Method, system, device and medium for reconstructing a motion boundary pressure field

Abstract

The application relates to a moving boundary pressure field reconstruction method, a system, a device and a medium, and the moving boundary pressure field reconstruction method comprises the following steps: acquiring moving boundary flow field data, wherein the moving boundary flow field data comprises a velocity field and a moving boundary; generating training data, wherein the training data comprises velocity supervision data, boundary supervision data and flow parameters; constructing a double neural network model according to preset parameters, wherein the double neural network model comprises a boundary network and a flow field network; training the double neural network through the training data; inputting the spatial coordinates of a to-be-predicted point; and the trained double neural network correspondingly outputs the pressure value of the point to predict the pressure field and the boundary under the moving boundary condition. The application obtains accurate boundary conditions and reduces the pressure reconstruction error of the flow field under the moving boundary.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of experimental fluid mechanics. In particular, it relates to a moving boundary pressure field reconstruction method, system, device and medium. BACKGROUND

[0002] Flow field pressure is a basic physical quantity of fluid dynamics, which directly affects the lift and drag of aircraft, ships and other vehicles. At the same time, flow field pressure and flow structure interact with each other, which is also an important factor leading to flow noise and structure vibration. The measurement of instantaneous pressure distribution inside the flow field has always been a difficulty in experimental fluid mechanics. At present, the main method is to obtain the velocity field by particle image velocimetry (PIV) technology and then to deduce the pressure field by combining physical equations. However, for moving curved boundary problems such as fish swimming, ventricular diastole and contraction, and bubble deformation, the traditional pressure reconstruction method is difficult to accurately calculate the pressure field of such moving curved boundary. The reason is that there is a large error in experimental measurement, mainly reflected in: first, experimental measurement cannot obtain accurate boundary shape and velocity, so it is impossible to obtain accurate boundary conditions; second, due to the limitation of spatial resolution, PIV cannot accurately analyze the flow near the wall; third, the traditional pressure reconstruction method needs to introduce complex boundary processing technology at the moving boundary. How to obtain accurate boundary conditions and reduce the pressure reconstruction error of flow field under moving boundary is a problem to be solved. SUMMARY

[0003] The present application provides a moving boundary pressure field reconstruction method, system, device and medium. To solve the problem that the traditional pressure reconstruction method is difficult to accurately calculate the pressure field of moving curved boundary.

[0004] To achieve the above-mentioned purpose, in a first aspect, the present application provides a moving boundary pressure field reconstruction method, comprising: obtaining moving boundary flow field data, the moving boundary flow field data comprising velocity field and moving boundary;

[0005] Generating training data, the training data comprising velocity supervision data, boundary supervision data and flow parameters, wherein the flow parameters at least include Reynolds number, characteristic length and characteristic velocity;

[0006] According to the preset parameters, a double neural network model is constructed, the double neural network model comprising a boundary network and a flow field network;

[0007] The double neural network is trained by the training data;

[0008] The spatial coordinates of the point to be predicted are input, and the trained double neural network outputs the pressure value of the point to predict the pressure field and boundary under the moving boundary condition.

[0009] Preferably, the training of the dual neural network by the training data comprises:

[0010] According to the input data label and the batch size, corresponding batch data is generated, which comprises flow field supervision data, boundary supervision data, equation residual points, motion boundary residual points and fixed boundary conditions;

[0011] The dynamic weight coefficients a, b and g are calculated;

[0012] The loss functions and the total loss function are calculated, and the gradient of the total loss function with respect to the to-be-trained parameters is calculated according to automatic differentiation, wherein the total loss function of the flow field network is composed of four items:

[0013] L total =L eqns +αL b.c. +βL fdat +γL bdat .

[0014] Wherein L eqns represents the residual of the Navier-Stokes equation; L b.c. represents the loss of boundary conditions; L fdat represents the loss of flow field data; L bdat represents the loss of boundary data;

[0015] The to-be-trained parameters are updated by using a deep learning optimization algorithm, which includes but is not limited to Adam algorithm and stochastic gradient descent method;

[0016] The above training process is repeated, the batch data is regenerated and iterative training is performed until the preset number of training times or the difference between the total loss functions of adjacent two iterations is less than 10 -6 , the trained dual neural network is saved.

[0017] Preferably, the dynamic weight coefficients a, b and g are calculated, which specifically comprises: setting the dynamic weight coefficients a, b and g to balance the convergence speed of each item, so that each item converges at a similar rate. When the first iteration, epoch = 0, the weight coefficient is set to the default value 1; for the rest of the iterations, the dynamic weight coefficients are updated according to the following formula:

[0018] Wherein represents the gradient of the loss function with respect to the neural network parameters, which is calculated by automatic differentiation; represents the average of the absolute value.

[0019] Preferably, the dual neural network model is constructed according to the preset parameters, which specifically comprises:

[0020] The boundary network input is time t and boundary initial position output is the boundary at the previous time where Θ b.c. represent the parameters to be trained of the boundary network, and the boundary velocity is obtained by automatic differentiation technique to obtain the complete boundary condition

[0021] The flow field network adopts a physical neural network, responsible for the approximate solution of the flow field, (U, p) = F flow (t, X; Θ flow ). The input is time t and spatial coordinate X, and the output is the velocity field U and the pressure field p, where Θ flow represents the parameters to be trained of the flow field network.

[0022] Preferably, the calculation of each loss function and the total loss function includes:

[0023] The residual of the incompressible Navier-Stokes equation is calculated by automatic differentiation technique, the boundary network F b.c. and the flow field network L b.c. F flow The velocity on the moving boundary is equal, and the loss function L b.c. of the boundary condition is minimized:

[0024] where N b.c. represents the number of boundary points, and ‖·‖2 represents the two-norm;

[0025] The total loss function L total is minimized to obtain the optimal network parameters.

[0026] To achieve the above purpose, in the second aspect, a method for reconstructing a three-dimensional flow field includes:

[0027] A data acquisition module is configured to acquire moving boundary flow field data, the moving boundary flow field data including a velocity field and a moving boundary;

[0028] A training data generation module is configured to generate training data, the training data including velocity supervision data, boundary supervision data, and flow parameters, wherein the flow parameters at least include Reynolds number, characteristic length, and characteristic velocity;

[0029] A model construction module is configured to construct a double neural network model according to preset parameters, the double neural network model including a boundary network and a flow field network;

[0030] A data training module is configured to train the double neural network through the training data;

[0031] The prediction module is used to input the spatial coordinates of the point to be predicted, and the trained dual neural network outputs the pressure value of the point to predict the pressure field and boundary under the motion boundary conditions.

[0032] Preferably, the model building module is specifically used to:

[0033] Generate corresponding batch data according to the input data label and the batch size, wherein the batch data includes flow field supervision data, boundary supervision data, equation residual points, motion boundary residual points and fixed boundary conditions;

[0034] Calculate dynamic weight coefficients α, β and γ;

[0035] Calculate each loss function and the total loss function, and calculate the gradient of the total loss function with respect to the parameters to be trained based on automatic differentiation, where the total loss function of the flow field network consists of four terms:

[0036] L total =L eqns +αL b.c. +βL fdat +γL bdat .

[0037] Among them L eqns represents the residual of the Navier-Stokes equation; L b.c. Indicates the loss of boundary conditions; L fdat Indicates the loss of flow field data; L bdat Indicates the loss of boundary data;

[0038] Using a deep learning optimization algorithm to update the parameters to be trained, the optimization algorithm includes but is not limited to the Adam algorithm and the stochastic gradient descent method;

[0039] Repeat the above training process, regenerate the batch data and perform iterative training until the preset number of training times is met or the difference between the total loss function of two adjacent iterations is less than 10 -6 , then save the trained dual neural network.

[0040] Preferably, the calculation of the dynamic weight coefficients α, β, and γ specifically includes: setting the dynamic weight coefficients α, β, and γ to balance the convergence speed of each item so that each item converges at a similar rate, when epoch=0 in the first iteration, the weight coefficient is set to a default value of 1; for the remaining iterations, the dynamic weight coefficient is updated according to the following formula:

[0041] in Represents the gradient of the loss function with respect to the neural network parameters, which is calculated by automatic differentiation; Indicates taking the average of the absolute values.

[0042] Preferably, the model building module is specifically used to:

[0043] The border network The input is time t and the initial position of the boundary Output is the boundary of the previous moment Among them, Θ b.c. Represents the parameters to be trained of the boundary network, and the boundary velocity is obtained through automatic differentiation technology To obtain the complete boundary conditions

[0044] The flow field network adopts a physical neural network to be responsible for approximate solution of the flow field.

[0045] (U,p)=F flow (t,X;Θ flow The input of ) is time t and spatial coordinate X, and the output is velocity field U and pressure field p, where Θ flow Represents the parameters to be trained of the flow field network.

[0046] To achieve the above-mentioned purpose, in a third aspect, the present invention also relates to an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the above-mentioned method for reconstructing a moving boundary pressure field when executing the computer program.

[0047] To achieve the above-mentioned purpose, in a fourth aspect, the present invention further relates to a computer-readable storage medium, in which instructions are stored, and when the instructions are run, the above-mentioned method for reconstructing a moving boundary pressure field is executed.

[0048] The present invention relates to a method, system, device, and medium for reconstructing a moving boundary pressure field. Compared with the prior art, the present invention has the following beneficial effects:

[0049] In order to solve the problem of pressure reconstruction of the flow field under a moving boundary, the present invention proposes a moving boundary pressure field reconstruction technology based on a neural network. The main feature of this technology is that it contains two neural networks, one network is used to track the Lagrangian boundary points, called the boundary network; the other physical neural network is used to approximate the flow field, called the flow field network; the two are coupled through the boundary conditions of the moving boundary to realize the solution of the pressure field under the curved moving boundary. The network can optimize the boundary conditions and velocity field at the same time according to the physical laws, greatly reducing the impact of measurement errors on pressure reconstruction. In order to improve the convergence speed and stability of network training, we further propose a dynamic weight update strategy that takes into account the loss size and gradient at the same time. Compared with the traditional pressure field calculation method, the advantages of this algorithm are: 1) it can calculate the pressure under any boundary motion form; 2) it can optimize the velocity field and boundary conditions at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Method flow for a motion boundary pressure field reconstruction method in embodiment one of the present application Figure 1 ;

[0051] Figure 2 Method flow for a motion boundary pressure field reconstruction method in embodiment one of the present application Figure 2 ;

[0052] Figure 3 Double neural network framework for calculating a curved motion boundary pressure field in a motion boundary pressure field reconstruction method in embodiment one of the present application

[0053] Figure 4 Calculation result diagram of example one of a motion boundary pressure field reconstruction method in embodiment one of the present application

[0054] Figure 5 Calculation result diagram of example two of a motion boundary pressure field reconstruction method in embodiment one of the present application

[0055] Figure 6 Structure schematic diagram of a motion boundary pressure field reconstruction system in embodiment two of the present application

[0056] Figure 7 Structure schematic diagram of an electronic device in embodiment three of the present application. DETAILED DESCRIPTION

[0057] The present application will be further described below in conjunction with the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application. In addition, it should be noted that, for the convenience of description, only the parts related to the present application are shown in the drawings, but not all the structures.

[0058] Embodiment one

[0059] A motion boundary pressure field reconstruction method, please refer to Figures 1-5 For dynamic boundary pressure field reconstruction, the present application proposes a dynamic boundary pressure field reconstruction technology based on a double neural network model. The neural network is composed of a boundary network and a flow field network. The boundary neural network is responsible for tracking the motion of Lagrangian boundary points. The flow field network is a physical neural network, responsible for the constraint solution of Euler flow field. The two are coupled through the boundary condition, so as to realize the pressure field solution under the curved motion boundary.

[0060] The method comprises the following steps: S101 to S105.

[0061] S101 obtains motion boundary flow field data, which includes velocity field and motion boundary.

[0062] The velocity field can be obtained through PIV or particle tracking velocimetry (PTV) technology, and the motion boundary can be obtained by grayscale processing of the image; the velocity field and boundary can also be obtained by numerical simulation.

[0063] S102 generates training data, where the training data includes velocity supervision data, boundary supervision data, and flow parameters, wherein the flow parameters include at least Reynolds number, characteristic length, and characteristic velocity.

[0064] Among them, velocity supervision data and boundary supervision data are generally generated by randomly uniformly selecting points, and flow parameters include Reynolds number, characteristic length, characteristic velocity, etc.

[0065] S103 constructs a dual neural network model according to preset parameters, where the dual neural network model includes a boundary network and a flow field network.

[0066] Among them, the preset parameters include the number of network layers, the number of neurons in each layer, the type of activation function, the learning rate, and the spatial discrete form of the equation points.

[0067] In this embodiment, S103 constructs a dual neural network model according to preset parameters, specifically including:

[0068] Border Network The input is time t and the initial position of the boundary Output is the boundary of the previous moment Among them, Θ b.c. Represents the parameters to be trained of the boundary network, and the boundary velocity is obtained through automatic differentiation technology To obtain the complete boundary conditions

[0069] The flow field network uses a physical neural network to approximate the flow field, (U, p) = F flow (t,X;Θ flow The input of ) is time t and spatial coordinate X, and the output is velocity field U and pressure field p, where Θ flow Represents the parameters to be trained for the flow network. The calculated velocity and pressure fields must satisfy the incompressible Navier-Stokes equations so that the flow field satisfies the physical constraints. Minimizing this residual ensures that the flow field satisfies the physical constraints.

[0070] S104 trains the dual neural network using the training data. The generated speed and boundary supervision data and flow parameters are input into the neural network, and parameters such as the number of iterations and batch size are set to start training the network.

[0071] in, Figure 2 This is a complete flow chart of this step, and the specific process includes: S1041-S1045.

[0072] S1041 generates corresponding batch data according to the input data label and the batch size, and the batch data includes flow field supervision data, boundary supervision data, equation residual points, motion boundary residual points and fixed boundary conditions.

[0073] S1042 calculates dynamic weight coefficients α, β and γ.

[0074] Since it is a multi-objective optimization task, in order to ensure the convergence of the neural network, we need to set dynamic weight coefficients α, β and g to balance the convergence speed of each item, so that each item converges at a similar rate.

[0075] In this embodiment: dynamic weight coefficients α, β and γ balance the convergence speed of each item, so that each item converges at a similar rate, when the first iteration epoch = 0, the weight coefficient is set to the default value 1; the rest of the iterations. Wherein L eqns represents the residual of the Navier-Stokes equation, L b.c. represents the loss of the boundary condition L fdat , represents the loss of the flow field data; L bdat represents the loss of the boundary data.

[0076] In this embodiment, the dynamic weight coefficients are updated according to the following formula:

[0077] The dynamic weight coefficients in the present application are updated according to the above formula to obtain the best convergence performance, wherein represents the gradient of the loss function with respect to the neural network parameters, which is calculated by automatic differentiation; represents the average of the absolute value, and k+1 is the iteration number.

[0078] S1043 calculates each loss function and the total loss function, and calculates the gradient of the total loss function with respect to the training parameters according to automatic differentiation, wherein the total loss function of the flow field network is composed of four items:

[0079] L total = L eqns + αL b.c. + βL fdat + γL bdat . (1)

[0080] Wherein L eqns represents the residual of the Navier-Stokes equation, which is obtained by automatic differentiation; L b.c. represents the loss of the boundary condition, that is, the velocity of the flow field on the moving boundary should be equal to the boundary motion velocity; L b.c. represents the loss of the boundary condition, that is, the deviation between the velocity field measured by PIV and the velocity field predicted by the neural network.fdat represents the loss of flow field data; L bdat represents the loss of boundary data, i.e. the deviation of the measured boundary from the boundary predicted by the neural network.

[0081] In this embodiment, S1043 calculates each loss function and the total loss function, including:

[0082] The residual of the incompressible Navier-Stokes equation is calculated by automatic differentiation technology, and the boundary network F b.c. and the flow field network L b.c. F flow The loss function L b.c. of the boundary condition is minimized when the velocity on the moving boundary is equal.

[0083] where N b.c. represents the number of boundary points, and ‖·‖2 represents the two-norm; the total loss function L total is minimized to obtain the optimal network parameters.

[0084] S1044 updates the to-be-trained parameters using a deep learning optimization algorithm, which includes but is not limited to the Adam algorithm and the stochastic gradient descent method.

[0085] Although the boundary condition obtained in the experiment contains noise, it can be used as a kind of supervised data to guide the convergence direction of the neural network. At this point, we only need to input the corresponding measurement data, and the neural network can obtain the optimal network parameters by minimizing the total loss function L total , and then calculate the boundary condition, velocity field and pressure field through forward propagation.

[0086] S1045 repeats the above training process, regenerates batch data and iteratively trains until the preset number of training times or the difference between the total loss functions of adjacent two iterations is less than 10 -6 , the trained double neural network is saved.

[0087] S105 inputs the spatial coordinates of the to-be-predicted point, and the trained double neural network outputs the pressure value of the point to predict the pressure field and boundary under the moving boundary condition.

[0088] In order to better illustrate the present application, two examples are given below:

[0089] Example 1:

[0090] Step 1: Obtain the velocity field and boundary data of the flow field. In this embodiment, we use direct numerical simulation to generate the oscillating cylindrical flow field. The Reynolds number based on the cylinder diameter D is 185, the dimensionless velocity of the incoming flow is 1, and the dimensionless diameter of the cylinder is 1. The cylinder is located at (0,0) and oscillates periodically in the vertical y direction. The motion equation of the cylinder is y c =0.2sin(2πf c t), where y c is the position of the center of the cylinder, t is the dimensionless time, f c is the dimensionless frequency of the cylindrical oscillation, which is set to 0.156 in this embodiment. In order to simulate the PIV measurement results, we intercepted the flow field with -1D≤x≤3D, -1D≤y≤1D (x is the flow direction), the spatial spacing between vectors is 1 / 20, and the time interval is 0.05. In order to be closer to the actual situation, we added Gaussian white noise to the velocity field. The intensity of Gaussian white noise is defined as the ratio of the noise amplitude to the velocity field amplitude, and σ is used. n In this embodiment, the noise intensity σ is added n =8%.

[0091] Step 2: Generate velocity supervision data, boundary supervision data and flow parameters. 1×10 6 data points, 0.5×10 6 boundary data points, 1×10 6 equation points, 1×10 6 It should be noted that the generated data does not include the pressure field.

[0092] Step 3: Construct a dual network model based on the preset parameters. In this embodiment, the boundary network contains 9 hidden layers, each with 32 neurons; the flow field network contains 13 hidden layers, each with 128 neurons. A total of 207,707 unknown parameters are generated. The initial learning rate is 5×10 -3 , with a step-wise decay, and the learning rate for the last 2000 epochs is set to 1×10 -5 .

[0093] Step 4: Input the generated training data into the neural network. The network epoch is set to 4000, each epoch is iterated 30 times, and the batch size is 10000.

[0094] Step 5: Calculate the dynamic weight coefficients α, β, and γ. In the first iteration (epoch = 0), the weight coefficients are set to the default value of 1; in the remaining iterations, the dynamic weight coefficients are calculated according to formula (2).

[0095] Step six: Calculate each loss function and total loss function according to formula (1), and calculate the gradient of the total loss function with respect to the training parameters according to automatic differentiation.

[0096] Step seven: Update the training parameters using a deep learning optimization algorithm. In this embodiment, the Adam algorithm is used to update the parameters.

[0097] Step eight: Repeat steps five to seven until 4000 epochs are completed, and save the network.

[0098] Step nine: Predict the pressure field and boundary under the motion boundary. In this embodiment, the prediction grid space interval is set to 0.01, and the time interval is set to 0.05. The final predicted pressure field is shown in Figure 4 . The error between the predicted result and the original pressure field is less than 4%.

[0099] Example two:

[0100] Test the performance of the application by fish swimming flow field, the specific steps are as follows:

[0101] Step one: Obtain the velocity field and boundary data of the flow field. In this embodiment, we use direct numerical simulation to generate the fish swimming flow field. The fish body is replaced by a NACA0012 airfoil, the head is located at the position (0, 0), and the head makes a wave-like swing in the vertical y direction. The Reynolds number based on the length L of the fish body is 1x10 4 , the incoming flow velocity is 0.1 m / s, the length L of the fish body is 0.1 m, the swing wavelength is equal to L, and the swing frequency is 2 Hz. In order to simulate the PIV measurement results, we intercept the flow field of -0.3≤x / L≤1.3, -0.3≤y / L≤0.3 (x is the flow direction), the spatial interval between vectors is L / 400, and the time interval is 2 times the direct numerical simulation interval, i.e. 2dt. In this embodiment, no Gaussian white noise is added.

[0102] Step two: Generate velocity supervision data, boundary supervision data, and flow parameters. From 300 numerical simulation velocity fields, we randomly and uniformly generated 2x10 6 data points, 1x10 6 boundary data points, 2x10 6 equation points, and 1x10 6 boundary condition points. It should be noted that the generated data does not include the pressure field.

[0103] Step three: Construct a double network model according to the preset parameters. In this embodiment, the boundary network contains 9 hidden layers, each containing 48 neurons; the flow field network contains 13 hidden layers, each containing 150 neurons. A total of 291,981 unknown parameters are formed. The initial learning rate is 5x10 -3, the learning rate is set to 1 x 10 -5 .

[0104] Step four: input the generated training data into the neural network. The network epoch is set to 18000, each epoch iteration is 30 times, and the batch size is 10000.

[0105] Step five: calculate the dynamic weight coefficients a, b and g. When the first iteration (epoch = 0), the weight coefficient is set to the default value 1; for the rest of the iterations, the dynamic weight coefficient is calculated according to formula (2).

[0106] Step six: calculate each loss function and the total loss function according to formula (1), and calculate the gradient of the total loss function with respect to the parameters to be trained according to automatic differentiation;

[0107] Step seven: update the parameters to be trained using a deep learning optimization algorithm. In this embodiment, the Adam algorithm is used to update the parameters.

[0108] Step eight: repeat steps five to seven until 18000 epochs are completed, and save the network.

[0109] Step nine: predict the pressure field and boundary under the motion boundary. In this embodiment, the prediction grid space interval is set to L / 400, and the time interval is 2dt. The final predicted pressure field is shown in Figure 5 The error between the predicted result and the original pressure field is less than 20%.

[0110] Embodiment two

[0111] A motion boundary pressure field reconstruction system, please refer to Figure 6 , comprising a data acquisition module 61, a training data generation module 62, a model construction module 63, a data training module 64 and a prediction module 65.

[0112] The data acquisition module 61 is used for acquiring motion boundary flow field data, and the motion boundary flow field data includes velocity field and motion boundary;

[0113] The training data generation module 62 is used for generating training data, and the training data includes velocity supervision data, boundary supervision data and flow parameters, wherein the flow parameters at least include Reynolds number, characteristic length and characteristic velocity;

[0114] The model construction module 63 is used for constructing a double neural network model according to a preset parameter, and the double neural network model includes a boundary network and a flow field network;

[0115] The data training module 64 is used for training the double neural network through the training data;

[0116] The prediction module 65 is configured to input the spatial coordinates of a to-be-predicted point, and the trained dual neural network outputs a pressure value of the point to predict the pressure field and the boundary under the motion boundary condition.

[0117] In some embodiments, the data training module 64 is specifically configured to:

[0118] generate corresponding batch data according to the input data label and the batch size, the batch data including flow field supervision data, boundary supervision data, equation residual points, motion boundary residual points, and fixed boundary conditions;

[0119] calculate dynamic weight coefficients a, b, and g;

[0120] calculate each loss function and a total loss function, and calculate the gradient of the total loss function with respect to the to-be-trained parameters according to automatic differentiation, wherein the total loss function of the flow field network is composed of four items:

[0121] L total = L eqns + aL b.c. + bL fdat + gL bdat .

[0122] wherein L eqns represents the residual of the Navier-Stokes equation; L b.c. represents the loss of the boundary condition; L fdat represents the loss of the flow field data; and L bdat represents the loss of the boundary data.

[0123] update the to-be-trained parameters by using a deep learning optimization algorithm, which includes but is not limited to the Adam algorithm and the stochastic gradient descent method;

[0124] repeat the above training process, regenerate the batch data and perform iterative training until the preset number of training times or the difference between the total loss functions of adjacent two iterations is less than 10 -6 , and save the trained dual neural network.

[0125] In some embodiments, the data training module 64 calculates the dynamic weight coefficients a, b, and g, and specifically includes: dynamically setting the weight coefficients a, b, and g to balance the convergence rates of each item, so that each item converges at a similar rate. When the first iteration is performed, epoch = 0, and the weight coefficients are set to the default value 1. For the remaining iterations, the dynamic weight coefficients are updated according to the following formula:

[0126] wherein represents the gradient of the loss function with respect to the neural network parameters, which is calculated by automatic differentiation; represents the average of the absolute value.

[0127] In some embodiments, the model construction module 63 is specifically configured to:

[0128] Boundary network The input is time t and the initial position of the boundary The output is the boundary at the previous time Where, Θ b.c. represents the to-be-trained parameters of the boundary network, and the boundary velocity is obtained through automatic differentiation technology to obtain the complete boundary condition

[0129] The flow field network adopts a physical neural network, which is responsible for the approximate solution of the flow field, (U, p) = F flow (t, X; Θ flow ). The input is time t and spatial coordinates X, and the output is the velocity field U and the pressure field p, wherein, Θ flow represents the to-be-trained parameters of the flow field network.

[0130] The motion boundary pressure field reconstruction system of the embodiment has the same implementation process, method and effect as the motion boundary pressure field reconstruction method described in Embodiment One, and will not be repeated here.

[0131] Embodiment Three

[0132] As shown in Figure 7 , the embodiment relates to an electronic device including at least one processor and a memory connected in communication with the at least one processor. The memory stores a computer program executable by the at least one processor. The computer program is executed by the at least one processor to enable the at least one processor to perform the motion boundary pressure field reconstruction method of Embodiment One, and achieve the corresponding beneficial effects of the motion boundary pressure field reconstruction method, which will not be repeated here. The electronic device provided by the embodiment can be a personal computer, such as a desktop computer, an all-in-one computer, a notebook computer, a tablet computer, etc. It can also be a terminal device such as a mobile phone, a wearable device, a palm computer, etc. The electronic device is only an example and should not limit the function and use range of the embodiments of the present application.

[0133] The components of the electronic device 3 can include but are not limited to the at least one processor 4 described above, the at least one memory 5 described above, and a bus 6 connecting different system components including the memory 5 and the processor 4.

[0134] The bus 6 includes a data bus, an address bus, and a control bus.

[0135] The memory 5 can include volatile memory, such as random access memory (RAM) 51 and / or cache memory 52, and / or non-volatile memory, such as read only memory (ROM) 53.

[0136] The memory 5 can also include a program / utility 55 having a set (at least one) of program modules 54, including but not limited to an operating system, one or more application programs, other program modules, and program data, each of which or a combination thereof, can include implementation of a network environment.

[0137] The processor 4, through running the computer program stored in the memory 5, executes various function applications and data processing, such as the above-mentioned motion boundary pressure field reconstruction method.

[0138] The electronic device 3 can also communicate with one or more external devices 7, such as a keyboard, a pointing device, etc. through an input / output (I / O) interface 8. Also, the electronic device 3 can communicate with one or more networks, such as a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet, through a network adapter 9. As Figure 5 illustrated, the network adapter 9 communicates with the other modules of the electronic device 3 through the bus 6. It should be appreciated that the network adapter 9 can be Figure 5 implemented by a plurality of network adapters. Also, other hardware and / or software modules can be used in conjunction with the electronic device 3, such as a microcode, a device driver, a redundant processor, an external disk drive array, a RAID (Redundant Array of Independent Disks) system, a tape drive, and a data backup storage system, etc. which are not shown in the figure.

[0139] It should be noted that although several units / modules or sub-units / modules of the electronic device are mentioned in the above detailed description, such division is merely exemplary and not mandatory. In fact, according to the embodiments of the present application, the features and functions of two or more units / modules described above can be embodied in one unit / module. Conversely, the features and functions of one unit / module described above can be further divided into a plurality of units / modules.

[0140] Embodiment Four

[0141] The present application relates to a computer readable storage medium, the storage medium stores instructions, the instructions run to implement the motion boundary pressure field reconstruction method of embodiment one, the run implementation process method and effect are the same as the motion boundary pressure field reconstruction method described in embodiment one, and will not be repeated here.

[0142] It should be noted that, in the present document, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element preceded by "comprises a" does not, without more constraints, foreclose the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0143] The above merely describes the preferred embodiments of the present application, and is not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation, or direct or indirect application in other related technical fields, made by using the content of the present application specification and drawings, are also included in the patent protection scope of the present application.

Claims

1. A method for reconstructing a moving boundary pressure field, characterized in that: It is used to reconstruct the dynamic boundary pressure field of the fish swimming surface. The flow field of the fish swimming is generated by direct numerical simulation. The fish body is replaced by a NACA0012 airfoil. The head is located at (0,0) and oscillates in a wave-like manner in the vertical y direction. The following are the results: Acquiring motion boundary flow field data, wherein the motion boundary flow field data includes a velocity field and a motion boundary; Generating training data, the training data including velocity supervision data, boundary supervision data, and flow parameters, wherein the flow parameters include at least a Reynolds number of the fish body length, a characteristic length, and a characteristic velocity, wherein the characteristic velocity is the incoming flow velocity and the characteristic length is the swing wavelength; Constructing a dual neural network model according to preset parameters, wherein the dual neural network model includes a boundary network and a flow field network; Training the dual neural network using the training data; The spatial coordinates of the point to be predicted are input, and the trained dual neural network outputs the corresponding pressure value of the point to predict the pressure field and boundary under the motion boundary condition; The dual neural network is trained using the training data, including: generating corresponding batch data according to input data labels and batch size, wherein the batch data includes flow field supervision data, boundary supervision data, equation residual points, motion boundary residual points, and fixed boundary conditions; calculating dynamic weight coefficients α, β, and γ; calculating various loss functions and a total loss function, and calculating the gradient of the total loss function with respect to the parameters to be trained according to automatic differentiation, wherein the total loss function of the flow field network is composed of four items: L total =L eqns +αL b.c. +βL fdat +γL bdat . Among them L eqns represents the residual of the Navier-Stokes equation; L b.c. Indicates the loss of boundary conditions; L fdat Indicates the loss of flow field data; L bdat represents the loss of boundary data; update the parameters to be trained using a deep learning optimization algorithm, which includes but is not limited to the Adam algorithm and the stochastic gradient descent method; repeat the above training process, regenerate the batch data and perform iterative training until the preset number of training times is met or the difference between two consecutive iterations of the total loss function is less than 10 -6 , then save the trained dual neural network; The dual neural network model is constructed according to the preset parameters, specifically including: the boundary network The input is time t and the initial position of the boundary Output is the boundary of the previous moment Among them, Θ b.c. Represents the parameters to be trained of the boundary network, and the boundary velocity is obtained through automatic differentiation technology To obtain the complete boundary conditions The flow field network adopts a physical neural network to solve the approximate flow field, (U, p) = F flow (t,X;Θ flow The input of ) is time t and spatial coordinate X, and the output is velocity field U and pressure field p, where Θ flow Represents the parameters to be trained of the flow field network.

2. A moving boundary pressure field reconstruction method according to claim 1, characterized in that: The calculation of the dynamic weight coefficients α, β, and γ specifically includes: setting the dynamic weight coefficients α, β, and γ to balance the convergence speed of each item so that each item converges at a similar rate. When epoch=0 for the first iteration, the weight coefficient is set to a default value of 1; for the remaining iterations, the dynamic weight coefficient is updated according to the following formula: in Represents the gradient of the loss function with respect to the neural network parameters, which is calculated by automatic differentiation; It means taking the average of the absolute values, and k+1 is the number of iterations.

3. The method for reconstructing a moving boundary pressure field according to claim 1, characterized in that: The calculation of each loss function and the total loss function includes: The residuals of the incompressible Navier-Stokes equations are calculated by automatic differentiation techniques, and the boundary network F b.c. and flow field network L b.c. F flow The speed on the moving boundary is equal, so the loss function L of the boundary condition is minimized b.c. : where N b.c. represents the number of boundary points, ‖·‖2 represents the two-norm; minimize the total loss function L total Get the optimal network parameters.

4. A moving boundary pressure field reconstruction system, characterized in that: It is used to reconstruct the dynamic boundary pressure field of the fish swimming surface. The flow field of the fish swimming is generated by direct numerical simulation. The fish body is replaced by a NACA0012 airfoil. The head is located at (0,0) and oscillates in a wave-like manner in the vertical y direction. The following are the results: A data acquisition module, configured to acquire motion boundary flow field data, wherein the motion boundary flow field data includes a velocity field and a motion boundary; A training data generation module is used to generate training data, wherein the training data includes speed supervision data, boundary supervision data, and flow parameters, wherein the flow parameters include at least the Reynolds number of the fish body length, the characteristic length, and the characteristic speed, wherein the characteristic speed is the incoming flow speed and the characteristic length is the swing wavelength; A model building module, configured to build a dual neural network model according to preset parameters, wherein the dual neural network model includes a boundary network and a flow field network; A data training module, configured to train the dual neural network using the training data; A prediction module, which is used to input the spatial coordinates of the point to be predicted, and the trained dual neural network outputs the pressure value of the point to predict the pressure field and boundary under the motion boundary condition; The model building module is specifically used to: Generate corresponding batch data according to the input data label and batch size, wherein the batch data includes flow field supervision data, boundary supervision data, equation residual points, motion boundary residual points, and fixed boundary conditions; calculate dynamic weight coefficients α, β, and γ; calculate various loss functions and the total loss function, and calculate the gradient of the total loss function with respect to the parameters to be trained by automatic differentiation, wherein the total loss function of the flow field network is composed of four terms: L total =L eqns +αL b.c. +βL fdat +γL bdat ., where L eqns represents the residual of the Navier-Stokes equation; L b.c. Indicates the loss of boundary conditions; L fdat Indicates the loss of flow field data; L bdat represents the loss of boundary data; update the parameters to be trained using a deep learning optimization algorithm, which includes but is not limited to the Adam algorithm and the stochastic gradient descent method; repeat the above training process, regenerate the batch data and perform iterative training until the preset number of training times is met or the difference between the total loss function of two adjacent iterations is less than 10 -6 , then save the trained dual neural network; The model building module is specifically used to: The border network The input is time t and the initial position of the boundary Output is the boundary of the previous moment Among them, Θ b.c. Represents the parameters to be trained of the boundary network, and the boundary velocity is obtained through automatic differentiation technology To obtain the complete boundary conditions The flow field network adopts a physical neural network to solve the approximate flow field, (U, p) = F flow (t,X;Θ flow The input of ) is time t and spatial coordinate X, and the output is velocity field U and pressure field p, where Θ flow Represents the parameters to be trained of the flow field network.

5. A moving boundary pressure field reconstruction system according to claim 4, characterized in that: The calculation of the dynamic weight coefficients α, β, and γ specifically includes: setting the dynamic weight coefficients α, β, and γ to balance the convergence speed of each item so that each item converges at a similar rate. When epoch=0 for the first iteration, the weight coefficient is set to a default value of 1; for the remaining iterations, the dynamic weight coefficient is updated according to the following formula: in Represents the gradient of the loss function with respect to the neural network parameters, which is calculated by automatic differentiation; It means taking the average of the absolute values, and k+1 is the number of iterations.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, a moving boundary pressure field reconstruction method according to any one of claims 1 to 3 is implemented.

7. A computer-readable storage medium, characterized in that: The storage medium stores instructions, which, when executed, execute a moving boundary pressure field reconstruction method according to any one of claims 1 to 3.

Images