Fast prediction method for airfoil streaming flow field based on Fourier neural operator

Abstract

The invention provides an airfoil profile streaming flow field rapid prediction method based on a Fourier neural operator, and belongs to the field of intelligent fluid mechanics. According to the method, machine learning and computational fluid mechanics are deeply fused, the future flow field state is rapidly predicted through a series of input and output data, and the calculation efficiency of the method is far higher than that of a traditional numerical method. According to the method, the calculation task of several hours or even several days of traditional computational fluid mechanics simulation can be shortened to the second level, the optimization iteration period of aircraft appearance design is greatly accelerated, and the dependence and cost of research and development on wind tunnel tests and high-performance calculation are remarkably reduced.

Description

Technical Field

[0001] This invention belongs to the field of intelligent fluid mechanics and relates to a method for rapid flow field prediction, particularly a method for rapid prediction of airfoil flow field based on Fourier neural operators. Background Technology

[0002] In the design and development of aircraft, flow field calculation and evaluation are crucial steps in optimizing aircraft shape and improving performance. However, while traditional numerical calculation methods and wind tunnel testing can provide high-precision flow field data, their computational and experimental costs are too high, and the time consumption is too long, making it difficult to meet the needs of rapid optimization and iteration of aircraft shape design in practical engineering. Therefore, combining advanced machine learning methods to achieve rapid prediction of aircraft flow fields is not only an important goal in the development of aerodynamics but also an urgent requirement for the development of aerospace technology.

[0003] Machine learning methods refer to algorithms that use computers to generate predictive models based on large amounts of empirical data. Machine learning can perform classification and recursive tasks based on input data. The core idea of ​​machine learning is to optimize model parameters by training algorithms and training data to predict unknown input data. In recent years, with the development of cloud computing and the increase in computing resources, the field of fluid mechanics has accumulated a large amount of flow data in different scenarios, which can be used to train machine learning models. Therefore, many machine learning methods have been widely applied to fluid mechanics problems, including turbulence modeling, hypersonic flow transition, flow field prediction, and aircraft aerodynamic shape optimization. Traditional computational fluid dynamics methods and experimental methods are costly and time-consuming, while machine learning-based flow prediction methods can achieve real-time, fast, and accurate flow field prediction, significantly shortening the time required for flow field calculations. Machine learning methods have powerful nonlinear computational capabilities and have a strong advantage in dealing with nonlinear problems. They can capture the nonlinear functional relationships of the flow field from a large amount of experimental or numerical simulation data, learn the nonlinear laws of the flow field, and thus reduce the dependence on traditional empirical models.

[0004] Most neural network models for flow field prediction learn mappings between finite-dimensional Euclidean spaces. The generalization ability of these models is limited by varying parameters, initial conditions, and boundary conditions. Traditional convolutional neural network (CNN)-based flow field prediction models have weak parameterization capabilities, making it difficult to accurately predict flow fields with different parameters. Furthermore, CNN-based flow field prediction models are typically fixed on the same grid as the training data, with fixed dimensions for input and output tensors, making it impossible to generalize to grids of different resolutions or topologies. Traditional CNN-based flow field prediction models rely on stacking convolutional layers to expand the receptive field and improve prediction accuracy. However, stacking convolutional layers significantly increases the number of parameters in the model, reducing training efficiency and increasing hardware costs. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a fast prediction method for airfoil flow field based on Fourier neural operators. This method can achieve fast and accurate prediction of airfoil flow field and significantly reduce the cost of wind tunnel testing and numerical simulation in the airfoil optimization process.

[0006] The technical solution of this invention is: In a first aspect, the present invention provides a method for rapid prediction of airfoil flow field based on Fourier neural operators, comprising: Acquire unsteady flow field data around the airfoil, wherein the flow field data includes at least the flow velocity, normal velocity, and pressure; Construct a Fourier neural operator model containing multiple Fourier layers; The training dataset is constructed by using the flow field data from the first N time steps as the model input and the flow field data from the (N+1)th time step as the model output label. The Fourier neural operator model was trained using the training dataset to minimize the multivariate relative error loss function between the predicted flow field and the actual flow field. Using a trained model, the future flow field state can be quickly predicted based on the input flow field sequence.

[0007] Preferably, the Fourier neural operator model contains 4 Fourier layers, and the number of Fourier modes in each Fourier layer is 12.

[0008] Preferably, the multivariate relative error loss function The definition is as follows:

[0009] in m It is the size of the output structure of the model. These represent the flow velocity, normal velocity, and pressure predicted by the Fourier neural operator model, respectively. These represent the flow velocity, normal velocity, and pressure in the actual flow field, respectively. It is the physical quantity of the i-th grid point.

[0010] Preferably, the GELU function is used as the activation function during the training of the Fourier neural operator model.

[0011] Preferably, the Adam algorithm is used as the optimization algorithm during the training of the Fourier neural operator model.

[0012] Preferably, the prediction of the future flow field state is achieved based on instantaneous prediction and iterative prediction strategies; instantaneous prediction directly maps the input of the model at the current time step to the prediction output of the next time step; iterative prediction uses the prediction output of the model at the current time step as part of the input to predict the flow field at the next time step, thereby realizing the sequential prediction of unsteady flow fields.

[0013] In a second aspect, the present invention provides a terminal device, comprising: Memory, used to store at least one program executed by a processor; A processor for executing a computer program stored in memory to implement the method described in the first aspect above.

[0014] Thirdly, the present invention provides a computer-readable storage medium storing a computer program that, when run on a computer, causes the computer to perform the above-described method.

[0015] The advantages of this invention compared to existing technologies are as follows: This invention combines flow field and Fourier neural operators, enabling the learning of mapping relationships in infinite-dimensional space and achieving super-resolution prediction of the flow field. Furthermore, compared to traditional convolutional neural network-based models, this invention offers higher computational efficiency, higher prediction accuracy, and lower hardware requirements. Attached Figure Description

[0016] Figure 1 This is a framework diagram of the Fourier neural operator used in this invention to predict the flow field around an airfoil; Figure 2 This is a graph showing the training and testing error of the Fourier neural operator in this invention. Figure 3 This is a dimensionless flow velocity cloud map at different time points predicted by the Fourier neural operator in this invention. Figure 4 This is a dimensionless normal velocity cloud map of different time points predicted by the Fourier neural operator in this invention. Figure 5This is a dimensionless pressure cloud map of different time points predicted by the Fourier neural operator in this invention.

[0017] Figure 6 These are the airfoil surface pressure coefficients predicted at different time points by the Fourier neural operator in this invention. Detailed Implementation

[0018] A fast prediction method for airfoil flow field based on Fourier neural operators includes the following steps: Acquire unsteady flow field data around the airfoil, wherein the flow field data includes at least the flow velocity, normal velocity, and pressure; Construct a Fourier neural operator model containing multiple Fourier layers; The training dataset is constructed by using the flow field data from the first N time steps as the model input and the flow field data from the (N+1)th time step as the model output label. The Fourier neural operator model was trained using the training dataset to minimize the multivariate relative error loss function between the predicted flow field and the actual flow field. Using a trained model, the future flow field state can be quickly predicted based on the input flow field sequence.

[0019] N is set to 5. In the deep learning model, the flow field data from the first five time points are used as input data, and the flow field data from the sixth time point is used as output data. The model has four Fourier layers, each with 12 modes. The GELU function and the Adam algorithm are chosen as the activation function and optimization algorithm, respectively. Relative error is used. The loss function for training FNO is as follows:

[0020] in m It is the size of the output structure of the model. These represent the flow velocity, normal velocity, and pressure predicted by the FNO, respectively. These represent the reference flow velocity, normal velocity, and pressure, respectively. It is the physical quantity of the i-th grid point.

[0021] Example: This embodiment includes the following steps: 1. Data preparation and preprocessing Unsteady flow field data around the airfoil were obtained using a high-precision computational fluid dynamics solver or wind tunnel experiments. Flow variables, including streamwise velocity *u*, normal velocity *v*, and pressure *p*, were extracted for each time step. The data were organized into a spatiotemporal sequence, with the flow field data from the first five time steps as input and the flow field data from the sixth time step as output. The data was normalized to improve the stability and convergence speed of the model training.

[0022] 2. Construction of Fourier Neural Operator Model Construct a Fourier neural operator model containing four Fourier layers, such as Figure 1 As shown. The number of Fourier modes in each Fourier layer is set to 12 to capture global dependencies in the flow field in the frequency domain. GELU (Gaussian Error Linear Unit) is chosen as the activation function to enhance the model's nonlinear expressive power.

[0023] 3. Model Training The model was trained using the Adam optimizer with an initial learning rate of 0.001 and a batch size of 5. Training was performed on a single RTX 3080 GPU, with 100 iterations. The training and test error curves during the iterations are shown below. Figure 2 As shown. The loss function uses multivariate relative error. Its definition is as follows:

[0024] in m It is the size of the output structure of the model. These represent the flow velocity, normal velocity, and pressure predicted by the FNO, respectively. These represent the reference flow velocity, normal velocity, and pressure, respectively. During training, a learning rate decay strategy can be introduced, such as halving the learning rate every 20 iterations, to improve model convergence accuracy.

[0025] 4. Flow field prediction The trained FNO model is used for rapid prediction of unknown flow fields. Inputting flow field data from the first five time steps, the model outputs the distribution of flow velocity, normal velocity, and pressure at the sixth time step. Contour plots of flow velocity, normal velocity, and pressure at different time points instantaneously predicted by the FNO are shown below. Figure 3-5 As shown. The airfoil surface pressure coefficients at different time points predicted instantaneously by the FNO are as follows: Figure 6 As shown, an iterative prediction strategy can be used to use the prediction results as the output of the next time step, thus enabling sequential prediction of unsteady flow fields.

[0026] 5. Model Evaluation and Validation The model's prediction accuracy is evaluated using a test set, and the relative errors of each physical quantity are calculated. Visualization tools can be used to compare the prediction results with computational fluid dynamics simulation results, such as... Figure 3-6 As shown, the model's ability to capture flow field structures is verified. The model's generalization ability under unseen flow conditions is evaluated. Figure 3-5 In the figure, (a), (b), (c) and (d) represent contour plots of the flow velocity, normal velocity and pressure at different times calculated by CFD, Unet and FNO, respectively. Figure 6 In the figure, (a), (b), (c) and (d) represent the pressure coefficient curves calculated by CFD, Unet and FNO at different times, respectively.

[0027] 6. Hardware and Software Environment Hardware: At least one RTX 3080 GPU is required, and at least 10GB of RAM is recommended. Software: Use the PyTorch or TensorFloW deep learning framework and install the extension library that supports Fast Fourier Transform. Operating system: Linux or Windows 10 / 11 is recommended.

[0028] This invention proposes a rapid prediction method for airfoil flow fields based on Fourier neural operators. This method can directly learn the mapping relationship between infinite-dimensional spaces through a series of input and output data. The Fast Fourier Transform (FFT) transforms the functions to the frequency domain for processing. Because the FFT is global, it can effectively capture long-range relationships between functions, and its computational efficiency is far higher than traditional numerical methods. This invention can achieve rapid and accurate instantaneous prediction of flow velocity, normal velocity, and pressure in the flow field. The Fourier neural operator can achieve sequential prediction of unsteady flow fields based on an iterative prediction strategy. This invention deeply integrates machine learning and computational fluid dynamics, providing a real-time flow field prediction tool. This invention can shorten the computational tasks of traditional computational fluid dynamics simulations, which take hours or even days, to seconds, greatly accelerating the optimization iteration cycle of aircraft shape design and significantly reducing the dependence and cost of wind tunnel testing and high-performance computing in R&D. Therefore, this invention has significant engineering practical significance for aircraft flow field prediction and shape optimization design.

[0029] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A method for rapid prediction of airfoil flow field based on Fourier neural operators, characterized in that, include: Acquire unsteady flow field data around the airfoil, wherein the flow field data includes at least the flow velocity, normal velocity, and pressure; Construct a Fourier neural operator model containing multiple Fourier layers; The training dataset is constructed by using the flow field data from the first N time steps as the model input and the flow field data from the (N+1)th time step as the model output label. The Fourier neural operator model was trained using the training dataset to minimize the multivariate relative error loss function between the predicted flow field and the actual flow field. Using a trained model, the future flow field state can be quickly predicted based on the input flow field sequence.

2. The method for fast prediction of airfoil flow field based on Fourier neural operators according to claim 1, characterized in that: The Fourier neural operator model contains four Fourier layers, and each Fourier layer has 12 Fourier modes.

3. The method for fast prediction of airfoil flow field based on Fourier neural operators according to claim 1, characterized in that: The multivariable relative error loss function The definition is as follows: in m It is the size of the output structure of the model. These represent the flow velocity, normal velocity, and pressure predicted by the Fourier neural operator model, respectively. These represent the flow velocity, normal velocity, and pressure in the actual flow field, respectively. It is the physical quantity of the i-th grid point.

4. The method for fast prediction of airfoil flow field based on Fourier neural operators according to claim 1, characterized in that: The GELU function is used as the activation function during the training of the Fourier neural operator model.

5. The method for fast prediction of airfoil flow field based on Fourier neural operators according to claim 1, characterized in that: The Adam algorithm is used as the optimization algorithm during the training of the Fourier neural operator model.

6. The method for fast prediction of airfoil flow field based on Fourier neural operators according to claim 1, characterized in that: The prediction of the future flow field state is achieved based on instantaneous prediction and iterative prediction strategies. Instantaneous prediction directly maps the input of the model at the current time step to the prediction output of the next time step. Iterative prediction uses the prediction output of the model at the current time step as part of the input to predict the flow field at the next time step, thereby realizing the sequential prediction of unsteady flow fields.

7. A terminal device, characterized in that, include: Memory, used to store at least one program executed by a processor; A processor for executing a computer program stored in memory to implement the method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when run on a computer, causes the computer to perform the method as described in any one of claims 1-6.

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