysis model sample points in the step 6.1, constructing an agent model by using a Kriging method based on the corrected low-precision pneumatic structure coupling analysis model sample information, and correcting the model y of the low-precision pneumatic structure coupling analysis modell s(x) Expressed as:
yl s(x)＝ρ0+ρ1yl(x) (2)
wherein y isl(x) For the response value of the sample point of the low-precision pneumatic structure coupling analysis model, correcting all sample point data of the low-precision pneumatic structure coupling analysis model by using the formula (2) to obtain a corrected model y of the low-precision pneumatic structure coupling analysis modell s(x) (ii) a Method for finishing correction model y of low-precision pneumatic structure coupling analysis model by using Kriging methodl s(x) Agent model y ofs s(x) Constructing;
step 6.3: calculating the error value delta (x) between the high-precision pneumatic coupling analysis model in the step 5 and the correction model of the low-precision pneumatic structure coupling analysis model in the step 6.2i) Error value delta (x)i) Obtained by calculation of equation (3):
δ(xi)＝yh(xi)-yl s(xi)＝yh(xi)-[ρ0+ρ1yl(xi)](i＝1,2,3…Nh) (3)
based on error information delta (x)i) Using Kriging method to complete the proxy model delta of error models(x) The structure of (1);
step 6.4: constructing a proxy model y from the modified model in step 6.2s s(x) Surrogate model delta to the error model in step 6.3s(x) Composed fusion model ys(x) As shown in formula (4):
ys(x)＝ys s(x)+δs(x) (4)
the fusion model ys(x) A proxy model for the high-precision pneumatic structure coupling analysis model;
and 7: based on the fusion model y established in step 6s(x) Using complex constraint in penalty function processing problem, using optimization algorithm to solve system optimization problem to obtain current fusion model ys(x) Of (2) an optimal solution
Figure FDA0002444997820000021
The penalty function is shown in equation (5):
F(x)＝f(x)+M*P(x)M＞0
Figure FDA0002444997820000022
wherein: f (x) is the processed optimization target, f (x) is the original optimization target, M is the penalty factor, P (x) is the constraint violation degree, gi(x) Is inequality constraint, hi(x) Is equality constraint, m is inequality constraint number, l is constraint total number;
and 8: calling the high-precision high-aspect-ratio wing aerodynamic structure coupling analysis model in the step 3 to obtain the optimal solution of the fusion model in the step 7
Figure FDA0002444997820000023
The true response value of (d); calculating a difference value between a real response value of the optimal solution and the fusion model, and judging whether the optimization result is credible according to the difference value; and if the model is not credible, returning to the step 4, increasing the number of sample points of the aerodynamic structure coupling analysis model of the low-precision high-aspect-ratio wing, repeating the steps 5, 6, 7 and 8 until a credible optimization result is obtained, and if the model is credible, outputting an optimal design result, namely completing the high-efficiency optimization design of the high-aspect-ratio wing considering the aerodynamic structure coupling problem.
2. The optimization design method of the high aspect ratio wing based on the model fusion method as claimed in claim 1, wherein: the specific implementation method of the step 2 is that,
step 2.1: establishing an optimization model of the structural discipline according to requirements;
in order to reduce the mass to the maximum extent while ensuring the structural strength, the size of each structural component of the wing is optimized in the structural analysis process; design variables include skin thickness, web thickness, flange radius; the optimization goal is that the structure quality is minimum; the constraint condition is that the maximum stress constraint and the maximum displacement deformation constraint are satisfied; the optimization of the structural disciplines is realized in a structural discipline analysis model;
step 2.2: establishing a system-level optimization model according to requirements;
selecting geometric design parameters as design variables in system level optimization, wherein the design variables comprise an aspect ratio, a root-tip ratio and a sweep angle, and determining upper and lower limits according to requirements; the maximum lift-drag ratio and the minimum structure mass are taken as optimization targets, and the constraint conditions comprise that the maximum structure stress is smaller than the allowable stress, the maximum structure displacement is smaller than the allowable displacement and the wing area is unchanged.
3. The optimization design method of the high aspect ratio wing based on the model fusion method as claimed in claim 1 or 2, wherein: and 3, realizing coordination of calculation precision and calculation cost through the density degree of the grid density of the pneumatic discipline, and establishing a high-precision and low-precision pneumatic structure coupling analysis model.
4. The high aspect ratio wing optimization design method based on the model fusion method as claimed in claim 3, wherein: in order to realize the high efficiency of the optimized design of the high-aspect-ratio wing considering the coupling problem of the aerodynamic structure, the experimental design method in the step 4 adopts a Latin hypercube experimental design method.
5. The method of claim 4, wherein the method comprises a step of optimizing the design of the high aspect ratio wing based on a model fusion methodIs characterized in that: the number of sample points in step 4 is determined according to theoretical analysis, experiment or empirical value, and N is takenh＝(nv+3)*(nv+2)，4Nh≤Nl≤6Nh。
6. The optimization design method of the high aspect ratio wing based on the model fusion method as claimed in claim 5, wherein: and 7, using an optimization algorithm to solve the system optimization problem and select a genetic algorithm to solve.
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