An aircraft flow field data prediction method based on physical information constraint

Abstract

The application discloses a kind of based on physical information constraint's aircraft flow field data prediction method, comprising the following steps: S1, data pre-processing and training embedding: the flow field data obtained by sampling is normalized, coding processing and linearization processing are carried out, and the embedding representation of flow field state variable is generated;S2, the training of Transformer module based on physical information constraint: the time series characteristics of flow field are captured by Transformer module, and physical information constraint is combined, and the network model suitable for unsteady flow field prediction is constructed;S3, flow field prediction: the unsteady flow field of bluff body around is predicted using the completed Transformer of training.The existing flow field prediction method depends on traditional computational fluid dynamics (CFD) simulation, often faces the problems such as low calculation efficiency, large resource consumption etc.The present application can efficiently predict complex flow field without relying on flow field prior experience by introducing physical information constraint and combining Transformer architecture, with high efficiency and small calculation overhead.

Description

Technical Field

[0001] This invention belongs to the field of unsteady flow field prediction technology, specifically relating to a method for predicting aircraft flow field data based on physical information constraints. Background Technology

[0002] The flow around a bluff body, a classic problem in fluid mechanics, involves flow separation, eddy shedding, and complex unsteady characteristics. These phenomena profoundly affect the pressure distribution and lift / drag on the surface of an object, making it a key research area in aerospace, architectural design, and mechanical engineering. While traditional computational fluid dynamics (CFD) methods can provide relatively accurate solutions to these problems with the development of numerical simulation techniques, they often require high computational costs, especially when handling large-scale, multi-condition flow analyses, where computational expenses increase dramatically. Therefore, how to reduce computational costs while maintaining high accuracy is a pressing challenge in current flow field prediction. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a method for predicting aircraft flow field data based on physical information constraints, which can significantly reduce computational overhead while ensuring high accuracy.

[0004] The technical solution adopted in this invention is as follows:

[0005] This application discloses a method for predicting aircraft flow field data based on physical information constraints, including the following steps:

[0006] S1. Data preprocessing and training embedding: Normalize, encode and linearize the sampled flow field data to generate embedded representations of the flow field state variables.

[0007] S2. Training of Transformer module based on physical information constraints: The Transformer module captures the time series characteristics of the flow field and combines them with physical information constraints to build a network model suitable for predicting unsteady flow fields.

[0008] S3. Flow field prediction: Predict the unsteady flow field around a bluff body using the trained Transformer.

[0009] As an optional technical solution, the data preprocessing and training embedding in step S1 includes the following steps:

[0010] S11. Data Sampling and Preprocessing: Acquire flow field data and normalize the acquired flow field data to normalize all flow field data to the open interval [-1, 1]; wherein, the flow field data includes the velocity field (u x u y), pressure field (p) and viscosity field (θ) expressed by kinematic viscosity;

[0011] S12: Encoding and linearizing the normalized flow field data: An automatic convolutional encoder is used to encode the normalized flow field data. During encoding, the feature map is first upsampled for size expansion, and then a standard convolution operation is applied. An auxiliary fully connected network is then used to predict the diagonal and off-diagonal elements of the Koopman operator for each viscosity, establishing a linear evolution relationship between observed variables based on the Koopman operator. The fully connected network is used to learn the flow field state variables (u...). x u y The embedding relationship between the observed variables (p, θ) and the observed variables;

[0012] S13: Decoding and Backpropagation: After the data is linearized by the Koopman operator, it is decoded through a deconvolution layer and then fed into the loss function for evaluation.

[0013] As an optional technical solution, when acquiring flow field data in step S11, a Cartesian grid is used for data sampling to improve computational efficiency and memory management.

[0014] As an optional technical solution, the training of the Transformer module based on physical information constraints in step S2 includes the following steps:

[0015] S21. Input for determining operating conditions and geometric information: The operating conditions of the flow around the cylinder are determined by the Reynolds number; the geometric information is represented by the signed distance function (SDF);

[0016] S22. Input flow field variables and time series prediction: The input to the model is the velocity field u. x u y The pressure field p and the kinematic viscosity θ of the fluid are encoded by a pre-trained convolutional neural network, and the encoded input dimension is 128. The model starts predicting from the steady state of the flow field. The flow field information obtained before prediction includes kinematic viscosity. After the prediction is completed for one time step, the Transformer uses the flow field data output from the previous time step as the input for predicting the next time step.

[0017] S23. Decoding and Evaluation of Transformer Predicted Data: The data predicted by the Transformer is output by the decoder, and the time step interval for data recording can be customized; the time dimension is eliminated after recording the time according to the specified number of steps; the predicted flow field variables are input into the loss function for evaluation, and then back to the Transformer through backpropagation.

[0018] As an optional technical solution, the loss function in step S23 is expressed as:

[0019] Loss=λ1L data +λ2n(L NS +L BC +L IC )

[0020] Where λ1 and λ2 represent the weights of the data-driven loss and the physical mechanism-driven loss at a given order of magnitude, respectively, and n is used to control the order of magnitude of the physical loss, such that L data It is on the same order of magnitude as physical losses; L data Let L be the mean square error between the predicted and actual values ​​of the three flow field variables. NS For the loss of the Navier-Stokes equation, L BC For boundary condition loss, L IC This represents the initial condition loss.

[0021] As an optional technical solution, the flow field prediction in step S3 includes the following steps:

[0022] S31. Input and preprocessing of flow field information: The flow field information provided to the model includes the geometric information of the flow field, initial conditions, boundary conditions, and the properties of the fluid itself. All data need to be normalized before input. The geometric information is represented by the sign distance function SDF, and the properties of the fluid itself include the fluid kinematic viscosity θ and density ρ.

[0023] S32. Determine the required time length and time step: After determining the time step and the time interval for recording data, begin flow field prediction.

[0024] S33. Prediction and Visualization: During the prediction process, the flow field will be visualized, and the velocity field (u) at each time step will be output. x ,u y The flow field data is visualized in contour plots for both the pressure field (p) and the flow field (g). Each visualization outputs a contour plot of the flow field data, with the resolution of the contour plot consistent with the resolution of the provided geometric and viscosity field information.

[0025] As an optional technical solution, the initial condition in step S31 is: when T = 0, u x =0, u y =0, P=P0, ρ=ρ0, θ=θ0.

[0026] As an optional technical solution, the boundary conditions in step S31 include velocity inlet boundary conditions, pressure outlet boundary conditions, and no-slip wall boundary conditions, wherein the velocity inlet boundary condition is: u x =1, u y=0; the pressure outlet boundary condition is: The no-slip wall boundary condition is: u x =0, u y =0.

[0027] The beneficial effects of this invention are as follows:

[0028] 1. This invention effectively improves the efficiency and accuracy of flow field prediction by introducing physical information constraints combined with the Transformer architecture. Specifically, the model achieves high-dimensional linear dynamic modeling and enhances the interpretability of low-dimensional physics through Koopman observable embedding; simultaneously, it leverages the advantages of the Transformer multi-head attention mechanism in time-series data processing to capture the unsteady characteristics of the flow field. By embedding the residuals, initial losses, and boundary losses of the governing equations into the loss function, the model ensures that the flow field output satisfies the laws of conservation of momentum and mass, thereby improving the physical consistency and reliability of the prediction results. In this way, the model can not only efficiently predict complex unsteady flow fields but also adapt to flow field prediction under different operating conditions, avoiding the accuracy problems caused by the lack of physical constraints in traditional methods.

[0029] 2. This application combines physical constraints with deep learning techniques. Specifically, it embeds the Navier-Stokes equations, initial conditions, and boundary conditions directly into the Transformer, thereby forcing the model to obey the fundamental laws of fluid mechanics during training. The initial conditions provide a particular solution to the Navier-Stokes equations, and automatic differentiation (AD) is used to solve the derivative terms in the Navier-Stokes equations and Neumann boundary conditions. Compared to traditional deep learning methods, the model of this invention has stronger generalization ability and can effectively adapt to flow field prediction tasks under new operating conditions. Simultaneously, the introduction of physical constraints significantly reduces the model's requirement for large amounts of high-quality labeled data, making it particularly suitable for situations where experimental data is scarce or operating conditions are complex.

[0030] 3. By incorporating physical constraints into the model, the proposed model not only solves the problem of high computational resource consumption in traditional CFD methods, but also avoids the problems of physical inconsistency and poor generalization ability encountered by traditional deep learning methods when dealing with flow field prediction. This model has broad application prospects, especially in aerospace, aerodynamic design, and building structure optimization, where it can significantly improve the efficiency and accuracy of flow field prediction, reduce computational overhead, and provide high-precision flow field prediction data for engineering design. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating an exemplary embodiment of a method for predicting aircraft flow field data based on physical information constraints.

[0032] Figure 2 This is a schematic diagram of a Koopman observable embedded training architecture in an exemplary embodiment. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The method steps of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0034] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0035] Example

[0036] like Figure 1 As shown, this application discloses a method for predicting aircraft flow field data based on physical information constraints, including the following steps:

[0037] S1. Data Preprocessing and Training Embedding: The sampled flow field data is normalized, encoded, and linearized to generate embedded representations of the flow field state variables. This includes the following processes:

[0038] S11: Data Sampling and Preprocessing. Acquire flow field data, including the velocity field (u). x u y This dataset contains four channels of flow field data, including pressure field (p) and viscosity field (θ) represented by kinematic viscosity. Cartesian grid sampling with equal-sized cells provides more efficient computation and memory management. The sampling resolution is 128×64, and the sampling area size is 16×8. After sampling, the data is normalized to an open interval [-1,1], eliminating dimensional differences and resulting in smoother gradient updates.

[0039] S12: Encoding the flow field data. An automatic convolutional encoder with a 3×3 kernel size is used. In the encoder part, the feature maps are first upsampled and then a standard convolution operation is applied. Additionally, two auxiliary fully connected networks are used to predict the diagonal and off-diagonal elements of the Koopman operator for each viscosity. This network is used to learn the flow field state variables (u...). x u yThe embedding relationships between the observed variables (p and θ) are established, with an embedding dimension of 128. Then, a linear evolution relationship between the observed variables is established based on the Koopman operator.

[0040] S13: Decoding and Backpropagation. After linearization by the Koopman operator, the data is decoded through the same six convolutional layers and then fed into the loss function for evaluation. The training loss function of the Koopman embedding model consists of three parts: 1. Reconstruction loss, ensuring a consistent mapping between embedding representations; 2. Koopman dynamics loss: This pushes the embedding states to follow linear dynamics based on the learned Koopman operator; 3. Koopman operator decay: This is a parameter for decaying the Koopman operator to help force the model to discover meaningful dynamic patterns and prevent overfitting.

[0041] S2. Transformer Module Training Based on Physical Information Constraints: The Transformer module captures the time-series characteristics of the flow field and, combined with physical information constraints, constructs a network model suitable for predicting unsteady flow fields. This specifically includes the following process:

[0042] S21. Determine the input of operating conditions and geometric information. The operating conditions for flow around a cylinder can be determined solely by the Reynolds number (for flow around an airfoil, the angle of attack must also be given). The Reynolds number is expressed in terms of kinematic viscosity as:

[0043]

[0044] Geometric information is represented by the symbolic distance function (SDF), and after the boundary conditions are given, the working conditions of the flow field can be determined solely by the kinematic viscosity of the fluid.

[0045] S22. Input flow field variables and time series prediction. The model input is the velocity field u. x u y The pressure field p and the kinematic viscosity θ of the fluid are used as input dimensions for the data. x ,u y ,p,θ∈R 4×64×128 The four-channel flow field variables are encoded using a pre-trained convolutional neural network, with the encoded input dimension being R. BatchSize×Time×128 The model starts predictions from the steady-state phase of the flow field. Before prediction, the only flow field information available is kinematic viscosity. When a prediction is completed at a given time step, the Transformer uses the flow field data (u) output from the previous time step. x ,u y ,p∈R 3×64×128 The input for predicting the next time step is θ. Due to the spatial uniformity and temporal independence of kinematic viscosity, the model no longer outputs θ, and the dimension is u. x ,uy ,p∈R 3×64×128 Three-channel flow field data.

[0046] S23. Backpropagation and Evaluation. The data predicted by the Transformer is output by the decoder, with data output every 20 time steps. The time dimension is eliminated, and the dimension of the state variables is restored to R. BatchSize×3×Hight×Wide The predicted flow field variables are then evaluated using a loss function, and subsequently backpropagated back into the Transformer.

[0047] The physical loss constraint consists of three parts: the loss L in the Navier-Stokes equations. NS Boundary condition loss L BC Initial condition loss L IC In addition, the state error L generated by data-driven processes data L NS This is the sum of squares of the Navier-Stokes (NS) equation residuals. The component form of the NS equation residuals for a 2D incompressible fluid, expressed using kinematic viscosity, is:

[0048]

[0049] The differential terms are calculated automatically. For gradient models without explicit functional relationships, a computational graph is created and the chain rule is used for calculation. Taking flow around a cylinder as an example, the boundary conditions (BCs) include: velocity inlet boundary conditions, u x =1, u y =0; Pressure outlet boundary condition, No-slip wall boundary conditions, u x =0, u y =0.

[0050] When the initial condition is (ICs)T = 0, we have:

[0051] u x =0, u y =0

[0052] P = P0

[0053] ρ=ρ0

[0054] θ=θ0

[0055] L data Let be the mean square error (MSE) between the predicted and actual values ​​of the three flow field variables. It can be expressed as:

[0056]

[0057] The model's loss function can be expressed as:

[0058] Loss=λ1L data +λ2n(L NS +L BC +L IC )

[0059] λ1 and λ2 represent the weights of the data-driven loss and the physical mechanism-driven loss at a given order of magnitude, respectively, and n is used to control the order of magnitude of the physical loss, such that L data The loss is on the same order of magnitude as the physical loss. The model's evaluation metric is the mean squared error (MSE) between the predicted and actual values. Once trained, the Transformer can be used to predict unsteady flow fields around bluff bodies.

[0060] S3. Flow Field Prediction: Predicting the unsteady flow field around a bluff body using a trained Transformer. This includes the following steps:

[0061] S31. Input and Preprocessing of Flow Field Information. The flow field information that needs to be provided to the model includes the geometric information of the flow field (represented by SDF), initial conditions ICs, boundary conditions BCs, and the fluid's inherent properties, including kinematic viscosity θ and density ρ. Besides flow around a cylinder, the incident angle of the incoming flow or its component form is also required. All data needs to be normalized to the open interval [-1,1] before input to eliminate dimensional differences.

[0062] S32. After determining the required prediction time length, time step, and time step interval for recording data, flow field prediction can begin.

[0063] S33. During the prediction process, the flow field is visualized simultaneously with the recorded data. The visualization resolution is consistent with the resolution of the provided geometric and viscosity field information. Each visualization outputs the velocity field u. x u y The flow field data cloud map, including pressure field p, as well as lift coefficient and drag coefficient.

[0064] To better understand this application, the following example of flow around a cylinder will be used to further illustrate the method of this application.

[0065] Specifically, the dataset used consisted of 40 Reynolds number intervals (100-750) data points for velocity, pressure, and viscosity fields around a cylinder. This included 27 training sets, 6 validation sets, and 7 test sets. Cartesian grid sampling was employed with a resolution of 128×64 and a sampling area size of 16×8. After sampling, the data was normalized to an open interval [-1, 1] to eliminate dimensional differences.

[0066] The embedding is then trained. The preprocessed flow field data is input into the model, with an input dimension of u.x u y p, θ∈R 4 ×64×128 The model learns the embedding relationship between flow field state variables and observed variables, with an embedding dimension of 128. Then, it establishes a linear evolution relationship between observed variables based on the Koopman operator. Finally, the flow field variables are decoded through a deconvolutional network, as shown below. Figure 2 As shown. The training process lasts for 300 epochs, and the model will automatically save the embedding method after the last training step as the frozen encoding method of the Transformer.

[0067] The processed flow field data is input into the Transformer. The embedding dimension after encoding by the pre-trained frozen encoder is R. BatchSize×Time×128 The data predicted by the Transformer is output by the decoder, with data output every 20 time steps. The time dimension is eliminated, and the dimension of the state variables is restored to R. Batch Size×3×Hight×Wide The visualization module generates contour maps of the velocity and pressure fields simultaneously with data recording. The predicted flow field variables are then input into the loss function for calculation. In the first step of training, the model calculates L... data With (L) NS +L BC +L IC The value of ) is then output, and n is adjusted so that the physical loss and data loss are on the same order of magnitude. The evaluation results for the first four samples of the example dataset are shown in Table 1:

[0068]

[0069] Table 1. Losses of the first four samples

[0070] Then at this time n = 10 5 The training loss of the model is then backpropagated to the Transformer to guide its optimization. A learning rate scheduler is used to dynamically adjust the learning rate during training, with four samples trained simultaneously at a time, while the batch size for validation is six. The Transformer is trained for a total of 250 epochs. During training, the flow field variable u... x u y p is explicitly output and monitored. The MSE (State Error) between the predicted result and the true value is used as the metric to evaluate the model's ability to predict the flow field. An evaluation is performed every 25 epochs during training (or a custom evaluation can be used), and the evaluation output will show... E pAnd state error. After Transformer training is complete, the state error of the model predicting the flow field will decrease to 10. -3 -10 -2 The order of magnitude of the sample datasets and their performance on different Reynolds number test sets are shown in Table 2.

[0071]

[0072] Table 2. Error of the model after training on the example dataset

[0073] This model can be used to predict the flow field around an unknown cylinder. The only flow field information required to perform the prediction is the fluid's kinematic viscosity θ, density ρ, and boundary conditions.

[0074] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. All technical solutions that fall within the scope of the claims of this invention are within the scope of protection of this invention.

Claims

1. A method for predicting aircraft flow field data based on physical information constraints, characterized in that, Includes the following steps: S1. Data preprocessing and training embedding: Normalize, encode and linearize the sampled flow field data to generate embedded representations of the flow field state variables. S2. Training of Transformer module based on physical information constraints: The Transformer module captures the time series characteristics of the flow field, and a loss function is constructed to apply physical information constraints, thereby constructing a network model suitable for predicting unsteady flow fields. S3. Flow field prediction: Predict the unsteady flow field around a bluff body using the trained Transformer. The loss function is expressed as: in, and These represent the weights of the data-driven loss component and the physical mechanism-driven loss component, respectively, within a given order of magnitude. Used to control the order of magnitude of physical loss, making It is on the same order of magnitude as physical losses; The mean square error between the predicted and actual values ​​of the three flow field variables is denoted as . For the loss of the Navier-Stokes equation, For boundary condition loss, Loss due to initial conditions; in, The sum of squares of the residuals of the Navier-Stokes equations is given by the component form of the Navier-Stokes equation residuals for a 2D incompressible fluid, expressed in terms of kinematic viscosity: The differential terms are calculated using automatic differentiation. For gradient models without explicit functional relationships, a computational graph is created and the chain rule is used for calculation.

2. The method for predicting aircraft flow field data based on physical information constraints according to claim 1, wherein the data preprocessing and training embedding in step S1 includes the following steps: S11. Data Sampling and Preprocessing: Acquire flow field data and normalize the acquired flow field data to ensure that all flow field data are normalized to a uniform standard. Within the open interval; wherein, the flow field data includes the velocity field, pressure field, and viscosity field represented by kinematic viscosity; S12: Encoding and linearizing the normalized flow field data: An automatic convolutional encoder is used to encode the normalized flow field data. During encoding, the feature map is first upsampled to expand its size, and then a standard convolution operation is applied. Then, an auxiliary fully connected network is used to predict the diagonal and off-diagonal elements of the Koopman operator for each viscosity, and a linear evolution relationship between the observed variables is established based on the Koopman operator. The fully connected network is used to learn the embedding relationship between the flow field state variables and the observed variables. S13: Decoding and Backpropagation: After the data is linearized by the Koopman operator, it is decoded through a deconvolution layer and then fed into the loss function for evaluation.

3. The method for predicting aircraft flow field data based on physical information constraints according to claim 2, characterized in that: In step S11, when acquiring flow field data, a Cartesian grid is used for data sampling to improve computational efficiency and memory management.

4. The method for predicting aircraft flow field data based on physical information constraints according to claim 1, characterized in that, The training of the Transformer module based on physical information constraints in step S2 includes the following steps: S21. Input of operating conditions and geometric information: The operating conditions of the flow around the cylinder are determined by the Reynolds number; the geometric information is represented by the signed distance function; S22. Input flow field variables and time series prediction: The model inputs are the velocity field, pressure field, and kinematic viscosity of the fluid. The flow field variables are encoded using a pre-trained convolutional neural network, and the encoded input dimension is 128. The model starts prediction from the steady-state period of the flow field. The flow field information obtained before prediction includes kinematic viscosity. After the prediction of one time step is completed, the Transformer uses the flow field data output from the previous time step as the input for predicting the next time step. S23. Decoding and Evaluation of Transformer Predicted Data: The data predicted by the Transformer is output by the decoder, and the time step interval for data recording can be customized; the time dimension is eliminated after recording the time according to the specified number of steps; the predicted flow field variables are input into the loss function for evaluation, and then back to the Transformer through backpropagation.

5. The method for predicting aircraft flow field data based on physical information constraints according to claim 1, characterized in that, The flow field prediction in step S3 includes the following steps: S31. Input and Preprocessing of Flow Field Information: The flow field information provided to the model includes the geometric information of the flow field, initial conditions, boundary conditions, and the properties of the fluid itself. All data needs to be normalized before input. The geometric information is represented by a signed distance function, and the fluid properties include the fluid kinematic viscosity. With density ; S32. Determine the required time length and time step: After determining the time step and the time interval for recording data, begin flow field prediction; S33. Prediction and Visualization: During the prediction process, the flow field will be visualized, and contour maps of the velocity and pressure fields at each time step will be output. Each visualization outputs a contour map of the flow field data, and the resolution of the contour map is consistent with the resolution of the provided geometric and viscosity field information.

6. The method for predicting aircraft flow field data based on physical information constraints according to claim 5, characterized in that, The initial condition in step S31 is: When =0, , ,in, For time, This represents the velocity component on the x-axis; This represents the velocity component on the y-axis. Pressure field Refers to the viscosity field.

7. The method for predicting aircraft flow field data based on physical information constraints according to claim 6, characterized in that, The boundary conditions in step S31 include velocity inlet boundary conditions, pressure outlet boundary conditions, and no-slip wall boundary conditions, wherein the velocity inlet boundary condition is: The pressure outlet boundary condition is as follows: The no-slip wall boundary condition is as follows: .

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