Boundary layer flow instability n-value prediction method based on data set and pattern recognition

Abstract

The application provides a boundary layer flow instability N value prediction method based on a data set and pattern recognition, comprising: establishing a boundary layer flow model according to the flow condition of a target scene; solving a disturbance control equation under the corresponding flow to generate disturbance data in Fourier space; when the disturbance data is restored to the physical space, different external disturbance sources are matched respectively to generate a rich disturbance field; determining the N value according to the disturbance data; collecting flow instability images in different slice planes of the disturbance field to generate an instability image data set; training a convolutional neural network by taking the instability image data set as a feature and taking the N value as a label; inputting the flow disturbance image under the target scene into the target convolutional neural network model to predict the flow instability N value under the target scene. When the flow parameters are unknown / incomplete or need to be predicted in real time, the traditional method is not applicable, and the application can efficiently predict the N value only by the observable features of the flow field.

Description

Technical Field

[0001] This invention belongs to the field of instability prediction technology, specifically relating to a method for predicting the N-value of boundary layer flow instability based on datasets and pattern recognition. Background Technology

[0002] Since Reynolds revealed the transition from laminar to turbulent flow through his circular tube experiments in 1883, the field of fluid mechanics has been deeply studying the transition process between the two. In most flows, turbulence typically begins with the violation of linear stability, i.e., instability. Instability is an important research direction in fluid mechanics, serving as the starting point for a system to evolve from a stable state to a more complex one, and it is widespread in nature and engineering applications. Whether it's vortex generation in atmospheric circulation or boundary layer transition in aerospace, instability plays a crucial role in flow structure and energy transfer. For example, the aerodynamic heat of the turbulent boundary layer is 3 to 8 times that of the laminar boundary layer; such a significant aerodynamic heat change can greatly affect aircraft materials and must be considered in aircraft design. Therefore, in-depth research into flow instability is of great significance for understanding the transition mechanism from laminar to turbulent flow and for designing and optimizing flow control schemes.

[0003] Over the past few decades, the academic community has conducted extensive research on instability. This research has not only broadened our understanding of flow and instability phenomena but also provided theoretical support for practical applications such as aerospace and energy transmission. Among these studies, linear stability theory (LST), as a crucial tool for studying flow instability, provides a theoretical foundation for understanding flow transition mechanisms and turbulence generation by solving eigenvalue problems such as the Orr-Sommerfeld equation. It is widely used to analyze the stability of boundary layer flows, predict transition locations, and delay turbulence through control measures. In recent years, with the deepening of research, the application of linear stability theory has expanded from classic flat plate boundary layers to more complex flow conditions. For example, Chen Xianliang and Fu Song analyzed the influence of thermochemical nonequilibrium effects on the linear stability of hypersonic flat plate boundary layers in 2022, showing that nonequilibrium processes mainly indirectly affect flow stability by changing the basic flow profile. Gloerfelt et al. found in 2020 that the dominant factors affecting the stability of tight gas boundary layers are isobaric specific heat and density-dependent viscosity. In 2014, Govindarajan and Sahu focused on viscosity stratification fluids under different conditions, summarizing the various effects of viscosity stratification on flow stability. In 2020, Chen Jianqiang et al. investigated the main flow field characteristics and boundary layer instability features at different angles of attack and Reynolds numbers using the HyTRV lifting body model, which exhibits typical characteristics of real aircraft. Besides enriching its application scenarios, a series of advances have revealed the influence of various factors such as surface roughness, pressure gradient, and fluid properties on flow stability.

[0004] With the rapid development of machine learning and data science, data-driven fluid dynamics research has entered a new stage. Many researchers have combined machine learning methods with flow stability analysis, driving the development of this field. For example, Cai Shengze et al. used particle image data for training to obtain a deep neural network model suitable for fluid motion estimation. DiLeoni et al. used deep operator networks to solve the forward prediction and backward prediction problems by mapping upstream disturbances to the downstream flow field. Mao et al. designed a DeepM&Mnet framework to predict the flow field after shock waves and improved prediction accuracy through data assimilation techniques in the case of data scarcity. Nie et al. proposed an eN method based on a substitution model, combined with radial basis function interpolation, to effectively predict the transition process in compressible boundary layers. Zafar et al. (2020) proposed a method based on a convolutional neural network (CNN) to successfully predict the local growth rate of disturbances by learning the boundary layer velocity profile and disturbance parameters. Fan et al. (2024) extended this approach to eigenvalue prediction of TS (Tollmien-Schlichting) waves and crossflow waves, and used PINN to solve for the corresponding eigenfunctions. Wu et al. (2024) proposed the SRGAN model based on low-resolution data to reproduce a two-dimensional super-resolution wall turbulence field containing multi-scale energy cascades. However, the above prediction processes rely on accurate flow field parameters, and no research has directly used visualization methods such as images for prediction, resulting in poor real-time performance. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for predicting the N-value of boundary layer flow instability based on datasets and pattern recognition, in order to meet the need for improved real-time prediction. To achieve the above objective, this invention provides the following technical solution:

[0006] According to a first aspect, the present invention provides a method for predicting the N-value of boundary layer flow instability based on datasets and pattern recognition, comprising: establishing a boundary layer flow model based on linear stability theory according to the flow conditions of a target scene, wherein the flow conditions include incompressibility and hypersonicity; solving the eigenvalue problem under the flow model according to the linearized Navier-Stokes (NS) equations to generate perturbation data in Fourier space; when performing inverse Fourier transform on the perturbation data in Fourier space, matching different preset external perturbation sources to generate multiple perturbation fields in physical space, wherein the external perturbation sources are determined according to the target scene; determining the N-value for each perturbation field in physical space based on the perturbation data; acquiring flow instability images in the target plane of each perturbation field in physical space to generate a flow instability image dataset; using the flow instability image dataset as training features and the corresponding N-values ​​as sample labels to train a convolutional neural network to obtain a trained target convolutional neural network; acquiring flow perturbation images under the target scene; inputting the flow perturbation images into the target convolutional neural network model to predict the N-value of flow instability under the target scene.

[0007] According to a second aspect, the present invention provides a boundary layer flow instability N-value prediction device based on dataset and pattern recognition, comprising: a model building module for establishing a flat plate boundary layer flow model under incompressible and hypersonic conditions based on linear stability theory; a disturbance data generation module for solving the eigenvalue problem under the flow model according to the linearized Navier-Stokes equations to generate disturbance data in Fourier space; a disturbance field generation module for matching different preset external disturbance sources when performing inverse Fourier transform on the disturbance data in Fourier space to generate multiple disturbance fields in physical space; and a label determination module for identifying the physical space. For each perturbation field, the N value is determined based on the perturbation data; the flow instability image dataset generation module is used to acquire flow instability images in the target plane of each perturbation field in physical space and generate a flow instability image dataset; the training module is used to train the convolutional neural network to be trained by using the flow instability image dataset as training features and the corresponding N value as sample labels, to obtain the target convolutional neural network after training; the image acquisition module is used to acquire flow perturbation images in the target scene; the N value prediction module is used to input the flow perturbation images into the target convolutional neural network model and predict the flow instability N value in the target scene.

[0008] According to a third aspect, embodiments of the present invention provide a computer storage medium storing computer instructions that, when executed by a processor, implement the steps of the boundary layer flow instability N-value prediction method based on dataset and pattern recognition as described in the first aspect or any embodiment of the first aspect.

[0009] This invention provides a method for predicting the N-value of boundary layer flow instability based on datasets and pattern recognition. Based on linear stability theory, its application is extended beyond traditional growth rate and dispersion relation predictions. First, LST (Limited-Site Transformation) is used to generate perturbation data in Fourier space, which is then transformed to physical space by matching it with predefined external perturbation sources. This constructs a large-scale flow instability dataset, which is then combined with machine learning to predict the N-value. Since a transition usually occurs when the N-value reaches a calibration threshold, the N-value predicted by this invention provides a foundation for pattern recognition and transition prediction in engineering applications. Furthermore, the proposed method can utilize observed patterns (such as those from wind tunnel tests and flight simulations) as input to a CNN model to predict the N-value, achieving accurate end-to-end mapping and providing a real-time instability prediction tool for key areas such as laminar flow control and hypersonic inlet design.

[0010] Other advantages, objectives and features of the invention will be set forth in the following description and will be apparent to those skilled in the art to some extent, or may be learned by practice of the invention. Attached Figure Description

[0011] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0012] Figure 1 Schematic diagram of different instability mechanisms of the X-51A hypersonic vehicle at typical external locations;

[0013] Figure 2 This is a flowchart illustrating a specific example of a boundary layer flow instability N-value prediction method based on dataset and pattern recognition according to the present invention.

[0014] Figure 3 This is a diagram illustrating the TS wave caused by point source vibration in this invention;

[0015] Figure 4 Figures (a), (b), and (c) are schematic diagrams illustrating the influence of external disturbances on the initial amplitude corresponding to different disturbance radii, different disturbance functions, and the number of disturbance sources in this invention.

[0016] Figure 5 This is a schematic diagram of the structure of the convolutional neural network in this invention;

[0017] Figure 6 Figures (a) and (b) are shown, respectively, the neutral surface plots of the Blasius basic flow incompressible example in the three-dimensional space (x,F,β) and the Mach 4.8 hypersonic example in the three-dimensional space (x,F,β).

[0018] Figure 7 Figures (a), (b), (c), and (d) are included. In this invention, Figure (a) is the neutral curve of the Blasius basic flow incompressible example under x-β, and Figures (b), (c), and (d) are the neutral curves of the Mach 4.8 hypersonic example under x-β, corresponding to the cases with only the first mode, both modes, and only the second mode, respectively.

[0019] Figure 8 The figures (a) and (b) represent the disturbance components in this invention. Distribution diagram of slices in different directions in physical space;

[0020] Figure 9 This includes two sets of figures: (a) and (b). Figure (a) shows a comparison of different perturbation components on the xz plane at positions close to the wall in the Blasius example, while figure (b) shows the perturbation components on the xz plane at different wall normal heights in the Blasius example. The comparison chart below also shows the maximum amplitude as a function of y;

[0021] Figure 10 The set of figures includes (a) and (b), which are comparison figures of different perturbation components on the xz plane at the position close to the wall in the hypersonic calculation example of the present invention, and xy plane slices at the perturbation center line in the hypersonic calculation example.

[0022] Figure 11 Figures (a), (b), (c), (d), and (e) show the three-dimensional space of the Blasius example in this invention under different external disturbances. Isosurface plot;

[0023] Figure 12 The diagrams include (a), (b), and (c), which are perturbation structure diagrams of the hypersonic calculation example in this invention at different frequencies close to the wall.

[0024] Figure 13 This is a sample image set of the flow field in this invention;

[0025] Figure 14 This is a graph showing the prediction performance of the CNN model in this invention, including (a) and (b). (a) represents the visualization of the sample, which is a heatmap overlaid with the original image. (b) is a comparison between the model prediction and the actual value of the corresponding sample.

[0026] Figure 15 Figures (a), (b), (c), and (d) represent the distribution of the average absolute error of the model in this invention across all different types of test samples.

[0027] Figure 16This is the overall technical roadmap of the present invention. Detailed Implementation

[0028] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. The technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0029] Flow instability is a complex and diverse problem, with different instability mechanisms occurring in different scenarios, such as... Figure 1 The diagram illustrates different instability mechanisms of the X-51A hypersonic vehicle at typical hull shapes. In the laminar boundary layer, TS wave instability is one of the classic instability modes, primarily caused by viscous and inertial forces. Mack mode instability mainly exists in the supersonic flat plate boundary layer, divided into a low-frequency first mode and a high-frequency second mode, with the second mode dominating while the first mode's instability resembles TS wave instability. Transverse instability typically occurs in the three-dimensional boundary layer, mainly caused by pressure distribution in the flow and the interaction between the boundary layer and the external fluid, and is crucial in swept-wing applications. Instability mechanisms occur in boundary layers with concave curvature surfaces, exhibiting vortex structures that develop along the flow direction due to flow inflection and curvature changes. Attachment line instability is common near the attachment line of surfaces such as airfoils, usually accompanied by flow separation and backflow phenomena. Furthermore, various factors influence the boundary layer's response to external disturbances, and a universally applicable transition theory has not yet been developed. Therefore, current research still faces several key challenges: a lack of systematic data support hinders comparisons between different instability mechanisms and their application in more complex real-world scenarios.

[0030] To advance research on flow instability and real-time prediction under unknown flow field parameters, this invention provides a method for predicting the N-value of boundary layer flow instability based on datasets and pattern recognition, such as... Figure 2 As shown, it includes:

[0031] S101, Based on the flow conditions of the target scenario, a boundary layer flow model is established based on the linear stability theory. The flow conditions include incompressibility and hypersonicity.

[0032] S102, Solve the eigenvalue problem under the flow model based on the linearized Navier-Stokes equations to generate perturbation data in Fourier space;

[0033] S103, when performing inverse Fourier transform on the perturbation data in Fourier space, different preset external perturbation sources are matched to generate multiple perturbation fields in physical space.

[0034] S104, for each perturbation field in the physical space, determine the value of N based on the perturbation data;

[0035] S105: Acquire flow instability images in the target plane of each disturbance field in the physical space and generate a flow instability image dataset.

[0036] S106, using the flow instability image dataset as training features and the corresponding N value as sample label, train the convolutional neural network to be trained to obtain the target convolutional neural network that has been trained.

[0037] S107, acquire the flow disturbance image in the target scene;

[0038] S108: Input the flow disturbance image into the target convolutional neural network model to predict the flow instability N value under the target scene.

[0039] For example, the overall technical solution of this embodiment is described as follows: When a small-amplitude point-source sinusoidal perturbation is introduced into the boundary layer of a flat plate, such as Figure 3 The diagram illustrates the TS wave caused by point-source vibrations, specifically showing the perturbation distribution in the physical space (spanning coordinate z) and Fourier space (wavenumber β) corresponding to the central slice. The growth of the downstream TS wave perturbation is consistent with the LST prediction. By matching the Fourier coefficients, the influence of different external conditions on the perturbation structure can be considered. Subsequently, planar visualization is used to characterize the flow evolution, thereby establishing a flow instability dataset in physical space. Based on this, a data-driven method is used to correlate the flow pattern with the instability parameters, achieving rapid and accurate prediction of the N value.

[0040] The following is a detailed explanation:

[0041] The target scenario can be either aerospace-related flow scenarios or industrial equipment flow scenarios, both of which involve boundary layer flow. This embodiment uses an aerospace-related flow scenario as an example for illustration, as accurately identifying transition points is crucial for guiding thermal protection. The flow conditions in the target scenario can be determined based on the aircraft's speed. When flying at low speeds, it can be considered an incompressible fluid; when flying at hypersonic speeds, it is a hypersonic fluid. Different boundary layer equations are constructed based on linear stability theory for different fluid types. For incompressible fluids, incompressible boundary layer equations are used to construct the flow model; for hypersonic fluids, compressible boundary layer equations are used.

[0042] The eigenvalue problem under the flow model is solved by applying a linearized Navier-Stokes equation, generating perturbation data in Fourier space. Linear stability theory, based on a linearization of the Navier-Stokes equation, is used to analyze small perturbations superimposed on laminar flow Q. The growth or decay of the flow. Linear stability theory is the existing technology for establishing boundary layer flow models, and will not be elaborated upon here. The instantaneous flow field is given by the following equation:

[0043]

[0044] In equation (1), the vectors q, Q and The equations include components of the fundamental flow; there are five components for compressible flow and four components for incompressible flow, where (x, y, z, t) represent three-dimensional spatial coordinates and time variables. To solve the linearized equations, a traveling wave solution is introduced:

[0045]

[0046] Where i is the imaginary unit, and cc represents the complex conjugate term. The linearized Navier-Stokes equations can be expressed as:

[0047]

[0048] Where α is the flow wavenumber, β is the spanwise wavenumber, ω is the disturbance frequency, Re is the Reynolds number, and Ma is the Mach number. This represents the perturbation data in Fourier space. The linear operator L depends on the fundamental flow and the dimensionless number characterizing the flow; its detailed expression is existing technology and will not be elaborated here. This embodiment takes a spatial stability problem as an example, where α and The eigenvalue problem is determined by solving equation (3), where the two represent eigenvalues ​​and eigenvectors, respectively. It is a four-dimensional matrix (x, ω, β; y) that encompasses perturbation data under different parameters. During the dimensionless transformation process, the superscript * is used to denote dimensional quantities, and the length reference scale used is the boundary layer thickness at the inlet. in, Represents the kinematic viscosity coefficient. The characteristic length is represented; the velocity reference scale is the incoming flow velocity.

[0049] Although Equation (2) establishes the connection between physical space and Fourier space, it is essentially a local representation that does not account for the cumulative growth of perturbations along the flow direction, while the linearity allows for harmonic decoupling. To address these issues, this embodiment superimposes all perturbations at the spanwise wavenumber β and multiplies them by an initial amplitude matched to the external perturbation. Thus Transform from Fourier space back to physical space.

[0050] Specifically, when performing an inverse Fourier transform on the perturbation data in Fourier space, different preset external perturbation sources are matched to generate multiple perturbation fields in physical space. This includes: determining perturbation modes for different spanwise wavenumbers based on the perturbation data; determining preset perturbation frequencies based on preset external perturbation sources, and performing Fourier transforms on the perturbation functions corresponding to the external perturbation sources to obtain the initial amplitudes for different spanwise wavenumbers. The preset external perturbation sources consist of different perturbation functions, perturbation radii, and the number of perturbation sources; matching the perturbation modes for different spanwise wavenumbers and the initial amplitudes of the corresponding spanwise wavenumbers in Fourier space to obtain the variation characteristics of the perturbations corresponding to different spanwise wavenumbers in physical space; and superimposing the variation characteristics of the perturbations corresponding to different spanwise wavenumbers in physical space to obtain the perturbation field of the external perturbation source at the corresponding frequency in physical space.

[0051] For example, the expression for a point-source type external disturbance source can be:

[0052]

[0053] Where n is the order of the polynomial, a0...a n Here are the polynomial coefficients, x and z are the coordinates on the xz plane, t represents time, and ω is the perturbation frequency. This is the initial phase.

[0054] Among them, representative functions include:

[0055]

[0056] in:

[0057]

[0058] In the formula x c z c Let R be the center of the disturbance and R be the radius of the disturbance. The above function guarantees that the double integral of the disturbance in the xz plane is always zero at any time, thus avoiding the introduction of additional noise. Moreover, the amplitude is maximum at the center of the disturbance, and the derivative is zero at the edge of the disturbance, which conforms to the characteristics of general disturbances in physical space. The actual external point source vibration is three-dimensional, but the research results show that using its two-dimensional center slice can effectively capture the main features. Therefore, this embodiment selects the three-dimensional disturbance in the xz plane. c The central slice at that point is transformed into Fourier space using Fourier transform, and decomposed into initial amplitudes under different β values. These amplitudes are then used as the initial perturbation for each wavenumber component in subsequent analyses, with the initial amplitude... The process of determining (β) includes: determining the spanwise signal value of each external disturbance source on the two-dimensional central slice of physical space according to the disturbance function corresponding to the preset external disturbance source; and determining the initial amplitude of different spanwise wavenumbers by using discrete Fourier transform based on the spanwise signal value of each external disturbance source on the two-dimensional central slice of physical space, as shown in the following formula:

[0059]

[0060] in, β represents the spanwise wavenumber in Fourier space. k The initial amplitude, k represents the wavenumber index, f(z) n f(z) is the spanwise signal value of the external disturbance source f on a two-dimensional central slice in physical space. n The disturbance function is determined based on the preset external disturbance source; this is existing technology and will not be elaborated upon. N z This refers to the number of signal sampling points. Wavenumber β k The relationship with k is:

[0061]

[0062] Equation (6) indicates that the external disturbance function directly affects the initial amplitude. like Figure 4 As shown, the figures (a), (b), and (c) on the left are the external disturbance profiles along the z-direction, and the right column shows the corresponding Fourier amplitudes, normalized to the value at β = 0. The Fourier amplitudes are represented by a stacked bar chart, where the values ​​are displayed as superimposed bars. Figure 4 As shown in (a), cases of R=200, R=300, and R=400 were selected. As the radius decreases, the physical disturbance becomes more concentrated at the center, resulting in a wider distribution of the Fourier components. Figure 4 Figure (b) illustrates the effects of different perturbation functions, causing amplitude fluctuations at the edges; among all factors, the number of perturbation sources has the greatest impact, such as... Figure 4 As shown in (c), the Fourier amplitude exhibits a dispersed characteristic as the number of values ​​changes. This can then be matched with data in the Fourier space to generate a rich variety of perturbation fields.

[0063] After fixing the frequency of external disturbances, it is possible to... Extract the corresponding three-dimensional data from the data and then... The perturbation mode matching is multiplied with the perturbation mode corresponding to β to obtain the variation characteristics of the perturbation in physical space corresponding to different spanwise wavenumbers. Then, the different wavenumbers are coupled and superimposed, and the perturbation is transformed from Fourier space back to physical space. The specific formula is as follows:

[0064]

[0065] in, For the physical space disturbance field of the external disturbance source, α r (β) represents the real part of the flow wavenumber when the spanwise wavenumber is β, exp(iα) r (β)x+iβz-iωt+N(β,x)) represents the perturbation mode of the spanwise wavenumber corresponding to β, and the imaginary part is integrated along the x-direction to obtain the value of N:

[0066]

[0067] Therefore, for each perturbation field in the physical space, the value of N is determined based on the perturbation data.

[0068] The above analysis concludes that different initial conditions affect the initial amplitude and disturbance data, further influencing the propagation process and distribution characteristics of flow field instability, with the main characteristic being the disturbance pattern. Therefore, the instability characteristics can be effectively predicted based on the pattern obtained from planar observations. Convolutional neural networks, as a type of deep learning model in machine learning, provide an effective solution for this task.

[0069] First, a flow instability image dataset needs to be constructed. After constructing multiple perturbation fields in the physical space according to formula (8), flow instability images are collected in the target plane of each perturbation field in the physical space to generate a flow instability image dataset. The target plane can be the xz and xy planes. Considering three different perturbation functions, three perturbation radii, and three perturbation source numbers, 27 different scenarios can be obtained by combining scenarios. After superimposing different frequencies, more instability images can be obtained. Taking the number of incompressible perturbation frequencies (number of encryption points) as 240 and the number of perturbation frequencies (number of encryption points) of Ma = 4.8 as 175 as an example, there are 6480 (incompressible) / 4725 (Ma = 4.8) instability images under the two slicing forms, thus constructing an instability image dataset.

[0070] CNNs are widely used in computer vision. Their unique feature lies in the introduction of convolutional and pooling layers, giving them strong feature learning capabilities. Convolutional layers use filters (kernels) to perform convolution operations on the input data, extracting features such as edges and corners. Pooling layers reduce the size of feature maps, lowering computational cost and enhancing model robustness. Finally, fully connected layers process these extracted features for classification or regression tasks. Classic CNN network architectures include LeNet (originally used for handwritten digit recognition, employing a relatively simple network structure), AlexNet (improving image classification accuracy and driving the application of deep learning), VGGNet (using stacked small convolutional kernels to deepen the network layers), and ResNet (introducing residual connections to solve the gradient vanishing problem in deep network training). CNNs have continued to evolve, resulting in a series of influential models, such as EfficientNet (using a composite scaling strategy to balance model depth, width, and resolution) and ConvNeXt (borrowing design principles from the Vision Transformer, achieving performance comparable to or even better than the Transformer within a convolutional framework).

[0071] These CNN models demonstrate excellent performance in image classification and provide a foundation for current research on flow instability prediction. This embodiment uses a flow instability image dataset as training features and the corresponding N values ​​as sample labels. Regression training is performed on the convolutional neural network to be trained, resulting in the target CNN model. The convolutional neural network used is as follows: Figure 5 As shown, the model includes: an input layer for inputting a grayscale image; three convolutional layers, each using a different number of convolutional kernels; a max-pooling layer, placed after each convolutional layer for feature downsampling; and three fully connected layers, placed after the last max-pooling layer for regression prediction, ultimately outputting N values. Specifically, the three convolutional layers are followed by a 2×2 max-pooling layer and three fully connected layers. The input is a 128×128 grayscale image, with the convolutional layers using 16, 32, and 64 3×3 convolutional kernels respectively, and stride and padding both being 1. Each convolutional layer is followed by a 2×2 max-pooling layer for feature downsampling. The extracted features are flattened and then input into the fully connected layers for regression prediction, with the number of neurons between layers being 2048 and 512 respectively, ultimately outputting 301 / 500 N values. The input data undergoes standard deviation normalization during the preprocessing stage.

[0072] After constructing the convolutional neural network, the unstable image dataset was divided into training, validation, and test sets in a 70%:15%:15% ratio. Hyperparameter optimization was performed on the validation set using random search, exploring parameters including: learning rate ∈ [0.0001, 0.001, 0.01], batch size ∈ [16, 32, 64], dropout rate ∈ [0.1, 0.2, 0.3, 0.4, 0.5], and activation function ∈ [ReLU, Leaky ReLU]. Twenty independent hyperparameter combinations were sampled and evaluated based on mean squared error (MSE). The configuration with the lowest error was selected for both training and testing the final model. After training, the model's performance was evaluated on the test set. Once the testing requirements were met, the trained target convolutional neural network was obtained. When capturing images of flow disturbances in aerospace-related flow scenarios, these images were input into the target convolutional neural network model to predict the N-value of flow instability in the target scenario.

[0073] This invention provides a method for predicting the N-value of boundary layer flow instability based on datasets and pattern recognition. In this method, LST is used to generate perturbation data in Fourier space, which is then transformed into physical space by matching it with predefined external perturbation sources. This approach constructs a large-scale flow instability dataset. By combining it with machine learning, and considering that a transition usually occurs when the N-value reaches a calibration threshold, the predicted N-value provides a foundation for pattern recognition and transition prediction in engineering applications. Furthermore, the proposed method can utilize observed patterns (such as those from wind tunnel tests and flight simulations) as input to a CNN model to predict the N-value, achieving accurate end-to-end mapping. This provides a real-time instability prediction tool for key areas such as laminar flow control of aircraft and hypersonic inlet design.

[0074] Regarding the above method, the process of constructing unstable image data and training convolutional neural networks for the Blasius basic flow incompressible example and the Mach 4.8 hypersonic example is explained in detail:

[0075] Before performing the analysis in physical space (x,y,z,t), the LST solution is calculated in Fourier space (x,ω,β;y). Taking Table 1 as an example, the mesh parameters are set according to requirements. This embodiment does not limit the mesh parameters, which are used to achieve high-precision numerical solutions for boundary layer perturbations using the LST. These parameters include the mesh range and number of points (only the configuration under positive β is listed; negative wavenumber data is generated from this). It is worth noting that this embodiment uses an adaptive Chebyshev mesh in the y-direction (all other dimensions are uniform meshes). iThe distribution of grid points is controlled to adapt to changes in boundary layer thickness. Note that solving hypersonic problems is more difficult and often requires a denser grid; the grid parameters shown here are only those retained after the solution is completed. The grid used in this embodiment has been verified for independence.

[0076] Table 1

[0077]

[0078] After solving, the imaginary parts of the eigenvalues ​​are used to draw the neutral surface and slice views on the xF plane, as shown below. Figure 6 As shown, the spatial distribution of the growth rate (global frequency F = ω / Re) is illustrated. For incompressible TS waves, the perturbation growth is most significant when β is 0, as shown in the figure. Figure 6 As shown in (a). At Mach 4.8, as Figure 6 As shown in (b), the second mode of instability has a higher growth rate, although its instability region is relatively narrow. This mode occurs because the disturbance control equations in hypersonic speeds have multiple solutions.

[0079] According to formula (4), a specific frequency is selected for subsequent analysis. For Blasius flow, such as Figure 7 The neutral curve under x-β, the solid white line represents the N value contour line, and the white dashed line represents the wave angle. Contour lines, when frequency F = 23 × 10 -6 At β = 0, the N value increases the fastest, reaching 10. If F is fixed at this point, a neutral curve is obtained at x - β, as shown below. Figure 7 As shown in (a). For the Mach 4.8 case, three representative frequencies were considered, corresponding to different instability scenarios: (i) F = 24 × 10 -6 Only the first mode of instability exists at that time. Figure 7 (b);(ii)F=135×10 -6 At that time, the first and second modes coexist, corresponding to upstream and downstream growth, respectively. Figure 7 (c)); (iii) at F = 179 × 10 -6 At that time, only the second mode of instability occurred. Figure 7 (d)).

[0080] The Fourier spatial perturbation data is converted back to physical space using formula (8). The data used satisfies the sampling theorem, that is, there are at least two sampling points within one wavelength. For example, in the x-direction, the wavelength range λ∈[110.05,2795.00] for the incompressible example has a spatial resolution Δx=49.00; while in the hypersonic case, the wavelength range λ∈[54.87,1.71×10 6], Δx=19.34. Therefore, at this time, the spatial structure of the disturbance can be effectively observed through the slice pattern.

[0081] Taking the Blasius fundamental flow as an example, the perturbation field at a position close to the wall normal is as follows: Figure 8 As shown, this represents the disturbance component. Distribution in physical space. As shown in Figure 8(a), the middle subplot is a slice of the xz plane near the wall; the left subplot is the corresponding single β wavenumber; and the right subplot is the yz plane slice at the position of the dashed line in the middle subplot. To better understand the mechanism formed by the superposition of different wavenumbers, the perturbation of a single β wavenumber is analyzed on the left. When x is small, the amplitudes of the various wavenumbers are not significantly different, and their superposition produces a "ripple" with a small radius. As x increases, wavenumbers with β close to 0 grow rapidly and gradually dominate the perturbation evolution process, while wavenumbers with larger β wavenumbers decay somewhat, thus increasing the radius of the "ripple".

[0082] Further analysis, as shown in Figure 8(b), also revealed the perturbation structures on the yz and xy planes (xy plane slices at the perturbation centerline (z = z)). c The left subplot represents the disturbance component. The right-hand subplot represents the instantaneous velocity field. +U), where the white dashed line in the figure represents the boundary layer thickness. The above Figure 8 In (b), the perturbation is mainly concentrated in the boundary layer region. It should be noted that when the perturbation amplitude is too large, the nonlinear term becomes non-negligible. Therefore, before addition, the nonlinear term should be... The scale was applied so that its maximum value did not exceed 10% of the basic flow (the basic flow is normalized to the flow velocity). This is equivalent to controlling the impact of the perturbation during propagation by scaling its initial magnitude.

[0083] In addition to the perturbation component outside, Figure 9 A Blasius example with perturbation comparison is provided. Figure 9 The middle (a) group of figures shows a comparison of different disturbance components on the xz plane at locations close to the wall for other flow components. The results show that, except for... Apart from that, the other three components have similar structures, only their amplitudes differ. Furthermore, as... Figure 9 As shown in Figure (b), these are the disturbance components on the xz plane at different wall normal heights. In comparison, for a certain component, the perturbation structure at different heights is very similar, and the different distributions of its perturbation maximum values ​​are very close to the eigenvector profile obtained from the linear stability analysis. The lower part of the figure shows the variation of the maximum amplitude with y on the xz plane.

[0084] The results in the hypersonic calculation example also confirm the conclusion of structural consistency among the above-mentioned perturbation components, such as... Figure 10 Figure (a) shows a comparison of different perturbation components on the xz plane near the wall. At this frequency, only the second mode is unstable. At this point, a "rope-like" structure appears on the xy plane, which is more significant in terms of density and temperature perturbations, as shown in Figure (a). Figure 10 Figure (b) shows a slice of the xy plane at the center line of the disturbance (z = z). c ), where the white dashed line represents the boundary layer thickness, and this structure is due to the difference in the distribution of the corresponding feature vectors.

[0085] In addition to the slicing operation described above, isosurfaces in three-dimensional space can also be drawn, such as... Figure 11 As shown, coloring was performed at different heights. The control cases were f=f1, R=200, and a single disturbance source ( Figure 11 (a)), corresponding to Figure 8 and Figure 9 The results are shown in the figure. When the frequency of the external disturbance increases to F = 41 × 10⁻⁶, -6 At that time (76% more than the control), the perturbation field was as follows Figure 11 As shown in (b), the disturbance amplitude at this frequency is small and exhibits a pattern of initial increase followed by decrease, due to a reduced growth rate and a narrower instability region. If we modify the form of the external disturbance (which directly affects...), Figure 4 The initial amplitude (shown in the Fourier space conversion) is obtained as follows: If the perturbation function is modified to f2, or the radius R is modified to 400, the results are as follows: Figure 11 As shown in (c) and 11(d), in both cases, the impact is mainly concentrated upstream, while the exponential amplification effect of the downstream disturbance overshadows the effects of the initial function modification. If the original external disturbance function remains, but two disturbance sources of the same frequency are placed at equal intervals along the z-axis, the result is as follows... Figure 11 As shown in (e), wave superposition and interference can be observed, and these interactions produce more complex structures.

[0086] As Figure 7 As mentioned above, under hypersonic conditions, different frequencies produce different combinations of instability. At relatively low frequencies, only the first mode exhibits instability, with a mechanism similar to incompressibility, but the dominant wavenumber is no longer β=0. The alternation of oblique waves causes the pattern to revolve around the centerline of the perturbation field (z=z). c The surrounding area exhibits characteristics similar to "waffles". Figure 12 (See Figure (a) in the diagram). As the frequency increases, instability characteristics of coexistence of the first and second modes begin to appear. In this case, instability of the first mode first occurs upstream, then the disturbance gradually decays, and grows again when it reaches the instability region of the second mode, as shown in Figure (a). Figure 12As shown in Figure (b) of the diagram. It is noteworthy that at the frequency shown in the figure, the disturbance amplitude does not show a significant decrease after leaving the instability region of the first mode. This is because the attenuation is mainly due to the larger wavenumbers, which have smaller initial amplitudes. Therefore, the overall instability structure is still determined by the smaller wavenumbers, which retain their initial amplitudes. As the frequency increases further, only the instability of the second mode occurs, as shown in... Figure 12 Figure (c) shows the disturbance amplitude before entering the instability region. To avoid excessive attenuation of the upstream disturbance leading to unclear subsequent characteristics, we kept the disturbance amplitude almost constant before entering the instability region, reflecting the spatial characteristics of the external disturbance. Upon entering the instability region, disturbances with smaller spanwise wavenumbers (β→0) begin to grow rapidly. This selective growth causes the disturbance structure to gradually evolve into a "shield-like" structure, characterized by the dominance of two-dimensional waves (similar to...). Figure 9 (Features observed in (a)).

[0087] After obtaining the aforementioned instability images, this invention employs a CNN to predict flow instability features. Figure 8 , Figure 12 The xz and xy plane types shown The velocity slice is taken as input, and the output is the value N. Here, the value N refers only to the variable x, such as... Figure 7 As shown, the N value is determined by selecting the maximum value under different wave numbers. Therefore, for the xz and xy planes, the model predicts the distribution of N values ​​along the x-direction of the flow.

[0088] According to Fourier space data Figure 7 (a) shows that the frequency range F in the incompressible case was chosen to be 6.7 × 10⁻⁶. -6 Up to 56.7×10 -6 Between, and encrypted into 240 points. For the case of Ma = 4.8, the range of F is 1.4 × 10. -6 Up to 285.7×10 -6 175 points. Two images are obtained at each frequency: the xz plane shows the slice near the wall, and the xy plane shows the slice along the perturbation centerline. To amplify the perturbation features, the boundaries of the images involving the y-dimensional area are not y-dimensional. max Instead, it is the maximum value of the boundary layer thickness, which is approximately 35 (incompressible) / 100 (Ma = 4.8).

[0089] In addition to encryption frequency, this paper also increases data diversity by enriching the forms of perturbation. Specifically, we consider scenarios with three different perturbation functions, three perturbation radii, and three numbers of perturbation sources, such as... Figure 4As shown. The above scene combinations can yield 27 different forms. When superimposed at different frequencies, the two slice forms result in 6480 (incompressible) / 4725 (Ma = 4.8) images respectively. Figure 13 As shown, these samples constitute the image dataset used in this invention.

[0090] According to the training process described in the above embodiments, after training is completed... Figure 14 The prediction results of the incompressible example for four samples in the cz plane are shown. Figure 14 The middle (a) group of figures shows the GradCAM visualization results. The highlighted areas highlight the regions in the input image that have a significant impact on CNN predictions, mainly concentrated near the TS wave of the samples, indicating that the CNN model has identified key features. The text in the upper left of the sub-figure represents the corresponding samples. For example, the first one, "f1r3s2 omega142", refers to a sample with perturbation function f1, radius 400 (i.e., the third type), two perturbation sources, and a frequency index of 142. Figure 14 The top of the figure in group (b) shows the predicted N value (solid line) of the corresponding sample CNN model and the N value calculated by LST (dots), while the bottom shows the error between the two. As can be seen from the figure, the CNN prediction result is highly consistent with the LST result, demonstrating good accuracy.

[0091] The above shows the prediction results for individual samples. For overall performance, the mean absolute error (MAE) of each sample in the test set can be displayed as a histogram. For example... Figure 15 As shown, the horizontal axis represents the magnitude of the error, and the vertical axis represents the frequency of occurrence. Figure (a) shows the xz plane under the incompressible condition; Figure (b) shows the xy plane under the incompressible condition; Figure (c) shows the xz plane under the hypersonic condition; and Figure (d) shows the xy plane under the hypersonic condition. The figures show that most errors fall within the range of ΔN < 0.2. To investigate the performance improvement brought by the optimized neural network, the test results of AlexNet, ResNet, and ConvNeXt on the incompressible xz plane are compared with the CNN architecture we used. ResNet-18 was selected for ResNet, and ConvNeXt-Tiny was selected for ConvNeXt. Minor modifications were made to these architectures to make them suitable for regression tasks. Quantitative comparisons are shown in Table 2.

[0092] Table 2

[0093]

[0094] The results show that the custom CNN uses a lightweight convolutional structure but employs a very large number of fully connected layers, resulting in the largest number of parameters, but actually lower FLOPs; AlexNet shows a slight improvement in performance compared to the custom CNN; ResNet has moderate parameters and high cost-effectiveness; ConvNeXt is a modern structure with the strongest fitting ability.

[0095] Based on the above description, the overall technical approach of the present invention is as follows: Figure 16 As shown, it includes theoretical analysis, data construction, and intelligent evaluation.

[0096] Theoretical Analysis: Based on stability theory, this paper analyzes the flow instability mechanism and uses LST to conduct an in-depth analysis of the instability characteristics of incompressible and hypersonic fluids. Through numerical simulation of flat plate boundary layer flow, it studies the critical conditions for instability, disturbance growth characteristics, and visualizes the flow evolution process.

[0097] Data Construction: The analysis of disturbance characteristics and the construction of a flow instability dataset reveal the evolutionary characteristics of disturbances from various dimensions, enrich the forms of external disturbances, and build a flow instability dataset based on this. The dataset primarily considers combinations of different frequencies, the number of disturbance sources, disturbance radii, and disturbance function forms, generating corresponding flow field instability patterns for different flow conditions.

[0098] Intelligent Assessment: Deep Learning-Based Flow Instability Prediction and Assessment. This approach applies deep learning techniques, such as CNNs, to the assessment and prediction of flow instability. By using simulated flow field images as input, the model can automatically extract key features from the images and accurately predict instability parameters and flow transitions based on these features. This provides new ideas and technical means for the optimal design of complex flow systems and the formulation of flow control strategies.

[0099] This invention provides a boundary layer flow instability N-value prediction device based on dataset and pattern recognition, comprising:

[0100] The model building module is used to establish a boundary layer flow model based on the linear stability theory according to the flow conditions of the target scenario.

[0101] The disturbance data generation module is used to solve the eigenvalue problem under the flow model based on the linearized Navier-Stokes equations and generate disturbance data in Fourier space.

[0102] The disturbance field generation module is used to match different preset external disturbance sources when performing inverse Fourier transform on the disturbance data in Fourier space, and generate multiple disturbance fields in physical space. The external disturbance sources are determined according to the target scene.

[0103] The label determination module is used to determine the N value for each perturbation field in the physical space based on the perturbation data.

[0104] The flow instability image dataset generation module is used to acquire flow instability images in the target plane of each perturbation field in physical space and generate a flow instability image dataset.

[0105] The training module is used to train the convolutional neural network to be trained by using the flow instability image dataset as training features and the corresponding N value as sample label, so as to obtain the target convolutional neural network after training.

[0106] The image acquisition module is used to acquire images of flow disturbances in the target scene;

[0107] The N-value prediction module is used to input the flow disturbance image into the target convolutional neural network model and predict the N-value of flow instability in the target scene.

[0108] This application also provides an electronic device, a processor, and a memory, wherein the processor and the memory can be connected via a bus or other means.

[0109] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or combinations of the above types of chips.

[0110] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the boundary layer flow instability N-value prediction method based on dataset and pattern recognition in this embodiment of the invention. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions, and modules stored in the memory.

[0111] The memory may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0112] The one or more modules are stored in the memory, and when executed by the processor, they perform actions such as... Figure 2 The embodiment shown illustrates a method for predicting the N-value of boundary layer flow instability based on datasets and pattern recognition.

[0113] For specific details regarding the aforementioned electronic devices, please refer to the relevant documentation. Figure 2 The relevant descriptions and effects in the illustrated embodiments are for understanding purposes only and will not be repeated here.

[0114] This embodiment also provides a computer storage medium storing computer-executable instructions that can execute the boundary layer flow instability N-value prediction method based on dataset and pattern recognition in any of the above method embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium may also include combinations of the above types of memory.

[0115] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A boundary layer flow instability based on dataset and pattern recognition Value prediction method, characterized in that, include: Based on the flow conditions of the target scenario, a boundary layer flow model is established using linear stability theory. The eigenvalue problem under the flow model is solved using the linearized Navier-Stokes equations, generating perturbation data in Fourier space. The linearized Navier-Stokes equations are then expressed as follows: in, For linear operators, For components of the basic flow, For the flow wave number, For spanwise wavenumber, The Reynolds number is... Mach number, This represents the perturbation data in Fourier space; When performing inverse Fourier transform on the perturbation data in Fourier space, different preset external perturbation sources are matched to generate multiple perturbation fields in physical space. The external perturbation sources are determined according to the target scene. For each perturbation field in physical space, determine based on the perturbation data. value; Flow instability images are acquired in the target plane of each perturbation field in physical space to generate a flow instability image dataset; Using the fluid instability image dataset as training features, the corresponding The values ​​are used as sample labels to train the convolutional neural network to obtain the target convolutional neural network after training. Acquire images of flow disturbances in the target scene; The flow disturbance image is input into the target convolutional neural network model to predict the flow instability in the target scene. value.

2. A boundary layer flow instability method based on dataset and pattern recognition as described in claim 1 Value prediction method, characterized in that, Flow conditions include incompressible and hypersonic, including: For hypersonic flow, the instability image dataset includes Mack's first-mode instability image, second-mode instability image, and instability image where the first and second modes coexist.

3. A boundary layer flow instability method based on dataset and pattern recognition as described in claim 1 Value prediction method, characterized in that, When performing an inverse Fourier transform on the perturbation data in Fourier space, different preset external perturbation sources are matched to generate multiple perturbation fields in physical space, including: Based on the perturbation data, determine the perturbation modes for different spanwise wavenumbers; Based on the preset external disturbance source, the preset disturbance frequency is determined, and the Fourier transform of the disturbance function corresponding to the external disturbance source is performed to obtain the initial amplitude of different spanwise wavenumbers. The preset external disturbance source consists of different disturbance functions, disturbance radii, and the number of disturbance sources. By matching the perturbation modes of different spanwise wavenumbers and the initial amplitudes of the corresponding spanwise wavenumbers in Fourier space, the variation characteristics of the perturbations corresponding to different spanwise wavenumbers in physical space are obtained. By superimposing the variation characteristics of disturbances in physical space corresponding to different spanwise wavenumbers, the disturbance field of the external disturbance source at the corresponding frequency in physical space is obtained.

4. A boundary layer flow instability method based on dataset and pattern recognition as described in claim 3. Value prediction method, characterized in that, The initial amplitudes of different spanwise wavenumbers are obtained by performing a Fourier transform on the disturbance function corresponding to the external disturbance source, including: Based on the preset disturbance function corresponding to the external disturbance source, determine the spanwise signal value of each external disturbance source on the two-dimensional central slice of physical space; Based on the spanwise signal values ​​of each external disturbance source on a two-dimensional central slice of physical space, the initial amplitudes of different spanwise wavenumbers are determined by discrete Fourier transform.

5. A boundary layer flow instability based on dataset and pattern recognition as described in claim 3 or 4 Value prediction method, characterized in that, Preset external disturbance sources to satisfy: ； in, , The location of the disturbance center. The disturbance radius is... Let be the order of the polynomial. ... For polynomial coefficients, , They are respectively Coordinate values ​​on the plane Indicates time, For the perturbation frequency, This is the initial phase.

6. A boundary layer flow instability method based on dataset and pattern recognition as described in claim 3. Value prediction method, characterized in that, The initial amplitudes of different spanwise wavenumbers are obtained by performing a Fourier transform on the disturbance function corresponding to the external disturbance source, including: ； in, Represents the spanwise wavenumber The initial amplitude, Indicates wavenumber index, External disturbance source The signal value spanned on the two-dimensional central slice It is the number of signal sampling points. It is the imaginary unit.

7. A boundary layer flow instability method based on dataset and pattern recognition as described in claim 3. Value prediction method, characterized in that, By matching the perturbation modes of different spanwise wavenumbers and their corresponding initial amplitudes in Fourier space, the physical variation characteristics of the perturbations corresponding to different spanwise wavenumbers are obtained, including: ； in, The physical space disturbance field of the external disturbance source. This represents the perturbation data in Fourier space. For spanwise wavenumber, The initial amplitude of the external disturbance source. For the spanwise wavenumber is The flow is directed towards the real part of the wavenumber. , Represents three-dimensional coordinates and time variables in physical space. The imaginary unit, Indicates complex conjugation.

8. A boundary layer flow instability method based on dataset and pattern recognition as described in claim 1 Value prediction method, characterized in that, Target convolutional neural networks include: Input layer, used to input grayscale images; Three convolutional layers, each using a different number of convolutional kernels; Max pooling layers are placed after each convolutional layer to perform feature downsampling; A three-layer fully connected layer, placed after the last max-pooling layer, is used for regression prediction, and the final output is... value.

9. A boundary layer flow instability based on dataset and pattern recognition Value prediction device, characterized in that, include: The model building module is used to establish a boundary layer flow model based on the linear stability theory according to the flow conditions of the target scenario. The disturbance data generation module is used to solve the eigenvalue problem under the flow model based on the linearized Navier-Stokes equations, generating disturbance data in Fourier space. The linearized Navier-Stokes equations are expressed as follows: in, For linear operators, For components of the basic flow, For the flow wave number, For spanwise wavenumber, The Reynolds number is... Mach number, This represents the perturbation data in Fourier space; The disturbance field generation module is used to match different preset external disturbance sources when performing inverse Fourier transform on the disturbance data in Fourier space, and generate multiple disturbance fields in physical space. The external disturbance sources are determined according to the target scene. The label determination module is used to determine the label for each perturbation field in the physical space, based on the perturbation data. value; The flow instability image dataset generation module is used to acquire flow instability images in the target plane of each perturbation field in physical space and generate a flow instability image dataset. The training module is used to take the dataset of flow instability images as training features, and the corresponding... The values ​​are used as sample labels to train the convolutional neural network to obtain the target convolutional neural network after training. The image acquisition module is used to acquire images of flow disturbances in the target scene; The value prediction module is used to input the flow disturbance image into the target convolutional neural network model to predict the flow instability in the target scene. value.

10. A computer storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the boundary layer flow instability based on dataset and pattern recognition as described in any one of claims 1-8. The steps of the value prediction method.

Images