Shock wave prediction method based on characteristic decomposition and deep neural network

Abstract

The invention discloses a shock wave prediction method based on characteristic decomposition and a deep neural network. The method comprises the steps of 1, collecting shock wave data and performing normalization processing on the shock wave data; 2, carrying out feature decomposition on the normalized data to extract a feature decomposition basic mode, and generating a feature decomposition basic mode projection coefficient; 3, building a deep neural network model; 4, training a deep neural network; and 5, reducing the shock wave pressure field to obtain predicted shock wave pressure field distribution, and completing shock wave prediction. The invention provides a shock wave prediction method based on characteristic decomposition and a deep neural network, flow field characteristics can be efficiently extracted through a characteristic decomposition method and dimension reduction processing is carried out, and the deep neural network realizes rapid prediction of a shock wave flow field by learning a relationship between the flow field characteristics and an inflow condition. And the method shows relatively strong generalization ability under different types of shock waves, and relatively high prediction precision is kept while the calculation time is greatly shortened.

Description

Technical Field

[0001] The present invention relates to the field of numerical simulation, and more specifically, to a shock wave prediction method based on eigendecomposition and deep neural network. Background Art

[0002] Shock waves are a common flow phenomenon in high-speed airflows and are widely present in the design and optimization of supersonic and hypersonic aircraft. Traditional shock wave calculation methods mainly rely on numerical simulations, such as computational fluid dynamics (CFD) and wind tunnel experiments. Although these methods have high accuracy, they usually require a lot of computing resources and time, and are limited by experimental conditions and the feasibility of numerical methods. Therefore, how to improve the computational efficiency of shock wave prediction while maintaining high accuracy has become an important research direction.

[0003] In recent years, deep learning has made some progress in the field of flow field prediction. By building a neural network model, the experimental cost and the time consumption of numerical calculations can be significantly reduced. However, the traditional deep learning method has the problem of insufficient generalization ability, that is, when the model faces diverse flow conditions or geometric shapes, the prediction time increases and the prediction accuracy may decrease significantly. Summary of the invention

[0004] An object of the present invention is to solve at least the above problems and / or disadvantages and to provide at least the advantages which will be described hereinafter.

[0005] In order to achieve these purposes and other advantages of the present invention, a shock wave prediction method based on feature decomposition and deep neural network is provided, comprising: step 1: collecting corresponding shock wave data based on the type of shock wave to be predicted, and normalizing the shock wave data respectively; Step 2: Perform eigendecomposition on the normalized data to select the mode with energy share ≥ 99% as the eigendecomposition base mode, and generate the eigendecomposition base mode coefficient I based on it; Step 3: Build a deep neural network model based on the characteristic decomposition fundamental mode coefficient I obtained in step 1-2; Step 4: By training the deep neural network model, the characteristic decomposition basis mode coefficient II is predicted; Step 5: Based on the characteristic decomposition fundamental mode coefficient II in step 4 and the characteristic decomposition fundamental mode in step 2, the reconstructed flow field data is obtained through calculation; The final predicted shock wave pressure field distribution is obtained by performing denormalization on the reconstructed flow field data, and the shock wave pressure field restoration is completed through shock wave prediction.

[0006] Preferably, the types of shock waves to be predicted in step 1 are divided into: oblique shock waves, shock expansion waves and detached shock waves; The data include parameterized flow field conditions and pressure fields of three shock waves under different flow field conditions, which are calculated respectively according to the flow field conditions.

[0007] Preferably, the feature decomposition in step 2 is: decomposing the normalized data matrix using singular value decomposition; The method for generating the characteristic decomposition fundamental mode coefficient I is as follows: projecting the normalized data matrix onto the selected characteristic decomposition fundamental mode to obtain the characteristic decomposition fundamental mode coefficient I; The specific method of the projection is: multiplying the normalized data matrix by the eigendecomposition base mode matrix.

[0008] Preferably, the deep neural network models in step 3 are three deep neural network models for oblique shock waves, shock expansion waves and detached shock waves, whose input layers are parameterized flow field conditions such as: incoming flow angle, plate inclination angle, blunt head radius, etc., and the output layer is the fundamental mode projection coefficient, and the middle hidden layer is composed of multiple fully connected layers.

[0009] Preferably, each hidden layer is followed by a parameterized rectified linear unit.

[0010] Preferably, the reconstructed flow field data in step 5 is calculated by performing matrix multiplication of the characteristic decomposition fundamental mode coefficient II in step 4 and the characteristic decomposition fundamental mode in step 2 to obtain the reconstructed flow field data.

[0011] The present invention has at least the following beneficial effects: First, the present invention can efficiently extract flow field features and perform dimensionality reduction processing through the feature decomposition (POD) method, while the deep neural network (DNN) can achieve rapid prediction of shock wave flow field by learning the relationship between flow field features and inflow conditions; this method can show strong generalization ability under different types of shock waves (such as oblique shock waves, shock expansion waves and detached shock waves), and maintain high prediction accuracy while greatly reducing the calculation time.

[0012] Secondly, the present invention enhances the nonlinear feature learning ability of the model through parameterized modified linear units, can effectively utilize limited data sets, is compatible with multiple shock wave types, reduces the computational cost and time of engineering applications, and greatly improves the efficiency of engineering design and aerodynamic optimization processes.

[0013] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is the oblique shock wave grid diagram; Figure 2 is the grid diagram of shock wave expansion wave; Figure 3 It is the mesh diagram of the detached shock wave; Figure 4 This is a diagram of CFD calculation results of oblique shock waves at an attack angle of -18.5° in Example 1 of the present invention; Figure 5 This is a diagram showing the prediction results of the oblique shock wave at an attack angle of -18.5° in Example 1 of the present invention; Figure 6 is an absolute error diagram of an oblique shock wave at an attack angle of -18.5° in Example 1 of the present invention; Figure 7 This is a diagram showing the CFD calculation results of expansion waves at an attack angle of -20° and an inclination angle of 20° in Example 1 of the present invention; Figure 8 This is a diagram showing the prediction results of expansion waves at an attack angle of -20° and an inclination angle of 20° in Example 1 of the present invention; Fig. 9 This is the absolute error diagram of expansion waves at an attack angle of -20° and an inclination angle of 20° in Example 1 of the present invention; Fig.10 This is a diagram showing the CFD calculation results of the detached shock wave at an attack angle of -18.5° in Example 1 of the present invention; Fig.11 This is a diagram showing the prediction results of the detached shock wave at an attack angle of -18.5° in Example 1 of the present invention; Fig.12 This is the absolute error diagram of the shock wave at an angle of attack of -18.5° in Example 1 of the present invention. Figure 4-12 The X-axis and Y-axis represent two mutually perpendicular directions in the two-dimensional space, and the unit is meter; the Z-axis represents the pressure or pressure difference in the two-dimensional space formed by the X-axis and Y-axis) DETAILED DESCRIPTION

[0015] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0016] A shock wave prediction method based on feature decomposition and deep neural network, comprising: Step 1: Collect the corresponding shock wave data based on the shock wave type to be predicted, and normalize the shock wave data respectively.

[0017] Generation of data sets. For the most common shock wave types, including oblique shock waves, shock expansion waves, and detached shock waves, three typical shock wave data sets are generated: Dataset 1: The flat plate is used as the research object to generate different oblique shock wave shapes by changing the incoming flow angle; Dataset 2: Shock wave expansion wave dataset, composed of a parallel plate and an inclined plate, changing the incoming flow angle and the inclination angle of the plate to capture the characteristics of the expansion wave; Dataset 3: The detached shock wave dataset generates different detached shock wave characteristics by changing the attack angle and blunt radius.

[0018] Use grid software to construct grid data of oblique shock wave, shock expansion wave and detached shock wave, such as Figure 1-3 shown.

[0019] Parameterized representation of shapes. Use parameterization as a representation for three simple shapes. The angle of attack represents the angle of the incoming flow. Figure 2 The mid-tilt angle indicates the angle at which the board deviates. Figure 3 The median radius indicates the radius size of the blunt tip.

[0020] CFD numerical calculation: In order to provide sufficient data for the neural network, CFD is used to calculate the pressure field P of the three shock waves in step 1 at different attack angles and parameters.

[0021] Data preprocessing. The three data sets are normalized separately, as shown in formula (1): (1) In the formula represents the normalized value, represents the sample value, represents the largest value in the sample. Indicates the smallest value in the sample.

[0022] Step 2: Perform eigendecomposition on the normalized data to efficiently extract the flow field features. Select the mode containing the main energy as the eigendecomposition base mode, and generate the eigendecomposition base mode coefficient I based on it.

[0023] Data feature decomposition. The POD technique is used to extract the main features of the flow field, and the normalized data matrix is ​​decomposed using singular value decomposition (SVD), as shown in formula (2): (2) Where X represents the normalized data matrix, U represents the left singular value matrix, and contains the orthogonal basis of POD. The diagonal matrix representing the singular values, the diagonal elements are the singular values, representing the energy of each mode point, and V is the right singular value matrix.

[0024] Selection of characteristic decomposition base modes. Select the first several modes containing the main energy, discard the modes with lower energy proportion to achieve dimensionality reduction processing, and ensure that the main characteristics of the flow field information are retained. The calculation method of the characteristic decomposition base mode energy proportion is shown in formula (3): (3) In the formula represents the eigendecomposition mode energy ratio, Represented as singular values, represents a counting variable, and k represents the total number of singular values. Select the energy ratio Sufficient flow field information can be retained.

[0025] Data projection. Project the normalized data matrix onto the selected eigendecomposition basis mode to obtain the eigendecomposition basis mode projection coefficient I. The specific method is to multiply the normalized data matrix by the eigendecomposition basis mode matrix.

[0026] Step 3: Build a deep neural network model based on the characteristic decomposition basis mode projection coefficient I obtained in step 1-2.

[0027] Deep neural network models for oblique shock waves, shock expansion waves, and detached shock waves are built respectively. The designed neural network model is a deep neural network, the input layer is the parameterized flow field conditions (such as the incoming flow angle, the inclination angle of the plate, the blunt head radius, etc.), and the output layer is the characteristic decomposition fundamental mode coefficient II. The hidden layer in the middle is composed of multiple fully connected layers, and each layer is followed by PReLU (parametric corrected linear unit) (Parametric ReLU), whose parameters are learned during the training process to enhance the model's adaptability to different data features. The model input parameters undergo multi-layer feature learning and mapping, and the corresponding characteristic decomposition fundamental mode coefficient II is output, which is used to predict shock wave characteristics under different flow field conditions.

[0028] Step 4: Train the deep neural network model and predict the eigendecomposition basis mode coefficients II.

[0029] Training neural network. Three different neural networks were trained using three data sets to correspond to three different shock wave types. The MSE loss function was used and the network was trained multiple times to make the loss function value as small as possible. The calculation formula is shown in formula (4): (4) In the formula represents the true value, Represents the predicted value, MSE represents the mean square error between the predicted value and the true value, N represents the total number of calculations, and the three trained models are used to predict the fundamental mode coefficients II of the characteristic decomposition of the pressure field of different shock wave types.

[0030] Step 5: Based on the characteristic decomposition fundamental mode coefficient II in step 4 and the characteristic decomposition fundamental mode in step 2, the reconstructed flow field data is obtained through calculation; The final predicted shock wave pressure field distribution is obtained by performing denormalization on the reconstructed flow field data, and the shock wave pressure field restoration is completed through shock wave prediction.

[0031] To restore the shock wave pressure field, perform matrix multiplication on the predicted characteristic decomposition fundamental mode coefficient II and the characteristic decomposition fundamental mode in step 2. The reconstructed flow field data = POD fundamental mode matrix × predicted POD fundamental mode coefficient. Denormalize the reconstructed data and restore it to the original scale to obtain the final predicted shock wave pressure field distribution.

[0032] Example 1 Different experiments are set up for the three common shock wave types (oblique shock wave, shock expansion wave, and detached shock wave).

[0033] Oblique shock wave: Given the incoming flow Mach number of Mach 3 and the angle of attack range of -10° to -30°, the pressure field is organized into a matrix, with each column representing the pressure field at an angle of attack. After POD decomposition, 7 POD modes are selected to train the model, with the input being the angle of attack; the output is the characteristic decomposition base mode coefficient II. The prediction results and CFD results of an oblique shock wave with a test sample of -18.5° are shown in Figure 2. Figure 4-6 As shown, the relative error is 0.5%.

[0034] Shock wave expansion wave: Given the incoming flow Mach number of 3 Mach, the angle of attack range is -10°~-40°, and the plate inclination angle is 10°~40°, and the plate inclination angle is 3°, 7 angle of attack transformations, 11 inclination transformations, and a data set of 77 data. 20 modes are selected to train the model, with the input being the angle of attack and the inclination angle; the output is the characteristic decomposition basic mode coefficient II. The expansion wave prediction results and CFD results of a test sample with an angle of attack of -20° and an inclination angle of 20° are shown in Figure 2. Figure 7-9 As shown, the relative error is 0.68%.

[0035] Debody shock wave: Given the incoming flow Mach number of 3 Mach, the angle of attack range of -10° to -30°, one is taken every 1°, the blunt radius is 0.0381, 0.0762, 0.1524, 15 modes are selected, the model is trained, the input is the angle of attack and the tilt angle; the output is the characteristic decomposition basic mode coefficient II. The expansion wave prediction results and CFD results of a test sample with an angle of attack of -18.5° and a blunt radius of 0.0381 are as follows Figure 10-12 As shown, the relative error is 0.77%.

[0036] The above solution is only an illustration of a preferred embodiment, but is not limited thereto. When implementing the present invention, appropriate replacement and / or modification can be performed according to user needs.

[0037] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and the embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily realized. Therefore, without departing from the general concept defined by the claims and equivalent scope, the present invention is not limited to the specific details and the illustrations shown and described here.

Claims

1. A shock wave prediction method based on feature decomposition and deep neural network, characterized in that: The method comprises: step 1: collecting corresponding shock wave data based on the shock wave type to be predicted, and normalizing the shock wave data respectively; Step 2: Perform eigendecomposition on the normalized data to select the mode with energy share ≥ 99% as the eigendecomposition base mode, and generate the eigendecomposition base mode coefficient I based on it; Step 3: Build a deep neural network model based on the characteristic decomposition fundamental mode coefficient I obtained in step 1-2; Step 4: By training the deep neural network model, the characteristic decomposition basis mode coefficient II is predicted; Step 5: Based on the characteristic decomposition fundamental mode coefficient II in step 4 and the characteristic decomposition fundamental mode in step 2, the reconstructed flow field data is obtained through calculation; The final predicted shock wave pressure field distribution is obtained by performing denormalization on the reconstructed flow field data, and the shock wave pressure field restoration is completed through shock wave prediction.

2. The shock wave prediction method based on feature decomposition and deep neural network according to claim 1, characterized in that: The types of shock waves to be predicted in step 1 are divided into: oblique shock wave, shock expansion wave and detached shock wave; The data include parameterized flow field conditions and pressure fields of three shock waves under different flow field conditions, which are calculated respectively according to the flow field conditions.

3. The shock wave prediction method based on feature decomposition and deep neural network according to claim 1, characterized in that: The eigendecomposition in step 2 is as follows: decomposing the normalized data matrix using singular value decomposition; The method for generating the characteristic decomposition fundamental mode coefficient I is as follows: projecting the normalized data matrix onto the selected characteristic decomposition fundamental mode to obtain the characteristic decomposition fundamental mode coefficient I; The specific method of the projection is: multiplying the normalized data matrix by the eigendecomposition base mode matrix.

4. The shock wave prediction method based on feature decomposition and deep neural network according to claim 2, characterized in that: The deep neural network models in step 3 are three deep neural network models for oblique shock waves, shock expansion waves and detached shock waves. The input layer is parameterized flow field conditions such as: incoming flow angle, plate inclination angle, blunt head radius, the output layer is the fundamental mode projection coefficient, and the hidden layer in the middle is composed of multiple fully connected layers.

5. The shock wave prediction method based on feature decomposition and deep neural network according to claim 4, characterized in that: Each hidden layer is followed by a parameterized rectified linear unit.

6. The shock wave prediction method based on eigendecomposition and deep neural network according to claim 1, characterized in that: The calculation method of the reconstructed flow field data in step 5 is: perform matrix multiplication of the characteristic decomposition fundamental mode coefficient II in step 4 and the characteristic decomposition fundamental mode in step 2 to obtain the reconstructed flow field data.

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