A flow field overpressure distribution nonlinear reduced-order prediction method

Abstract

The application provides a flow field overpressure distribution nonlinear reduction prediction method, which is suitable for nonlinear dimension reduction and rapid prediction of flow field overpressure distribution data, and aims to overcome the limitation that traditional linear dimension reduction method is difficult to process high-dimensional complex aerodynamic data. The method firstly generates a design variable sample set based on the parameterized shape of the aircraft, and obtains corresponding high-dimensional overpressure distribution data through CFD simulation; then the overpressure distribution data is nonlinearly reduced by using a Gaussian process hidden variable model to extract hidden space variables and reconstruct the model; then the mapping relationship between the design variables and the hidden space variables is established by using a Kriging surrogate model, so that the rapid prediction from the design variables to the overpressure distribution is realized. The method does not need to solve the flow control equation, and can complete the reconstruction and prediction of the overpressure distribution within seconds, significantly improving the efficiency of the aircraft aerodynamic layout design, and is suitable for rapid design and evaluation of high-performance aircraft such as low sonic boom aircraft.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft aerodynamic layout design, in particular to a nonlinear dimension reduction method suitable for overpressure distribution data in aircraft flight flow field. BACKGROUND

[0002] With the increasing requirements for the comprehensive performance of the aircraft (lift-drag ratio, sound blast, stealth, etc.), aerodynamic layout design has become a key link in the whole aircraft development process. Currently, high-precision computational fluid dynamics (CFD) methods are generally used to obtain aerodynamic data, but when facing hundreds to thousands of dimensions of flow field information, CFD-level simulation is not only computationally intensive and time-consuming, but also difficult to quickly reflect the influence of shape fine-tuning on local flow field in iterative design.

[0003] Traditional aerodynamic optimization algorithms often simplify the optimization target to macroscopic aerodynamic forces such as lift or drag, and regard the flow field data containing rich local features as intermediate results, failing to fully explore their potential laws. Because the conventional optimization model has weak data processing capability, it is difficult to effectively summarize and extract the feature relationship of massive data, which leads to the need for designers to perform "manual modification" on the local wing or fuselage, resulting in low efficiency and being easily disturbed by subjective factors. Linear dimension reduction methods, such as principal component analysis, can reduce the data dimension to a certain extent, but due to the limitations of linear methods, they cannot accurately capture complex nonlinear flow mechanisms. SUMMARY

[0004] The present application aims to provide a nonlinear dimension reduction method suitable for overpressure distribution data in flow field, which overcomes the limitations of traditional linear dimension reduction methods and is suitable for processing complex data. The flow field data ignored by traditional design methods are summarized and analyzed using the dimension reduction method provided by the present application, thereby providing good support for layout optimization. The nonlinear dimension reduction method provided by the present application extracts low-dimensional features from high-dimensional data and achieves high-precision prediction of overpressure distribution data, providing an efficient prediction model for aerodynamic layout design.

[0005] To achieve the purpose of the present application, the technical solution adopted is as follows:

[0006] S1 Sample data generation.

[0007] First, the design variables x describing the aircraft shape are obtained using a parameterization method based on the reference shape of the aircraft. The design variable sample set X to be calculated and analyzed is obtained using a design of experiment method. Each row Xi of the sample set X represents a set of design variables x, corresponding to a new aerodynamic shape. For each new aerodynamic shape, three-dimensional flow field data are obtained by CFD method, and the overpressure distribution of the specified spatial position corresponding to the design variables x is recorded as y. The overpressure distribution corresponding to each shape is extracted to form a high-dimensional training data set Y.

[0008] In some embodiments, the data of interest to the designer can be extracted for the spatial location of interest. For example, the overpressure distribution y at a certain location of the fuselage is closely related to the aircraft blast characteristics, and the design of the overpressure distribution y can reduce the aircraft blast.

[0009] S2 nonlinear dimension reduction model training.

[0010] The high-dimensional training data set Y is reduced by using a Gaussian process latent variable model (GP-LVM) to obtain a low-dimensional latent space variable Z. On this basis, the Gaussian process latent variable model establishes a reconstruction model f through a Gaussian process, thereby realizing the reconstruction of the latent space to the physical space.

[0011] Generally, it is assumed that the high-dimensional training data set Y has a certain structure in the low-dimensional latent space, and the data dimension reduction adopts a Gaussian process latent variable model (GP-LVM). For a given low-dimensional latent space variable Z, the posterior probability of the high-dimensional training data set Y is represented as:

[0012] (1)

[0013] where N is a multivariate Gaussian distribution, D is the data dimension, Y represents the high-dimensional training data set, is the i-th column of Y, d Z is the latent space variable, is the kernel matrix.

[0014] The dimension reduction and reconstruction of the high-dimensional training data set Y are performed by inputting a set of latent variables, and the prediction probability distribution of the target is as follows:

[0015] (2)

[0016] where the subscript * represents the target, represents the overpressure distribution of the target, represents the target latent space variable, represents the target kernel function, represents the kernel function value of the target latent space, N is the size of the sample data set, k represents the kernel function, W represents the W-th latent variable, N represents the N-th latent variable, T represents the matrix transpose.

[0017] The expectation value of the prediction probability distribution is taken as the prediction value of the dimension reduction and reconstruction data of the high-dimensional training data set Y, and the variance of the prediction probability distribution is used to measure the uncertainty of the prediction value. From equation (3), the expectation value and the variance can be represented as follows:

[0018] (3)

[0019] E denotes the mathematical expectation, V denotes the variance, p denotes the probability distribution function.

[0020] The kernel function characterizes the similarity between the data set and the input data, and determines the characteristics of the model. The model is trained to maximize the probability in equation (3), and a gradient-based optimization is used to

[0021] Loss function is minimized, which is defined as follows:

[0022]

[0023] S3 Hidden space surrogate model training.

[0024] A surrogate model of the design variable x and the hidden space variable Z is established, and a total of n surrogate models are needed, where n is the spatial dimension of the hidden space. For each dimension of the hidden space, a surrogate model g between the design variable x and the hidden space variable Z is established to obtain the mapping relationship of x→Z. The training input of the surrogate model is the design variable x, and the training output is the hidden space variable Z. After the model training is completed, given any design variable x*, the model can predict the corresponding hidden space variable Z*. The surrogate model can use a conventional surrogate model, such as a common Kriging, or a model with stronger generalization ability such as a deep neural network.

[0025] S4 Overpressure distribution prediction.

[0026] Overpressure distribution prediction, i.e., prediction of the aerodynamic characteristics of the aircraft, so far, the present application has obtained an overpressure distribution reduced-order model and a hidden space surrogate model, which can realize rapid prediction of the overpressure distribution corresponding to the design variable.

[0027] Specifically, when a new design variable x is given, the corresponding hidden space variable Z is obtained through the surrogate model g, and the overpressure distribution y is predicted through the reconstruction model f, and the overpressure distribution data corresponding to the overpressure distribution data The overpressure distribution data can be used to carry out aerodynamic layout design and realize overpressure distribution prediction without CFD solution.

[0028] The present application has the beneficial effect that the high-precision prediction model established does not involve time-consuming CFD calculation, and can obtain overpressure distribution data in seconds, realizing efficient prediction of overpressure distribution data, and greatly shortening the aircraft design iteration cycle. BRIEF DESCRIPTION OF DRAWINGS

[0029] In order to more clearly illustrate the technical solutions of the present application, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other embodiments can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0030] Figure 1 is a flow field overpressure distribution nonlinear reduction method flow chart provided by the present application;

[0031] Figure 2 is a schematic diagram of overpressure distribution data extraction at a specific position below a supersonic aircraft;

[0032] Figure 3 is a high-precision prediction of overpressure distribution and CFD comparison provided by the present application. DETAILED DESCRIPTION

[0033] The present application will now be further described in detail in conjunction with the method embodiments. The present application will be further described in detail in conjunction with the drawings and specific embodiments. The following embodiments are only descriptive, not limiting, and cannot limit the protection scope of the present application.

[0034] Figure 1 is a flow field overpressure distribution nonlinear reduction method flow chart provided by the present application.

[0035] First, sample data generation is performed. Given the aerodynamic shape of the aircraft, a parameterization method is selected to parameterize the aerodynamic shape. The change of the aircraft aerodynamic shape can be described by the parameter change. The design variable x describing the aircraft shape is obtained by using the parameterization method. A set of parameters (design variables) is given, and a corresponding aerodynamic shape is obtained.

[0036] A commonly used three-dimensional shape parameterization method is a free-form deformation parameterization method, which can control the change of the aerodynamic shape within the control frame by controlling the change of the vertex position of the control frame.

[0037] After determining the range of design variables, an experimental design method such as Latin hypercube method is used to randomly sample in the design space to obtain a design variable sample set, which is denoted as X. Each row of the sample set X represents a set of design variables x, corresponding to a new aerodynamic shape. For each new aerodynamic shape, three-dimensional flow field data is obtained by CFD method. The overpressure distribution corresponding to the design variable x is denoted as y, and the overpressure distribution y is extracted at the predetermined spatial position to form a high-dimensional training data set Y.

[0038] In some embodiments, data of interest to the designer can be extracted for specific spatial locations. For example, the overpressure distribution y at a certain distance from the fuselage is closely related to the aircraft's sonic boom characteristics, and designing the overpressure distribution y can reduce the aircraft's sonic boom.

[0039] In one embodiment, the number of design variables is selected as 33, and the sample set size is 100. Then, CFD calculations and analyses were performed on each set of design variables in the sample set to obtain data of interest to the designers, such as near-field overpressure distribution data for supersonic aircraft. .

[0040] Figure 2 This is a schematic diagram illustrating the overpressure distribution data extracted at a specific location beneath a supersonic aircraft. The aircraft's fuselage length is... L At the bottom of the fuselage H Extracting overpressure distribution data, generally H = 3 L ~ 5 L .

[0041] Then, nonlinear dimensionality reduction is performed on the obtained data. The high-dimensional training dataset Y is reduced in dimensionality using the Gaussian process latent variable model (GP-LVM) to obtain the low-dimensional latent space variables Z. Based on this, the Gaussian process latent variable model establishes a reconstruction model f through a Gaussian process, thereby realizing the reconstruction from the latent space to the physical space.

[0042] Generally, assuming that the high-dimensional training dataset Y has a specific structure in the low-dimensional latent space, and the data dimensionality reduction uses the Gaussian process latent variable model (GP-LVM), the posterior probability of the high-dimensional training dataset Y for a given low-dimensional latent space variable Z is expressed as:

[0043] (1)

[0044] Where N is a multivariate Gaussian distribution, D It refers to the data dimension, where Y represents the high-dimensional training dataset. It is the first one d Column Z is a latent space variable. It is a kernel matrix.

[0045] The dimensionality reduction and reconstruction of the high-dimensional training dataset Y are performed by inputting a set of latent variables, and the predicted probability distribution of the target is as follows:

[0046] (2)

[0047] The subscript * indicates the target. Indicates the target overpressure distribution. denotes the target latent space variable, N is the size of the sample data set, k denotes the kernel function, W denotes the Wth latent variable, N denotes the Nth latent variable, T denotes the matrix transpose.

[0048] The expectation value of the prediction probability distribution is taken as the prediction value of the reduced and reconstructed data of the high-dimensional training data set Y, while the variance of the prediction probability distribution is used to measure the uncertainty of the prediction value. From equation (3), the expectation value and the variance can be expressed as follows:

[0049] (3)

[0050] The kernel function characterizes the similarity between the data set and the input data and determines the characteristics of the model. The training model is trained to maximize the probability in equation (3), and a gradient-based optimization is used to minimize the loss function , which is defined as follows:

[0051] (4)

[0052] For the high-dimensional training data set Y, it is reduced to the latent space variable Z by using the Gaussian latent variable model, and the dimension of the high-dimensional training data set Y is D , D The size is determined by the flow field calculation space grid discretization, which is generally in the order of hundreds to thousands, and in this embodiment, the number of overpressure distribution points is 1000, so . The dimension of the reduced latent space is n , n < D . Generally, it is preferable that n =2~5, and in this embodiment, n = 4. The high-dimensional training data set Y is input into the Gaussian latent variable model as training data to train the model hyperparameters. After the model training is completed, given any latent space variable Z, the corresponding overpressure distribution data C p , i.e. the flow field data, can be obtained.

[0053] Secondly, a proxy model of the design variable x and the latent space variable Z is established, and a total of n proxy models are needed, wherein n is the spatial dimension of the latent space. For each dimension of the latent space, a proxy model g between the design variable x and the latent space variable Z is established to obtain the mapping relationship of x→Z.

[0054] Since the dimension of Z is n , it is necessary to establish n= 4 surrogate models. The Kriging model is selected to establish the mapping relationship between the design variable x and the latent space variable Z.

[0055] Finally, based on the trained nonlinear dimensionality reduction model and surrogate model, the overpressure distribution data is reduced in order and rapidly predicted. Overpressure distribution prediction, i.e., the prediction of aircraft aerodynamic characteristics, is addressed by this invention, which obtains an overpressure distribution reduction model and a latent space surrogate model, enabling rapid prediction of the overpressure distribution corresponding to design variables.

[0056] Overpressure distribution prediction essentially reflects the evolution of an aircraft's aerodynamic characteristics under different design parameters. Through the reduced-order overpressure distribution model and latent space surrogate model constructed in this invention, rapid prediction of overpressure distribution based on design variables can be achieved without the need for complex CFD simulation calculations.

[0057] When a new design variable x is given, the corresponding latent space variable Z is first obtained through the surrogate model g, then its overpressure distribution y is predicted through the reconstruction model f, and finally the corresponding overpressure distribution data C is predicted using the overpressure distribution reduction model. p The obtained C p This is the aerodynamic flow field distribution result under the design variable, enabling overpressure distribution prediction without CFD solution.

[0058] Specifically, given the design variable x, using n Each surrogate model predicts the variable Z in each dimension of the latent space, obtaining the latent space variable Z corresponding to the design variable x. Z is then used as input to a nonlinear dimensionality reduction model to obtain the corresponding overpressure distribution data C. p This refers to flow field data. Thus, rapid prediction of overpressure distribution data is achieved. Taking low-sonic-bang design as an example, designers can use the predicted overpressure distribution to further solve the acoustic propagation equation, obtain the near-field signal, and then calculate the sonic boom value. This process avoids solving the flow equation, greatly improving design efficiency.

[0059] In the process of aircraft design, the method provided by this invention can be used to reduce the order of overpressure distribution and make rapid predictions, which are of concern to designers.

[0060] Figure 3 A set of overpressure distributions predicted by design variables are presented. After CFD verification, they are in good agreement with the model predictions. The mean square error of the two sets of overpressure distribution curves is 0.08%, indicating that the model prediction accuracy is very high and fully meets the requirements for rapid prediction of overpressure distribution in the design process.

[0061] The application is based on generating a design variable sample set of an aircraft parameterized shape, and obtaining corresponding high-dimensional overpressure distribution data through CFD simulation; then using a Gaussian process hidden variable model to perform nonlinear dimensionality reduction on the overpressure distribution data, extract hidden space variables and reconstruct the model; further, through a Kriging or other surrogate model, a mapping relationship between the design variables and the hidden space variables is established, realizing fast prediction from the design variables to the overpressure distribution.

[0062] The core advantage of the method is that the method does not need to solve the flow control equation, and can complete the reconstruction and prediction of the overpressure distribution within seconds, significantly improving the efficiency of aircraft aerodynamic layout design, and is suitable for rapid design and evaluation of high-performance aircraft such as low sonic boom aircraft.

[0063] Taking the aerodynamic shape design of a low sonic boom aircraft as an example, the designer can further solve the sound propagation equation based on the predicted overpressure distribution of the application, obtain the near-field pressure waveform signal, and calculate the corresponding sonic boom index accordingly. This process significantly reduces the consumption of computing resources and design cycle, and greatly improves the design efficiency.

[0064] In summary, in the process of aircraft aerodynamic design, for the key performance indicator of the designer's attention, the overpressure distribution, the application provides a method integrating dimensionality reduction modeling and surrogate modeling, which can realize the order reduction expression and fast prediction of the overpressure distribution data, and provides an efficient and reliable support means for aerodynamic layout optimization.

[0065] The above only describes the preferred embodiments of the application and is not intended to limit the application. For those skilled in the art, the application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application. It should be noted that the technical features in the above embodiments can be freely combined by those skilled in the art, and the technical solutions formed also belong to the embodiments disclosed in the present application.

[0066] Further, without departing from the principles of the present application, the present application can be improved and modified in several ways, and these improvements and modifications also fall within the protection scope of the claims of the present application.

Claims

1. A method for nonlinear order reduction prediction of overpressure distribution in a flow field, characterized in that, Includes the following steps: S1 Sample Data Generation: The design variable x is obtained by parameterizing the reference shape of the aircraft. The design variable x is obtained by using the experimental design method. Each set of design variables x in the sample set X corresponds to a new aerodynamic shape. For each new aerodynamic shape, the three-dimensional flow field data is obtained by CFD method, and the overpressure distribution y is extracted at a predetermined spatial location to form a high-dimensional training dataset Y. S2 Nonlinear Dimensionality Reduction Model Training: The high-dimensional training dataset Y is reduced in dimension using a Gaussian process latent variable model to obtain low-dimensional latent space variables Z; based on this, the Gaussian process latent variable model establishes a reconstruction model f through a Gaussian process, thereby realizing the reconstruction from latent space to physical space; S3 Latent Space Proxy Model Training: For each dimension of the latent space, establish a proxy model g between the design variable x and the latent space variable Z to obtain the mapping relationship between the design variable x and the latent space variable Z; S4 Overpressure Distribution Prediction: When a new design variable is input, the corresponding latent space variable Z is first obtained through the surrogate model g, and then its overpressure distribution data is predicted through the reconstruction model f, thus realizing overpressure distribution prediction.

2. The nonlinear order reduction prediction method for flow field overpressure distribution according to claim 1, characterized in that: In step S1, the experimental design method is the Latin hypercube method, which is used to perform random sampling to obtain the sample set X of the design variable x.

3. The nonlinear order reduction prediction method for flow field overpressure distribution according to claim 1, characterized in that: In step S1, the predetermined spatial position is position H directly below the aircraft fuselage, where H = 3L ~ 5L, and L represents the length of the aircraft fuselage.

4. The nonlinear order reduction prediction method for flow field overpressure distribution according to claim 1, characterized in that: In step S3, the Kriging model is used to establish the mapping relationship between the design variable x and the latent space variable Z.

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