Wing static aeroelastic optimization design method based on MWORKS software platform

Abstract

The present invention discloses a wing static aeroelastic optimization design method based on the MWORKS software platform, including: obtaining design variables of the wing shape and structural layout, and determining the fitness function according to the optimization objectives and constraints. A genetic algorithm is used for global optimization, and the individual fitness is quickly calculated through a high-precision proxy model to finally obtain the optimal individual. The proxy model obtained by the adaptive modeling method of the present invention has higher accuracy. The adaptive sampling algorithm helps to dig out sample points that can significantly improve the fitting accuracy of the proxy model, thereby improving the efficiency of the proxy model construction. The point addition strategy SPMPD method disclosed in the present invention can achieve the required accuracy requirements with fewer sample points.

Description

Technical Field

[0001] The invention belongs to the technical field of wing static aeroelastic optimization design, and in particular relates to a wing static aeroelastic optimization design method based on a MWORKS software platform. Background Art

[0002] When designing an aircraft wing, in order to fully consider the coupling relationship between aerodynamic and structural disciplines, give play to the synergistic effect of multiple disciplines, and reduce repeated modifications in the design process, it is necessary to conduct a comprehensive aerodynamic structural design of the wing, namely, aeroelastic optimization design. This optimization design method comprehensively considers the requirements of aerodynamic performance and structural strength. Through efficient optimization design methods, it rationally weighs the design indicators of each discipline to obtain the overall optimal solution that meets the indicators of each discipline. As aeroelastic analysis methods continue to pursue higher accuracy, the calculation time also increases, which brings challenges to aeroelastic optimization design.

[0003] In order to speed up the static aeroelastic optimization design, a proxy model is used to replace the static aeroelastic calculation, which can significantly improve the optimization speed and save optimization time during optimization. However, the traditional proxy model construction method is generally used to generate all sample points at one time, and then calculate the response values ​​of these sample points to build the proxy model. The construction of a high-precision high-dimensional proxy model requires a large number of sample points as a basis, which results in a lot of time to calculate the response values ​​of these sample points using aeroelastic analysis technology. This method, which lacks a priori knowledge of the proxy model, will result in a waste of computing resources. In addition, it is difficult for researchers to determine the right samples at one time.

[0004] Therefore, it is proposed to use an adaptive method to construct a proxy model. Compared with the traditional proxy model construction method, the feedback link is introduced in the construction process of the adaptive proxy model. First, the proxy model is established with the initial sample points, and then new sample points are obtained in the design space according to the point addition strategy, and then the proxy model is established until the termination condition (such as the maximum allowable error value) is met, and the update of the sample points is stopped to obtain the final proxy model. In the process of building an adaptive proxy model, useful information can be extracted from the established proxy model to obtain high-quality sample points, so as to build a high-precision proxy model with as few sample points as possible. The key to the adaptive proxy model technology lies in how to intelligently add new sample points in the design space to build a high-precision model with as few sample points as possible. Static aeroelastic optimization problems have the characteristics of many design variables and a large design space. At present, the commonly used point addition strategy is the single-point addition criterion, such as the maximum prediction variance criterion, the minimum confidence lower limit criterion, the maximum expectation criterion, etc. These single-point addition criteria are difficult to improve the accuracy of the proxy model to the set value when facing optimization problems with high dimensions and high complexity in the design space. Summary of the invention

[0005] To solve the above technical problems, the present invention proposes a wing static aeroelastic optimization design method based on the MWORKS software platform. In view of the problems of low efficiency and slow optimization speed of static aeroelastic optimization design, it is proposed to adopt an efficient multi-point plus point strategy to construct an adaptive proxy model to replace the static aeroelastic calculation method, establish an efficient, accurate and engineering application value static aeroelastic optimization design method based on an adaptive proxy model, which can perform fast and accurate static aeroelastic optimization design of the wing.

[0006] To achieve the above object, the present invention provides a wing static aeroelastic optimization design method based on the MWORKS software platform, comprising:

[0007] Obtain initial sample points, obtain design variables of wing shape and structural layout, and determine fitness function according to optimization objectives and constraints;

[0008] Perform static aeroelastic calculations, add sample points to the sample library, and establish a Kriging model based on the sample library;

[0009] The Kriging model is globally optimized to obtain an adaptive proxy model, and individual fitness is calculated based on the adaptive proxy model to obtain an optimal result and complete the design.

[0010] Optionally, the process of obtaining the initial sample points includes: generating the initial sample points by sampling the low-discrepancy sequence.

[0011] Optionally, the process of obtaining design variables for the wing shape and structural layout includes:

[0012] Acquire a wing of a target passenger aircraft, establish a wing digital model based on the wing of the target passenger aircraft, and establish an aerodynamic parameterized model and a structural parameterized model based on the wing digital model;

[0013] Acquiring wing aerodynamic shape design parameters based on the aerodynamic parameterized model;

[0014] The wing structure layout parameters are obtained based on the structural parameterized model.

[0015] Optionally, the wing aerodynamic shape design parameters include inner / outer wing aspect ratio, inner / outer wing root-to-tip ratio, inner / outer wing anhedral angle, and wing leading edge sweep angle;

[0016] The wing structure layout parameters include the chordwise positions of the front and rear spars at the wing root, kink point and wing tip, respectively.

[0017] Optionally, the process of performing static aeroelastic calculation and adding sample points to the sample library includes:

[0018] Based on the aerodynamic parameterized model and the structural parameterized model, a low-order panel method is used to perform static aeroelastic calculation on the initial sample points;

[0019] Interpolate the structural displacements onto the aerodynamic parameterized model to calculate the aerodynamic forces;

[0020] Interpolate aerodynamic loads onto the structural parameterized model for static analysis;

[0021] If the displacement converges, the static aeroelastic analysis results are output, and the static aeroelastic analysis results are the response values ​​of the sample points. The sample points and their response values ​​are added to the sample library.

[0022] Optionally, the process of globally optimizing the Kriging model to obtain the adaptive proxy model includes:

[0023] The optimization result of the Kriging model is verified based on the leave-one-out cross-validation method. If the optimization result converges, an adaptive proxy model is obtained; if the optimization result does not converge, global optimization is continued.

[0024] Optionally, the optimization result of the Kriging model is verified based on a leave-one-out cross-validation method. If the optimization result converges, the adaptive proxy model is obtained and the following formula is used for verification:

[0025]

[0026] In the formula, is the average of the true response values ​​of all sample points, y i is the true response value of the sample point, is the predicted value of the surrogate model; is R 2 Determination coefficient, if the determination coefficient meets the preset accuracy index, it is judged that the optimization result converges and the adaptive proxy model is obtained.

[0027] Optionally, if the optimization result does not converge, the process of continuing the global optimization includes:

[0028] The design space is divided by the k-means clustering algorithm, and new sample points are obtained by using the mixed addition criterion.

[0029] Optionally, the process of partitioning the design space using a k-means clustering algorithm includes:

[0030] Based on the k-means clustering algorithm, the sample points in the current sample library are divided into several categories;

[0031] Using sample points in any one or more categories as a test set and the remaining sample points as a training set to build a proxy model, and using the test set to calculate the normalized absolute error of the proxy model;

[0032]

[0033] In the formula, q is the total number of sample points, s is the number of sample points in each category, is the predicted response value of the test point, is the mean of the true response values ​​of all sample points;

[0034] According to the ranking of normalized absolute errors, the value ranges of the first m types of sample points with larger errors in the design space are taken as m reconstruction domains.

[0035] Optionally, the process of obtaining new sample points by using the mixed point addition criterion includes:

[0036] In the entire design space and each reconstruction domain, the three point addition criteria of minimizing the surrogate model prediction criterion, maximizing the prediction mean square error criterion, and improving the expectation criterion are mixed to find the new sample points;

[0037] Calculate the Euclidean distance between the newly added sample point and the original sample point. If the distance is less than the preset threshold, remove the newly added sample point.

[0038] Technical effects of the present invention:

[0039] The present invention discloses a wing static aeroelastic optimization design method based on the MWORKS software platform. Compared with the prior art, the present invention adopts an adaptive modeling method to obtain a proxy model with higher accuracy. The adaptive sampling algorithm helps to dig out sample points that can significantly improve the fitting accuracy of the proxy model, thereby improving the efficiency of the proxy model construction. The point addition strategy SPMPD method disclosed in the present invention can achieve the required accuracy requirements with fewer sample points. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0041] Figure 1 It is a flow chart of static aeroelastic optimization design in an embodiment of the present invention;

[0042] Figure 2 A flow chart for constructing an adaptive Kriging model in an embodiment of the present invention;

[0043] Figure 3 This is a flow chart of the operation of the main control program in an embodiment of the present invention;

[0044] Figure 4 R for establishing proxy models for the two methods in the embodiments of the present invention 2 Comparison chart;

[0045] Figure 5 is the R of the Powell8 function proxy model in the embodiment of the present invention 2 Change graph;

[0046] Figure 6 It is a flow chart of static aeroelastic optimization design based on adaptive proxy model in an embodiment of the present invention;

[0047] Figure 7 is a graph showing changes in the determination coefficient of the proxy model in an embodiment of the present invention;

[0048] Figure 8 It is a graph showing the optimal individual objective function value changing with evolutionary algebra in an embodiment of the present invention;

[0049] Fig. 9 Graphs showing how the optimal individual constraint function value in an embodiment of the present invention changes with the number of evolutionary generations, wherein (a) is a graph showing how the wing mass changes with the number of evolutionary generations, (b) is a graph showing how the wing drag changes with the number of evolutionary generations, (c) is a graph showing how the wingtip relative displacement changes with the number of evolutionary generations, and (d) is a graph showing how the wingtip relative twist angle changes with the number of evolutionary generations. DETAILED DESCRIPTION

[0050] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0051] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0052] Embodiment 1

[0053] The flow chart of static aeroelastic optimization design of the wing is as follows: Figure 1 As shown. The genetic algorithm is used for global optimization in the illustrated process. First, the design variables of the wing shape and structural layout are determined, and the fitness function is determined according to the optimization objectives and constraints. The genetic algorithm is used for global optimization, and the individual fitness is quickly calculated through the high-precision proxy model to finally obtain the optimal individual. The construction of the high-precision proxy model is the core of the entire process diagram.

[0054] The construction flow chart of the proxy model is as follows: Figure 2 The adaptive proxy model here is based on the Kriging model, and the point adding strategy adopts an adaptive sampling algorithm (SPMPD) based on design space partitioning and hybrid point adding criteria.

[0055] The specific steps are as follows:

[0056] (1) Determine the initial sample points. For high-dimensional static aeroelastic optimization design problems, the initial sample points need to be evenly distributed in the design space. Sobol low-discrepancy sequence sampling is more balanced than pseudo-random sequence distribution and can efficiently generate evenly distributed sample points in high-dimensional space. Therefore, the present invention adopts Sobol low-discrepancy sequence sampling to obtain the initial sample points.

[0057] (2) Use the real model to perform simulation analysis to obtain the real response value of the sample, and add the sample points to the sample library. Construct the Kriging model based on the sample library.

[0058] (3) The determination coefficient R of the Kriging model was calculated using the leave-one-out cross-validation method. 2 , the determination coefficient calculation formula is:

[0059]

[0060] In the formula, is the average of the true response values ​​of all sample points, y i is the true response value of the sample point, is the predicted value of the proxy model. 2 Whether the accuracy index is met. If not, go to step (4) to increase sample points and repeat steps (2) and (3). If it is met, output the Kriging model.

[0061] (4) Adopt an adaptive sampling algorithm based on design space partitioning and hybrid point addition criteria to obtain additional sample points:

[0062] ① Use the k-means clustering algorithm to divide the q sample points in the current sample library into n categories;

[0063] ② Use the leave-one-out cross-validation method to calculate the normalized absolute error (NAE) of each type of sample point. Use a certain type of sample point as the test set and the remaining sample points as the training set to build a proxy model, and use the test set to calculate the normalized absolute error of the constructed proxy model:

[0064]

[0065] In the formula, q is the total number of sample points, s is the number of sample points in each category, is the predicted response value of the test point, is the mean of the true response values ​​of all sample points;

[0066] ③ According to the ranking of normalized absolute error, the value range of the first m types of sample points with larger errors in the design space is taken as m reconstruction domains;

[0067] ④ In the entire design space and each reconstruction domain, the three point addition criteria of minimizing the proxy model prediction criterion (MSP), maximizing the mean square error of prediction criterion (MSE), and improving the expected criterion (EI) are mixed to find the new sample points;

[0068] ⑤Remove update points that are highly correlated with the original sample points: Calculate the Euclidean distance between the new sample points and the original sample points. If the distance is less than a certain threshold, it is considered that the update point is highly correlated with the original sample point and needs to be removed.

[0069] Program implementation:

[0070] The present invention adopts the domestic software MWORKS to write the program main control module, and the operation flow of the main program is:

[0071] ① Generate initial sample points and calculate the true response of the sample points to build an initial sample library;

[0072] ②According to the initial sample library, a high-precision adaptive proxy model is established using an adaptive sampling algorithm based on design space partitioning and hybrid point addition criteria;

[0073] ③ Use the established high-precision proxy model to quickly calculate individual fitness to complete global optimization and output the optimization results.

[0074] Figure 3 It is the flow chart of the main control program, which calls a series of application modules. sobol.exe: generates initial sample points through low-difference sequence sampling method; aswj.exe: generates files required for static aeroelastic calculation according to the design variable value; count.exe: performs static aeroelastic calculation; extract.exe: generates initial sample library; creatr.exe: updates sample points through adaptive sampling algorithm based on design space partition and mixed point addition criterion to establish sample library for building high-precision proxy model; creatmodel.exe: establishes high-precision Kriging proxy model; TyGlobalOptimization: built-in optimization toolbox of MWORKS software.

[0075] Technical effects of the present invention:

[0076] (1) Effect of building an adaptive proxy model

[0077] In order to verify that the adaptive sampling algorithm (SPMPA) proposed in this paper can improve the efficiency of proxy model construction, it is compared with the method of directly using the same number of sample points to establish a proxy model. These two methods are used to establish a proxy model for the 5-dimensional Powell5 function. The function independent variable range is x 1，2，3，4，5 ∈[-4,5].

[0078] According to the range of the function's independent variable, a low-discrepancy sequence sampling method is used to generate 300 sample points. The first 50 sample points are taken as the initial sample points for building the adaptive proxy model, and new sample points are gradually added using the adaptive sampling algorithm. As a control, the first m sample points are also taken from these 300 sample points to directly build the proxy model, where m is the number of sample points used in the adaptive proxy model construction process.

[0079] Figure 4 This is a comparison of the modeling accuracy of these two proxy model building methods. When the number of sample points used to build the proxy model is the same, the proxy model obtained by the adaptive modeling method is more accurate. The adaptive sampling algorithm helps to mine sample points that can significantly improve the fitting accuracy of the proxy model, thereby improving the efficiency of proxy model construction.

[0080] In order to verify that the proposed point-adding strategy can improve the efficiency of agent model construction, the Powell8 function is used to test the effectiveness of the proposed point-adding strategy. The expression of the Powell8 function is:

[0081]

[0082] The function variable range is x 1，2，3，4，5，6，7，8 ∈[-4,5].

[0083] The proposed SPMPPD method is compared with MSE and MASA. To reduce the impact of randomness, the algorithm is run 10 times and the results are averaged. The number of initial sample points is 40, and the proxy model R is recorded. 2 The sample size N1 when it first reaches 0.8 and the R 2 The total number of samples N2 when reaching 0.8. The results are shown in Table 1. Compared with the other two methods, the SPMPD method can achieve the required accuracy with fewer sample points. This is mainly due to the partitioning of the design space and the mixed use of multiple point addition criteria in the area with poor fitting accuracy.

[0084] Table 1

[0085]

[0086] In addition, the SPMPD method is compared with the three point addition criteria of MSP, MSE, and EI alone, and the three point addition criteria of mixed use without partitioning. The comparison results are as follows: Figure 5As shown in the figure, when building an adaptive proxy model for high-dimensional input, it is difficult to further improve the accuracy of the proxy model in the middle and late stages of adding points by using a single-point adding strategy. This problem can be effectively avoided by using a hybrid adding algorithm. At the same time, if the design space is not partitioned and only the hybrid adding criterion is used, the R2 of the proxy model will become unstable and have poor robustness.

[0087] In summary, the SPPMPD adaptive Kriging model construction method proposed in the present invention can establish a high-precision high-dimensional input proxy model with fewer sample points.

[0088] (2) Static aeroelasticity optimization effect

[0089] The wings of the passenger aircraft are optimized to keep the airfoil and wing root chord length unchanged. The wing has a turning point at the kink point, so it is divided into inner and outer wing sections. The aerodynamic shape design parameters of the wing include: inner / outer wing aspect ratio, inner / outer wing root tip ratio, inner / outer wing anhedral angle, and wing leading edge sweep angle, a total of 7 parameters; the structural layout parameters of the wing include: the chord-wise position of the front and rear beams at the wing root, kink point, and wing tip, respectively, a total of 6 parameters. There are a total of 13 design variables.

[0090] The static aeroelastic optimization design of the wing aims to maximize the lift-to-drag ratio while meeting the constraints of wing mass, wing drag, and structural strength and stiffness. The constraints for the static aeroelastic optimization design of the wing are: ① wing mass less than 3500kg; ② wing drag less than 65kN; ③ wingtip relative displacement less than 0.07; ④ wingtip relative twist angle less than 0.16° / m.

[0091] The genetic algorithm is used for optimization, with 400 individuals per generation and a total of 500 generations. Table 2 The values ​​of the objective function and constraints before and after optimization. From the comparison before and after optimization in the table, it can be seen that: the lift-to-drag ratio before optimization is relatively low, and the wing drag is large and does not meet the constraints. After optimization, the lift-to-drag ratio has been significantly improved, and the wing drag has decreased to meet the constraints; the wing tip relative displacement and wing tip relative twist angle have increased slightly after optimization, but both meet the constraints.

[0092] Table 2

[0093]

[0094] Embodiment 2

[0095] like Figure 6 As shown, this embodiment provides a wing static aeroelastic optimization design method based on the MWORKS software platform, including:

[0096] Obtain initial sample points, obtain design variables of wing shape and structural layout, and determine fitness function according to optimization objectives and constraints;

[0097] Perform static aeroelastic calculations, add sample points to the sample library, and establish a Kriging model based on the sample library;

[0098] The Kriging model is globally optimized to obtain an adaptive proxy model, and individual fitness is calculated based on the adaptive proxy model to obtain an optimal result and complete the design.

[0099] As an implementation method in this embodiment, the process of obtaining the initial sample points includes: generating the initial sample points by sampling the low-discrepancy sequence.

[0100] As an implementation method in this embodiment, the process of obtaining the design variables of the wing shape and structure layout includes:

[0101] Acquire a wing of a target passenger aircraft, establish a wing digital model based on the wing of the target passenger aircraft, and establish an aerodynamic parameterized model and a structural parameterized model based on the wing digital model;

[0102] Acquiring wing aerodynamic shape design parameters based on the aerodynamic parameterized model;

[0103] The wing structure layout parameters are obtained based on the structural parameterized model.

[0104] As an implementation in this embodiment, the wing aerodynamic shape design parameters include inner / outer wing aspect ratio, inner / outer wing root-tip ratio, inner / outer wing anhedral angle, and wing leading edge sweep angle;

[0105] The wing structure layout parameters include the chordwise positions of the front and rear spars at the wing root, kink point and wing tip, respectively.

[0106] As an implementation method of this embodiment, the process of performing static aeroelastic calculation and adding sample points to the sample library includes:

[0107] Based on the aerodynamic parameterized model and the structural parameterized model, a low-order panel method is used to perform static aeroelastic calculation on the initial sample points;

[0108] Interpolate the structural displacements onto the aerodynamic parameterized model to calculate the aerodynamic forces;

[0109] Interpolate aerodynamic loads onto the structural parameterized model for static analysis;

[0110] If the displacement converges, the static aeroelastic analysis result is output, and the static aeroelastic analysis result is input into the sample library as a sample point.

[0111] As an implementation method of this embodiment, the process of globally optimizing the Kriging model to obtain the adaptive proxy model includes:

[0112] The optimization result of the Kriging model is verified based on the leave-one-out cross-validation method. If the optimization result converges, an adaptive proxy model is obtained; if the optimization result does not converge, global optimization is continued.

[0113] As an implementation method in this embodiment, the optimization result of the Kriging model is verified based on the leave-one-out cross-validation method. If the optimization result converges, the adaptive proxy model is obtained, and the following formula is used to verify:

[0114]

[0115] In the formula, is the average of the true response values ​​of all sample points, y i is the true response value of the sample point, is the predicted value of the surrogate model; is R 2 Determination coefficient, if the determination coefficient meets the preset accuracy index, it is judged that the optimization result converges and the adaptive proxy model is obtained.

[0116] As an implementation method of this embodiment, if the optimization result does not converge, the process of continuing the global optimization includes:

[0117] The design space is divided by the k-means clustering algorithm, and new sample points are obtained by using the mixed addition criterion.

[0118] As an implementation method in this embodiment, the process of dividing the design space by the k-means clustering algorithm includes:

[0119] Based on the k-means clustering algorithm, the sample points in the current sample library are divided into several categories;

[0120] Using sample points in any one or more categories as a test set and the remaining sample points as a training set to build a proxy model, and using the test set to calculate the normalized absolute error of the proxy model;

[0121]

[0122] In the formula, q is the total number of sample points, s is the number of sample points in each category, is the predicted response value of the test point, is the mean of the true response values ​​of all sample points;

[0123] According to the ranking of normalized absolute errors, the value ranges of the first m types of sample points with larger errors in the design space are taken as m reconstruction domains.

[0124] As an implementation method of this embodiment, the process of obtaining new sample points by using the mixed point addition criterion includes:

[0125] In the entire design space and each reconstruction domain, the three point addition criteria of minimizing the surrogate model prediction criterion, maximizing the prediction mean square error criterion, and improving the expectation criterion are mixed to find the new sample points;

[0126] Calculate the Euclidean distance between the newly added sample point and the original sample point. If the distance is less than the preset threshold, remove the newly added sample point.

[0127] Embodiment 3

[0128] The static aeroelastic optimization of the wing was carried out, and the passenger aircraft wing was selected as the research object, and the numerical model of the passenger aircraft was established. According to the numerical model, the aerodynamic and structural parameterized models were established respectively.

[0129] The static aeroelastic optimization design of the above passenger aircraft model in the cruising state was carried out. The optimized state was the cruising state, with a flight altitude of 11200m, a flight Mach number of 0.78, an angle of attack of 1.4°, and elevator and aileron deflections of 0.

[0130] This time, the wings of the passenger plane were optimized to keep the airfoil and wing root chord length unchanged. The wing has a turning point at the kink point, so it is divided into inner and outer wing sections. The aerodynamic shape design parameters of the wing include: inner / outer wing aspect ratio, inner / outer wing root tip ratio, inner / outer wing anhedral angle, and wing leading edge sweep angle, a total of 7 parameters; the structural layout parameters of the wing include: the chord-wise position of the front and rear beams at the wing root, kink point, and wing tip, respectively, a total of 6 parameters. There are a total of 13 design variables.

[0131] The static aeroelastic optimization design of the wing aims to maximize the lift-to-drag ratio while satisfying the constraints of wing mass, wing drag, and structural strength and stiffness. For the evaluation of the strength and stiffness of the wing structure, multiple complex factors need to be considered. Since only the structural layout is optimized in the present invention, it can be simplified to use the wingtip twist angle, wingtip relative twist angle, and wingtip relative displacement to evaluate the stiffness and strength of the wing structure.

[0132] The constraints for the static aeroelastic optimization design of the wing are: ① the wing mass is less than 3500kg; ② the wing drag is less than 65kN; ③ the wingtip relative displacement is less than 0.07; ④ the wingtip relative twist angle is less than 0.16° / m.

[0133] After determining the design variables, the wing mass and wing shape parameters can be obtained. Therefore, it is only necessary to build a proxy model to predict the four parameters of lift coefficient, drag coefficient, wingtip relative displacement, and wingtip relative twist angle. The lift-to-drag ratio of the objective function and the wing drag and wingtip twist angle in the constraint conditions can be calculated through the design variable values ​​and the proxy model prediction values.

[0134] According to the previously determined design variables and their value ranges, 130 initial sample points were established using Sobol sequence sampling. The adaptive proxy model construction method was used to establish a proxy model for predicting the four parameters of drag coefficient, lift coefficient, wingtip relative displacement, and wingtip relative twist angle. Figure 7 This is a graph showing the change in the proxy model determination coefficient during the process of building the proxy model. From the graph, we can see that adding new sample points in the early stage can significantly improve the global fitting accuracy of the proxy model. The final proxy model determination coefficients are all above 0.95.

[0135] Genetic algorithm is used for optimization, with 400 individuals in each generation and a total of 500 generations. Figure 8 and Fig. 9 It is a graph of changes in the lift-to-drag ratio, wing mass, wing drag, wingtip relative displacement, and wingtip relative twist angle of the optimal individual in each generation during the evolutionary process. Fig. 9 (a) is the graph of wing mass changing with the evolutionary generation, (b) is the graph of wing drag changing with the evolutionary generation, (c) is the graph of wing tip relative displacement changing with the evolutionary generation, and (d) is the graph of wing tip relative twist angle changing with the evolutionary generation. It can be seen from the figure that as the optimization process proceeds, the lift-to-drag ratio of the optimal individual of each generation continues to increase and finally tends to a certain value; the wing mass, wing drag, wing tip relative displacement and wing tip relative twist angle of the optimal individual of each generation have large fluctuations in the early stage of evolution, and tend to be stable in the middle and late stages of evolution and meet the constraints. Table 3 The values ​​of objective functions and constraints before and after optimization.

[0136] Table 3

[0137]

[0138]

[0139] From the comparison before and after optimization in the table above, we can see that: before optimization, the lift-to-drag ratio is relatively low, and the wing drag is large and does not meet the constraints. After optimization, the lift-to-drag ratio has been significantly improved, and the wing drag has decreased to meet the constraints. The wingtip relative displacement and wingtip relative twist angle have increased slightly after optimization, but both meet the constraints.

[0140] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. Wing static aeroelastic optimization design method based on MWORKS software platform, It is characterized in that include: Obtain initial sample points, obtain design variables of wing shape and structural layout, and determine fitness function according to optimization objectives and constraints; Perform static aeroelastic calculations, add sample points to the sample library, and establish a Kriging model based on the sample library; Performing global optimization on the Kriging model to obtain an adaptive proxy model, calculating individual fitness based on the adaptive proxy model, obtaining an optimal result, and completing the design; The process of obtaining the initial sample points includes: generating the initial sample points by sampling the low-discrepancy sequence; The process of obtaining the design variables of the wing shape and structural layout includes: Acquire a wing of a target passenger aircraft, establish a wing digital model based on the wing of the target passenger aircraft, and establish an aerodynamic parameterized model and a structural parameterized model based on the wing digital model; Acquiring wing aerodynamic shape design parameters based on the aerodynamic parameterized model; Acquiring wing structure layout parameters based on the structural parameterized model; The wing aerodynamic shape design parameters include the inner / outer wing aspect ratio, the inner / outer wing root-to-tip ratio, the inner / outer wing anhedral angle, and the wing leading edge sweep angle; The wing structure layout parameters include the chordwise positions of the front and rear spars at the wing root, kink point, and wing tip, respectively; The process of performing static aeroelastic calculations and adding sample points to the sample library includes: Based on the aerodynamic parameterized model and the structural parameterized model, a low-order panel method is used to perform static aeroelastic calculation on the initial sample points; Interpolate the structural displacements onto the aerodynamic parameterized model to calculate the aerodynamic forces; Interpolate aerodynamic loads onto the structural parameterized model for static analysis; If the displacement converges, the static aeroelastic analysis results are output, and the static aeroelastic analysis results are the response values ​​of the sample points. The sample points and their response values ​​are added to the sample library; The process of globally optimizing the Kriging model to obtain an adaptive proxy model includes: The optimization result of the Kriging model is verified based on the leave-one-out cross-validation method. If the optimization result converges, an adaptive proxy model is obtained; if the optimization result does not converge, global optimization is continued; The optimization result of the Kriging model is verified based on the leave-one-out cross-validation method. If the optimization result converges, the adaptive proxy model is obtained and the following formula is used to verify: In the formula, is the average of the true response values ​​of all sample points, y i is the true response value of the sample point, is the predicted value of the surrogate model; is R 2 Determination coefficient: if the determination coefficient meets the preset accuracy index, the optimization result is judged to be converged and the adaptive proxy model is obtained; If the optimization result does not converge, the process of continuing the global optimization includes: The design space is divided by the k-means clustering algorithm, and new sample points are obtained by using the mixed point addition criterion; The process of partitioning the design space using the k-means clustering algorithm includes: Based on the k-means clustering algorithm, the sample points in the current sample library are divided into several categories; Using sample points in any one or more categories as a test set and the remaining sample points as a training set to build a proxy model, and using the test set to calculate the normalized absolute error of the proxy model; In the formula, q is the total number of sample points, s is the number of sample points in each category, is the predicted response value of the test point, is the mean of the true response values ​​of all sample points; According to the ranking of normalized absolute errors, the value ranges of the first m types of sample points with larger errors in the design space are taken as m reconstruction domains; The process of obtaining new sample points using the mixed point addition criterion includes: In the entire design space and each reconstruction domain, the three point addition criteria of minimizing the surrogate model prediction criterion, maximizing the prediction mean square error criterion, and improving the expectation criterion are mixed to find the new sample points; Calculate the Euclidean distance between the newly added sample point and the original sample point. If the distance is less than the preset threshold, remove the newly added sample point.

Images