A method, apparatus, readable storage medium, and computer program product for low-computational-cost data assimilation and flow field reconstruction using neural networks.

Abstract

This invention belongs to the field of flow field measurement in aerospace, and relates to a method for spatial flow field reconstruction using data assimilation of physical quantity measurement data from the wing surface. The method includes steps such as wing geometric modeling and mesh generation, solver setup and mesh convergence analysis, construction of a simulation dataset within the wind tunnel experimental range, VAE model construction and flow field dimensionality reduction, construction of an aerodynamic surrogate model using the Gaussian process regression (GPR) method, obtaining flow field priors based on experimental conditions, data assimilation using the ensemble Kalman filter method, iterative iteration and convergence judgment, and completion of flow field reconstruction. This invention combines the surrogate model with the ETKF algorithm, which improves the efficiency of the flow field reconstruction process, making it possible to quickly and accurately reconstruct the entire flow field in wind tunnel experiments. It is a powerful tool for the analysis and optimization of wing aerodynamic characteristics.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of flow field measurement in the field of aerospace, more particularly, to a method of spatial flow field reconstruction using data assimilation with wing surface physical quantity measurement data. BACKGROUND

[0002] Wing is a key component of aircraft, and it is essential to study the aerodynamic characteristics of the wing. The aerodynamic characteristics of the wing can be studied by two methods, computational fluid dynamics (CFD) and experimental fluid dynamics (EFD). The CFD method solves the fluid control equation (N-S equation), which can obtain the global multi-physical quantity flow field information around the model by setting specific model and boundary conditions, and is an important tool for aerodynamic performance analysis. Experimental fluid dynamics (EFD) is the closest experimental method to actual flight conditions. The aerodynamic characteristics of airfoils are usually studied by wind tunnel experiments. However, wind tunnel experiments are very expensive, and the physical quantities that can be measured are limited. Usually, only single flow field information can be obtained at a time, and most of the measurement data are sparse. For example, for wind tunnel experiments of airfoils, ordinary experiments such as pressure hole measurement of airfoil surface pressure distribution can only obtain the pressure distribution of the wall surface, but cannot obtain the spatial velocity field and pressure field information. The spatial flow field around the airfoil involves some important aerodynamic phenomena of the airfoil, such as boundary layer transition at low speed, flow separation at high angle of attack, and shock at high speed.

[0003] To address the spatial limitations of single-point measurements in wind tunnel experiments, researchers introduced data assimilation methods. This method fuses full-field flow data obtained from computational fluid dynamics (CFD) simulations with high-precision local observation data from wind tunnel measurements, achieving a more accurate reconstruction of complex flow fields. Data assimilation techniques were initially widely applied in fields such as weather forecasting. The core idea is to optimize algorithms by adjusting the initial conditions, boundary conditions, or key parameters of numerical models to minimize the difference between model predictions and experimental observations, thus allowing the numerical simulation results to continuously approach the true physical state. Based on different theoretical foundations, data assimilation methods can be mainly divided into variational methods and sequential assimilation methods (such as ensemble Kalman filters). Among them, ensemble transform Kalman filtering (ETKF), as an improvement on sequential assimilation methods, shows significant advantages in flow field reconstruction. The ETKF method uses a "set" reflecting the state of a system, updates this set using observational data, and finally obtains the boundary conditions closest to the experimentally measured state by averaging the set, thereby achieving high-precision flow field reconstruction. Existing research shows that ETKF can effectively correct the predictions of turbulence models, such as calibrating uncertainties in key parameters like angle of attack and Mach number in the flow field around an airfoil, thereby significantly improving the accuracy of flow field reconstruction. In dynamic systems containing uncertainties, this method can effectively combine observational data with physical models to obtain predictions closer to the actual state. However, the ETKF method requires constructing a set reflecting the system state and iterating continuously based on measurement data, relying on batch CFD simulations, which incurs high computational and time costs.

[0004] therefore, Summary of the Invention To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a low-computational-cost data assimilation flow field reconstruction method that integrates neural networks. The purpose of this method is to solve the technical problem that existing technologies require the use of CFD for batch solutions when reconstructing flow fields in wind tunnel measurements, which results in large computational loads and low efficiency.

[0005] To achieve the above objectives, according to one aspect of the present invention, a low-computational-cost data assimilation flow field reconstruction method incorporating neural networks is provided, comprising: Step 1: Wing geometry modeling and mesh generation; Construct a 3D model of the wing to be tested, generate a structured mesh for the external flow field of the wing model, and convert it into an unstructured mesh for computational fluid dynamics calculations; Step 2: Solver setup and mesh convergence analysis; refine and sparse the unstructured mesh obtained in Step 1, import it into Fluent, select the K-omega turbulence model, and simulate with the same boundary conditions; set and compare the surface aerodynamic loads calculated by sparse, medium, and dense mesh densities, and select the mesh with the highest accuracy and lower density to balance the calculation efficiency. Step 3: Constructing the simulation dataset within the wind tunnel experimental range; determining the incoming flow boundary based on the wind tunnel experimental conditions, using the free flow velocity. Angle of attack Define the parameter space; obtain uniform samples within the parameter space. For each sample, a batch CFD simulation was performed using a mesh with acceptable accuracy and lower density obtained in step two; the pressure field was retained. With corresponding incoming flow conditions Build a dataset for subsequent comparison and iteration with experimental measurements; Step 4: Flow field dimensionality reduction; using a variational autoencoder based on a neural network, the high-dimensional pressure field data is compressed into a low-dimensional latent space to obtain latent space variables. The neural network-based variational autoencoder uses the pressure field dataset obtained in step three. Pre-trained neural network acquisition; Step 5: Construction of the aerodynamic surrogate model using the Gaussian process regression method; establishing the aerodynamic parameters for the incoming flow condition using the Gaussian process regression method. With the latent spatial variables in step four The mapping relationship between them is used to generate an aerodynamic surrogate model of the force field, thereby realizing the input aerodynamic parameters. Directly predict the corresponding pressure field; Step Six: Obtain the flow field prior based on the experimental conditions; based on the set conditions of the wind tunnel experiment, perform Latin hypercube sampling around the set conditions to form a flow field containing... Set of incoming flow conditions under different operating conditions Then, the aerodynamic surrogate model obtained in step five is used to predict the pressure field of all members in the set, and the prior distribution matrix of the flow field is obtained. ; Step 7: Data assimilation using the Kalman filter method; processing the wing surface pressure measurement data obtained from the pressure orifice tests in the wind tunnel. Error analysis was performed on the prior flow field distribution from step six to determine the Kalman gain matrix. Then according to Calculate the posterior distribution ; Step 8: Iteration and Convergence Check; Determine if the current iteration has converged using the preset convergence criterion. If the convergence condition is not met, update the boundary condition set and repeat steps 6 to 8 until the convergence condition is met. Then, exit the iteration and output the boundary conditions in the posterior distribution. ; Step 9: Complete flow field reconstruction; based on the final boundary conditions output in Step 8 after iteration. Using the mesh and parameters set in step two, CFD simulation is performed to obtain the final reconstructed result of the flow field data assimilation.

[0006] Furthermore, the construction and training method of the variational autoencoder based on the neural network described in step four is as follows; The basic architecture of a variational autoencoder (VAE) based on a neural network is represented as follows: (1) in, This represents the flow field information after encoding, compression, decoding, and reconstruction. The encoder compresses the complete physical field into the latent space, that is, Mapping to latent variables , Representing high-dimensional physical field vectors: (2) in, Represents the mean of the latent variables. Represents the variance of latent variables. Represents an encoder neural network; To make this latent space regular, latent variables are specified. The distribution follows a standard normal distribution: (3) in, This represents the probability distribution of latent variables relative to the flow field. Represents a normal distribution; During training, a new latent variable is generated through reparameterization. : (4) in, It's Gaussian noise. It is a standard normal distribution. The identity matrix represents a matrix with a variance of 1. The input is then fed into a symmetric network with the same mesh architecture as the encoder, but in the opposite direction, called the decoder: (5) in, Represents a decoder neural network; The loss function used when training the decoder neural network includes MSE reconstruction error and KL divergence, which are adjusted by... This adjusts the weight of the KL divergence in the loss function, thereby regularizing the orthogonality of the low-dimensional latent space, as shown in formula (6). (6) in, This represents the loss function of the VAE neural network. This represents the root mean square error between the input and output of a VAE. This represents the weight of the KL divergence in the loss function. Denotes KL divergence, This indicates that the flow field data and the underlying spatial variables conform to a normal distribution; By training a VAE neural network to obtain a dimensionality reduction model of a high-dimensional physical field, the high-dimensional physical field is compressed and encoded into a low-dimensional latent vector, thus using only... Low-dimensional latent vectors of order Adding a decoder to represent the high-dimensional flow field distribution .

[0007] Furthermore, in step five, a low-dimensional latent vector is constructed using the Gaussian process regression (GPR) method. and boundary conditions ( The relationship between them; the Gaussian process regression method (GPR) is as follows: First, the aerodynamic parameters are expressed as ,in It is a specific working condition, and the low-dimensional latent variables are represented as... This represents the value of a potential variable corresponding to a specific flow condition. The incoming flow condition and the value of the potential variable from step four are combined to form a training sample set D: (7) in, Indicates the number of samples in the training set; For each dimension of the potential space Construct an independent Gaussian process regression model for each: (8) in, , The independent and identically distributed Gaussian noise is about unknown mapping function For unknown mapping functions Satisfies the prior assumptions of a Gaussian process: (9) in, To represent a Gaussian process, the mean is usually taken as 0, i.e., the mean is zero. ;and The covariance function, also known as the kernel function, is used to describe the correlation between different aerodynamic operating conditions. This represents the incoming flow parameters for a different operating condition; the kernel function consists of a linear kernel function and a Matern32 kernel function. (10) Where the linear kernel function The definition of is: (11) The Matern32 kernel function The definition of is: (12) in: (13) in, As an intermediate variable; , and Noise variance These are all hyperparameters of the GPR method, which need to be determined by optimization learning. The optimization objective is to maximize the log-marginal likelihood of the observations, as shown in the formula: (14) in, This represents the log-marginal likelihood of the observed data Z given the hyperparameter θ, achieved by maximizing... The optimal hyperparameters are found by taking their values. represents the covariance matrix calculated by the kernel function, and n represents the number of training samples; Solve for the hyperparameter values ​​that maximize equation (14), and thus determine the mapping function in equation (8). Gaussian distribution characteristics, and then through the mapping function The set of mapping functions For a new set of incoming flow conditions Output the values ​​of the latent variables. ; New incoming flow conditions Predict the mean with the corresponding mapping function , is represented as: (15) variance Represented as: (16) For a new incoming flow condition and its boundary The latent spatial variable Z predicted by GPR is expressed as : (17) in, This indicates the values ​​of the latent spatial variables predicted by the GPR process; Subsequently, the predicted values ​​of the latent spatial variables are input into the variational decoder in step four to obtain the complete pressure field. : (18) Therefore, the aerodynamic proxy model constructed using formulas (17) and (18) can be used to obtain the flow field under any incoming flow condition.

[0008] Furthermore, in step six, Latin hypercube sampling is performed around the set operating parameters based on the experimental conditions to form an inflow condition set. ,in, The specific steps for obtaining the data assimilation prior matrix using an aerodynamic surrogate model for c different incoming flow conditions formed through Latin hypercube sampling are as follows: First, the potential space value corresponding to the flow condition is obtained according to formula (17). : (19) in, This represents the mean vector of the latent space predicted by the model under the prior set of incoming flow conditions. This represents the covariance between the prior load case and all training load cases, calculated using the kernel function. This represents the values ​​of the potential spatial variables corresponding to the prior flow conditions; Then, according to formula (18), the predicted latent spatial variable values ​​are decoded by a variational decoder to obtain the complete prior set of the pressure field. : (20) Therefore, the pneumatic proxy model is expressed as: (twenty one).

[0009] Furthermore, in step seven, the set transformation Kalman filter utilizes Kalman gain. The estimation results of the system model and the experimental observation data are assigned corresponding weights to obtain the optimal state matrix that integrates the system model information and the measured data; the prior distribution is constructed using the CFD flow field set obtained in step six. : (twenty two) in, This represents the flow field information corresponding to the set of prior incoming flow conditions, with a sample size of c; Calculate the mean of the prior distribution vectors of all obtained elements. ,in The prior distribution of the flow field is represented as follows: (twenty three)

[0010] (twenty four) Through the mean matrix Obtain the deviation matrix : (25) From the observation noise covariance matrix Covariance matrix of set members The simultaneous calculations yielded: (26) in, Kalman gain, superscript This is the transpose of the matrix. The projection matrix is ​​set to 1 at the corresponding positions of the airfoil mesh and the experimental model measurements, and 0 at the other positions. Experimental measurement data obtained from wind tunnel experiments Constructed filter experimental measurement data matrix For reference, the experimental measurement data were obtained from the pressure measurement holes, and there are a total of One measurement point: (27) For the existing prior mean matrix The posterior mean matrix is ​​obtained by correcting using Kalman gain. Using the posterior mean matrix and posterior bias matrix Find the posterior distribution after processing. The calculation formula is as follows: (31).

[0011] Furthermore, in step eight, a convergence criterion is used to determine whether the iteration process has ended. The iteration stops when the convergence criterion reaches a preset threshold. (32) in, This represents the root mean square error between the prior and posterior pressure fields; During the iterative loop, the boundary conditions corresponding to the posterior distribution are used as the initial values ​​of the boundary conditions for the next iteration, in order to obtain the prior distribution vector for the next iteration: (33) After the iteration terminates, take the result obtained from the last iteration. Calculate the average value of the group of boundary conditions, and then use this average value. The final modified boundary conditions were re-introduced into the CFD solver to conduct numerical simulations, and the reconstructed high-fidelity global flow field was obtained.

[0012] According to another aspect of the invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the low computational cost data assimilation flow field reconstruction method as described in any of the preceding claims.

[0013] According to another aspect of the invention, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the low-computational-cost data assimilation flow field reconstruction method as described in any of the preceding claims.

[0014] According to another aspect of the invention, a computer program product is provided, including a computer program that, when executed by a processor, implements the low computational cost data assimilation flow field reconstruction method as described in any of the preceding claims.

[0015] In summary, the technical solutions conceived in this invention, compared with the prior art, can achieve the following beneficial effects: 1. To address the limitations of wall measurements in terms of spatial coverage during wind tunnel experiments and the high computational cost of the ETKF method due to its reliance on batch CFD simulations, this invention introduces a neural network surrogate model to replace the traditional CFD solver, constructing an efficient computational path within a data assimilation framework—an effective solution. Specifically, the surrogate model, as a computationally inexpensive approximation model, can replace the complex and time-consuming original simulation model (CFD simulation), significantly improving the efficiency of optimization and analysis while maintaining accuracy. Combining the surrogate model with the ETKF algorithm enhances the efficiency of the flow field reconstruction process, making it possible to rapidly and accurately reconstruct the entire flow field in wind tunnel experiments—a powerful tool for analyzing and optimizing airfoil aerodynamic characteristics.

[0016] 2. This invention uses a neural network-based surrogate model instead of a CFD solver as the tool for updating the prior flow field in the ensemble transformation Kalman filter iterative process. This reduces the number of CFD solver calls and effectively improves the efficiency of data assimilation. Actual experiments show that for the same 2D airfoil mesh and the same working condition, the CFD solver takes approximately 5 minutes to obtain results, while the aerodynamic surrogate model takes approximately 50 ms. This significantly increases overall efficiency without compromising accuracy. Attached Figure Description

[0017] Figure 1 This is a flowchart of the data assimilation flow field reconstruction method of the fusion neural network proxy model according to a preferred embodiment of the present invention; Figure 2 This is a CFD mesh diagram of the NCAC0012 airfoil, a preferred embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0019] This invention addresses the need for rapid sensing of complete multiphysics fields in wind tunnel airfoil experiments in aerospace. It proposes a method for reconstructing the flow field around the airfoil using pressure distribution data measured on the airfoil surface, combined with data assimilation. To address the high computational and time costs associated with frequent calls to the CFD solver during data assimilation, a low-cost data assimilation flow field reconstruction method incorporating a neural network surrogate model is proposed. The specific implementation is as follows: Pressure distribution data on the wing surface was measured using a pressure orifice and pressure scanning valve measurement scheme. To improve the efficiency of data assimilation, an ensemble transformation Kalman filter data assimilation method incorporating a neural network surrogate model was proposed. The implementation steps are as follows, and the detailed flowchart is attached. Figure 1 : Step 1: Wing geometry modeling and mesh generation. A 3D model of the wing to be tested is constructed. The external flow field of the wing model is then meshed using a structured mesh and converted into an unstructured mesh for computational fluid dynamics calculations.

[0020] Step 2: Solver Setup and Mesh Convergence Analysis. The basic mesh is refined and thinned, imported into Fluent, and a suitable turbulence model is selected for simulation with identical boundary conditions. The surface aerodynamic loads of the three meshes are compared, and the mesh with sufficient accuracy and low density is selected to balance the computational efficiency.

[0021] Step 3: Constructing the simulation dataset within the wind tunnel experimental range. Determine the incoming flow boundary based on the wind tunnel experimental conditions, using the free flow velocity... Angle of attack Define the parameter space; uniformly sample from the parameter space. For each sample, set up batch CFD simulation according to step two; retain the pressure field. With corresponding incoming flow conditions Build a dataset for subsequent comparison and iteration with experimental measurements.

[0022] Step 4: VAE Model Construction and Flow Field Dimensionality Reduction. A variational autoencoder (VAE) based on a neural network is constructed, mainly consisting of an encoder, a latent space, and a decoder, using the pressure field dataset obtained in Step 3. This neural network is trained to compress high-dimensional stress field data into a low-dimensional latent space using an encoder. In addition, a decoder can be used to decode the high-dimensional pressure field from the latent space. .

[0023] Step 5: Construction of the Gaussian Process Regression (GPR) aerodynamic surrogate model. The Gaussian process regression method is used to establish the aerodynamic parameters for the incoming flow condition. ) and the latent spatial variables in step four The mapping relationship between them is used to generate an aerodynamic surrogate model of the pressure field, realizing the input aerodynamic parameters ( It can directly predict the corresponding pressure field, effectively reducing the use of CFD and lowering the computational cost.

[0024] Step Six: Obtain the flow field prior based on the experimental conditions. Based on the set conditions of the wind tunnel experiment, perform Latin hypercube sampling around the set conditions to form a set of incoming flow conditions. Its number of elements is represent For different operating conditions, the aerodynamic surrogate model obtained in step five is used to predict the pressure field of all members in the set, and the prior distribution matrix of the flow field is obtained. .

[0025] Step 7: Data assimilation using the ensemble Kalman filter method. Perform error analysis on the obtained measurement data and flow field verification distribution to determine the Kalman gain matrix. Then, based on the wing surface pressure measurement data obtained from the pressure orifices during wind tunnel testing... Calculate the posterior distribution .

[0026] Step 8: Iteration and Convergence Check. Determine if the current iteration has converged using the convergence criterion. If the convergence condition is not met, update the boundary condition set and repeat steps 6 through 8 until the convergence condition is met. Exit the iteration and output the boundary conditions in the posterior distribution. ).

[0027] Step Nine: Complete the flow field reconstruction. Based on the final boundary conditions after iteration output in Step Eight ( Using the mesh and other parameters set in step two, CFD simulation is performed to obtain the final reconstructed result of the flow field data assimilation.

[0028] Furthermore, this invention addresses the problem of high computational complexity and low efficiency associated with CFD batch solutions for flow field reconstruction during wind tunnel measurements. It proposes a low-cost data assimilation flow field reconstruction method. This method can assimilate various wind tunnel measurement data, such as temperature, surface pressure, surface friction drag, and spatial velocity fields. The technical solution is illustrated here using surface pressure measured through pressure holes on a common airfoil surface as an example: Pressure measurement orifices are used by drilling small holes in the wing surface and connecting them to a pressure scanner via pressure measurement tubes to read the pressure at each orifice. This measurement method offers high single-point measurement accuracy and is a mature pressure measurement method widely used in wind tunnels. While pressure orifices can measure discrete surface pressure data, obtaining parameters such as spatial velocity field, pressure field, and turbulence intensity field under the same operating conditions requires a flow field reconstruction method based on data assimilation. To improve the efficiency of data assimilation, a neural network surrogate model is introduced to replace the traditional CFD simulator, constructing an efficient computational path within the data assimilation framework. A set transformation Kalman filter data assimilation method integrating the neural network surrogate model is proposed, with the following implementation steps: Step 1: Wing Geometric Modeling and Meshing. A 3D model of the wing under test is constructed and geometrically simplified, retaining the geometric features with the greatest impact on aerodynamics. The wing model is then meshed with a structured mesh for the external flow field and converted into an unstructured mesh for computational fluid dynamics calculations.

[0029] Step 2: Simulation Verification and Mesh Convergence Analysis. The basic mesh is refined and then sparsed. The resulting external flow field mesh is imported into the Fluent fluid dynamics solver. A suitable turbulence model is selected for simulation, and the same boundary conditions are set. The surface aerodynamic load information of the three meshes with different densities is compared. The mesh with the lower density is selected to balance computational efficiency while ensuring computational accuracy.

[0030] Step 3: Constructing the simulation dataset within the wind tunnel experimental range. Based on the experimental conditions of the wind tunnel, determine the boundaries of the incoming flow conditions for the simulation dataset, typically using the free-flow velocity. Angle of attack Two aerodynamic parameters are defined. Within a two-dimensional parameter space formed by the maximum and minimum values ​​of these two parameters, a uniform sampling method is used to sample data from the parameter space. 10 samples, representing a uniform distribution. Different operating conditions. Using the simulation settings from step two, combined with sampling... A set of random aerodynamic parameters ( Batch fluid dynamics simulations were performed. The flow field dataset was retained for subsequent iterative comparison with experimental measurements; here, the experimental measurements are surface pressure distributions, therefore the pressure field is retained. and the corresponding incoming flow conditions ( ) Construct the dataset.

[0031] Step 4: Construct and train a variational autoencoder (VAE) model to achieve dimensionality reduction of the flow field. Construct a neural network-based variational autoencoder (VAE), which mainly consists of an encoder, a latent space, and a decoder, using the pressure field dataset obtained in Step 3. This neural network is trained to compress high-dimensional stress field data into a low-dimensional latent space using an encoder. In addition, a decoder can be used to decode the high-dimensional pressure field from the latent space. .

[0032] Step 5: Construct an aerodynamic surrogate model using the Gaussian process regression (GPR) method. Establish the aerodynamic parameters for the incoming flow condition using the Gaussian process regression method. ) and the latent spatial variables in step four The mapping relationship between them is used to generate an aerodynamic surrogate model of the pressure field, realizing the input aerodynamic parameters ( It can directly predict the corresponding pressure field, effectively reducing the use of CFD and lowering the computational cost.

[0033] Step Six: Obtain the flow field prior based on the experimental conditions. Based on the set conditions of the wind tunnel experiment, perform Latin hypercube sampling around the set conditions to form a set of incoming flow conditions. The set has c elements representing c different operating conditions. The aerodynamic surrogate model obtained in step five is used to predict the pressure field of all members in the set, thus obtaining the prior distribution matrix of the flow field. .

[0034] Step 7: Assimilate the boundary conditions using the Kalman filter method. Perform error analysis on the obtained measurement data and flow field verification distribution to determine the Kalman gain matrix. Then, based on the rarefaction pressure data of the wing surface measured in the wind tunnel test using pressure orifices... Calculate the posterior distribution .

[0035] Step 8: Iterate through the loop and determine if convergence has occurred. Determine if the current iteration has converged using the convergence criterion. If the convergence condition is not met, update the boundary condition set and repeat steps 6 through 8 until the convergence condition is met. Exit the loop iteration and output the boundary conditions in the posterior distribution. ).

[0036] Step Nine: Complete the flow field reconstruction. Based on the final boundary conditions after iteration output in Step Eight ( Using the mesh and other parameters set in step two, CFD simulation is performed to obtain the final reconstructed result of the flow field data assimilation.

[0037] The specific method for constructing a network-based variational autoencoder (VAE) model in step four is as follows. The pressure field retained in step three... Represented as a high-dimensional physical field vector Dimensional reduction to potential space In this context, the dimension of the physical field is originally smaller than the dimension of the potential space. Therefore, dimensionality reduction of high-dimensional physical fields is achieved. The basic principle of VAE is to reduce the dimensionality of the data space. The input data X is mapped to the latent space (the mapping relationship is represented as follows). The decoder network reconstructs the input data from the latent space representation (the mapping is represented as...). It's important to note that the encoder and decoder designs are typically symmetrical. In the bottleneck structure between the encoder and decoder networks, data is compressed into the latent space Z. Therefore, the basic architecture of a VAE can be represented as: (1) in, This represents the flow field information after encoding, compression, decoding, and reconstruction. The encoder uses a convolutional neural network (or a fully connected layer, depending on the form of the retained field) to compress the complete physical field into the latent space, that is,... Mapping to latent variables : (2) in, Represents the mean of the latent variables. Represents the variance of latent variables. This represents the encoder neural network.

[0038] To make this latent space regular, latent variables are specified. The distribution follows a standard normal distribution: (3) in, This represents the probability distribution of latent variables relative to the flow field. This indicates a normal distribution.

[0039] Therefore, a new latent variable is generated during training through reparameterization. : (4) in, It's Gaussian noise. It is a standard normal distribution. The identity matrix represents a variance of 1. This design ensures that the process of taking values ​​of latent variables is differentiable, making the low-dimensional latent space continuous.

[0040] The input is then fed into a symmetric network with the same mesh architecture as the encoder, but in the opposite direction, called the decoder: (5) in, This represents the decoder neural network.

[0041] The loss function used when training this network includes MSE reconstruction error and KL divergence, which can be adjusted by... This adjusts the weight of the KL divergence in the loss function, thereby regularizing the orthogonality of the low-dimensional latent space, as shown in Equation (6).

[0042] (6) in, This represents the loss function of the VAE neural network. This represents the root mean square error between the input and output of a VAE. This represents the weight of the KL divergence in the loss function. Denotes KL divergence, This indicates that the flow field data and the potential spatial variables conform to a normal distribution.

[0043] In this way, by training this VAE neural network, we obtain a dimensionality reduction model of the high-dimensional physical field, thus reducing the high-dimensional ( The physical quantity field is compressed and encoded into a low-dimensional latent vector. We can use only Low-dimensional latent vectors of order Adding a decoder allows for the representation of high-dimensional flow field distributions. .

[0044] In step five, we use the Gaussian process regression (GPR) method to construct a low-dimensional latent vector. and boundary conditions ( The connection between them allows us to directly input boundary conditions. Obtaining low-dimensional latent variables By using a variational decoder to decode latent variables and obtain the flow field results corresponding to the boundary conditions, without the need for a CFD solver, the efficiency of data assimilation can be greatly improved. Gaussian process regression (GPR) is a nonlinear regression method based on a probabilistic framework. Its core advantages lie in its ability to quantify prediction uncertainties, flexibly fit complex data relationships, and perform robustly on small sample data.

[0045] First, we express the aerodynamic parameters as follows: in It is a specific working condition, and the low-dimensional latent variables are represented as... To represent the value of a latent variable corresponding to a specific flow condition, the incoming flow condition and the latent variable values ​​from step four can be combined to form a training sample set D: (7) in, This indicates the number of samples in the training set.

[0046] Then for each dimension of the potential space Able to construct an independent Gaussian process regression model: (8) in, The independent and identically distributed Gaussian noise is about unknown mapping function According to the prior assumptions of Gaussian processes, for unknown mapping functions... It satisfies the prior assumptions of a Gaussian process: (9) in, To represent a Gaussian process, the mean is usually taken as 0, i.e., the mean is zero. .and The covariance function (also called the kernel function) is used to describe the correlation between different aerodynamic operating conditions. This represents the incoming flow parameters for a different operating condition. The key to GPR lies in determining the kernel function. Here, to simultaneously characterize the linear trend and nonlinear variation characteristics between aerodynamic parameters and latent variables, a combined kernel function is chosen, consisting of a linear kernel function and a Matern32 kernel function: (10) Where the linear kernel function The definition of is: (11) The Matern32 kernel function The definition of is: (12) in: (13) in, As an intermediate variable, , and These are all hyperparameters of the kernel function, plus the noise variance. The hyperparameters belonging to the GPR method need to be determined through optimization learning. The optimization objective is to maximize the log-marginal likelihood of the observations, as shown in the formula: (14) in, This represents the log-marginal likelihood of the observed data Z given the hyperparameters θ. It is the objective function in GPR used to optimize the hyperparameters of the kernel function; maximizing this value is used to find the optimal hyperparameters. Let represent the covariance matrix calculated by the kernel function, and n represent the number of training samples.

[0047] Numerical methods such as gradient descent and ARD autocorrelation determination can be used to find the hyperparameter values ​​that maximize the above function. Once the hyperparameter values ​​are determined, the mapping function in formula (8) is determined. The Gaussian distribution characteristics can be obtained through the mapping function. The set of mapping functions For a new set of incoming flow conditions Output the values ​​of the latent variables. .

[0048] New incoming flow conditions Predict the mean with the corresponding mapping function , can be represented as: (15) variance It can be represented as: (16) Gaussian process regression is a probabilistic regression model, therefore, for a completely new inflow condition... Its output is not a fixed value, but a mean (15) and a variance (16), where the mean is the predicted value and the variance represents determinism. Therefore, for a new inflow condition and its boundary... We can express the values ​​of the latent spatial variable Z predicted by GPR as follows: : (17) in, This represents the values ​​of the latent spatial variables predicted by the GPR process. Subsequently, the predicted latent variables are input into the variational decoder in step four to obtain the complete pressure field. : (18) Therefore, we can use formulas (17) and (18) to construct an aerodynamic proxy model, which can quickly obtain the flow field under a certain inflow condition without the need for a CFD solver.

[0049] In step six, a set of incoming flow conditions is formed by performing Latin hypercube sampling around the set operating parameters based on the experimental conditions. ,in, The specific steps for obtaining the data assimilation prior matrix using a surrogate model, representing c different incoming flow conditions formed through Latin hypercube sampling, are as follows: First, the potential space value corresponding to the flow condition is obtained according to formula (17). : (19) in, This represents the mean vector of the latent space predicted by the model under the prior set of incoming flow conditions. This represents the covariance between the prior load case and all training load cases, calculated using the kernel function. This represents the value of the potential spatial variable corresponding to the prior flow condition.

[0050] Then, according to formula (18), the predicted latent spatial variable values ​​are decoded by a variational decoder to obtain the complete prior set of the pressure field. : (20) Therefore, the pneumatic surrogate model can be expressed as: (twenty one) In step seven, the set transformation Kalman filter utilizes Kalman gain. The estimation results of the system model and the experimental observation data are assigned corresponding weights to obtain the optimal state matrix that integrates the system model information and the measured data. The prior distribution is constructed using the CFD flow field set obtained in step six. : (twenty two) in, This represents the flow field information corresponding to the prior flow condition set (sample size c).

[0051] Calculate the mean of the prior distribution vectors of all obtained elements. ,in The prior distribution of the flow field is represented as follows: (twenty three)

[0052] (twenty four) Through the mean matrix Obtain the deviation matrix : (25) Determining Kalman Gain using the Set Transform Kalman Filter Method The minimum variance optimal estimation is essentially a weighted allocation of coefficients between the model's prior information and the experimental observation information, derived from the observation noise covariance matrix. Covariance matrix of set members The simultaneous calculations yielded: (26) in, Kalman gain, superscript This is the transpose of the matrix. This is the projection matrix, with a value of 1 at the corresponding positions of the airfoil mesh and the experimental model measurements, and 0 at the other positions.

[0053] Experimental measurement data obtained from wind tunnel experiments Constructed filter experimental measurement data matrix For reference, the experimental measurement data were obtained from the pressure measurement holes, and there are a total of One measurement point: (27) For the existing prior mean matrix The posterior mean matrix is ​​obtained by correcting using Kalman gain. In this matrix, the H matrix is ​​the transformation matrix, which transforms the prior pressure field into the corresponding points measured by pressure. Represent the posterior distribution: (28) Next, the posterior bias matrix is ​​obtained. , where the matrix It is a symmetric positive definite matrix, and its singular value decomposition yields the eigenvector matrix. and eigenvalue matrix : (29) (30) Using the posterior mean matrix and posterior bias matrix The posterior distribution after processing can be obtained. The calculation formula is as follows: (31) In step eight, a convergence criterion is used to determine whether the iteration process has ended. Here, surface pressure data is measured using a flexible sensor for data assimilation. Therefore, the convergence criterion is set to stop iteration when the mean square error (MSE) of the physical quantities at the grid points before and after data assimilation decreases to 1% of that in the first iteration. This threshold condition indicates that continued iteration is unlikely to achieve a more significant correction gain on the prior distribution. (32) in, This represents the root mean square error between the prior and posterior pressure fields.

[0054] During the iterative loop, the boundary conditions corresponding to the posterior distribution are used as the initial values ​​of the boundary conditions for the next iteration, in order to obtain the prior distribution vector for the next iteration: (33) After the iteration terminates, take the result obtained from the last iteration. Calculate the average value of the group of boundary conditions, and then use this average value. The final modified boundary conditions were re-introduced into the CFD solver to conduct numerical simulations, and the reconstructed high-fidelity global flow field was obtained.

[0055] In summary, by using a neural network-based surrogate model instead of a CFD solver as a tool for updating the prior flow field in the set transformation Kalman filter iterative process, the number of CFD solver calls can be reduced, effectively improving the efficiency of data assimilation.

[0056] Actual experiments have shown that, with the addition of Figure 2 Taking the NACA0012 airfoil with a two-dimensional C-type mesh as an example, the number of meshes is approximately 32,000. Under the same mesh, the CFD solver (SA turbulence model) takes about 5 minutes to obtain the result, while the aerodynamic surrogate model takes about 50 ms to obtain the result. Without affecting the accuracy, the overall efficiency is greatly improved.

[0057] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A low-computational-cost data assimilation flow field reconstruction method incorporating neural networks, characterized in that, include: Step 1: Wing geometry modeling and mesh generation; Construct a 3D model of the wing to be tested, generate a structured mesh for the external flow field of the wing model, and convert it into an unstructured mesh for computational fluid dynamics calculations; Step 2: Solver setup and mesh convergence analysis; refine and sparse the unstructured mesh obtained in Step 1, import it into Fluent, select the K-omega turbulence model, and simulate with the same boundary conditions; set and compare the surface aerodynamic loads calculated by sparse, medium, and dense mesh densities, and select the mesh with the highest accuracy and lower density to balance the calculation efficiency. Step 3: Constructing the simulation dataset within the wind tunnel experimental range; determining the incoming flow boundary based on the wind tunnel experimental conditions, using the free flow velocity. Angle of attack Define the parameter space; obtain uniform samples within the parameter space. For each sample, a batch CFD simulation was performed using a mesh with acceptable accuracy and lower density obtained in step two; the pressure field was retained. With corresponding incoming flow conditions Build a dataset for subsequent comparison and iteration with experimental measurements; Step 4: Flow field dimensionality reduction; using a variational autoencoder based on a neural network, the high-dimensional pressure field data is compressed into a low-dimensional latent space to obtain latent space variables. The neural network-based variational autoencoder uses the pressure field dataset obtained in step three. Pre-trained neural network acquisition; Step 5: Construction of the aerodynamic surrogate model using the Gaussian process regression method; establishing the aerodynamic parameters for the incoming flow condition using the Gaussian process regression method. With the latent spatial variables in step four The mapping relationship between them is used to generate an aerodynamic surrogate model of the force field, thereby realizing the input aerodynamic parameters. Directly predict the corresponding pressure field; Step Six: Obtain the flow field prior based on the experimental conditions; based on the set conditions of the wind tunnel experiment, perform Latin hypercube sampling around the set conditions to form a flow field containing... Set of incoming flow conditions under different operating conditions Then, the aerodynamic surrogate model obtained in step five is used to predict the pressure field of all members in the set, and the prior distribution matrix of the flow field is obtained. ; Step 7: Data assimilation using the Kalman filter method; processing the wing surface pressure measurement data obtained from the pressure orifice tests in the wind tunnel. Error analysis was performed on the prior flow field distribution from step six to determine the Kalman gain matrix. Then according to Calculate the posterior distribution ; Step 8: Iteration and Convergence Check; Determine if the current iteration has converged using the preset convergence criterion. If the convergence condition is not met, update the boundary condition set and repeat steps 6 to 8 until the convergence condition is met. Then, exit the iteration and output the boundary conditions in the posterior distribution. ; Step 9: Complete flow field reconstruction; based on the final boundary conditions output in Step 8 after iteration. Using the mesh and parameters set in step two, CFD simulation is performed to obtain the final reconstructed result of the flow field data assimilation.

2. The low-computational-cost data assimilation flow field reconstruction method fused with neural networks according to claim 1, characterized in that, The construction and training method of the neural network-based variational autoencoder described in step four is as follows; The basic architecture of a variational autoencoder (VAE) based on a neural network is represented as follows: (1) in, This represents the flow field information after encoding, compression, decoding, and reconstruction. The encoder compresses the complete physical field into the latent space, that is, Mapping to latent variables , Representing high-dimensional physical field vectors: (2) in, Represents the mean of the latent variables. Represents the variance of latent variables. Represents an encoder neural network; To make this latent space regular, latent variables are specified. The distribution follows a standard normal distribution: (3) in, This represents the probability distribution of latent variables relative to the flow field. Represents a normal distribution; During training, a new latent variable is generated through reparameterization. : (4) in, It's Gaussian noise. It is a standard normal distribution. The identity matrix represents a matrix with a variance of 1. The input is then fed into a symmetric network with the same mesh architecture as the encoder, but in the opposite direction, called the decoder: (5) in, Represents a decoder neural network; The loss function used when training the decoder neural network includes MSE reconstruction error and KL divergence, which are adjusted by... This adjusts the weight of the KL divergence in the loss function, thereby regularizing the orthogonality of the low-dimensional latent space, as shown in formula (6). (6) in, This represents the loss function of the VAE neural network. This represents the root mean square error between the input and output of a VAE. This represents the weight of the KL divergence in the loss function. Denotes KL divergence, This indicates that the flow field data and the underlying spatial variables conform to a normal distribution; By training a VAE neural network to obtain a dimensionality reduction model of a high-dimensional physical field, the high-dimensional physical field is compressed and encoded into a low-dimensional latent vector, thus using only... Low-dimensional latent vectors of order Adding a decoder to represent the high-dimensional flow field distribution .

3. The low-computational-cost data assimilation flow field reconstruction method fused with neural networks according to claim 2, characterized in that, In step five, a low-dimensional latent vector is constructed using the Gaussian process regression (GPR) method. and boundary conditions ( The relationship between them; the Gaussian process regression method (GPR) is as follows: First, the aerodynamic parameters are expressed as ,in It is a specific working condition, and the low-dimensional latent variables are represented as... This represents the value of a potential variable corresponding to a specific flow condition. The incoming flow condition and the value of the potential variable from step four are combined to form a training sample set D: (7) in, Indicates the number of samples in the training set; For each dimension of the potential space Construct an independent Gaussian process regression model for each: (8) in, , The independent and identically distributed Gaussian noise is about unknown mapping function For unknown mapping functions Satisfies the prior assumptions of a Gaussian process: (9) in, To represent a Gaussian process, the mean is usually taken as 0, i.e., the mean is zero. ;and The covariance function, also known as the kernel function, is used to describe the correlation between different aerodynamic operating conditions. This represents the incoming flow parameters for a different operating condition; the kernel function consists of a linear kernel function and a Matern32 kernel function. (10) Where the linear kernel function The definition of is: (11) The Matern32 kernel function The definition of is: (12) in: (13) in, As an intermediate variable; , and Noise variance These are all hyperparameters of the GPR method, which need to be determined by optimization learning. The optimization objective is to maximize the log-marginal likelihood of the observations, as shown in the formula: (14) in, This represents the log-marginal likelihood of the observed data Z given the hyperparameter θ, achieved by maximizing... The optimal hyperparameters are found by taking their values. represents the covariance matrix calculated by the kernel function, and n represents the number of training samples; Solve for the hyperparameter values ​​that maximize equation (14), and thus determine the mapping function in equation (8). Gaussian distribution characteristics, and then through the mapping function The set of mapping functions For a new set of incoming flow conditions Output the values ​​of the latent variables. ; New incoming flow conditions Predict the mean with the corresponding mapping function , is represented as: (15) variance Represented as: (16) For a new incoming flow condition and its boundary The latent spatial variable Z predicted by GPR is expressed as : (17) in, This indicates the values ​​of the latent spatial variables predicted by the GPR process; Subsequently, the predicted values ​​of the latent spatial variables are input into the variational decoder in step four to obtain the complete pressure field. : (18) Therefore, the aerodynamic proxy model constructed using formulas (17) and (18) can be used to obtain the flow field under any incoming flow condition.

4. The low-computational-cost data assimilation flow field reconstruction method fused with neural networks according to claim 3, characterized in that, In step six, Latin hypercube sampling is performed around the set operating parameters based on the experimental conditions to form an inflow condition set. ,in, The specific steps for obtaining the data assimilation prior matrix using an aerodynamic surrogate model for c different incoming flow conditions formed through Latin hypercube sampling are as follows: First, the potential space value corresponding to the flow condition is obtained according to formula (17). : (19) in, This represents the mean vector of the latent space predicted by the model under the prior set of incoming flow conditions. This represents the covariance between the prior load case and all training load cases, calculated using the kernel function. This represents the values ​​of the potential spatial variables corresponding to the prior flow conditions; Then, according to formula (18), the predicted latent spatial variable values ​​are decoded by a variational decoder to obtain the complete prior set of the pressure field. : (20) Therefore, the pneumatic proxy model is expressed as: (21)。 5. A low-computational-cost data assimilation flow field reconstruction method incorporating neural networks according to claim 4, characterized in that, In step seven, the set transformation Kalman filter utilizes Kalman gain. The estimation results of the system model and the experimental observation data are assigned corresponding weights to obtain the optimal state matrix that integrates the system model information and the measured data; the prior distribution is constructed using the CFD flow field set obtained in step six. : (22) in, This represents the flow field information corresponding to the set of prior incoming flow conditions, with a sample size of c; Calculate the mean of the prior distribution vectors of all obtained elements. ,in Represents the prior distribution of the flow field: (23) (24) Through the mean matrix Obtain the deviation matrix : (25) From the observation noise covariance matrix Covariance matrix of set members The simultaneous calculations yielded: (26) in, Kalman gain, superscript This is the transpose of the matrix. The projection matrix is ​​set to 1 at the corresponding positions of the airfoil mesh and the experimental model measurements, and 0 at the other positions. Experimental measurement data obtained from wind tunnel experiments Constructed filter experimental measurement data matrix For reference, the experimental measurement data were obtained from the pressure measurement holes, and there are a total of One measurement point: (27) For the existing prior mean matrix The posterior mean matrix is ​​obtained by correcting using Kalman gain. Using the posterior mean matrix and posterior bias matrix Find the posterior distribution after processing. The calculation formula is as follows: (31)。 6. A low-computational-cost data assimilation flow field reconstruction method incorporating neural networks according to claim 5, characterized in that, In step eight, a convergence criterion is used to determine whether the iteration process has ended. The iteration stops when the convergence criterion reaches a preset threshold. (32) in, This represents the root mean square error between the prior and posterior pressure fields; During the iterative loop, the boundary conditions corresponding to the posterior distribution are used as the initial values ​​of the boundary conditions for the next iteration, in order to obtain the prior distribution vector for the next iteration: (33) After the iteration terminates, take the result obtained from the last iteration. Calculate the average value of the group of boundary conditions, and then use this average value. The final modified boundary conditions were re-introduced into the CFD solver to conduct numerical simulations, and the reconstructed high-fidelity global flow field was obtained.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the low computational cost data assimilation flow field reconstruction method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the low computational cost data assimilation flow field reconstruction method according to any one of claims 1 to 6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the low computational cost data assimilation flow field reconstruction method according to any one of claims 1 to 6.

Images