Aerodynamic optimization design method suitable for high-dimensional design variables of three-dimensional shape of aircraft

Abstract

The application belongs to the field of aircraft design, and particularly relates to an aerodynamic optimization design method suitable for three-dimensional shape high-dimensional design variables of an aircraft, which comprises the following steps: step 1: selecting a characteristic section, parameterizing a three-dimensional shape of an aircraft to be optimized, and determining design variables and a design space; step 2: dividing the characteristic section into zones, making the design variable values of the same zone equal, and sampling to obtain a global sample; step 3: carrying out aerodynamic calculation on the sample points to obtain a sample aerodynamic data set; step 4: obtaining zone sorting and zone design spaces based on a decision tree algorithm; and step 5: according to the zone sorting order, carrying out optimization in each zone by using an optimization framework based on a proxy model to obtain an optimized shape. The application can automatically and effectively extract prior knowledge based on the sensitivity of each zone design variable to a target function, and then obtain zone sorting, and the optimization based on the zone sorting can effectively avoid the dimension disaster problem, and has high optimization efficiency and good precision.

Description

Technical Field

[0001] This invention relates to the field of aircraft design technology, specifically to an aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape, mainly used in the aerodynamic shape optimization design of high-dimensional design variables of three-dimensional aircraft shape for various types of aircraft. Background Technology

[0002] Among surrogate optimization algorithms based on the Kriging model, the efficient global optimization (EGO) method, which improves the expectation criterion, has been widely used in aerospace and other fields in recent years due to its efficiency, globality, and excellent performance in handling optimization design problems in engineering. However, when performing more refined aerodynamic shape optimization design, we need more design variables for parametric modeling to obtain a more sufficient design space. But a large number of design variables inevitably leads to problems such as difficulty in surrogate model optimization search and a decrease in surrogate model accuracy. This is also the biggest problem with the EGO method—the "curse of dimensionality".

[0003] Currently, the EGO method for handling high-dimensional optimization problems mostly utilizes hierarchical optimization methods to reduce the dimensionality of the design space. The paper "Research on Complex Aerodynamic Optimization and Robust Design Methods Based on CFD" by Zhao Ke, doctoral dissertation of Northwestern Polytechnical University, 2014, published a hierarchical optimization method—cooperative optimization design based on a partitioned proxy model. It achieves hierarchicalization through physical flow mechanisms and human design experience, which can effectively handle the problems caused by high-dimensional input variables. However, this method also has its limitations. It is highly dependent on the designer's engineering experience. For complex design problems, due to the lack of prior knowledge, this method lacks applicability and seriously affects the efficiency and quality of optimization design. The paper "Research on Nash-EGO Algorithm for High-Dimensional Optimization Problems and Its Aerodynamic Applications" by Xu Shengguan, doctoral dissertation of Nanjing University of Aeronautics and Astronautics, 2018, published a Nash-EGO algorithm. By introducing Nash equilibrium theory from the field of economics, it can transform high-dimensional problems into a series of low-dimensional problems, thereby effectively avoiding the dimensionality curse of the EGO algorithm. However, the grouping method and number of groups for parameter splitting (i.e., hierarchicalization) in its algorithm are monotonous and lack universality. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes an aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shapes. Based on the traditional hierarchical optimization method based on the EGO algorithm, this invention introduces a machine learning method—the decision tree algorithm—which can automatically and effectively extract prior knowledge based on the sensitivity of design variables, thereby obtaining partitioning order information. Then, optimization design is performed according to the partitioning order, thus solving the problem of difficulty in obtaining effective prior knowledge and obtaining effective grouping and grouping forms, and avoiding the curse of dimensionality.

[0005] This invention is achieved through the following technical solution:

[0006] An aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape includes the following steps:

[0007] Step 1: Select several feature profiles to parameterize the 3D shape of the aircraft to be optimized, and determine the design variables X = (x1, x2, ..., x...). n ) T and design space R;

[0008] Step 2: Divide the design variables into regions according to the feature profiles selected by the parametric method. Treat the design variables in the same region as a whole, that is, make the design variable values ​​in the same region equal. Then sample within the design space to obtain global samples.

[0009] Specifically, assuming the parametric method selects m feature profiles, the design variables X = (x1, x2, ..., x...) are arranged according to the feature profiles. n ) T Divide the sample into m partitions; during sampling, set the design variable values ​​within each partition to the same value. Then, the design variables in the global sample are q1, q2, ..., q. m ;

[0010] Step 3: Use CFD methods to calculate the aerodynamic performance of the sample points and obtain the aerodynamic dataset of the samples;

[0011] Furthermore, step 3 specifically involves performing aerodynamic calculations on the sample points based on the RANS method, storing the design variables and the calculated aerodynamic data according to the partitioning in step 2, and obtaining the aerodynamic dataset of the sample points.

[0012] Furthermore, the aerodynamic data in step 3 includes lift coefficient, drag coefficient, and pitching moment coefficient;

[0013] Step 4: Use the decision tree algorithm to perform data mining on the sample aerodynamic dataset obtained in Step 3 to obtain optimization design knowledge; the optimization design knowledge includes the sensitivity ranking of each partition to the objective function and the design space of each partition;

[0014] Furthermore, the decision tree algorithm in step 4 is the Classification and Regression Tree (CART) algorithm;

[0015] Step 5: Based on the partitioning results and partitioning order of the decision tree method in Step 4, an optimization framework based on the surrogate model is used to find the optimal shape within the design space of each partition.

[0016] Furthermore, step 5 specifically includes the following sub-steps:

[0017] Step 51: Starting from partition 1, sample and calculate the sample aerodynamic dataset of partition 1 within its design space using the Latin hypercube sampling method, and construct a surrogate model of partition 1; optimize based on the surrogate model to obtain the optimal shape of partition 1.

[0018] Step 52: Determine whether the optimization of the next partition needs to continue based on the set criteria. If the optimization of the next partition needs to continue, keep the optimal shape of the previous partition unchanged and start the optimization of the next partition; if the optimization of the next partition does not need to continue, end the optimization and obtain the final optimized shape.

[0019] Furthermore, when optimizing the next partition in step 52, the optimal value of the previous partition needs to be passed to the next partition. Specifically, the Latin hypercube sampling method is used to sample and calculate the sample aerodynamic dataset of the next partition within the design space, and the optimal value of the previous partition is added to the sample of the next partition to construct a surrogate model of the next partition. Based on the surrogate model, the optimal shape of the next partition is obtained.

[0020] Furthermore, the judgment criterion for step 52 is that if the optimization target value of the current partition decreases by more than 1%, then the next partition optimization needs to be performed; otherwise, the next partition optimization does not need to be performed.

[0021] Furthermore, the present invention also provides a computer device, including: a processor, a storage medium and a bus, wherein the storage medium stores program instructions executable by the processor, and when the computer device is running, the processor communicates with the storage medium via the bus, and when the processor executes the program instructions, it is used to implement the aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional shape of aircraft.

[0022] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program, which, when run by a computer, is used to implement the aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape.

[0023] Beneficial effects

[0024] This invention proposes an aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shapes. Based on traditional hierarchical optimization using the EGO algorithm, this method introduces a machine learning approach—the decision tree algorithm—to automatically and effectively extract prior knowledge based on the sensitivity of each partition's design variables to the objective function, thereby obtaining partition order information. This method has a clear source of prior knowledge, providing a valid basis for the grouping method and number of groups, thus solving the problem that traditional methods struggle to obtain effective prior knowledge and rely on designer experience for grouping, leading to difficulties in obtaining effective grouping and grouping forms. Finally, this method optimizes the design according to the partition order, effectively avoiding the curse of dimensionality. Attached Figure Description

[0025] Figure 1 This is a flowchart of the three-dimensional wing optimization design method of the present invention;

[0026] Figure 2 This is the reference plan view of the ONERA-M6 wing;

[0027] Figure 3 A schematic diagram of the FFD parameterization method for the ONERA-M6 wing;

[0028] Figure 4 The decision tree partitioning results and partitioning order;

[0029] Figure 5 To optimize the comparison of wing and initial shape pressure cloud maps;

[0030] in, Figure 5 (a) shows the surface pressure cloud diagram of the optimized shape and the initial shape using the Efficient Global Optimization (EGO) method; Figure 5 (b) shows the surface pressure contours of the optimized shape and the initial shape using the sequential partitioning optimization method (PT); Figure 5 (c) shows the surface pressure cloud diagram of the optimized shape and the initial shape using the optimization method (DMTPT) of the present invention;

[0031] Figure 6 To optimize the pressure distribution and geometry at different spanwise positions of the wing, and to compare the initial shape with the overall shape;

[0032] in, Figure 6 (a) and (b) represent the results at the spanwise position η = 0.01; Figure 6 (c) and (d) represent the results at the spanwise position η = 0.2; Figure 6 (e)(f) represent the results at the spanwise position η = 0.4; Figure 6 (g)(h) represent the results at the spanwise position η = 0.62; Figure 6(i)(j) represent the results at the spanwise position η = 0.84; Figure 6 (k)(l) represents the result at the spanwise position η = 0.96;

[0033] Figure 7 The error convergence curve is shown (the first 200 iterations). Detailed Implementation

[0034] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer and to enable those skilled in the art to better understand the invention, the invention will be further described in detail and in full below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0035] This embodiment utilizes the aerodynamic optimization design method proposed in this invention, applicable to high-dimensional design variables of three-dimensional aircraft shapes. Taking the ONERA-M6 wing as an example, under transonic design conditions: Mach number 0.8395, design lift coefficient 0.28, angle of attack 3.06°, Reynolds number 11.72 × 10⁻⁶. 6 The following describes the aerodynamic drag reduction optimization design of a three-dimensional airfoil. The mathematical descriptions of the objective function and constraints are as follows:

[0036] min C D

[0037] st C L =0.28

[0038] t opt ≥t0

[0039] Where C D C is the drag coefficient. L t is the lift coefficient. opt To optimize the target wing thickness, t0 is the initial wing thickness.

[0040] This embodiment is achieved through the following steps:

[0041] Step 1: Select several feature profiles to perform shape parameterization on the ONERA-M6 wing, and determine the design variables and design space;

[0042] In this embodiment, specifically, the FFD parameterization method is used to select six airfoil profiles along the wing span as feature profiles for parameterization of the three-dimensional wing. The feature profiles and control points are as follows: Figure 3 As shown, the z-coordinate of the control point is used as the design variable. There are 10 design variables on the upper and lower surfaces of each airfoil profile, for a total of 120 design variables. That is, the optimization problem in this embodiment is 120-dimensional, which is a typical high-dimensional design variable problem. The range of the design variables is ±0.2, forming the design space.

[0043] Step 2: Divide the design variables into partitions according to the feature profiles selected by the parametric method. Treat the design variables in the same partition as a whole, that is, make the design variable values ​​in the same partition equal. Then, use Latin hypercube sampling in the design space to obtain global samples.

[0044] In this embodiment, the 120-dimensional design variables are divided into 6 partitions according to 6 airfoil profiles. The airfoil profile at the wing root is named the first profile, and the profiles from the wing root to the wingtip are named the first to the sixth profiles. Partitions 1 to 6 refer to the first to the sixth airfoil profiles, respectively. During sampling, the design variable values ​​within the same partition are set to be equal, so the design variables in the global sample are q1, q2, ..., q6. A total of 1000 sample points are extracted in the global sample.

[0045] Step 3: Perform aerodynamic performance calculations on the sample points to obtain the aerodynamic dataset of the samples;

[0046] In this embodiment, specifically, aerodynamic calculations are performed on sample points based on the RANS method, and the design variables and the calculated aerodynamic data are stored by partition to obtain the aerodynamic dataset of the sample points; the aerodynamic data is the drag coefficient.

[0047] Step 4: Use the Classification and Regression Tree (CART) algorithm to perform data mining on the sample aerodynamic dataset obtained in Step 3 to obtain optimization design knowledge; the optimization design knowledge includes the ranking of the sensitivity of design variables to the objective function in 6 different partitions and the design space of each partition;

[0048] Figure 4 This diagram shows the partitioning results using the CART decision tree algorithm in this embodiment. In the diagram, x1-x6 represent partitions 1-6, respectively. The triangle symbol represents the root node of the decision tree. Each root node contains partitioning information and corresponding design space information. The vertical order of the root nodes indicates the partitioning order. Root nodes in the same row mean that the partitions corresponding to these root nodes have roughly the same sensitivity to the objective function, and the design variables of several partitions in the same row can be optimized together as a single category. Figure 4 Based on the results, the partitioning results and sorting of the decision tree algorithm are partition 1, partition 3+6, partition 4+5, partition 2, namely the first section, the third and sixth sections, the fourth and fifth sections, and the second section;

[0049] Step 5: Based on the partitioning results and partitioning order of the decision tree method in Step 4, i.e., partition 1 is the first partition, partitions 3+6 are the second partition, partitions 4+5 are the third partition, and partition 2 is the fourth partition, an optimization framework based on a surrogate model is used within the design space of each partition to obtain the optimized shape; specifically, it includes the following sub-steps:

[0050] Step 51: The first round of optimization starts with partition 1, i.e., partition 1. Within its design space, the Latin hypercube sampling method is used to sample and calculate the sample aerodynamic dataset of the partition, and the Kriging surrogate model of the partition is constructed. Based on the surrogate model, the optimal shape of the partition is obtained.

[0051] Step 52: Determine whether the next round of partition optimization needs to be carried out based on the set criteria. The criterion is that if the current partition's optimization target value decreases by more than 1%, then the next round of partition optimization needs to be carried out; otherwise, the next round of partition optimization does not need to be carried out.

[0052] If a next round of partition optimization is required, the optimal shape from the previous round of partition optimization is kept unchanged, and the next round of partition optimization begins. During the next round of partition optimization, the optimal value from the previous round needs to be passed to the next round's partition. Specifically, Latin hypercube sampling is used to sample and calculate the aerodynamic dataset for that partition within the next round's partition design space. The optimal value from the previous round of partition optimization is added to the samples of that partition, constructing a Kriging surrogate model for that partition. Based on this surrogate model, optimization is performed to obtain the optimal shape for that partition. If a next round of partition optimization is not required, the optimization ends, and the final optimized shape is obtained.

[0053] To verify the effectiveness of the aerodynamic optimization design method of the present invention for high-dimensional design variables of three-dimensional aircraft shape, this embodiment also uses two methods, Efficient Global Optimization (EGO) and traditional Sequential Partition Optimization (PT), as a comparison. In the accompanying drawings, EGO represents the Efficient Global Optimization method, PT represents the Sequential Partition Optimization method, and DMTPT represents the decision tree partitioning optimization method of the present invention. The EGO method optimization employed 400 sample points and 400 rounds of optimization. The sequential partition optimization corresponds to the traditional hierarchical optimization method. In this embodiment, the specific processing involves dividing the wing into regions according to the airfoil profile, and then dividing it into first to sixth profile regions in the spanwise direction of the downstream flow, from the wing root to the wingtip. The sequential partition optimization performed three rounds of partition optimization, with each round consisting of partition 1+2, partition 3+4, and partition 5+6, i.e., the first and second profiles, the third and fourth profiles, and the fifth and sixth profiles. Each round employed 100 sample points and 200 rounds of optimization. The optimization method of this invention also performed three rounds of partition optimization, with each round consisting of partition 1, partition 3+6, and partition 4+5, i.e., the first profile, the third and sixth profiles, and the fourth and fifth profiles. Each round employed 100 sample points and 200 rounds of optimization. The optimization of partition 2 met the optimization stopping condition because the shock wave on the wing surface was basically eliminated when the third round of partition optimization reached partition 4+5.

[0054] Table 1 shows the optimization results for each partition; Table 2 shows the optimization results for three different methods. The initial drag coefficient of the M6 ​​wing is 0.01899. By comparing the parameter values, it can be seen that in the EGO method optimization, the drag coefficient decreased from the initial 0.01899 to 0.01586, and the drag decreased by 16.5%. In the sequential partition optimization, the drag coefficient decreased from the initial 0.01899 to 0.01508, and the drag decreased by 20.6%. In the decision tree-based partition optimization, the drag coefficient decreased from the initial 0.01899 to 0.01479, and the drag decreased by 22.1%. The decision tree-based partition optimization obtained the best optimization result, which shows that the optimization method of the present invention can achieve better results than the traditional EGO method and the traditional sequential partition optimization method.

[0055] Table 1 Comparison of specific partitioning parameters based on decision tree partitioning optimization

[0056] <![CDATA[C l ]]> <![CDATA[C d ]]> <![CDATA[C m ]]> Error Partition 1 0.28 0.01623 -0.00530 0.00018 Partition 3+6 0.28 0.01512 -0.02222 0.00027 Partition 4+5 0.28 0.01479 -0.02566 0.00106

[0057] Table 2 Comparison of wing parameters based on decision tree partitioning optimization, EGO method optimization, and sequential partitioning optimization.

[0058] <![CDATA[C l ]]> <![CDATA[C d ]]> <![CDATA[C m ]]> Error t initial shape 0.28 0.01899 0.010195 / / EGO 0.28 0.01586 -0.02989 0.00222 42 hours 6 minutes 42 seconds Sequential partitioning 0.28 0.01508 -0.03111 0.00024 19:39:15 Decision tree partitioning 0.28 0.01479 -0.02566 0.00106 19:28:13

[0059] Figure 5A comparison of pressure contour plots for the initial shape and the optimized shapes obtained by three optimization methods is presented. Figure 6 The paper presents the pressure distribution and geometric shape comparison between the optimized shape obtained by three optimization methods at different spanwise positions and the initial shape, where η represents different spanwise positions. Figure 6 (a) and (b) represent the results at the spanwise position η = 0.01. Figure 6 (c) and (d) represent the results at the spanwise position η = 0.2. Figure 6 (e)(f) represent the results at the spanwise position η = 0.4. Figure 6 (g)(h) represent the results at the spanwise position η = 0.62. Figure 6 (i)(j) represent the results at the spanwise position η = 0.84. Figure 6 (k)(l) represent the results at the spanwise position η = 0.96. The comparison shows that the surface shock waves of the optimized shape are better eliminated after optimization by the method of this invention.

[0060] Figure 7 A comparison of the surrogate model accuracy of the three optimization methods is presented. It can be seen that the optimization method of the present invention has higher surrogate model accuracy than the EGO optimization method and the sequential partitioning surrogate model optimization method, and performs well in dimensionality reduction.

[0061] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape, characterized in that, Includes the following steps: Step 1: Select several feature profiles, parameterize the three-dimensional shape of the aircraft to be optimized, and determine the design variables and design space; Step 2: Divide the design variables into regions according to the feature profiles selected by the parametric method. Treat the design variables in the same region as a whole, that is, make the design variable values ​​in the same region equal. Then sample within the design space to obtain global samples. Step 3: Use CFD methods to calculate the aerodynamic performance of sample points in the global sample to obtain the aerodynamic dataset of the global sample. Step 4: Use the decision tree algorithm to perform data mining on the sample aerodynamic dataset obtained in Step 3 to obtain optimization design knowledge; the optimization design knowledge includes the sensitivity ranking of each partition to the objective function and the design space of each partition; Step 5: Based on the partitioning results and partitioning order of the decision tree method in Step 4, an optimization framework based on a surrogate model is used within the design space of each partition to obtain the optimized shape. This specifically includes the following sub-steps: Step 51: Starting from partition 1, sample and calculate the sample aerodynamic dataset of partition 1 within its design space using the Latin hypercube sampling method, and construct a surrogate model of partition 1; optimize based on the surrogate model to obtain the optimal shape of partition 1. Step 52: Determine whether the optimization of the next partition needs to continue based on the set criteria. If the optimization of the next partition needs to be carried out, keep the optimal shape of the previous partition unchanged and start the optimization of the next partition. If no further partition optimization is needed, the optimization process ends, and the final optimized shape is obtained.

2. The aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape according to claim 1, characterized in that, Step 3 specifically involves: performing aerodynamic calculations on the sample points based on the RANS method, storing the design variables and the calculated aerodynamic data according to the partitioning in step 2, and obtaining the aerodynamic dataset of the sample points.

3. The aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape according to claim 2, characterized in that, The aerodynamic data includes lift coefficient, drag coefficient, and pitching moment coefficient.

4. The aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape according to claim 1, characterized in that, The decision tree algorithm in step 4 is the Classification and Regression Tree (CART) algorithm.

5. The aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape according to claim 1, characterized in that, When optimizing the next partition in step 52, the optimal value of the previous partition needs to be passed to the next partition. Specifically, the Latin hypercube sampling method is used to sample and calculate the sample aerodynamic dataset of the next partition in the design space, and the optimal value of the previous partition is added to the sample of the next partition to construct the surrogate model of the next partition. Based on the surrogate model, the optimal shape of the next partition is obtained.

6. The aerodynamic optimization design method applicable to high-dimensional design variables of three-dimensional aircraft shape according to claim 1, characterized in that, The judgment criterion for step 52 is that if the optimization target value of the current partition decreases by more than 1%, then the next partition needs to be optimized; otherwise, the next partition does not need to be optimized.

7. A computer device, comprising: A processor, a storage medium, and a bus, wherein the storage medium stores program instructions executable by the processor, characterized in that: when the computer device is running, the processor communicates with the storage medium via the bus, and when the processor executes the program instructions, it implements the method of any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program thereon, characterized in that: The computer program is executed by a computer to implement the method of any one of claims 1 to 6.

Images