An airfoil aerodynamic stealth design rule extraction method based on data mining
By performing data mining on an airfoil aerodynamic stealth sample dataset and utilizing algorithms such as random forest, adaptive augmented inheritance, and self-organizing mapping, the high-dimensional multi-objective airfoil aerodynamic stealth optimization problem was solved, achieving a reduction in design space and objective function, and improving optimization efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-11-27
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies are insufficient to effectively solve the multidisciplinary optimization problem of high-dimensional, multi-objective airfoil aerodynamic stealth. The large amount of computation and the difficulty in convergence of optimization search algorithms lead to increased computational costs and timelines for aircraft design.
Multiple data mining algorithms were used to mine the sample dataset of airfoil aerodynamic stealth to obtain the feature importance of design variables and their coupling correlation with the target. Random forest, adaptive augmented inheritance, self-organizing mapping and equimetric mapping algorithms were used to reduce the design space and objective function.
It effectively improves the optimization efficiency of multidisciplinary, high-dimensional, and multi-objective problems in airfoil aerodynamic stealth, reduces the design space and objective function, and improves the efficiency of optimization design.
Smart Images
Figure CN117787117B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of aircraft design technology, specifically to a method for extracting airfoil aerodynamic stealth design rules based on data mining. Background Technology
[0002] Aerodynamic stealth integrated design plays a guiding role in the shape design of modern fighter jets. The aerodynamic stealth multidisciplinary optimization of airfoils is a typical high-dimensional, multi-objective problem. It is characterized by high-dimensional design variables, a large number of objective functions (the number of objective functions is greater than 3), and a large design space. Due to the diversity of objectives and variables and their mutual coupling, the computational load is huge, the optimization search algorithm is difficult to converge, and the Pareto front is a hypersurface, which makes decision-making difficult. This increases the computational cost and cycle of aircraft optimization design.
[0003] For high-dimensional, multi-objective problems, design space reduction and objective dimensionality reduction provide a solution. Traditional surrogate model methods only perform simple fitting of sample data to predict the aerodynamic performance of new shapes. They lack further mining of the sample data obtained by consuming huge computational resources. In fact, the sample data contains features such as the importance of design variables and the correlation between objective functions, which need to be further mined and utilized to guide the optimization design. Currently, in this area, the paper "Self-organizing map of pareto solutions obtained from multiobjective supersonic wing design, 40th AIAA Aerospace Sciences Meeting & Exhibit. 2002" discloses a mining method that uses a self-organizing mapping algorithm to analyze four aerodynamic targets of a supersonic wing. The three-dimensional pareto front is successfully mapped onto a two-dimensional self-organizing map, revealing the influence of aerodynamic performance on wing thickness and camber. The paper "Data mining based multipoint design of next-generation transonic wing with small sweep back, 27th Congress of the international council of the aeronautical sciences, 2010" discloses a mining method that uses the Analysis of Total Variation (ANOVA) algorithm to analyze the characteristics of the multidisciplinary design optimization space of the wing. It finds that the sweep angle, wing root thickness, and wing root leading edge radius are important parameters affecting the drag coefficient under transonic / subsonic conditions. Although the above methods use data mining to analyze the aerodynamic performance and design variables of the aircraft, they only solve the simple multi-objective aerodynamic optimization problem and cannot solve the multi-disciplinary, high-dimensional, multi-objective problem of aerodynamic stealth with a larger design space and more objective functions. Summary of the Invention
[0004] To address the problems existing in the prior art, this invention proposes a data mining-based method for extracting aerodynamic stealth design rules for airfoils. By employing various data mining algorithms to mine sample datasets containing aerodynamic stealth target parameters, the method obtains the feature importance of design variables and their coupling correlation with the target. This effectively reduces the design space and design target, thereby significantly improving the optimization efficiency of aerodynamic stealth multidisciplinary high-dimensional multi-objective problems.
[0005] This invention is achieved through the following technical solution:
[0006] A method for extracting aerodynamic stealth design rules for airfoils based on data mining includes the following steps:
[0007] Step S1: Based on the specific problem of airfoil aerodynamic stealth optimization, establish a mathematical model for the optimization problem;
[0008] Specifically, the optimization state, optimization objective and constraints are determined, a reference airfoil is selected, a CFD calculation mesh is generated around the reference airfoil, the reference airfoil is parameterized, the design variables and design space are determined, and samples are taken in the design space to obtain samples within the design space.
[0009] Step S2: Perform aerodynamic stealth performance calculations on the airfoil samples obtained in Step S1 to obtain the aerodynamic stealth dataset of the samples.
[0010] Step S3: Use data mining algorithms to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2 to obtain optimization design knowledge;
[0011] Step S4: Based on the optimization design knowledge obtained in step S3, obtain the reduced design space and objective function.
[0012] Furthermore, the optimization objectives in step S1 include: lift-to-drag ratio objective function, lift objective function, drag objective function, pitch moment coefficient objective function, vertically polarized TE wave incident radar cross-section objective function, and horizontally polarized TM wave incident radar cross-section objective function.
[0013] Furthermore, step S2 includes the following sub-steps:
[0014] Step S21: Based on the RANS method, perform aerodynamic calculations on the airfoil within the sample, store the design variables and the calculated aerodynamic data, and obtain the aerodynamic dataset of the sample points; the aerodynamic data includes lift coefficient, drag coefficient, lift-to-drag ratio, and pitching moment coefficient;
[0015] Step S22: Based on the method of moments, perform stealth calculations on the airfoils within the sample, and add the calculated stealth data to the aerodynamic dataset of the sample points obtained in step S21 to obtain the aerodynamic stealth dataset of the sample points; the stealth data includes the incident radar cross-section of vertically polarized TE waves and the incident radar cross-section of horizontally polarized TM waves.
[0016] Furthermore, the optimization design knowledge in step 3 includes the characteristic importance of design variables and the coupling correlation between design variables and objectives;
[0017] Furthermore, step S3 includes the following sub-steps:
[0018] Step S31: Use the Random Forest (RF) data mining algorithm to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2. The specific process is as follows:
[0019] (1) Divide the sample dataset into n subsets using the Bootstrap self-sampling method;
[0020] (2) In the subset, randomly select features from the dataset and choose the best splitting attribute as a node to build a decision tree;
[0021] (3) Repeat the above two steps multiple times to build multiple decision trees;
[0022] (4) Multiple decision trees form a random forest. Based on the random forest, the final result is determined by voting, thereby obtaining the feature importance of the design variables.
[0023] Step S32: The AdaBoost adaptive augmented inheritance data mining algorithm is used to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2. The specific process is as follows:
[0024] (1) Let the sample aerodynamic stealth dataset be denoted as Dataset={(x1,y1),(x2,y2),…(x n ,y n The weight distribution of )} is as follows:
[0025]
[0026] Among them, w i is the weight of each training sample, and n is the number of training sample points;
[0027] (2) Iterate t∈[1,T] times and update the weight distribution:
[0028]
[0029]
[0030] Among them, D t+1 It updates the weight distribution of the training samples, e t It is a weak classifier H t In distribution D t Error on;
[0031] (3) Based on weight Combining weak classifiers yields a strong classifier, which in turn determines the feature importance of the design variables.
[0032]
[0033] Among them, H bestThe feature importance of H is the design variable of a strong classifier. t The feature importance is the design variable for the weak classifier, where T is the number of iterations and e is the feature importance. t It is a weak classifier H t In distribution D t Error on;
[0034] Step S33: The self-organizing map (SOM) data mining algorithm is used to perform data mining on the sample aerodynamic stealth dataset obtained in step S2. The specific process is as follows:
[0035] (1) Initialize the weights W of the m*m neurons in the output layer. j ={w j1 ,w j2 ,…w jm},j=1,2...,m;
[0036] (2) Select the sample aerodynamic stealth dataset as the input sample and search for the best neuron (BMU):
[0037] BMU = argmin{||x i (s)-w j (s)||}
[0038] Where, x i represents the high-dimensional sample input data, and s represents the number of iterations;
[0039] (3) Find neighboring neurons of the BMU using the neighborhood function, with a neighborhood radius of:
[0040]
[0041] Where S is the maximum number of iterations and N0 is the initial neighborhood radius;
[0042] (4) Update the weights of the BMU and neighboring neurons:
[0043]
[0044] Where α0 is the initial learning rate;
[0045] In the specific training process, the final weight coefficient matrix and BMU are obtained by iterating from step (2) to step (4), thereby obtaining the coupling correlation between design variables and targets;
[0046] Step S34: Use the Isomap data mining algorithm to perform data mining on the sample dataset obtained in Step S2. The specific process is as follows:
[0047] (1) Determine the k nearest neighbors of the sample point xi, set the distance between xi and the k nearest neighbors as the Euclidean distance, and set the distance to other points as infinity;
[0048] (2) Calculate the distance dist(x) between sample points using the shortest path algorithm. i ,x j );
[0049] (3) Dist(x) i ,x j The sample aerodynamic stealth dataset is used as input to the multidimensional scaling (MDS) algorithm to obtain the mapping of the sample aerodynamic stealth dataset in low-dimensional space;
[0050] (4) The analysis is carried out based on the mapping of the sample aerodynamic stealth dataset in low-dimensional space, so as to obtain the coupling correlation of design variables / targets.
[0051] Furthermore, step S4 includes the following sub-steps:
[0052] Step S41: Based on the feature importance of the design variables obtained by the random forest data mining algorithm and the adaptive reinforcement inheritance data mining algorithm in steps S31 and S32, sort the design variables from largest to smallest to obtain the quantitative impact of each design variable on the objective function, and select the decision tree containing important design variables from the random forest to achieve design space reduction.
[0053] Step S42: Based on the comparative analysis of the design variable / objective coupling correlation obtained by the self-organizing map data mining algorithm and the isometric map data mining algorithm in steps S33 and S34, obtain the objective function trade-off relationship. Based on this trade-off relationship, determine one or more objective functions (less than the initial number of objectives) to achieve dimensionality reduction of the objective function.
[0054] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a computer, performs steps S1 to S4 of the method for extracting airfoil aerodynamic stealth design rules based on data mining.
[0055] Beneficial effects
[0056] This invention provides a data mining-based method for extracting aerodynamic stealth design rules for airfoils. By employing random forest data mining, adaptive augmented inheritance data mining, self-organizing map data mining, and metric map data mining algorithms, the method mines sample datasets containing aerodynamic stealth target parameters to obtain the feature importance of design variables and their coupling correlation with the target. This effectively reduces the design space and design objectives, thereby significantly improving the optimization efficiency of multidisciplinary, high-dimensional, multi-objective problems related to aerodynamic stealth of airfoils. Attached Figure Description
[0057] Figure 1 This is a flowchart of a method for extracting airfoil aerodynamic stealth design rules based on data mining, according to an embodiment of the present invention.
[0058] Figure 2 This is a schematic diagram of the CST parameter station location in the airfoil parameterization method of this invention.
[0059] Figure 3 This is a flowchart of the training samples in an embodiment of the present invention;
[0060] Figure 4 This is a flowchart illustrating data mining of a sample dataset according to an embodiment of the present invention;
[0061] Figure 5 This is a schematic diagram of the random forest data mining algorithm according to an embodiment of the present invention;
[0062] Figure 6 This is a schematic diagram of the adaptive enhanced inheritance data mining algorithm according to an embodiment of the present invention;
[0063] Figure 7 This is a schematic diagram of the topology of the self-organizing adaptive data mining algorithm according to an embodiment of the present invention;
[0064] Figure 8 This is a schematic diagram of data dimensionality reduction using the isometric mapping data mining algorithm according to an embodiment of the present invention;
[0065] Figure 9 A flowchart for designing space / target reduction in an embodiment of the present invention;
[0066] Figure 10 The ranking of design variables based on the adaptive enhanced inheritance data mining algorithm of this invention.
[0067] Figure 11 The ranking of design variables based on the random forest data mining algorithm in this embodiment of the invention;
[0068] Figure 12 The coloring result of the objective function obtained by the self-organizing map data mining algorithm in this embodiment of the invention;
[0069] Figure 13 The coloring result of the objective function obtained by the isometric mapping data mining algorithm in this embodiment of the invention; Detailed Implementation
[0070] 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.
[0071] This embodiment utilizes a data mining-based airfoil aerodynamic stealth design rule extraction method proposed in this invention. For a certain type of aircraft airfoil, a high-dimensional multi-objective optimization design space / objective reduction analysis is carried out on the airfoil, focusing on the two core issues of airfoil aerodynamic stealth.
[0072] like Figure 1 As shown, a method for extracting airfoil aerodynamic stealth design rules based on data mining includes the following steps:
[0073] Step S1: Based on the specific problem of airfoil aerodynamic stealth optimization, establish a mathematical model for the optimization problem;
[0074] Specifically, the optimization state, optimization objective and constraints are determined, NACA2424 is selected as the reference airfoil, a CFD calculation grid is generated around the reference airfoil, the reference airfoil is parameterized, the design variables and design space are determined, and samples are taken in the design space to obtain samples in the design space.
[0075] In this embodiment, the optimization state is: H = 10km, Ma = 0.5, α = 2°, and there are six optimization objectives, making it a typical high-dimensional multi-objective optimization problem. The six objective functions are as follows:
[0076] The maximum lift-to-drag ratio is achieved, i.e., the objective function reaches its maximum value as follows:
[0077]
[0078] Where K is the lift-to-drag ratio, the superscript subsonic indicates that the design state is subsonic, and the subscript L represents lift and D represents drag.
[0079] Maximum lift is achieved, i.e., the objective function reaches its maximum value as follows:
[0080]
[0081] Among them, C L Here, L represents the lift coefficient, V represents the inflow velocity, and S represents the reference area.
[0082] Minimize resistance, i.e., minimize the following objective function:
[0083]
[0084] Among them, C DHere, D represents the drag coefficient, V represents the inflow velocity, and S represents the reference area.
[0085] The absolute value of the pitch moment coefficient is minimized, i.e., the objective function is minimized as follows:
[0086]
[0087] Among them, C M Here, M represents the pitching moment coefficient, V represents the incoming flow velocity, and S represents the reference area. Indicates the mean aerodynamic chord length;
[0088] The vertically polarized TE wave incident radar has the smallest scattering area, i.e., the following objective function takes a minimum value:
[0089]
[0090] Wherein, the superscript s represents the scattered field, i represents the incident field, H represents the magnetic field, and R represents the distance from the target to the radar receiver;
[0091] The horizontally polarized TM wave incident radar has the smallest scattering area, i.e., the following objective function takes a minimum value:
[0092]
[0093] Wherein, the superscript s represents the scattered field, i represents the incident field, E represents the electric field, and R represents the distance from the target to the radar receiver;
[0094] In this embodiment: the perturbation CST parameterization method is used to parameterize the airfoil. The CST basis function is in the form of: B(x)=C(x)·S(x), where the class function C(x)=x N1 ·(1-x) N2 Used to define the geometric shape, N1 and N2 are parameters that control the characteristics of the shape function, specifically N1 = 0.5, N2 = 1; shape function The basis functions are used to describe the geometric features of the shape in detail. The specific value of N is: N = 4; the coefficient A i These are the design variables. For the NACA2424 airfoil in this embodiment, a total of 10 design variables are used, 5 for the upper surface and 5 for the lower surface. Among them, A0 to A4 are used to describe the shape of the upper surface, and A5 to A9 are used to describe the shape of the lower surface. The parameter positions are as follows: Figure 2 As shown in Table 1, the initial values of the design variables and the design space are shown below. The Latin hypercube method is used for sampling to obtain 5000 sample points in the design space.
[0095] Table 1 Design Variables and Design Space
[0096]
[0097] Step S2: Perform aerodynamic stealth performance calculations on the airfoil samples obtained in Step S1 to obtain the aerodynamic stealth dataset of the samples; such as... Figure 3 As shown, it specifically includes the following sub-steps:
[0098] Step S21: Based on the RANS method, perform aerodynamic calculations on the airfoil within the sample, store the design variables and the calculated aerodynamic data, and obtain the aerodynamic dataset of the sample points; the aerodynamic data includes lift coefficient, drag coefficient, lift-to-drag ratio, and pitching moment coefficient; in this embodiment, a self-developed CFD solver is used to calculate the aerodynamic performance of the airfoil, and the specific process is as follows: the flow field control equation adopts the RANS equation, the SA-equation turbulence model closed equation set is adopted, the spatial discretization adopts the Roe scheme, and the time propagation adopts the LU-SGS implicit scheme;
[0099] Step S22: Based on the method of moments, perform stealth calculations on the airfoil within the sample, and add the calculated stealth data to the aerodynamic dataset of the sample points obtained in step S21 to obtain the aerodynamic stealth dataset of the sample points; the stealth data includes the incident radar cross-section of vertically polarized TE waves and the incident radar cross-section of horizontally polarized TM waves; in this embodiment, a self-developed electromagnetic stealth solver is used to calculate the stealth performance of the airfoil. The specific process is as follows: the electromagnetic field distribution is represented as a linear combination of a set of basis functions, and then, by applying appropriate boundary conditions to the basis functions, a set of linear equations describing the relationship between charge distribution and electromagnetic field are obtained. Solve these linear equations to obtain the distribution of the electromagnetic field.
[0100] Step S3: Data mining algorithms are used to mine the sample aerodynamic stealth dataset obtained in Step S2 to obtain optimization design knowledge; the optimization design knowledge includes the feature importance of design variables and the coupling correlation between design variables and the target; such as... Figure 4 As shown, it specifically includes the following sub-steps:
[0101] Step S31: Use the Random Forest (RF) data mining algorithm to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2, such as... Figure 5 As shown, the specific process is as follows:
[0102] (1) Divide the sample dataset into n subsets using the Bootstrap self-sampling method;
[0103] (2) In the subset, randomly select features from the dataset and choose the best splitting attribute as a node to build a decision tree;
[0104] (3) Repeat the above two steps multiple times to build multiple decision trees;
[0105] (4) Multiple decision trees form a random forest. Based on the random forest, the final result is determined by voting, thereby obtaining the feature importance of the design variables.
[0106] Step S32: Use the Adaptive Enhanced Inheritance Data Mining Algorithm (AdaBoost) to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2, such as... Figure 6 As shown, the specific process is as follows:
[0107] (1) Let the sample aerodynamic stealth dataset be denoted as Dataset={(x1,y1),(x2,y2),...(x n ,y n The weight distribution of )} is as follows:
[0108]
[0109] Among them, w i is the weight of each training sample, and n is the class label of the training sample;
[0110] (2) Iterate t∈[1,T] times and update the weight distribution:
[0111]
[0112]
[0113] Among them, D t+1 It updates the weight distribution of the training samples, e t It is a weak classifier H t In distribution D t Error on;
[0114] (3) Based on weight Combining weak classifiers yields a strong classifier, which in turn determines the feature importance of the design variables.
[0115]
[0116] Among them, H best The feature importance of H is the design variable of a strong classifier. t The feature importance is the design variable for the weak classifier, where T is the number of iterations and e is the feature importance. t It is a weak classifier H t In distribution D t Error on;
[0117] Step S33: Use the Self-Organizing Map (SOM) data mining algorithm to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2, such as... Figure 7 As shown, the specific process is as follows:
[0118] (1) Initialize the weights W of the m*m neurons in the output layer. j ={w j1 ,w j2 ,...w jm},j=1,2...,m;
[0119] (2) Select the sample aerodynamic stealth dataset as the input sample and search for the best neuron (BMU):
[0120] BMU = argmin{||x i (s)-w j (s)||}
[0121] Where, x i represents the high-dimensional sample input data, and s represents the number of iterations;
[0122] (3) Find neighboring neurons of the BMU using the neighborhood function, with a neighborhood radius of:
[0123]
[0124] Where S is the maximum number of iterations and N0 is the initial neighborhood radius;
[0125] (4) Update the weights of the BMU and neighboring neurons:
[0126]
[0127] Where α0 is the initial learning rate.
[0128] In the specific training process, the final weight coefficient matrix and BMU are obtained by iterating from step (2) to step (4), thereby obtaining the coupling correlation between design variables and targets;
[0129] Step S34: Use the Isomap data mining algorithm to perform data mining on the sample dataset obtained in Step S2. The specific process is as follows:
[0130] (1) Determine the k nearest neighbors of the sample point xi, set the distance between xi and the k nearest neighbors as the Euclidean distance, and set the distance to other points as infinity;
[0131] (2) Calculate the distance dist(x) between sample points using the shortest path algorithm. i ,x j );
[0132] (3) Dist(x) i ,x j This is used as input to the Multidimensional Scaling (MDS) algorithm to obtain the mapping of the sample aerodynamic stealth dataset in a low-dimensional space, such as... Figure 8 As shown;
[0133] (4) The analysis is carried out based on the mapping of the sample aerodynamic stealth dataset in low-dimensional space, so as to obtain the coupling correlation of design variables / targets.
[0134] Step S4: Based on the optimization design knowledge obtained in Step S3, obtain the reduced design space and objective function; such as Figure 9 As shown, it specifically includes the following sub-steps:
[0135] Step S41: Based on the feature importance of the design variables obtained by the random forest data mining algorithm and the adaptive reinforcement inheritance data mining algorithm in steps S31 and S32, sort the design variables from largest to smallest to obtain the quantitative impact of each design variable on the objective function, select the decision tree containing important design variables from the random forest, and realize the reduction of design space.
[0136] Figure 10 The ranking of design variables based on the adaptive enhanced inheritance data mining algorithm in this embodiment. Figure 11 The ranking of the importance of design variables obtained by the random forest data mining algorithm in this embodiment; from... Figure 10 and Figure 11 It can be seen that for the CL target, the most important design variable is A9, followed by A7 and A6. That is, for lift, the airfoil trailing edge camber is a relatively important design variable; a smaller trailing edge camber can improve the aerodynamic efficiency of the airfoil and reduce the generation of wake vortices and turbulence. For the CD drag coefficient, the most important design variables are A1, A2, and A0, meaning the wing leading edge camber, i.e., the radius of curvature of the leading edge, is a relatively important design variable. A curved leading edge helps to smooth the airfoil surface and eliminate sharp edges, allowing radiated and scattered signals to disperse in different directions. For the vertically polarized TE wave incident radar cross-section, taking the airfoil pitch ±30° sector as the main radar threat area, A1 and A5 are very important design variables; that is, the airfoil leading edge camber basically determines stealth performance. Similarly, for the target function vertically polarized TM wave incident radar cross-section, A1 and A5 also determine its stealth performance.
[0137] Combining the data obtained from the two methods, for the six design objectives, A0, A1, A2, A5, A6, and A9, namely the leading and trailing edge camber of the airfoil, are relatively important design variables. Decision trees containing the above important design variables are selected from the random forest. A new design space is obtained based on the selected decision trees, thereby reducing the design space. Table 2 shows the reduced design space with the lift-to-drag ratio K as an example.
[0138] Table 2. Design space after reducing lift-to-drag ratio K
[0139]
[0140] Step S42: Based on the comparative analysis of the design variable / objective coupling correlation obtained by the self-organizing map data mining algorithm and the isometric map data mining algorithm in steps S33 and S34, obtain the objective function trade-off relationship. Based on this trade-off relationship, determine one or more (less than the initial number of objectives) objective functions to achieve dimensionality reduction of the objective function.
[0141] Figure 12 The coloring result of the objective function obtained by the self-organizing map data mining algorithm in this embodiment is shown below. Figure 13 This is the coloring result of the objective function obtained by the isometric mapping data mining algorithm in this embodiment; to ensure that darker colors represent better design objectives, the objective values CD, TE, and TM are negative. Figure 12 and Figure 13 It can be seen that there are relatively complex relationships between the objective functions of the optimization problem in this embodiment: the most obvious conclusion is that the lift coefficient CL and the lift-to-drag ratio K are quite consistent, and their optimal solution regions overlap significantly; secondly, the TE vertical polarization and TM horizontal polarization are quite consistent, and their regions overlap significantly. For the lift coefficient CL and the drag coefficient CD, both the self-organizing mapping algorithm and the isometric mapping algorithm indicate a conflicting trade-off between them. Similarly, there is a strong conflicting trade-off between the pitch moment coefficient CM and the drag coefficient CD. In the results given by the self-organizing mapping algorithm, for the lift-to-drag ratio K and the TE vertical polarization and TM horizontal polarization, except for some overlap in the upper left region, the two are negatively correlated in most regions. The results of the isometric mapping algorithm also show that the lift-to-drag ratio K and the TE vertical polarization and TM horizontal polarization have a conflicting relationship; and the relationship between the lift coefficient CL and the TE vertical polarization and TM horizontal polarization, as seen through the isometric mapping algorithm, shows a conflicting trade-off between the optimal values in the lower left region and the remaining regions.
[0142] Based on the above results, the multi-objective optimization problem of airfoil aerodynamic stealth in this embodiment does not have a solution where all six objective functions take the optimal value. Compromises must be made. According to the trade-off relationship of the above objective functions and the actual airfoil aerodynamic stealth design requirements, one or more (less than the initial number of 6) objective functions are determined to achieve dimensionality reduction of the objective functions.
[0143] This embodiment also provides a computer-readable storage medium storing a computer program, which, when executed by a computer, performs steps S1 to S4 of the data mining-based airfoil aerodynamic stealth design rule extraction method.
[0144] 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. A method for extracting airfoil aerodynamic stealth design rules based on data mining, characterized in that, Includes the following steps: Step S1: Based on the specific problem of airfoil aerodynamic stealth optimization, establish a mathematical model for the optimization problem; Specifically, the optimization state, optimization objective and constraints are determined, a reference airfoil is selected, a CFD calculation mesh is generated around the reference airfoil, the reference airfoil is parameterized, the design variables and design space are determined, and samples are taken in the design space to obtain samples within the design space. Step S2: Perform aerodynamic stealth performance calculations on the airfoil samples obtained in Step S1 to obtain the aerodynamic stealth dataset of the samples. Step S3: Use data mining algorithms to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2 to obtain optimization design knowledge; the data mining algorithms include random forest data mining algorithm, adaptive augmented inheritance data mining algorithm, self-organizing map data mining algorithm, and equimetric map data mining algorithm. Step S4: Based on the optimization design knowledge obtained in Step S3, obtain the reduced design space and objective function, which specifically includes the following sub-steps: Step S41: Sort the design variables from largest to smallest according to the feature importance obtained by the random forest data mining algorithm and the adaptive augmented inheritance data mining algorithm, obtain the quantitative impact of each design variable on the objective function, and select the decision tree containing important design variables from the random forest to achieve design space reduction. Step S42: Based on the comparative analysis of the coupling correlation between design variables and objectives obtained by the self-organizing map data mining algorithm and the equimetric map data mining algorithm, the objective function trade-off relationship is obtained. Based on this trade-off relationship, an objective function with fewer than the initial number of objectives is determined, thereby achieving dimensionality reduction of the objective function.
2. The method of claim 1, wherein the method is characterized by: In step S1, the optimization objectives include: lift-to-drag ratio objective function, lift objective function, drag objective function, pitch moment coefficient objective function, vertically polarized TE wave incident radar cross-section objective function, and horizontally polarized TM wave incident radar cross-section objective function.
3. The method for extracting airfoil aerodynamic stealth design rules based on data mining according to claim 1, characterized in that, Step S2 includes the following sub-steps: Step S21: Based on the RANS method, perform aerodynamic calculations on the airfoil within the sample, store the design variables and the calculated aerodynamic data, and obtain the aerodynamic dataset of the sample points; the aerodynamic data includes lift coefficient, drag coefficient, lift-to-drag ratio, and pitching moment coefficient; Step S22: Based on the method of moments, perform stealth calculations on the airfoils within the sample, and add the calculated stealth data to the aerodynamic dataset of the sample points obtained in step S21 to obtain the aerodynamic stealth dataset of the sample points; the stealth data includes the incident radar cross-section of vertically polarized TE waves and the incident radar cross-section of horizontally polarized TM waves.
4. The method for extracting airfoil aerodynamic stealth design rules based on data mining according to claim 1, characterized in that, The optimization design knowledge in step S3 includes the characteristic importance of design variables and the coupling correlation between design variables and objectives.
5. The method for extracting airfoil aerodynamic stealth design rules based on data mining according to claim 1, characterized in that, Step S3 includes the following sub-steps: Step S31: Use the Random Forest (RF) data mining algorithm to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2. The specific process is as follows: (1) The sample dataset is divided into n subsets using the Bootstrap self-sampling method; (2) In the subset, randomly select features from the dataset and choose the best splitting attribute as a node to build a decision tree; (3) Repeat the above two steps multiple times to build multiple decision trees; (4) Multiple decision trees form a random forest. Based on the random forest, the final result is determined by voting, thereby obtaining the feature importance of the design variables; Step S32: The AdaBoost adaptive augmented inheritance data mining algorithm is used to perform data mining on the sample aerodynamic stealth dataset obtained in Step S2. The specific process is as follows: (1) The sample aerodynamic stealth dataset is denoted as Its weight distribution is as follows: in, is the weight of each training sample, and n is the number of training sample points; (2) Iteration Next, update the weight distribution: in, It updates the weight distribution of the training samples. It is a weak classifier In distribution Error on; (3) According to the weight Combining weak classifiers yields a strong classifier, which in turn determines the feature importance of the design variables. in, The feature importance of the design variables for strong classifiers. The design variables for the weak classifier are the feature importance, and T is the number of iterations. It is a weak classifier In distribution Error on; Step S33: The self-organizing map (SOM) data mining algorithm is used to perform data mining on the sample aerodynamic stealth dataset obtained in step S2. The specific process is as follows: (1) Initialize the output layer Weights of each neuron ; (2) Select the sample aerodynamic stealth dataset as the input sample and search for the best neuron (BMU): in, represents the high-dimensional sample input data, and s represents the number of iterations; (3) Find the neighboring neurons of the BMU using the neighborhood function, with the neighborhood radius being: Where S is the maximum number of iterations. It is the initial neighborhood radius; (4) Update the weights of the BMU and neighboring neurons: in, It is the initial learning rate; In the specific training process, the final weight coefficient matrix and BMU are obtained by iterating from step (2) to step (4) to obtain the coupling correlation of design variables / targets. Step S34: Use the Isomap data mining algorithm to perform data mining on the sample dataset obtained in Step S2. The specific process is as follows: (1) Determine the k nearest neighbors of the sample point xi, set the distance between xi and the k nearest neighbors as the Euclidean distance, and set the distance to other points as infinity; (2) Use the shortest path algorithm to calculate the distance between sample points. ; (3) As input to the Multidimensional Scaling (MDS) algorithm, the mapping of the sample aerodynamic stealth dataset in low-dimensional space is obtained; (4) Based on the mapping of the sample aerodynamic stealth dataset in low-dimensional space, the design variables / target coupling correlation is obtained.
6. A computer-readable storage medium storing a computer program, wherein the computer program is executed by a computer to perform the airfoil aerodynamic stealth design rule extraction method according to any one of claims 1 to 5.