Aircraft aerodynamic configuration optimization design method based on manifold learning dimensionality reduction mapping

Abstract

The invention discloses an aircraft aerodynamic configuration optimization design method based on manifold learning dimensionality reduction mapping, and relates to the technical field of aerodynamic configuration design, and the method comprises the steps: defining design variable parameters of an aircraft aerodynamic configuration, and determining a design variable parameter sample and pressure distribution sample data according to a variable value range; training a preset Bayesian manifold learning dimensionality reduction mapping model, and determining a latent variable by using the trained target Bayesian manifold learning dimensionality reduction mapping model and the pressure distribution sample data; training a preset multi-output deep neural network model based on the design variable parameter sample and the latent variable; and performing pressure distribution prediction based on the trained target multi-output deep neural network model, the target Bayesian manifold learning dimensionality reduction mapping model and the variable value range, optimizing target pressure distribution in the variable value range by using a pressure distribution prediction result, and determining a target design variable parameter value. The problem of high-dimensional mapping precision in existing related schemes can be solved, and the design accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of aerodynamic shape design, and in particular to an aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping. Background Art

[0002] For a long time, due to limitations in design concepts, methods, and computer hardware, existing approaches have relied on computational fluid dynamics (CFD) to determine aircraft aerodynamic characteristics, requiring high-precision numerical simulations. Since aircraft aerodynamic shape design is a high-dimensional problem, massive amounts of data (millions of them) not only require significant storage but also easily lead to the curse of dimensionality during model training. Therefore, effective data dimensionality reduction is crucial.

[0003] However, existing CFD-based aerodynamic shape optimization schemes have significant limitations, hindering their effective application in aircraft design. Principal component analysis (PCA), a traditional and widely used linear dimensionality reduction method, is often employed in these schemes. However, it struggles to establish a complex and accurate reduced-order model for massive, high-dimensional data with complex structures, resulting in poor design efficiency and accuracy. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide an aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping. This method can solve the problem of high-dimensional mapping accuracy in existing related solutions, achieve efficient dimensionality reduction and efficient global optimization of pressure distribution, thereby improving the efficiency, precision, accuracy, and reliability of aircraft aerodynamic shape design and enhancing the user experience. The specific scheme is as follows:

[0005] In a first aspect, the present application provides a method for optimizing the aerodynamic shape of an aircraft based on manifold learning and dimensionality reduction mapping, comprising:

[0006] Defining design variable parameters of the aircraft's aerodynamic shape based on free-form deformation technology, and determining design variable parameter samples and pressure distribution sample data corresponding to the design variable parameter samples according to the variable value range;

[0007] Training a preset Bayesian manifold learning dimensionality reduction mapping model based on a preset training strategy, and performing nonlinear dimensionality reduction on the pressure distribution sample data using the trained target Bayesian manifold learning dimensionality reduction mapping model to determine corresponding latent variables;

[0008] Training a preset multi-output deep neural network model based on the design variable parameter samples and the latent variables to determine a trained target multi-output deep neural network model;

[0009] Pressure distribution prediction is performed based on the target Bayesian manifold learning dimensionality reduction mapping model, the target multi-output deep neural network model and the variable value range, and the corresponding pressure distribution prediction results, target pressure distribution and global optimization algorithm are used to search for the optimal value within the variable value range to determine the target design variable parameter values ​​and complete the aircraft aerodynamic shape optimization design operation.

[0010] Optionally, the defining of design variable parameters of the aircraft aerodynamic shape based on the free-form deformation technology, and determining design variable parameter samples and pressure distribution sample data corresponding to the design variable parameter samples according to the variable value range, includes:

[0011] parameterizing the aerodynamic shape of the aircraft based on free-form deformation technology, and defining a set of design variable parameters of the aerodynamic shape of the aircraft using corresponding parameterization results;

[0012] Within the variable value range corresponding to each of the design variable parameters, respectively selecting design variable parameter samples that meet a first preset number based on a preset random sampling algorithm to determine a design variable parameter sample set;

[0013] The pressure distribution sample data corresponding to each of the design variable parameter samples is obtained according to the numerical results of the computational fluid dynamics simulation to determine the pressure distribution sample data set.

[0014] Optionally, the training of a preset Bayesian manifold learning dimensionality reduction mapping model based on a preset training strategy includes:

[0015] The pressure distribution sample data set is input into a preset Bayesian manifold learning dimensionality reduction mapping model, so that the preset Bayesian manifold learning dimensionality reduction mapping model is based on the variational inference framework and the pressure distribution sample data set, and a nonlinear mapping from the latent space to the target high-dimensional space is established through a Gaussian process to complete the training of the model hyperparameters and determine the trained target Bayesian manifold learning dimensionality reduction mapping model.

[0016] Optionally, the training of a preset multi-output deep neural network model based on the design variable parameter samples and the latent variables to determine a trained target multi-output deep neural network model includes:

[0017] Obtaining a preset multi-output deep neural network model; the preset multi-output deep neural network model is a Bayesian neural network composed of multiple layers of Bayesian dense layers;

[0018] The design variable parameter samples are input into the preset multi-output deep neural network model so that the preset multi-output deep neural network model processes the design variable parameter samples based on the Bayesian dense layer for abstraction and feature extraction, and completes training based on the processing results and the latent variables to determine a trained target multi-output deep neural network model.

[0019] Optionally, the pressure distribution prediction based on the target Bayesian manifold learning dimensionality reduction mapping model, the target multi-output deep neural network model and the variable value range includes:

[0020] For any design variable parameter within the variable value range, determining a target latent variable corresponding to the current design variable parameter based on the target multi-output deep neural network model;

[0021] The target latent variable is input into the target Bayesian manifold learning dimensionality reduction mapping model to determine a pressure distribution prediction result corresponding to the current design variable parameters.

[0022] Optionally, the optimization is performed within the variable value range using the corresponding pressure distribution prediction result, the target pressure distribution, and a global optimization algorithm, including:

[0023] By defining the root mean square error between the target pressure distribution and the pressure distribution prediction result as the objective function of the global optimization algorithm, and using the global optimization algorithm to search for the optimal value within the variable value range, the target design variable parameter values ​​that meet the target pressure distribution are determined.

[0024] Optionally, after determining the target design variable parameter value, the method further includes:

[0025] Based on the computational fluid dynamics solver, it is judged whether the target design variable parameter value meets the preset aircraft aerodynamic shape design target to determine the corresponding judgment result.

[0026] Optionally, after determining the corresponding judgment result, the method further includes:

[0027] If the judgment result indicates that the target design variable parameter value does not meet the preset aircraft aerodynamic shape design target, the process jumps back to the step of defining the design variable parameters of the aircraft aerodynamic shape based on the free form deformation technology.

[0028] It can be seen that in the present application, the design variable parameters of the aerodynamic shape of the aircraft are defined based on the free-form deformation technology, and the design variable parameter samples and the pressure distribution sample data corresponding to the design variable parameter samples are determined according to the variable value range; the preset Bayesian manifold learning dimensionality reduction mapping model is trained based on the preset training strategy, and the trained target Bayesian manifold learning dimensionality reduction mapping model is used to perform nonlinear dimensionality reduction on the pressure distribution sample data to determine the corresponding latent variables; the preset multi-output deep neural network model is trained based on the design variable parameter samples and the latent variables to determine the trained target multi-output deep neural network model; the pressure distribution is predicted based on the target Bayesian manifold learning dimensionality reduction mapping model, the target multi-output deep neural network model and the variable value range, and the corresponding pressure distribution prediction results, target pressure distribution and global optimization algorithm are used to perform optimization within the variable value range to determine the target design variable parameter values ​​and complete the aircraft aerodynamic shape optimization design operation. That is to say, in this application, the design variable parameters of the aircraft's aerodynamic shape are first defined, and then the design variable parameter samples and corresponding pressure distribution sample data are determined based on the value range. Then, based on these samples, a preset Bayesian manifold learning dimensionality reduction mapping model and a preset multi-output deep neural network model are trained respectively. The trained target Bayesian manifold learning dimensionality reduction mapping model, target multi-output deep neural network model and variable value range are used to predict the pressure distribution, and the target design variable parameter values ​​are determined in combination with the target pressure distribution and the global optimization algorithm. In this way, the problem of high-dimensional mapping accuracy in existing related solutions can be solved, and efficient dimensionality reduction and efficient global optimization of pressure distribution can be achieved, thereby improving the efficiency, precision, accuracy and reliability of aircraft aerodynamic shape design and enhancing the user experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0030] Figure 1 A flow chart of an aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping provided in this application;

[0031] Figure 2 A schematic diagram of a specific model training process provided for this application;

[0032] Figure 3 A specific optimization design framework and a schematic diagram of the optimization design solution and verification process provided for this application;

[0033] Figure 4 A schematic diagram of an M6 wing grid provided for this application;

[0034] FIG5( a ) is a schematic diagram showing a comparison between a target pressure distribution of a cross section 1 and a pressure distribution of an initial configuration at the cross section 1 provided by the present application;

[0035] FIG5( b ) is a schematic diagram showing a comparison between a target pressure distribution at a cross section 2 provided by the present application and a pressure distribution at the cross section 2 of an initial configuration;

[0036] FIG5( c ) is a schematic diagram showing a comparison between a target pressure distribution at section 3 provided by the present application and the pressure distribution at section 3 of the initial configuration;

[0037] FIG5( d ) is a schematic diagram showing a comparison between a target pressure distribution at a cross section 4 provided by the present application and a pressure distribution at the cross section 4 of an initial configuration;

[0038] FIG6 (a) is a schematic diagram comparing the pressure distribution at section 1 of an optimized design configuration provided by this application and an initial configuration;

[0039] FIG6 (b) is a schematic diagram comparing the pressure distribution at section 2 of an optimized design configuration provided by this application and an initial configuration;

[0040] FIG6 (c) is a schematic diagram comparing the pressure distribution at section 3 of an optimized design configuration provided by this application and an initial configuration;

[0041] FIG6 (d) is a schematic diagram comparing the pressure distribution at section 4 of an optimized design configuration provided by this application and an initial configuration;

[0042] FIG7 (a) is a schematic diagram showing a comparison of an airfoil of an optimized design configuration provided by the present application and an initial configuration at section 1;

[0043] FIG7( b ) is a schematic diagram showing a comparison of an optimized design configuration provided by the present application and an initial configuration at section 2 of the airfoil;

[0044] FIG7 (c) is a schematic diagram showing a comparison of an optimized design configuration provided by the present application and an initial configuration at section 3 of the airfoil;

[0045] FIG7( d ) is a schematic diagram showing a comparison of an airfoil of an optimized design configuration provided by the present application and an initial configuration at section 4;

[0046] Figure 8 This application provides a wing surface pressure cloud map before and after optimization design. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] There are some obvious limitations in the optimization design related schemes in the existing CFD-based aerodynamic shape design schemes, which make it impossible to use them efficiently in aircraft design. The principal component analysis model that is more commonly used in the scheme is a traditional and widely used linear dimensionality reduction method, but it is difficult to establish a complex and accurate reduction model for massive high-dimensional data with complex structures, resulting in poor design efficiency and accuracy. To this end, the present application provides an aircraft aerodynamic shape optimization design scheme based on manifold learning dimensionality reduction mapping, which can solve the problem of high-dimensional mapping accuracy in existing related schemes, achieve efficient dimensionality reduction of pressure distribution and efficient global optimization, thereby improving the efficiency, precision, accuracy and reliability of aircraft aerodynamic shape design, and enhancing user experience.

[0049] See also Figure 1 As shown, an embodiment of the present invention discloses a method for optimizing the aerodynamic shape of an aircraft based on manifold learning and dimensionality reduction mapping, comprising:

[0050] Step S11 : defining design variable parameters of the aerodynamic shape of the aircraft based on the free-form deformation technology, and determining design variable parameter samples and pressure distribution sample data corresponding to the design variable parameter samples according to the variable value range.

[0051] Specifically, in this embodiment, firstly, sample data related to the aircraft or a part of the aircraft is required, such as Figure 2 As shown, taking the wing design of an aircraft as an example, relevant sample data is generated based on the baseline wing (referring to the wing model used as a reference or benchmark in the design).

[0052] It should be understood that in order to generate relevant sample data, the aerodynamic shape of the aircraft is first parameterized based on the free-form deformation technology, and the corresponding parameterization results are used to define a set of design variable parameters of the aerodynamic shape of the aircraft; then, within the variable value range corresponding to each of the design variable parameters, the design variable parameter samples that meet the first preset number are selected based on the preset random sampling algorithm to determine the design variable parameter sample set; the pressure distribution sample data corresponding to each of the design variable parameter samples are obtained according to the numerical results of the computational fluid dynamics simulation to determine the pressure distribution sample data set. In other words, the aerodynamic shape of the aircraft or a part of the aircraft is first parameterized using the free-form deformation (FFD) technology. The change in the aerodynamic shape can be described by the parameterization change, and a set of n design variable parameters is defined to correspond to an aerodynamic shape. Then, within the variable value range of the design variable parameters, a preset random sampling algorithm is used to extract m design variable parameter samples. Each group of n design variable parameters is a design variable parameter sample, and the design variable parameter sample set is , where T represents transpose, is the first design variable parameter sample in the sample set, is the mth design variable parameter sample in the sample set. Through CFD (Computational Fluid Dynamics, computational fluid dynamics) numerical calculation analysis, the corresponding pressure distribution sample data set can be obtained ,in, is the first pressure distribution sample data in the sample data set, and correspond; is the mth pressure distribution sample data in the sample data set, and Correspondingly, the preset random sampling algorithm may be a Latin Hypercube Sampling algorithm (LHS).

[0053] Step S12: training a preset Bayesian manifold learning dimensionality reduction mapping model based on a preset training strategy, and performing nonlinear dimensionality reduction on the pressure distribution sample data using the trained target Bayesian manifold learning dimensionality reduction mapping model to determine corresponding latent variables.

[0054] In this embodiment, after generating the sample data, the generated sample data is used to train a Bayesian manifold learning dimensionality reduction mapping model. That is, the pressure distribution sample data set is input into a preset Bayesian manifold learning dimensionality reduction mapping model, so that the preset Bayesian manifold learning dimensionality reduction mapping model, based on the variational inference framework and the pressure distribution sample data set, establishes a non-linear mapping from the latent space to the target high-dimensional space through a Gaussian process to complete the training of the model hyperparameters and determine the trained target Bayesian manifold learning dimensionality reduction mapping model.

[0055] It should be understood that regarding the specific implementation of the training of the Bayesian manifold learning dimensionality reduction mapping model, in the aircraft aerodynamic shape optimization design framework in this embodiment (as Figure 3 shown), it includes a step of non-linearly reducing the dimensionality of the pressure distribution sample data in the pressure distribution sample data set . The dimensionality reduction model used, that is, the preset Bayesian manifold learning dimensionality reduction mapping model, can be a Bayesian Gaussian Process Latent Variable Model (Bayesian GP-LVM). This model is a Bayesian method for non-linear dimensionality reduction. Based on the Gaussian Process Latent Variable Model (GP-LVM), it performs Bayesian training through variational inference, which can make the model more robust in the dimensionality reduction task and automatically select the dimension of the latent space. Assume that there is a specific low-dimensional structure Zr in the high-dimensional pressure distribution data, where r << m. A non-linear mapping from the latent space to the target high-dimensional space is established through a Gaussian process. Given the latent variable Zr, the probability density of the high-dimensional pressure distribution data is defined as:

[0056] ; (1)

[0057] where, is a multivariate Gaussian distribution, D is the high-dimensional data dimension, represents the high-dimensional target matrix, represents <000第d dimension of , Zr is the latent variable matrix. KNN is the covariance matrix calculated by the kernel function, is the noise precision, represents the identity matrix, and N represents N Gaussian distributions.

[0058] The Bayesian GP-LVM model sets a prior distribution for the latent variable Zr instead of treating Z as an inherent parameter to be optimized, so that the distribution of the latent variable is considered during the training process, thus being able to capture the inherent uncertainty in the data. Bayesian GP-LVM uses the variational inference framework to introduce a variational distribution q(Zr) to approximate the posterior By integrating the latent variable Zr, the model no longer relies on a single point estimate, but instead considers all possible Zr values, which is the core of the Bayesian method. As training samples, training is performed by maximizing the variational lower bound of the log-marginal likelihood.

[0059] After the model is trained, the probability distribution of high-dimensional data corresponding to the latent variables can be predicted. At this time, the joint probability distribution of the training samples and the reconstructed new data output satisfies the following Gaussian distribution:

[0060] ; (2)

[0061] in, is the training sample, Zr is the latent space data corresponding to the training sample, * represents the reconstruction target, Reconstructing new data, Represents the latent space data corresponding to the reconstruction of new data, K is the covariance matrix of the training data, is the cross-kernel covariance between the training sample data and the reconstruction target, T represents the transpose, is the reconstructed target sample (i.e. ). According to the definition of Gaussian conditional probability distribution, the predicted probability distribution of the reconstructed target is as follows:

[0062] ; (3)

[0063] Predicting the expectation of a probability distribution To reconstruct the predicted value of new data, the variance To reconstruct the uncertainty of new data prediction, the kernel function represents the similarity between the dataset and the input data. Bayesian GP-LVM uses the Automatic Relevance Determination Squared Exponential (ARD-SE) kernel function to select the dimension of the latent variable, and maximizes the log-marginal likelihood of the output data. The variational lower bound of is obtained, and the gradient optimization method is used to estimate the model parameters and determine the model characteristics. After the model parameters are optimized, the independent length scale parameters in the kernel function will have significant differences, and the amplitudes corresponding to some dependent variables will be close to 0. In this case, it can be assumed that the latent variable does not carry information about the process variable, and therefore this dimension can be ignored during dimensionality reduction.

[0064] Step S13: training a preset multi-output deep neural network model based on the design variable parameter samples and the latent variables to determine a trained target multi-output deep neural network model.

[0065] In this embodiment, after completing the training of the popular mapping model, the pressure distribution sample data can be obtained by step S12. The corresponding low-dimensional latent variable Zr is further used to establish the design variable parameters A multi-output deep neural network model with latent variables Zr, that is, deep neural network model training is performed, specifically, a preset multi-output deep neural network model is first obtained; the preset multi-output deep neural network model is a Bayesian neural network composed of multiple layers of Bayesian dense layers; the design variable parameter samples are input into the preset multi-output deep neural network model, so that the preset multi-output deep neural network model processes the design variable parameter samples based on the Bayesian dense layers for abstraction and feature extraction, and completes the training based on the processing results and the latent variables to determine the trained target multi-output deep neural network model.

[0066] It should be understood that regarding deep neural network model training, the preset multi-output deep neural network model in this embodiment is a Bayesian neural network composed of multiple layers of Bayesian dense layers, with a total of 5 layers. These are the input layer and 4 Bayesian dense layers. The first three layers are hidden layers used for abstraction and feature extraction, and the last layer is the output layer. After model training is completed, for any design variable parameter within a given design space (i.e., the range of variable values), the model can accurately predict the corresponding latent space variables.

[0067] Step S14: Predicting the pressure distribution based on the target Bayesian manifold learning dimensionality reduction mapping model, the target multi-output deep neural network model, and the variable value range, and using the corresponding pressure distribution prediction results, target pressure distribution, and global optimization algorithm to perform optimization within the variable value range to determine the target design variable parameter values ​​and complete the aircraft aerodynamic shape optimization design operation.

[0068] In this embodiment, after completing the deep neural network model training, this embodiment will perform a rapid prediction of the pressure distribution. At this point, the Bayesian nonlinear probability dimensionality reduction model of the high-dimensional pressure distribution and the latent space multi-output deep neural network proxy model have been established and trained. It can achieve rapid prediction of the design variable parameters to the pressure distribution. Specifically, given any design variable parameter x in the design space, its specific position z in the latent space can be obtained through the target multi-output deep neural network model, and then the pressure distribution data corresponding to z can be predicted through the target Bayesian manifold learning dimensionality reduction mapping model. That is, for any design variable parameter within the variable value range, the target latent variable corresponding to the current design variable parameter is determined based on the target multi-output deep neural network model; the target latent variable is input into the target Bayesian manifold learning dimensionality reduction mapping model to determine the pressure distribution prediction result corresponding to the current design variable parameter.

[0069] Furthermore, this embodiment performs an optimization design of the aerodynamic shape based on the pressure distribution prediction results obtained by rapid prediction. The target Bayesian manifold learning dimensionality reduction mapping model and the target multi-output deep neural network model are combined with the global optimization algorithm to form the following Figure 3 The overall framework of the optimization design is shown in the figure. The target pressure distribution of the optimization is set in advance, and the predicted pressure distribution value in the pressure distribution prediction result is used. The global optimization algorithm objective function is defined as the root mean square error (RMSE) between the predicted pressure distribution and the target pressure distribution. The global optimization algorithm is then used to optimize within the design space to determine the optimal design shape parameters that meet the target pressure distribution. Specifically, the global optimization algorithm objective function is defined as the RMS error (RMSE) between the target pressure distribution and the predicted pressure distribution. The global optimization algorithm is then used to optimize within the range of variable values ​​to determine the target design variable parameter values ​​that meet the target pressure distribution. This completes one round of the aerodynamic shape optimization design process.

[0070] Furthermore, after obtaining the target design variable parameter values, the CFD solver can be used to verify whether the optimal shape design meets the design goals. If the requirements are met, it is the optimal design shape; if the design requirements are not met, steps S11 to S14 are repeated, and the sample data is updated in step S11 or the target pressure distribution is reset in step S14. That is, after determining the target design variable parameter values, the computational fluid dynamics solver is used to determine whether the target design variable parameter values ​​meet the preset aircraft aerodynamic shape design goals to determine the corresponding judgment results. If the judgment result indicates that the target design variable parameter values ​​do not meet the preset aircraft aerodynamic shape design goals, the process jumps back to the step of defining the design variable parameters of the aircraft aerodynamic shape based on the free form deformation technology.

[0071] In summary, this embodiment proposes an aerodynamic shape optimization design framework based on manifold learning dimensionality reduction mapping and deep neural network models. This framework uses manifold learning dimensionality reduction mapping methods to extract low-dimensional features from high-dimensional flow field data. Furthermore, a deep neural network model is used to establish an accurate multi-output proxy model between shape design variable parameters and low-dimensional latent space. This allows for high-precision prediction of high-dimensional flow field data given a given shape. Furthermore, the framework combines global optimization algorithms for optimization and local optimization algorithms for fine-tuning to achieve the optimal aerodynamic shape given a given flow field distribution. This framework provides an efficient and feasible aerodynamic shape optimization design solution, which has the following beneficial effects:

[0072] (1) Efficient prediction and optimization of pressure distribution. This solution uses the Bayesian Gaussian process latent variable model dimensionality reduction mapping method to model the pressure distribution, which can achieve high-precision prediction of the pressure distribution and provide the uncertainty of the predicted pressure distribution. At the same time, it achieves efficient dimensionality reduction of the pressure distribution, reducing the nearly thousand-dimensional pressure distribution data to about four dimensions, and then establishes a multi-output proxy model of the shape design variable parameters and the low-dimensional latent space through the deep neural network model. Combined with the global optimization algorithm, efficient global optimization is achieved.

[0073] (2) During the design process, there is no need to call a time-consuming CFD solver. By using the trained Bayesian manifold mapping model and deep neural network model, the optimized design can be achieved within a few minutes, enabling rapid iteration of the design scheme.

[0074] It can be seen that the design variable parameters of the aerodynamic shape of the aircraft are defined based on the free-form deformation technology, and the design variable parameter samples and the pressure distribution sample data corresponding to the design variable parameter samples are determined according to the variable value range; the preset Bayesian manifold learning dimensionality reduction mapping model is trained based on the preset training strategy, and the trained target Bayesian manifold learning dimensionality reduction mapping model is used to perform nonlinear dimensionality reduction on the pressure distribution sample data to determine the corresponding latent variables; the preset multi-output deep neural network model is trained based on the design variable parameter samples and the latent variables to determine the trained target multi-output deep neural network model; the pressure distribution is predicted based on the target Bayesian manifold learning dimensionality reduction mapping model, the target multi-output deep neural network model and the variable value range, and the corresponding pressure distribution prediction results, target pressure distribution and the global optimization algorithm are used to perform optimization within the variable value range to determine the target design variable parameter values ​​and complete the aircraft aerodynamic shape optimization design operation. That is to say, in this application, the design variable parameters of the aircraft's aerodynamic shape are first defined, and then the design variable parameter samples and corresponding pressure distribution sample data are determined based on the value range. Then, based on these samples, a preset Bayesian manifold learning dimensionality reduction mapping model and a preset multi-output deep neural network model are trained respectively. The trained target Bayesian manifold learning dimensionality reduction mapping model, target multi-output deep neural network model and variable value range are used to predict the pressure distribution, and the target design variable parameter values ​​are determined in combination with the target pressure distribution and the global optimization algorithm. In this way, the problem of high-dimensional mapping accuracy in existing related solutions can be solved, and efficient dimensionality reduction and efficient global optimization of pressure distribution can be achieved, thereby improving the efficiency, precision, accuracy and reliability of aircraft aerodynamic shape design and enhancing the user experience.

[0075] The following combination Figures 2 to 8 The disclosed schematic diagram specifically illustrates the technical solution of the embodiment of the present application.

[0076] In this embodiment, combined with Figure 2 and Figure 3 As shown, the aerodynamic shape design related to the M6 ​​wing is carried out. First, sample data is generated. Given the aerodynamic shape of the M6 ​​wing, a parameterization method is selected to parameterize the aerodynamic shape of the selected baseline wing. The change of the aerodynamic shape of the M6 ​​wing can be described by the parameterization change. A set of design variable parameters is given to correspond to an aerodynamic shape. Free form deformation parameterization technology is used for the M6 ​​wing. The change of the aerodynamic shape within the control frame is controlled by changing the vertex position of the control, and the design variable parameters of the aerodynamic shape are defined. After determining the value range of the design variable parameters, 2000 design variable parameter samples are extracted in the design space using the LHS algorithm. Perform CFD numerical analysis on each set of design variable parameters. The grid diagram of the M6 ​​wing is shown in the figure below. Figure 4 As shown in the figure. Based on the CFD numerical results, the sections of the M6 ​​wing at 25%, 50%, 75% and 95% of the span (sections 1, 2, 3 and 4, respectively) are selected to obtain the pressure distribution data of each section. The pressure distribution data of the four sections of each wing are grouped into a column to form a set of pressure distribution training data. Finally, the pressure distribution sample data set can be obtained. .

[0077] Then the Bayesian manifold learning dimensionality reduction mapping model training is carried out. Nonlinear dimensionality reduction is performed using the Bayesian Gaussian process latent variable model to reduce it to the latent space Zr. The size of the pressure distribution sample data is determined by the discreteness of the flow field calculation grid, generally in the hundreds to thousands. According to the pressure distribution sample data points in the previous step, the number of points is 921. The dimension of the latent space after dimensionality reduction is r, r<<921, generally 2-10, and in this embodiment, r=8. Pressure distribution sample data set The training samples are fed into the Bayesian Gaussian process latent variable model to train the model hyperparameters. After the model training is complete, for any given latent space variable z, the corresponding physical space pressure distribution data y can be quickly obtained.

[0078] After that, the deep neural network model is trained. Through the previous step, the pressure distribution sample data can be obtained The corresponding low-dimensional latent variable , further establish the design variable parameter X and latent variable This multi-output deep neural network model is a Bayesian neural network consisting of five layers, each consisting of an input layer and four Bayesian dense layers. The first three layers are hidden layers used for abstraction and feature extraction, and the last layer is the output layer. After model training, given any design variable parameter x in the design space, the model can accurately predict the corresponding latent space variable z.

[0079] At this point, the Bayesian nonlinear probability dimensionality reduction model and the latent space multi-output deep neural network proxy model for high-dimensional pressure distribution have been established and trained. Based on the trained nonlinear probability dimensionality reduction model and the multi-output deep neural network proxy model, the pressure distribution dimensionality reduction and rapid prediction can be achieved. Specifically, given any design variable parameter x in the design space, its specific position z in the latent space can be quickly and accurately obtained through the latent space neural network multi-output proxy model. Then z is used as the input of the Bayesian nonlinear probability dimensionality reduction model to quickly obtain the corresponding pressure distribution data The two-step process allows for rapid prediction of pressure distribution data, typically within seconds.

[0080] Then the aerodynamic shape optimization design is carried out. The Bayesian nonlinear probability dimensionality reduction model and the latent space multi-output deep neural network agent model are combined with the global optimization algorithm to form the overall framework of the optimization design. The M6 ​​wing is selected along the span of 25%, 50%, 75% and 95% of the total four design sections (sections 1, 2, 3, and 4, respectively). The wing is parameterized using the FFD parameterization method, with a total of 110 design variable parameters. The M6 ​​wing is optimized and the design state is: Mach number , angle of attack a=3.06, Reynolds number . Figure 4 A grid diagram of the M6 ​​wing is shown. Optimization design requires a target pressure distribution. This embodiment directly modifies the pressure distribution on the four sections of the initial configuration to produce a target pressure distribution that reduces drag. The principle of the target pressure distribution is to smooth out areas where shock waves and pressure fluctuations exist. Figures 5(a)-5(d) compare the initial configuration pressure distribution on sections 1, 2, 3, and 4, respectively, with the given target pressure distribution. While it is impossible for the designed target pressure distribution to completely match the target pressure distribution in the figure, the target pressure distribution in the figure can guide the design process toward weakening shock waves and reducing pressure distribution fluctuations.

[0081] Finally, the CFD solver is used to verify whether the optimal shape design meets the design objectives. If it does, it is considered the optimal design shape. If it does not, the aforementioned steps are repeated, and the sample data is updated in the first step or the target pressure distribution is reset in a later step. Figures 6(a)-6(d) are comparisons of the airfoil surface pressure distribution at sections 1, 2, 3, and 4 between the optimized design configuration and the initial configuration, respectively. As can be seen from the figures, compared to the initial configuration, the pressure distribution of the inverse design configuration at each section basically matches the target pressure distribution without shock waves, with a mean square error of 0.0187%, indicating that the optimization design method of the present invention has high prediction accuracy. Figures 7(a)-7(d) are comparisons of the airfoil surface pressure distribution at sections 1, 2, 3, and 4 between the optimized design configuration and the initial configuration, respectively. Figure 8It is the pressure cloud map of the wing surface before and after optimization. It can be seen from the figure that the shock waves at other spanwise positions on the wing upper surface are weakened after optimization.

[0082] To summarize the above analysis, this embodiment proposes an aerodynamic shape optimization design framework based on manifold learning dimensionality reduction mapping and a deep neural network model. The results of the embodiment show that the design intent has been achieved, and the M6 ​​wing has quickly obtained the optimization result under the optimization design framework.

[0083] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from the other embodiments. Reference can be made to the descriptions of the identical or similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and the relevant parts can be referred to the descriptions of the methods.

[0084] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0085] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0086] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or device comprising the element.

[0087] The above is a detailed introduction to the technical solution provided by the present application. Specific examples are used herein to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea. At the same time, for those skilled in the art, according to the ideas of the present application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present application.

Claims

1. A method for optimizing the aerodynamic shape of an aircraft based on manifold learning and dimensionality reduction mapping, characterized in that: include: Defining design variable parameters of the aircraft's aerodynamic shape based on free-form deformation technology, and determining design variable parameter samples and pressure distribution sample data corresponding to the design variable parameter samples according to the variable value range; Training a preset Bayesian manifold learning dimensionality reduction mapping model based on a preset training strategy, and performing nonlinear dimensionality reduction on the pressure distribution sample data using the trained target Bayesian manifold learning dimensionality reduction mapping model to determine corresponding latent variables; Training a preset multi-output deep neural network model based on the design variable parameter samples and the latent variables to determine a trained target multi-output deep neural network model; Pressure distribution prediction is performed based on the target Bayesian manifold learning dimensionality reduction mapping model, the target multi-output deep neural network model and the variable value range, and the corresponding pressure distribution prediction results, target pressure distribution and global optimization algorithm are used to search for the optimal value within the variable value range to determine the target design variable parameter values ​​and complete the aircraft aerodynamic shape optimization design operation.

2. The aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping according to claim 1 is characterized in that: The method of defining the design variable parameters of the aircraft aerodynamic shape based on the free-form deformation technology and determining the design variable parameter samples and the pressure distribution sample data corresponding to the design variable parameter samples according to the variable value range includes: parameterizing the aerodynamic shape of the aircraft based on free-form deformation technology, and defining a set of design variable parameters of the aerodynamic shape of the aircraft using corresponding parameterization results; Within the variable value range corresponding to each of the design variable parameters, respectively selecting design variable parameter samples that meet a first preset number based on a preset random sampling algorithm to determine a design variable parameter sample set; The pressure distribution sample data corresponding to each of the design variable parameter samples is obtained according to the numerical results of the computational fluid dynamics simulation to determine the pressure distribution sample data set.

3. The aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping according to claim 2 is characterized in that: The training of the preset Bayesian manifold learning dimensionality reduction mapping model based on the preset training strategy includes: The pressure distribution sample data set is input into a preset Bayesian manifold learning dimensionality reduction mapping model, so that the preset Bayesian manifold learning dimensionality reduction mapping model is based on the variational inference framework and the pressure distribution sample data set, and a nonlinear mapping from the latent space to the target high-dimensional space is established through a Gaussian process to complete the training of the model hyperparameters and determine the trained target Bayesian manifold learning dimensionality reduction mapping model.

4. The aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping according to claim 1, characterized in that: The step of training a preset multi-output deep neural network model based on the design variable parameter samples and the latent variables to determine a trained target multi-output deep neural network model includes: Obtaining a preset multi-output deep neural network model; the preset multi-output deep neural network model is a Bayesian neural network composed of multiple layers of Bayesian dense layers; The design variable parameter samples are input into the preset multi-output deep neural network model so that the preset multi-output deep neural network model processes the design variable parameter samples based on the Bayesian dense layer for abstraction and feature extraction, and completes training based on the processing results and the latent variables to determine a trained target multi-output deep neural network model.

5. The aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping according to claim 1 is characterized in that: The pressure distribution prediction based on the target Bayesian manifold learning dimensionality reduction mapping model, the target multi-output deep neural network model and the variable value range includes: For any design variable parameter within the variable value range, determining a target latent variable corresponding to the current design variable parameter based on the target multi-output deep neural network model; The target latent variable is input into the target Bayesian manifold learning dimensionality reduction mapping model to determine a pressure distribution prediction result corresponding to the current design variable parameters.

6. The aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping according to claim 1, characterized in that: The optimization is performed within the variable value range using the corresponding pressure distribution prediction results, target pressure distribution and global optimization algorithm, including: By defining the root mean square error between the target pressure distribution and the pressure distribution prediction result as the objective function of the global optimization algorithm, and using the global optimization algorithm to search for the optimal value within the variable value range, the target design variable parameter values ​​that meet the target pressure distribution are determined.

7. The aircraft aerodynamic shape optimization design method based on manifold learning and dimensionality reduction mapping according to claim 1 is characterized in that: After determining the target design variable parameter value, the method further includes: Based on the computational fluid dynamics solver, it is judged whether the target design variable parameter value meets the preset aircraft aerodynamic shape design target to determine the corresponding judgment result.

8. The aircraft aerodynamic shape optimization design method based on manifold learning dimensionality reduction mapping according to claim 7 is characterized in that: After determining the corresponding judgment result, the method further includes: If the judgment result indicates that the target design variable parameter value does not meet the preset aircraft aerodynamic shape design target, the process jumps back to the step of defining the design variable parameters of the aircraft aerodynamic shape based on the free form deformation technology.

Images