Aircraft flow field and aerodynamic performance joint prediction method and system based on multi-task learning

Abstract

The invention relates to an aircraft flow field and aerodynamic performance joint prediction method and system based on multi-task learning. The method comprises the following steps: collecting flow field data sets of different symmetric airfoils; after data preprocessing is carried out on the flow field data set, an input and output data set is constructed; constructing a neural network model, wherein the neural network model comprises a backbone network, a branch network and a fusion network; taking the space time sequence coordinates as input of the backbone network, and outputting backbone features; taking the static input characteristics and the historical flow field time sequence data as inputs of the branch network, and correspondingly outputting flow field prediction branch characteristics and aerodynamic coefficient prediction branch characteristics respectively; outputting a predicted value through the fusion network; constructing a weighted loss function; training the neural network model; and carrying out neural network model lightweight processing, and carrying out flow field prediction. The flow field characteristic prediction of the aircraft under the flow condition is realized quickly and accurately.

Description

Technical Field

[0001] This invention relates to the field of aircraft aerodynamic design and fluid dynamics technology, and in particular to a method and system for joint prediction of aircraft flow field and aerodynamic performance based on multi-task learning. Background Technology

[0002] Flow field prediction in aircraft aerodynamic design is a key factor affecting flight performance and aerodynamic optimization. Flow field characteristics, especially under high-speed, transonic, or supersonic flight conditions, directly determine the overall aerodynamic performance of the aircraft. Under these conditions, the unsteady flow characteristics of the aircraft become more complex, with phenomena such as vortex shedding, flow separation, and shock wave oscillations. These unsteady effects significantly impact the aerodynamic performance and flight safety of the aircraft. Therefore, accurately predicting unsteady flow fields is a major challenge in aircraft design.

[0003] Traditional methods for predicting flow fields in aircraft primarily rely on wind tunnel experiments and computational fluid dynamics (CFD) techniques. While wind tunnel experiments provide realistic experimental data, their high cost, long development time, and poor adaptability to complex operating conditions limit their rapid application in aircraft design. Although CFD technology can obtain accurate flow field simulation results by solving Navier-Stokes (NS) simulations numerically, it still requires significant computational resources and time for large-scale parameter scans, long-term unsteady flow simulations, or flow field prediction under high-speed flight environments, becoming a bottleneck in aircraft aerodynamic design.

[0004] With the development of deep learning technology, AI-based flow field prediction methods have gradually become an effective supplement to traditional CFD. Deep learning models, especially convolutional neural networks and deep neural networks, have made significant progress in aerodynamic parameter prediction and aerodynamic performance analysis, particularly in handling simple flow fields or static flow problems, where computational efficiency has been greatly improved. Some researchers have used convolutional neural networks based on airfoil image input to achieve high-precision prediction of lift coefficients. For predicting unsteady characteristics, state-space neural networks developed using wind tunnel data have surpassed traditional dynamic stall models, accurately predicting the unsteady aerodynamic characteristics of airfoils. Compared with traditional neural networks, deep operator networks (DeepONet) exhibit stronger expressive power and higher prediction efficiency when handling high-dimensional and nonlinear problems. In recent years, deep operator networks have shown promising application prospects in airfoil aerodynamic characteristic prediction, turbulence modeling, and flow field reconstruction. Deep operator neural networks learn linear or nonlinear operators based on data, possessing advantages such as fast convergence speed and strong generalization ability, and have been used to solve differential equations and boundary layer unstable waves.

[0005] However, these methods still face many challenges when dealing with complex unsteady flow fields, especially under complex flow conditions. (1) Current methods can only predict flow field results or aerodynamic coefficients, which is difficult to meet the aerodynamic design of aircraft. The corresponding results need to be obtained at the same time to meet the design requirements. (2) Existing methods are difficult to combine with historical flow field data to predict the future. Most of them need to start from the initial state, which greatly reduces efficiency. (3) Current methods do not combine the corresponding physical equations as constraints, resulting in insufficient physical consistency of the prediction results.

[0006] Therefore, it is necessary to significantly improve the computational efficiency of aircraft flow field prediction while ensuring high accuracy, and to provide a new deep learning method for aircraft aerodynamic design and optimization, which is particularly suitable for the aerodynamic design and optimization of high-speed, transonic or supersonic aircraft. Summary of the Invention

[0007] To address these issues, this invention provides a method and system for joint prediction of aircraft flow field and aerodynamic performance based on multi-task learning. It aims to solve the problems of high computational cost, long prediction cycle, insufficient joint prediction capability of multiple physical quantities, and limited high-frequency feature capture capability of traditional computational fluid dynamics methods in aircraft aerodynamic design. It is suitable for aerodynamic performance analysis and optimization of aircraft under flow conditions, and can quickly and accurately predict flow field characteristics, thereby optimizing aerodynamic performance in the aircraft design process.

[0008] To address the aforementioned technical problems, this invention provides a method for jointly predicting the flow field and aerodynamic performance of aircraft based on multi-task learning, comprising:

[0009] Collect flow field datasets for different symmetrical airfoils; wherein, the flow field datasets include CFD simulation data of different airfoils under different operating conditions;

[0010] After preprocessing the flow field dataset, an input and output dataset is constructed. The input data includes spatial temporal coordinates, static input features, and historical flow field temporal data. The static input features include Mach number, angle of attack, and airfoil geometric parameters including maximum thickness and the location of maximum thickness. The output data includes flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0011] A neural network model is constructed, which includes a backbone network, branch networks, and a fusion network. The branch networks include a flow field branch network and an aerodynamic performance branch network.

[0012] The spatial temporal coordinates are used as input to the backbone network to output backbone features; the static input features and historical flow field temporal data are used as input to the branch network to output flow field prediction branch features and aerodynamic coefficient prediction branch features, respectively.

[0013] After fusing the main features and the flow field prediction branch features, a fused feature is obtained. The fused feature and the aerodynamic coefficient prediction branch feature are then processed by the fusion network to obtain an output prediction value that includes flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0014] We construct a flow field loss function to measure the error between the flow field data predicted by the model and the actual flow field data, an aerodynamic performance loss function to measure the prediction error of the lift coefficient and drag coefficient, and a physical consistency loss function. We then weight the three functions to obtain a weighted loss function.

[0015] The neural network model is trained based on the weighted loss function and the input / output dataset;

[0016] The trained neural network model is lightweighted to predict the flow field under different operating conditions and airfoil conditions.

[0017] In one embodiment of the present invention, the flow field datasets for different symmetrical airfoils are collected, including:

[0018] Flow field data of different aircraft airfoils are collected as the flow field dataset, and flow field data of at least one of the aircraft airfoils are used as the validation set; wherein, the flow field dataset includes flow field simulation results with Mach number range of 0.2-0.5 and angle of attack range of 25°-55°, and the flow field simulation results include pressure field and velocity field variables;

[0019] Based on the flow field data of different airfoils, after meshing, flow field simulation was performed under different operating conditions, including changes in Mach number, angle of attack, and airfoil parameters.

[0020] Based on the simulation results, the flow field pressure, velocity in the X and Y directions, and lift-drag aerodynamic coefficients near the airfoil are obtained.

[0021] In one embodiment of the present invention, after preprocessing the flow field dataset, an input-output dataset is constructed, including:

[0022] The flow field dataset is cleaned and anomaly handled, and missing values ​​are filled in using linear interpolation to ensure data integrity and continuity.

[0023] Based on aerodynamic principles and data-driven analysis methods, the original static parameters in the flow field dataset are screened; the importance of each original static parameter is evaluated using a random forest model, and finally the static input features are selected.

[0024] The input and output are aligned with coordinate axes and time indices. The static input features, spatial time coordinates, and historical flow field time data are used as inputs, and the corresponding flow field pressure, X and Y direction velocities, and lift and drag aerodynamic systems are used as outputs to form an input-output dataset for the neural network model.

[0025] In one embodiment of the present invention, the spatial temporal coordinates are used as input to the backbone network, and backbone features are output. The static input features and historical flow field temporal data are used as input to the branch network, and flow field prediction branch features and aerodynamic coefficient prediction branch features are output respectively. The backbone features and the flow field prediction branch features are fused to obtain fused features. The fused features and the aerodynamic coefficient prediction branch features are processed by the fusion network to obtain output predicted values ​​including flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients, including:

[0026] The backbone network adopts a multilayer perceptron architecture, which performs feature extraction and nonlinear mapping on the spatial temporal coordinates through multiple fully connected layers, and finally generates a 64-dimensional temporal feature vector.

[0027] The flow field prediction branch network first uses a 1×1 convolutional layer to compress the static input features, reducing the feature dimension, and then uses the ReLU activation function for nonlinear processing to enhance the model's fitting ability. Next, the network further extracts higher-level spatial features through a multi-layer convolutional structure, and finally outputs a flow field image with a size of B×256×256×3, where B represents the batch size, 256 represents the resolution, and the three channels correspond to the two components of the pressure field and velocity field in the flow field, respectively.

[0028] The flow field prediction branch network includes a bidirectional long short-term memory network (Bi-LSTM) to capture the temporal evolution characteristics of the flow field. The bidirectional long short-term memory network consists of two LSTM layers. The first LSTM layer contains 128 memory units, and the second LSTM layer contains 64 memory units. Dropout layers are used for regularization to prevent overfitting.

[0029] The aerodynamic performance prediction branch network is stacked through a multi-layer fully connected structure to extract global flow field information features including Mach number, flow velocity, and airfoil parameters, and finally outputs lift and drag aerodynamic coefficients with a size of B×2.

[0030] The fusion network adopts a three-way parallel fusion strategy, which concatenates the backbone features, the flow field features extracted from the flow field prediction branch, and the element-wise product features of the two to obtain a feature vector containing multi-level, cross-domain information.

[0031] In one embodiment of the present invention, the expression for the flow field loss is:

[0032] L flow = ;

[0033] Among them, L flow It is the flow field loss;

[0034] and These are the pressure and velocity components in the predicted flow field data, respectively.

[0035] and These are the pressure and velocity components in real flow field data;

[0036] N is the number of spatial sample points.

[0037] In one embodiment of the present invention, the expression for the aerodynamic performance loss is:

[0038] L aer = ;

[0039] Among them, L aer It is a loss of aerodynamic performance;

[0040] and These are the predicted lift coefficient and drag coefficient, respectively.

[0041] and These are the actual values ​​of the lift coefficient and drag coefficient;

[0042] N represents the number of sample operating conditions.

[0043] In one embodiment of the present invention, the expression for the physical consistency loss is:

[0044] L cont = MSE )+MSE( )+MSE( );

[0045] in,

[0046] ;

[0047] ;

[0048] ;

[0049] Among them, L cont This represents a loss of physical consistency.

[0050] This represents the residual due to mass conservation.

[0051] This represents the residual due to the conservation of momentum.

[0052] Represents the residual due to energy conservation.

[0053] MSE() represents the mean squared error, MSE = ,in, For the target value, Here, N represents the model's predicted value, and N is the number of samples.

[0054] Represents the gradient operator;

[0055] Represents momentum density;

[0056] Indicates total energy density;

[0057] Indicates fluid density;

[0058] Represents the tensor product;

[0059] Represents the pressure tensor;

[0060] Represents the viscous stress tensor;

[0061] Represents the fluid velocity vector;

[0062] Represents the heat flux vector;

[0063] t represents time.

[0064] In one embodiment of the present invention, the expression for the weighted loss function is:

[0065] L total = λ1L flow +λ2L aer +λ3L cont ;

[0066] Where λ1, λ2, and λ3 are the weight coefficients of the loss function, used to control the contribution of each loss function to the total loss.

[0067] In one embodiment of the present invention, training the neural network model based on the weighted loss function and the input-output dataset includes:

[0068] The neural network model is trained in a distributed parallel manner based on the PyTorch deep learning framework.

[0069] During training, mixed precision training is applied to reduce memory usage, and dropout layers with a dropout rate of 0.2 are set in each network layer to prevent overfitting.

[0070] The AdamW optimizer is used to update the network parameters, with an initial learning rate of 1×10⁻⁶. -4 And L1 regularization is introduced to improve the robustness of the model;

[0071] An early stopping strategy was set during training, and model checkpoints were saved every 5 epochs. After training for 100 epochs, convergence was achieved on the validation set.

[0072] The trained neural network model is lightweighted using a structured pruning strategy. This includes determining the importance of neurons based on the absolute value of the weights, removing low-importance neuron connections according to a preset pruning rate, fine-tuning the pruned network, and restoring model accuracy through a learning rate decay strategy. This achieves the structured lightweighting of the neural network model.

[0073] This invention also provides a joint prediction system for aircraft flow field and aerodynamic performance based on multi-task learning, comprising:

[0074] The flow field dataset acquisition module is used to collect flow field datasets for different symmetrical airfoils; wherein, the flow field dataset includes CFD simulation data of different airfoils under different operating conditions;

[0075] The input / output dataset acquisition module is used to preprocess the flow field dataset and then construct the input / output dataset. The input data includes spatial temporal coordinates, static input features, and historical flow field temporal data. The static input features include Mach number, angle of attack, and airfoil geometric parameters including maximum thickness and the location of maximum thickness. The output data includes flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0076] A neural network model building module is used to build a neural network model, which includes a backbone network, branch networks, and a fusion network. The branch networks include a flow field branch network and an aerodynamic performance branch network.

[0077] The prediction branch feature acquisition module is used to take the spatial temporal coordinates as input to the backbone network and output backbone features; and to take the static input features and historical flow field temporal data as input to the branch network and output flow field prediction branch features and aerodynamic coefficient prediction branch features respectively.

[0078] The output prediction value acquisition module is used to fuse the main features and the flow field prediction branch features to obtain fused features. The fused features and the aerodynamic coefficient prediction branch features are then processed by the fusion network to obtain output prediction values ​​that include flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0079] The weighted loss function construction module is used to construct a flow field loss function to measure the error between the flow field data predicted by the model and the actual flow field data, an aerodynamic performance loss function to measure the prediction error of the lift coefficient and drag coefficient, and a physical consistency loss function, and the weighted loss function is obtained by weighting the three.

[0080] The training module is used to train the neural network model based on the weighted loss function and the input-output dataset;

[0081] The flow field prediction module is used to perform lightweight processing on the trained neural network model in order to predict the flow field under different operating conditions and different airfoil conditions.

[0082] The technical solution of the present invention has the following advantages compared with the prior art:

[0083] This invention discloses a method and system for joint prediction of aircraft flow field and aerodynamic performance based on multi-task learning. This method effectively improves the accuracy and efficiency of aircraft flow field prediction and aerodynamic performance evaluation by introducing a multi-task learning framework, a bidirectional long short-term memory network, a combination of branch and backbone networks, and a weighted loss function. Through the multi-task learning framework, the model can simultaneously optimize multiple tasks, including flow field prediction loss, lift and drag prediction loss, and flow field continuity loss, avoiding the limitation of traditional methods that can only handle single physical quantities. This effectively improves the overall performance of aerodynamic design. Furthermore, this method effectively models the dynamic characteristics of the flow field evolution over time using a bidirectional LSTM, especially capturing complex flow phenomena such as vortex shedding and flow separation, thereby enhancing the processing capability of flow field time-series data. Attached Figure Description

[0084] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0085] Figure 1This is a flowchart of a multi-task joint prediction method for the flow field and aerodynamic performance of an aircraft proposed in this invention.

[0086] Figure 2 This is a diagram of the AirFoil-Deeponet flow field prediction framework of the present invention.

[0087] Figure 3 This is a diagram of the AirFoil-Deeponet network architecture of the present invention. Detailed Implementation

[0088] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0089] In this invention, when directions (up, down, left, right, front, and back) are described, it is only for the convenience of describing the technical solution of this invention, and does not indicate or imply that the technical features referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0090] In this invention, "several" means one or more, "multiple" means two or more, "greater than," "less than," "exceeding," etc., are understood to exclude the stated number; "above," "below," "within," etc., are understood to include the stated number. In the description of this invention, the terms "first" and "second" are used only to distinguish technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0091] In this invention, unless otherwise explicitly defined, the terms "setting," "installing," and "connecting" should be interpreted broadly. For example, they can refer to a direct connection or an indirect connection through an intermediate medium; a fixed connection, a detachable connection, or an integrally formed connection; a mechanical connection, an electrical connection, or a connection capable of mutual communication; or the internal connection of two components or the interaction between two components. Those skilled in the art can reasonably determine the specific meaning of the above terms in this invention based on the specific content of the technical solution.

[0092] Example 1 To address the problems of high computational cost, long prediction cycle, insufficient joint prediction capability of multiple physical quantities, and limited high-frequency feature capture capability in traditional aircraft flow field prediction, this embodiment provides a joint prediction method for aircraft flow field and aerodynamic performance based on multi-task learning. The overall process is as follows: Figure 1 As shown, it includes the following steps:

[0093] S1. Collect flow field datasets for different symmetrical airfoils; wherein, the flow field datasets include CFD simulation data of different airfoils under different operating conditions.

[0094] Specifically, in step S1, flow field datasets for different symmetrical airfoils are collected, including:

[0095] S11. Collect flow field data of different aircraft airfoils as the flow field dataset, and use the flow field data of at least one of the aircraft airfoils as a validation set (test set); In this embodiment, the flow field data of different symmetrical aircraft airfoils include NACA0006, NACA0012, NACA0018 and NACA0024, of which NACA0024 is used as the validation set;

[0096] The flow field dataset includes flow field simulation results with Mach numbers ranging from 0.2 to 0.5 and angles of attack ranging from 25° to 55°. The flow field simulation results include pressure field and velocity field variables; all data are sourced from the UIUC airfoil database.

[0097] S12. Based on the flow field data of different airfoils, after mesh generation, CFD flow field simulations were performed under different operating conditions, including variations in Mach number, angle of attack, and airfoil parameters. Specifically, high-precision mesh generation was performed for the flow field simulation data of different airfoils, with each airfoil containing approximately 615,200 mesh elements and 200 mesh nodes on the airfoil surface. The far-field boundary was positioned 10 times the airfoil chord length to minimize the influence of the far-field boundary conditions on local flow characteristics. During data generation, flow field simulations were performed for different operating parameters (including Mach number, angle of attack, and airfoil geometric parameters) with a simulation time step of 0.002 s and a total simulation duration of 1.2 s.

[0098] S13. The pressure and velocity field data of the region near the airfoil were obtained through the above simulation, and a flow field dataset for training the neural network model was constructed accordingly.

[0099] S2. After preprocessing the flow field dataset, construct the input and output datasets. The input data includes spatial time-series coordinates, static input features, and historical flow field time-series data (coordinates and time in the X and Y directions). The static input features include Mach number, angle of attack, and airfoil geometric parameters including maximum thickness and the location of maximum thickness. The output data includes flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0100] Specifically, step S2 includes:

[0101] S21. Perform data cleaning and anomaly handling on the flow field dataset (remove outliers using the 3σ principle) and use linear interpolation to fill in missing values ​​to ensure data integrity and continuity.

[0102] S22. Based on aerodynamic principles and data-driven analysis methods, the original static parameters in the flow field dataset are screened. A random forest model is used to evaluate the importance of each original static parameter, ultimately selecting the static aerodynamic parameters. These static aerodynamic parameters include Mach number, angle of attack, and airfoil geometry parameters including maximum thickness and the location of maximum thickness. These static features can effectively describe the aerodynamic characteristics of the aircraft and provide strong support for subsequent flow field prediction and aerodynamic performance prediction. Simultaneously, spatial coordinates and historical time-series data are also used as input features, allowing the model to capture dynamic information about flow field changes at different times.

[0103] S24. Align the input and output with the coordinate axes and time index (x, y, t), take the static aerodynamic parameters and dynamic spatiotemporal coordinate features as input, and the pressure field and velocity field components of the corresponding flow field as output, to form an input-output dataset for the neural network model.

[0104] It should be noted that during the dataset construction phase, the data required for flow field prediction and aerodynamic performance prediction are first divided into two types of inputs. Corresponding input and output datasets are constructed to meet the different input requirements of the flow field and aerodynamic performance branches. The inputs and outputs are aligned using coordinate axes and time indices (x, y, t). Static input features, spatial temporal coordinates (x, y, t), and historical flow field time-series data are used as inputs, while flow field pressure, velocities in the X and Y directions, and lift / drag aerodynamic coefficients are used as output data. This pairing forms the final dataset, facilitating model training and prediction.

[0105] In this way, the flow field branch network of the subsequently constructed AirFoil-Deeponet neural network model can receive flow field data based on spatial coordinates and flight conditions, while the aerodynamic performance branch network of the neural network model receives aerodynamic performance data based on flight conditions. This structure ensures that the input data of the two branch networks can be processed separately, while also enabling joint training through a shared feature layer.

[0106] S3. Construct the (AirFoil-Deeponet) neural network model. The process prediction architecture diagram is as follows: Figure 2 As shown, the overall network architecture is as follows: Figure 3 As shown. The neural network model includes a backbone network, branch networks, and a fusion network, wherein the branch networks include a flow field branch network and an aerodynamic performance branch network.

[0107] S4. Use the spatial temporal coordinates as input to the backbone network and output the backbone features; use the static input features and historical flow field temporal data as input to the branch network and output the flow field prediction branch features and aerodynamic coefficient prediction branch features respectively.

[0108] S5. After fusing the main features and the flow field prediction branch features, a fused feature is obtained. The fused feature and the aerodynamic coefficient prediction branch feature are processed by the fusion network to obtain an output prediction value that includes flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0109] The output prediction values ​​include joint predictions of pressure field, velocity field and aerodynamic parameters, which are applicable to the aerodynamic design and optimization of high-speed and transonic aircraft. Furthermore, it can achieve a calculation speed of seconds during inference, which can significantly improve the computational efficiency of flow field prediction, especially in flow field prediction and aerodynamic performance optimization under complex flight conditions.

[0110] By fusing the outputs of the flow field branch network and the main network, the ability to jointly predict multiple physical quantities of flow field and aerodynamic parameters is improved.

[0111] Specifically, the backbone network adopts a multilayer perceptron (MLP) architecture, which extracts features and performs nonlinear mapping on the spatial temporal coordinates through multiple fully connected layers, ultimately generating a 64-dimensional temporal feature vector; this structure captures the deep features of the flow field data by learning the complex relationships of the data layer by layer.

[0112] Specifically, the flow field branching network predicts the flow field data. The aerodynamic performance branching network predicts the lift coefficient and drag coefficient.

[0113] The flow field prediction branch network first uses a 1×1 convolutional layer to compress the static input features, reducing the feature dimension, and then uses the ReLU activation function for nonlinear processing to enhance the model's fitting ability. Next, the network further extracts higher-level spatial features through a multi-layer convolutional structure, and finally outputs a flow field image with a size of B×256×256×3, where B represents the batch size, 256 represents the resolution, and the three channels correspond to the two components of the pressure field and velocity field in the flow field, respectively.

[0114] The flow field prediction branch network includes a bidirectional long short-term memory (Bi-LSTM) network to capture the temporal evolution characteristics of the flow field. The Bi-LSTM network consists of two LSTM layers, with the first LSTM layer containing 128 memory units and the second LSTM layer containing 64 memory units. Dropout layers are used for regularization to prevent overfitting. The Bi-LSTM network can effectively learn the temporal dependence of the flow field data, enhancing the model's performance in dynamic prediction.

[0115] The aerodynamic performance prediction branch network is stacked through a multi-layer fully connected structure to extract global flow field information features including Mach number, flow velocity, and airfoil parameters, and finally outputs lift and drag aerodynamic coefficients with a size of B×2. The aerodynamic performance prediction branch network uses the features learned by the fully connected layers to accurately predict lift and drag coefficients, thereby providing key reference values ​​for aerodynamic design.

[0116] The fusion network adopts a three-way parallel fusion strategy, which concatenates the backbone features, the flow field features extracted from the flow field prediction branch, and the element-wise product features of the two to obtain a feature vector containing multi-level, cross-domain information. The element-wise product term explicitly introduces nonlinear interaction information between aerodynamic parameters and spatiotemporal location, thereby enhancing the expressive power of the model. The fused features further improve the accuracy of aerodynamic performance prediction and the accuracy of flow field generation.

[0117] Furthermore, by designing the AirFoil-Deeponet neural network architecture, aerodynamic parameters are used as inputs to branch networks, including flow parameters, airfoil parameters, and historical time-series data, to generate feature representations related to their flow field solutions. The branch networks are divided into two networks: flow field prediction and aerodynamic coefficient prediction. The outputs of the flow field prediction branch network and the main network are fused. Through the fused network, the pressure and velocity components in the flow field of the airfoil under different incoming flow conditions can be predicted. The aerodynamic coefficient prediction network predicts the aerodynamic performance coefficients (lift and drag). AirFoil-Deeponet uses a bidirectional long short-term memory network to model time-series data to capture the dynamic characteristics of the flow field evolution over time.

[0118] It should be noted that the input layer of the AirFoil-Deeponet neural network model includes the space coordinates of the aircraft (N×2), physical parameters (B×3), where B is the batch size, 3 represents the aircraft structural parameters such as thickness ratio, maximum height, and altitude, historical flow field data (B×128), and flow parameters (B×2), where 2 represents the angle of attack, Mach number, etc. The historical flow field time-series data is processed using Bi-LSTM to capture the dynamic characteristics of the flow field changing over time. The Bi-LSTM consists of two layers: the first LSTM layer has 128 units, and the second LSTM layer has 64 units. Dropout layers are used for regularization to prevent overfitting. Finally, these temporal features are compressed into a 32-dimensional feature vector, which is then further processed and output through multiple fully connected layers.

[0119] S6. Construct a flow field loss function to measure the error between the model-predicted flow field data and the actual flow field data, an aerodynamic performance loss function to measure the prediction error of the lift coefficient and drag coefficient, and a physical consistency loss function. These three functions are weighted to obtain a weighted loss function. The weight coefficients of the weighted loss function are dynamically adjusted according to the importance of each task. This effectively captures phenomena in complex flow fields, such as vortex shedding and shock wave oscillations, enhancing the ability to express the high-frequency dynamic behavior of the flow field.

[0120] Specifically, the flow field loss uses mean square error (MSE), which is expressed as follows:

[0121] L flow = ;

[0122] Among them, L flow It is the flow field loss;

[0123] and These are the pressure and velocity components in the predicted flow field data, respectively.

[0124] and These are the pressure and velocity components in real flow field data;

[0125] N is the number of spatial sample points.

[0126] Specifically, the aerodynamic performance loss uses mean square error (MSE), which is expressed as follows:

[0127] L aer = ;

[0128] Among them, L aer It is a loss of aerodynamic performance;

[0129] and These are the predicted lift coefficient and drag coefficient, respectively.

[0130] and These are the actual values ​​of the lift coefficient and drag coefficient;

[0131] N represents the number of sample operating conditions.

[0132] Specifically, the physical consistency loss, based on the residuals of the Navier-Stokes equations, ensures that the flow field prediction conforms to physical laws. The physical loss typically calculates the residuals of the flow field data and measures these residuals using the MSE (Mean Sequence of Exclusion). For each residual:

[0133] ;

[0134] ;

[0135] ;

[0136] Furthermore, the physical loss can be calculated:

[0137] L cont = MSE )+MSE( )+MSE( );

[0138] in,

[0139] Among them, L cont This represents a loss of physical consistency.

[0140] This represents the residual due to mass conservation.

[0141] This represents the residual due to the conservation of momentum.

[0142] Represents the residual due to energy conservation.

[0143] MSE() represents the mean squared error, MSE = ,in, For the target value, Here, N represents the model's predicted value, and N is the number of samples.

[0144] Represents the gradient operator;

[0145] Represents momentum density;

[0146] Indicates total energy density;

[0147] Indicates fluid density;

[0148] Represents the tensor product;

[0149] Represents the pressure tensor;

[0150] Represents the viscous stress tensor;

[0151] Represents the fluid velocity vector;

[0152] Represents the heat flux vector;

[0153] t represents time.

[0154] Specifically, the expression for the weighted loss function is:

[0155] L total = λ1L flow +λ2L aer +λ3L cont ;

[0156] Where λ1, λ2, and λ3 are the weighting coefficients of the loss function, used to control the contribution of each loss function to the total loss. Finally, the weighted loss function sums the errors of all physical quantities in a weighted manner to obtain the total loss value.

[0157] The model's loss function consists of three parts: flow prediction loss (Loss_flow), lift and drag prediction loss (Loss_aer), and flow continuity loss (Loss_cont). This ensures the continuity and physical rationality of the flow prediction. This weighted loss design can ensure the balance of various tasks and avoid over-optimizing one task and affecting the performance of other tasks.

[0158] S7. Train the neural network model based on the weighted loss function and the input / output dataset.

[0159] S8. The trained neural network model is lightweighted to predict the flow field under different operating conditions and different airfoil conditions.

[0160] It should be noted that steps S6 to S8 set the hyperparameters for training the AirFoil-Deeponet neural network, minimize the MSE prediction error, and train the constructed AirFoil-Deeponet neural network model. The loss function adopts a weighted loss function. By optimizing the flow field prediction loss, lift and drag coefficient prediction loss, and flow field continuity loss, the model's performance in multi-task learning is improved, the optimal model is obtained, and the number of model parameters is optimized through pruning.

[0161] Specifically, in step S8, training the neural network model based on the weighted loss function and the input / output dataset includes:

[0162] The neural network model is trained in a distributed parallel manner based on the PyTorch deep learning framework.

[0163] During training, mixed precision training is applied to reduce memory usage, and dropout layers with a dropout rate of 0.2 are set in each network layer to prevent overfitting.

[0164] The AdamW optimizer is used to update the network parameters, with an initial learning rate of 1×10⁻⁶. -4 And L1 regularization is introduced to improve the robustness of the model;

[0165] An early stopping strategy was set during training, and model checkpoints were saved every 5 epochs. After training for 100 epochs, convergence was achieved on the validation set.

[0166] The trained neural network model is lightweighted using a structured pruning strategy. This includes determining the importance of neurons based on the absolute value of the weights, removing low-importance neuron connections according to a preset pruning rate, fine-tuning the pruned network, and restoring model accuracy through a learning rate decay strategy. This achieves the structured lightweighting of the neural network model.

[0167] It should be noted that step S7 includes training hyperparameters through the AirFoil-Deeponet neural network, minimizing the MSE prediction error, training the constructed model, and obtaining the optimal model. In step S8, lightweight processing refers to optimizing the number of model parameters through pruning.

[0168] The training hyperparameters specifically refer to the model training loss function using mean squared error (MSE), the optimizer being AdamW, the learning rate being 0.0001, and the use of early stopping during training to prevent overfitting.

[0169] Model pruning optimization specifically refers to the lightweighting of the AirFoil-Deeponet neural network after initial training using a structured pruning strategy. The specific steps include: determining neuron importance based on weight absolute values, removing low-importance neuron connections according to a preset pruning rate, fine-tuning the pruned network, and restoring model accuracy using a learning rate decay strategy.

[0170] Furthermore, during model training, the neural network model is trained in a distributed parallel manner based on the PyTorch deep learning framework, using a hardware configuration of four GPUs with 32GB of video memory and a 12-core Intel Xeon Platinum 8352V CPU. During training, mixed precision training is applied to reduce video memory usage, and dropout layers with a dropout rate of 0.2 are set in each layer of the network to prevent overfitting.

[0171] The AdamW optimizer is used to update the network parameters, with an initial learning rate of 1×10⁻⁶. -4 L1 regularization is introduced to improve the robustness of the model. The mean squared error (MSE) is used as the loss function to measure the difference between the model's predicted value and the target value. The model outputs pressure P and velocity components U and V at the same time. The prediction errors of the three components are weighted and summed to form the total loss value.

[0172] An early stopping strategy was set during training, and model checkpoints were saved every 5 epochs. After training for 100 epochs, convergence was achieved on the validation set.

[0173] After training, the importance of neurons is determined based on the absolute value of the weights. Low-importance neuron connections are removed according to a preset pruning rate. The pruned network is then fine-tuned and trained. The model accuracy is restored through a learning rate decay strategy, thereby achieving the structured and lightweight processing of the neural network model.

[0174] In summary, this multi-task flow field and aerodynamic performance joint prediction model can accurately process flow field data under different operating conditions and provide accurate flow field prediction results. It is applicable to industrial fields such as aircraft aerodynamic design, unsteady flow field modeling, and flow field reconstruction. Therefore, this invention provides an efficient and accurate solution for flow field prediction by combining deep learning methods and traditional fluid mechanics theory, and has broad application prospects.

[0175] Example 2 Based on the same inventive concept, this embodiment provides a joint prediction system for aircraft flow field and aerodynamic performance based on multi-task learning. The principle of solving the problem is similar to that of the joint prediction method for aircraft flow field and aerodynamic performance based on multi-task learning, and the repeated parts will not be described again.

[0176] This embodiment provides a joint prediction system for aircraft flow field and aerodynamic performance based on multi-task learning, including:

[0177] The flow field dataset acquisition module is used to collect flow field datasets for different symmetrical airfoils; wherein, the flow field dataset includes CFD simulation data of different airfoils under different operating conditions;

[0178] The input / output dataset acquisition module is used to preprocess the flow field dataset and then construct the input / output dataset. The input data includes spatial temporal coordinates, static input features, and historical flow field temporal data. The static input features include Mach number, angle of attack, and airfoil geometric parameters including maximum thickness and the location of maximum thickness. The output data includes flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0179] A neural network model building module is used to build a neural network model, which includes a backbone network, branch networks, and a fusion network. The branch networks include a flow field branch network and an aerodynamic performance branch network.

[0180] The prediction branch feature acquisition module is used to take the spatial temporal coordinates as input to the backbone network and output backbone features; and to take the static input features and historical flow field temporal data as input to the branch network and output flow field prediction branch features and aerodynamic coefficient prediction branch features respectively.

[0181] The output prediction value acquisition module is used to fuse the main features and the flow field prediction branch features to obtain fused features. The fused features and the aerodynamic coefficient prediction branch features are then processed by the fusion network to obtain output prediction values ​​that include flow field pressure, velocity in the X and Y directions, and lift and drag aerodynamic coefficients.

[0182] The weighted loss function construction module is used to construct a flow field loss function to measure the error between the flow field data predicted by the model and the actual flow field data, an aerodynamic performance loss function to measure the prediction error of the lift coefficient and drag coefficient, and a physical consistency loss function, and the weighted loss function is obtained by weighting the three.

[0183] The training module is used to train the neural network model based on the weighted loss function and the input-output dataset;

[0184] The flow field prediction module is used to perform lightweight processing on the trained neural network model in order to predict the flow field under different operating conditions and different airfoil conditions.

[0185] This method and system employ a multi-task learning framework, combining the aerodynamic design characteristics of the aircraft, flow field conditions, and historical time-series data to accurately predict the flow field and evaluate aerodynamic performance. The model combines branch and backbone networks, using the aircraft's coordinates, flow field physical parameters, and historical flow field data as input. It utilizes a bidirectional long short-term memory network to model the time-series data, capturing the dynamic characteristics of the flow field over time. During training, a novel weighted loss function is proposed, with the optimization objective simultaneously incorporating flow field prediction loss, lift and drag prediction loss, and flow field continuity loss, thereby improving the model's performance across multiple tasks. This model can not only accurately predict the aircraft's flow field but also provide predictions of aerodynamic parameters such as lift and drag, helping designers quickly obtain the aircraft's aerodynamic characteristics. While maintaining high accuracy, it significantly improves computational efficiency, with a single inference time on the order of seconds. This provides an efficient unsteady flow field prediction tool for aircraft aerodynamic design and has significant application prospects.

[0186] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0187] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0188] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0189] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0190] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for jointly predicting flow field and aerodynamic performance of an aircraft based on multi-task learning, characterized in that, The method comprises the following steps: Collecting flow field data sets of different symmetrical airfoils; wherein the flow field data sets comprise CFD simulation data of different airfoils under different working conditions; After data preprocessing of the flow field data sets, an input-output data set is constructed; wherein the input data comprises spatial time-series coordinates, static input features and historical flow field time-series data, the static input features comprise Mach number, angle of attack, airfoil geometric parameters including maximum thickness and maximum thickness position, and the output data comprises flow field pressure, X and Y direction velocity and lift-drag aerodynamic coefficients; A neural network model is constructed, which comprises a backbone network, a branch network and a fusion network, and the branch network comprises a flow field branch network and an aerodynamic performance branch network; The spatial time-series coordinates are taken as the input of the backbone network to output backbone features; the static input features and the historical flow field time-series data are taken as the input of the branch network to correspondingly output flow field prediction branch features and aerodynamic coefficient prediction branch features; After feature fusion of the backbone features and the flow field prediction branch features, fusion features are obtained, and the fusion features and the aerodynamic coefficient prediction branch features are processed through the fusion network to obtain output prediction values comprising flow field pressure, X and Y direction velocity and lift-drag aerodynamic coefficients; A flow field loss function for measuring the error between the model prediction flow field data and the real flow field data, an aerodynamic performance loss function for measuring the prediction error of the lift coefficient and the drag coefficient, and a physical consistency loss function are constructed, and a weighted loss function is obtained by weighting the three functions; The neural network model is trained based on the weighted loss function and the input-output data set; The trained neural network model is subjected to lightweight processing to predict the flow field under different working conditions and different airfoil conditions.

2. The method of claim 1, wherein, Collecting flow field data sets of different symmetrical airfoils, comprising: Collecting flow field data of different aircraft airfoils as the flow field data set, and taking the flow field data of at least one of the aircraft airfoils as a validation set; wherein the flow field data set comprises flow field simulation results with a Mach number range of 0.2-0.5 and an angle of attack range of 25°-55°, and the flow field simulation results comprise pressure field, velocity field variables; Based on the flow field data of different airfoils, grid division is performed, and flow field simulation is performed under different working conditions, wherein the working conditions include changes in Mach number, angle of attack and airfoil parameters; According to the simulation results, the flow field pressure, X and Y direction velocity and lift-drag aerodynamic coefficients near the airfoil are obtained.

3. The method of claim 1, wherein, After data preprocessing of the flow field data set, an input-output data set is constructed, comprising: Data cleaning and abnormality processing are performed on the flow field data set, and missing values are filled in by linear interpolation to ensure the integrity and continuity of the data; Based on the principles of aerodynamics and data-driven analysis methods, the original static parameters in the flow field data set are screened; the importance of each original static parameter is evaluated by using a random forest model, and finally the static input features are selected. The input and output are aligned with the coordinate axis and time index, the static input feature and spatial time sequence coordinates and historical flow field time sequence data are taken as inputs, and corresponding flow field pressure, X and Y direction velocity and lift and drag force aerodynamic coefficients are taken as outputs to form an input and output data set for a neural network model.

4. The method of claim 1, wherein, The spatial time sequence coordinates are taken as inputs of the backbone network, and backbone features are output. The static input feature and historical flow field time sequence data are taken as inputs of the branch network, and corresponding flow field prediction branch features and aerodynamic coefficient prediction branch features are output, the backbone features and the flow field prediction branch features are fused to obtain fusion features, and the fusion features and the aerodynamic coefficient prediction branch features are processed by the fusion network to obtain output prediction values including flow field pressure, X and Y direction velocity and lift and drag force aerodynamic coefficients, comprising: The backbone network adopts a multi-layer perceptron architecture, and a plurality of fully connected layers are used to extract and nonlinearly map the spatial time sequence coordinates to finally generate a 64-dimensional time sequence feature vector; The flow field prediction branch network first uses a 1x1 convolution layer to compress the static input feature, reduce the feature dimension, and perform nonlinear processing through a ReLU activation function to enhance the fitting ability of the model; next, the network further extracts higher-level spatial features through a multi-layer convolution structure, and finally outputs a flow field image with a size of Bx256x256x3, where B represents batch size, 256 represents resolution, and the three channels correspond to the pressure field and two components of the velocity field in the flow field; The flow field prediction branch network includes a bidirectional long short-term memory network (Bi-LSTM) for capturing the time evolution characteristics of the flow field; the bidirectional long short-term memory network is composed of two LSTM layers, the first LSTM layer includes 128 memory cells, and the second LSTM layer includes 64 memory cells, and a dropout layer is used for regularization to prevent overfitting; The aerodynamic performance prediction branch network is stacked through a multi-layer fully connected structure, extracts global information features of the flow field including Mach number, flow velocity and airfoil parameters, and finally outputs lift and drag force aerodynamic coefficients with a size of Bx2; The fusion network adopts a three-way parallel fusion strategy, which concatenates the backbone features, the flow field features extracted by the flow field prediction branch, and the element-wise product features of the two to obtain a feature vector containing multi-level and cross-domain information.

5. The method of claim 1, wherein, The expression of the flow field loss is: L flow = ； wherein L flow is the flow field loss; and are the pressure and velocity components in the predicted flow field data, respectively; and are the pressure and velocity components in the real flow field data; N is the number of spatial sample points.

6. The method of claim 1, wherein, The expression of the aerodynamic performance loss is: L aer = ； wherein L aer is the aerodynamic performance loss; and are the predicted lift and drag coefficients, respectively; and are the true values of the lift and drag coefficients; N is the number of sample working conditions.

7. The method of claim 1, wherein, The expression of the physical consistency loss is: L cont =MSE( )+MSE( )+MSE( ) wherein, ； ； ； wherein L cont is a physical consistency loss; represents the mass conservation residual error; represents the momentum conservation residual; represents an energy conservation residual error; MSE() represents the mean squared error, MSE = ,in, For the target value, The value is the model prediction, and N is the number of samples. denotes the gradient operator; denotes the momentum density; denotes the total energy density; represents the fluid density; denotes the tensor product; denotes the pressure tensor; denotes the viscous stress tensor; represents the fluid velocity vector; represents the heat flow vector; t represents time.

8. The method of claim 1, wherein, The expression of the weighted loss function is: L total = λ1L flow +λ2L aer +λ3L cont ; wherein λ1, λ2, and λ3 are weight coefficients of the loss function, used to control the contribution of each loss function in the total loss.

9. The method of claim 1, wherein, The neural network model is trained based on the weighted loss function and the input and output data set, comprising: The neural network model is distributed and parallel trained based on a PyTorch deep learning framework; During the training process, mixed precision training is applied to reduce GPU memory usage, and a Dropout layer with a dropout rate of 0.2 is set in each layer of the network to prevent overfitting; The network parameters are updated using the AdamW optimizer with an initial learning rate of 1x10 -4 and L1 regularization is introduced to improve the robustness of the model. During the training process, an early stopping strategy is set and a model checkpoint is saved every 5 epochs, and convergence is achieved on the validation set after 100 epochs of training; The trained neural network model is subjected to lightweight processing using a structured pruning strategy, including determining the importance of neurons based on the absolute value of weights, removing low-importance neuron connections according to a preset pruning rate, and fine-tuning the pruned network to restore model accuracy through a learning rate decay strategy, thereby achieving structured lightweight processing of the neural network model.

10. An aircraft flow field and aerodynamic performance joint prediction system based on multi-task learning, characterized in that, It comprises: a flow field dataset acquisition module for collecting flow field datasets of different symmetrical airfoils; wherein the flow field dataset includes CFD simulation data of different airfoils under different working conditions; an input-output dataset acquisition module for constructing an input-output dataset after data preprocessing of the flow field dataset; wherein the input data includes spatial time-series coordinates, static input features, and historical flow field time-series data, the static input features include Mach number, angle of attack, and airfoil geometric parameters including maximum thickness and maximum thickness position, and the output data includes flow field pressure, X and Y direction velocities, and lift and drag force aerodynamic coefficients; a neural network model construction module for constructing a neural network model, the neural network model including a backbone network, a branch network, and a fusion network, the branch network including a flow field branch network and an aerodynamic performance branch network; a predicted branch feature acquisition module for inputting the spatial time-series coordinates as the input of the backbone network to output backbone features, and inputting the static input features and historical flow field time-series data as the input of the branch network to correspondingly output flow field predicted branch features and aerodynamic coefficient predicted branch features; an output prediction value acquisition module for fusing the backbone features and the flow field predicted branch features to obtain fusion features, and processing the fusion features and the aerodynamic coefficient predicted branch features through the fusion network to obtain output prediction values including flow field pressure, X and Y direction velocities, and lift and drag force aerodynamic coefficients; a weighted loss function construction module for constructing a flow field loss function for measuring the error between the predicted flow field data and the real flow field data, an aerodynamic performance loss function for measuring the prediction error of the lift coefficient and the drag coefficient, and a physical consistency loss function, and weighting the three to obtain a weighted loss function; a training module for training the neural network model based on the weighted loss function and the input-output dataset; a flow field prediction module for lightweight processing of the trained neural network model to predict flow fields under different working conditions and different airfoil conditions.

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