A three-dimensional sparse velocity field encryption method, device and storage medium

Abstract

The application discloses a three-dimensional sparse velocity field encryption method and device and a storage medium, and the method comprises the following steps: extracting a three-dimensional sparse velocity field from cross-correlation calculation, and preprocessing to determine the encryption position coordinates. Then, according to the principle of light field PIV, the three-dimensional experimental velocity data is sliced into a two-dimensional flow field, input into a fully connected layer neural network for training, and the corresponding neural network weight is obtained. In addition, by calculating the residual of Navier-Stokes equation and incorporating it into the loss function, the neural network is physically constrained to verify whether the network meets the physical equation and reaches the preset convergence value. Finally, the predicted velocity component and the corresponding encryption position are output. The application is suitable for post-processing encryption prediction of single-camera light field PIV technology, can effectively avoid the adverse effects caused by complex factors such as bad values, noise, stretching effect and spatial filtering effect, and is helpful to improve the spatial resolution of three-dimensional flow field measurement.

Description

Technical Field

[0001] This invention relates to the fields of flow measurement and artificial intelligence, specifically a method, device, and storage medium for encrypting a three-dimensional sparse velocity field. Background Technology

[0002] Complex flows exist within compressors, turbines, and other components, making the improvement of the internal flow field crucial for high-performance engine design. Developing advanced three-dimensional flow field measurement techniques to improve quantitative velocity measurement accuracy facilitates the optimization of flow channel structures and enhances overall engine performance. Particle image velocimetry (PIV), based on optical field imaging, is a single-camera three-dimensional flow field testing technique developed in recent years. Its advantages include reduced requirements for the optical window of the measurement environment and avoidance of complex multi-camera system calibration, thus expanding its application range. However, single-camera optical field PIV suffers from a significant problem: low spatial resolution in flow field measurement. This is primarily due to limitations in post-processing algorithms and the presence of noise and out-of-range values ​​in the experimental data itself. Traditional post-processing algorithms mainly include reconstruction and cross-correlation calculations. The stretching effect introduced by reconstruction algorithms reduces the accuracy of velocity field calculations, resulting in a spatial resolution typically above 2mm × 2mm × 2mm. Cross-correlation algorithms exhibit spatial averaging effects, only calculating the average velocity within a suitable window and unable to calculate the instantaneous velocity at arbitrary locations. The spatial resolution limitations of optical field PIV are particularly pronounced when analyzing the fine structural features of complex flows. To address the complex impact of traditional post-processing algorithms and noise-related outliers, it is necessary to consider adding a post-processing encryption method after obtaining the sparse velocity field through cross-correlation calculation to improve the overall spatial resolution.

[0003] With the development of intelligent-enabled fluid mechanics, new post-processing methods can be adopted in two ways: firstly, traditional data assimilation algorithms, such as ensemble Kalman filtering or intrinsic orthogonal decomposition, can be used; secondly, pure neural networks can be employed as a primary approach to improve spatial resolution. Unlike traditional data assimilation, which relies entirely on the physical framework and lacks experimental realism, neural networks rely on experimental data to extract feature information from the real flow field, inductively learn, and make the prediction results more consistent with the actual flow field. However, neural networks relying entirely on experimental data can lead to a "black box" problem, meaning it is difficult to extract reliable physical information from the data, making the prediction results potentially only consistent with the observation data and not with physical laws. Noise and outliers in the experimental data itself can also affect the generalization ability of the model. Post-processing encryption methods that conform to single-camera light field PIV technology should consider the actual situation of both some data and some physical laws. Summary of the Invention

[0004] To address the shortcomings of the existing methods, this invention provides a three-dimensional sparse velocity field encryption method using high spatial resolution single-camera light field PIV technology.

[0005] The solution to the technical problem of this invention is:

[0006] This invention first provides a three-dimensional sparse velocity field encryption method, comprising:

[0007] A cryptographic model is constructed and trained. The input to the cryptographic model is a three-dimensional sparse velocity field obtained from cross-correlation calculations, and the output of the prediction model is the three-dimensional cryptographic velocity field. The activation function and loss function of the cryptographic model are as follows:

[0008] The activation function uses an adaptive swish function, expressed as:

[0009]

[0010] In the formula, β is a trainable parameter and n is a scaling factor;

[0011] The total loss function L is expressed as:

[0012] L = L data +αL eqns

[0013] Among them, L data The loss function for data prediction; L eqns The loss function is defined by the physical equation constraints, and α is the weighting coefficient.

[0014]

[0015] In the formula, N u N represents the number of velocity components u in the mainstream direction, where the subscript u represents the velocity component in the mainstream direction; v N represents the number of velocity components v perpendicular to the mainstream direction, where the subscript v represents the velocity component perpendicular to the mainstream direction; eqns This indicates the number of observation points used in the calculation of the Navier-Stokes equations; the subscript eqns represents the Navier-Stokes equations. data (X i , t i (x) represents the position X i and time t i The corresponding known mainstream velocity component, X i =(x i y i ) represents numbers from 1 to N u The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the i-th position in the traversal i Representing numbers from 1 to N u The i-th time of the traversal; v data (X j , t j (x) represents the position X j and time t jThe corresponding known velocity component perpendicular to the main flow direction, X j =(x j y j ) represents numbers from 1 to N v The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the j-th position during traversal i Representing numbers from 1 to N u The i-th time of the traversal; u pred (X i , t i (x) represents the position X i and time t i The corresponding neural network predicts the mainstream direction velocity component, X. i =(x i y i ) represents numbers from 1 to N u The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the i-th position in the traversal i Representing numbers from 1 to N u The i-th time of the traversal; v pred (X j , t j (x) represents the position X j and time t j The corresponding neural network predicts the velocity component perpendicular to the mainstream direction, X. j =(x j y j ) represents numbers from 1 to N v The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the j-th position during traversal i Representing numbers from 1 to N u The i-th time of the traversal; e k (X m , t m (x) represents the position X m and time t m Next, calculate the residual of the k-th physical equation, where k ranges from 1 to 3, representing the residuals of the three physical equations, X. m =(x m y m ) represents numbers from 1 to N eqns The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the m-th position during traversal m Representing numbers from 1 to N eqns The i-th time point during the traversal;

[0016] Determine the coordinates of the locations in the 3D sparse velocity field that need to be encrypted; input the coordinates of the locations to be encrypted into the encryption model, and predict the velocity components of the corresponding encryption locations based on the weights.

[0017] The present invention also provides an electronic device, comprising:

[0018] One or more processors;

[0019] Memory, used to store one or more programs;

[0020] When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of a three-dimensional sparse velocity field encryption method as described in any one of claims 1-6.

[0021] A storage medium storing a computer program that, when executed by a processor, implements the aforementioned three-dimensional sparse velocity field encryption method.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] (1) Based on the actual situation of single-camera light field PIV technology, and in response to the complex influences that lead to limited spatial resolution of the obtained flow field, including bad values, noise, stretching effect and spatial filtering effect, this invention adds a third post-processing encryption method in post-processing as a comprehensive step to solve the complex influences and improve spatial resolution.

[0024] (2) The present invention establishes a prediction model based on the principle of single-camera light field PIV image acquisition, and uses experimental data of single-camera light field PIV post-processing for training, testing and prediction, so that the model has practical significance for improving the spatial resolution of single-camera light field PIV. Attached Figure Description

[0025] Figure 1 Schematic diagram of a high-resolution optical field PIV post-processing system;

[0026] Figure 2 A diagram of the physical information neural network structure based on the Navier-Stokes equations;

[0027] Figure 3 The xy-plane flow field vector diagram of the flow around a cylinder at a flow rate of 98 L / h obtained by cross-correlation calculation;

[0028] Figure 4 The vector diagram of the flow field in the xy plane around a cylinder with a flow rate of 98 L / h, obtained for precision prediction. Detailed Implementation

[0029] The present invention will now be described in detail with reference to the accompanying drawings. The present invention includes, but is not limited to, the following examples:

[0030] This invention provides a post-processing encryption method for high spatial resolution single-camera light field PIV technology, located in the third step after cross-correlation calculation, such as... Figure 1 As shown, the implementation steps are as follows:

[0031] (1) Flow field data preprocessing: Extract the three-dimensional flow field (t, x, y, u, v) obtained from cross-correlation calculation, where t, x, y, u, v represent time, position component in the mainstream direction, position component perpendicular to the mainstream direction, velocity component in the mainstream direction, and velocity component perpendicular to the mainstream direction, respectively. 80% of this data is used as training data for the neural network, and 20% is used as test data. The corresponding (t, x, y) data is used as known data for calculating the residuals of the Navier-Stokes equations, such as... Figure 1 The three-dimensional sparse velocity field is extracted from cross-correlation calculations. Due to the constraints of the Navier-Stokes equations, the input data must satisfy the conditions of the Navier-Stokes equations. This includes time, velocity components, and their corresponding position components. The time in the steady-state flow field is a constant value, while the time in the transient flow field is a continuously changing value. The velocity components and their corresponding position components are extracted based on the principle of optical field PIV (Pilot-In-Video). Optical field PIV involves sequentially acquiring flow field information on the same plane at different depths to obtain two-dimensional optical field images at different depths. Figure 1 As shown, a reconstruction algorithm integrates a two-dimensional light field image into a three-dimensional spatial distribution, and cross-correlation calculations are performed to obtain a sparse velocity field, such as... Figure 3 The image shows the sparse velocity field in the xy plane of the flow around a cylinder, obtained by optical field PIV. Based on depth, the sparse velocity field can be independently divided into two-dimensional flow field information for different planes. The two-dimensional flow fields corresponding to all depths are then predicted sequentially.

[0032] (2) Setting physical equation constraints for the model: Each training iteration is constrained by the residuals of the physical equations until the loss function meets the convergence value. The Navier-Stokes equations (NS equations) and the continuity equation, which describe two-dimensional fluid motion, are used as prior physical information and embedded into the loss function of the residual neural network in the form of partial differential equations. The residual terms corresponding to the NS equations can be expressed as equations e1 and e2, and the residual terms corresponding to the continuity equation can be expressed as equation e3.

[0033]

[0034] e3 = u x +v y

[0035] In the formula, U represents the resultant velocity vector, U=(u,v), u represents the velocity component in the mainstream direction, and v represents the velocity component perpendicular to the mainstream direction; Represents the gradient operator in spatial coordinates. It is a vector differential operator representing the convection term in the Navier-Stokes equations. Indicates the sign of the partial derivative. This indicates taking the partial derivative with respect to the x-direction. This represents taking the partial derivative with respect to the y-direction. The first-order partial derivative of the velocity component u with respect to the x-direction describes the rate of change of the function with respect to the x-direction. Re represents the first-order partial derivative of the velocity component v with respect to the y-direction, describing the rate of change of the function with respect to the y-direction; Re represents the Reynolds number of the flow; u t Let u be the derivative of the u component with respect to time t; x Let u be the derivative of the u component with respect to the x component; v t v is the derivative of the v component with respect to time t; y p is the derivative of the v component with respect to the y component. t p is the derivative of the pressure component p with respect to time t; x Let p be the derivative of the p component with respect to the x component; p y is the derivative of the p component with respect to the y component; It's the Laplacian operator, it's the gradient. The divergence is expressed as Multiplying by the velocity component represents the viscous term in the Navier-Stokes equations; This represents the second partial derivative of the velocity component u with respect to the x-direction, measuring the rate of change of velocity in the x-direction. It represents the second partial derivative of the velocity component u with respect to the y-direction, and measures the rate of change of velocity in the y-direction; This represents the second partial derivative of the velocity component v with respect to the x-direction, measuring the rate of change of velocity in the x-direction. It represents the second partial derivative of the velocity component v with respect to the y-direction, and measures the rate of change of velocity in the y-direction; and For partial derivative terms in neural networks and The calculation is based on the chain rule and uses an automatic difference method.

[0036] The loss function is based on the data prediction L data and physical equation constraints L eqns Composition. v pred and u pred These are the mainstream velocity component and the perpendicular-mainstream velocity component predicted by the neural network based on position X and time t, respectively. data and u data These are the velocity components along the main direction and the velocity components perpendicular to the main direction, which are known from the neural network training set. The loss function L for data prediction is... data It calculates the average of the sum of squared differences between the predicted and known velocity components at all the same location and time, and then sums the calculations for the two velocity components. The loss function L is constrained by the physical equations. eqnsIt calculates the average of the sum of squares of the three residuals at all the same location and time, and then sums the three residuals together.

[0037]

[0038] L = L data +αL eqns

[0039] In the formula, N u N represents the number of velocity components u in the mainstream direction, where the subscript u represents the velocity component in the mainstream direction; v This indicates the number of velocity components v perpendicular to the mainstream direction. The subscript v represents the velocity component perpendicular to the mainstream direction. Generally, N u =N v N eqns This indicates the number of observation points used in the calculation of the Navier-Stokes equations; the subscript eqns represents the Navier-Stokes equations. data (X i , t i (x) represents the position X i and time t i The corresponding known mainstream velocity component, X i =(x i y i ) represents numbers from 1 to N u The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the i-th position in the traversal i Representing numbers from 1 to N u The i-th time of the traversal; v data (X j , t j (x) represents the position X j and time t j The corresponding known velocity component perpendicular to the main flow direction, X j =(x j y j ) represents numbers from 1 to N v The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the j-th position during traversal i Representing numbers from 1 to N u The i-th time of the traversal; u pred (X i , t i (x) represents the position X i and time t i The corresponding neural network predicts the mainstream direction velocity component, X. i =(x i y i ) represents numbers from 1 to N uThe mainstream direction position component x and the perpendicular mainstream direction position component y, t of the i-th position in the traversal i Representing numbers from 1 to N u The i-th time of the traversal; v pred (X j , t j (x) represents the position X j and time t j The corresponding neural network predicts the velocity component perpendicular to the mainstream direction, X. j =(x j y j ) represents numbers from 1 to N v The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the j-th position during traversal i Representing numbers from 1 to N u The i-th time of the traversal; e k (X m , t m (x) represents the position X m and time t m Next, calculate the residual of the k-th physical equation, where k ranges from 1 to 3, representing the residuals of the three physical equations, X. m =(x m y m ) represents numbers from 1 to N eqns The mainstream direction position component x and the perpendicular mainstream direction position component y, t of the m-th position during traversal m Representing numbers from 1 to N eqns The i-th time step in the traversal. α represents the residual weight of the loss function, typically chosen as 1, indicating that the weights of the loss function for data prediction and the loss function constrained by the Navier-Stokes equations are consistent. This completes the construction of a high-resolution velocity field prediction model using a physical information neural network, such as... Figure 2 As shown. By Figure 2 It can be seen that by putting position and time into a fully connected neural network to predict velocity and pressure, the predicted velocity and known velocity are used to calculate the loss function term, the residual terms of the Navier-Stokes equation and the continuity equation are calculated based on the predicted velocity and pressure to obtain the physical constraint loss function term, and the two loss function terms are combined into the total loss function according to the weight α.

[0040] (3) Set the neural network parameters of the model: Use a pure neural network with fully connected layers, 7 layers, and 64 neurons in each layer. Pre-set the convergence value of the loss function. If the total loss function calculated from the speed predicted by the test set does not reach the convergence value after one training cycle, update the neural network parameters, retrain, until the loss function converges, terminate the loop, save the neural network parameters, and perform encrypted prediction.

[0041] The neural network uses an adaptive momentum estimation Adam optimizer to train and update its parameters. The activation function of the neural network is an adaptive swish function. This is represented as...

[0042]

[0043] In the formula, β is the trainable parameter, n is the scaling factor, and a = nβ. Without the scaling factor n, the adaptive parameter a will slowly converge to the optimal value due to the small learning rate. n ≥ 1 can accelerate the convergence process to find the optimal a. Therefore, the scaling factor n is set to 10, and the initial value of β is set to 0.1.

[0044] (4) Training process: The entire training process involves changing the slice depth four times, predicting and integrating the output of the corresponding slices in a loop. Assume that the dimensions of the u, v, and w components obtained from the cross-correlation calculation are all m×k×n;

[0045] First, the three-dimensional experimental data is sliced ​​according to depth z to obtain the corresponding xy-plane flow field as a two-dimensional training set. The u' and v' components are predicted, and the integrated and encrypted dimension is 2m×2k×n. Among them, in the xy-plane, x is the position component in the mainstream direction, y is the position component perpendicular to the mainstream direction, u' is the velocity component in the mainstream direction in the xy-plane, and v' is the velocity component perpendicular to the mainstream direction in the xy-plane.

[0046] Then, x is sliced ​​as depth to obtain the corresponding yz plane flow field, and v' and w' components are predicted. The encryption dimension is 2m×k×2n. In the yz plane, y is the position component in the mainstream direction, z is the position component perpendicular to the mainstream direction, v' is the velocity component in the mainstream direction in the yz plane, and w' is the velocity component perpendicular to the mainstream direction in the yz plane.

[0047] Next, from the encrypted velocity components, the u” and w” components are encrypted in the xz plane with a y depth of 2m, and integrated to obtain an encryption dimension of 2m×2k×2n. In the xz plane, x represents the position component in the mainstream direction, z represents the position component perpendicular to the mainstream direction, u” represents the velocity component in the mainstream direction in the xz plane, and w” represents the velocity component perpendicular to the mainstream direction in the xz plane.

[0048] Finally, from the encrypted velocity components, the u” and v” components are encrypted in the xy plane at a z depth of 2n. Integrating the three predicted velocity components yields a new encryption dimension of 2m×2k×2n. In the xy plane, x represents the position component in the mainstream direction, y represents the position component perpendicular to the mainstream direction, u” represents the velocity component in the mainstream direction in the xy plane, and y” represents the velocity component perpendicular to the mainstream direction in the xy plane.

[0049] Based on a four-step two-dimensional encryption method, an eight-fold encrypted prediction of the cross-correlation velocity field is achieved. Figure 4 It can be seen that it is caused by Figure 3 The xy-plane flow field of the cylinder obtained as a refined prediction of the original flow field. Figure 3 and Figure 4 A distinct vortex can be seen in the area circled in the lower middle part. Figure 3 The right side of the center (circled above) shows a tendency for the presence of a vortex, but due to limited resolution, the entire vortex cannot be accurately captured. Figure 4 At the same location on the right side of the middle (circled above), a distinct vortex can be seen, which is consistent with the principle that alternating vortices are generated when a cylinder flows around it. Figure 3 and Figure 4 The comparison shows that the model of the present invention can improve the spatial resolution of single-camera light field PIV post-processing while repairing the flow field according to the flow equation.

[0050] The entire model only requires modification of the Reynolds number, flow field size, and number of locations requiring encryption according to different flow field types; the remaining slicing, training prediction, and integrated output are all automated. This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a three-dimensional sparse velocity field encryption method.

Claims

1. A method for encrypting a three-dimensional sparse velocity field, characterized in that, include: A cryptographic model is constructed and trained. The input to the cryptographic model is a three-dimensional sparse velocity field obtained from cross-correlation calculations, and the output of the prediction model is the three-dimensional cryptographic velocity field. The activation function and loss function of the cryptographic model are as follows: The activation function uses an adaptive swish function, expressed as: wherein, β are trainable parameters, n is a scale factor; Total loss function L is represented as: wherein, L data is a loss function for data prediction; L eqns is a loss function for physical equation constraint, α is a weight coefficient; In the formula, N u Represents the velocity component in the mainstream direction u The number of components, where the subscript u represents the velocity component in the mainstream direction; N v Represents the velocity component perpendicular to the mainstream direction. v The number of components, where the subscript v represents the velocity component perpendicular to the mainstream direction; N eqns This indicates the number of observation points used in the calculation of the Navier-Stokes equations; the subscript eqns represents the Navier-Stokes equations. u data ( X i , t i ) is the location X i and time t i The corresponding known mainstream velocity components are as follows. X i =( x i , y i ) represents from 1 to N u The mainstream direction position component of the i-th position during traversal x and vertical mainstream direction position components y , t i Representing from 1 to N u The i-th time point during the traversal; v data ( X j , t j ) is the location X j and time t j The corresponding known velocity components perpendicular to the mainstream direction are as follows. X j =( x j , y j ) represents from 1 to N v The mainstream direction position component at the j-th position during traversal x and vertical mainstream direction position components y , t i Representing from 1 to N u The i-th time point during the traversal; u pred ( X i , t i ) is the location X i and time t i The corresponding neural network predicts the mainstream direction velocity components. X i =( x i , y i ) represents from 1 to N u The mainstream direction position component of the i-th position during traversal x and vertical mainstream direction position components y , t i Representing from 1 to N u The i-th time point during the traversal; v pred ( X j , t j ) is the location X j and time t j The corresponding neural network predicts the velocity component in the vertical mainstream direction. X j =( x j , y j ) represents from 1 to N v The mainstream direction position component at the j-th position during traversal x and vertical mainstream direction position components y , t i Representing from 1 to N u The i-th time point during the traversal; e k ( X m , t m ) is the location X m and time t m Next, calculate the residual of the k-th physical equation, where k ranges from 1 to 3, representing the residuals of the three physical equations. X m =( x m , y m ) represents from 1 to N eqns The mainstream direction position component at the m-th position during traversal x and vertical mainstream direction position components y , t m Representing from 1 to N eqns The i-th time point during the traversal; Determine the coordinates of the locations in the 3D sparse velocity field that need to be encrypted; input the coordinates of the locations to be encrypted into the encryption model, and predict the velocity components of the corresponding encryption locations based on the weights; Training methods for encryption models include: Flow field data preprocessing: Extracting the three-dimensional sparse velocity field obtained from cross-correlation calculation ( t , x , y , u , v ), and divided into training data and test data for the encrypted model. t, x, y, u, v These are time, position component in the mainstream direction, position component perpendicular to the mainstream direction, velocity component in the mainstream direction, and velocity component perpendicular to the mainstream direction; corresponding to ( t , x , y () as known data for calculating the residuals of the Navier-Stokes equations; The three-dimensional sparse velocity field is independently divided into two-dimensional flow field information in different planes; the loss function of the data prediction residual is calculated based on the predicted velocity components and the actual experimental velocity components; the residual of the Navier-Stokes equation is calculated based on the corresponding position and the predicted velocity to obtain the loss function of physical constraints; the loss function of the data prediction residual and the residual of the Navier-Stokes equation are added together by weights to obtain the total loss function. After each training session, the encrypted model first performs forward and backward propagation on the training data to update the weights, and then runs forward propagation on the test data to calculate the specified loss and performance metrics in order to observe changes in model performance. The training process of the encryption model includes: The encryption model is constrained by physical equations: each training iteration is subject to the residuals of the physical equations until the loss function converges; the Navier-Stokes equations and continuity equations describing two-dimensional fluid motion are used as prior physical information and embedded into the loss function of the residual neural network in the form of partial differential equations; the residual terms corresponding to the Navier-Stokes equations are expressed as follows: e 1 and e 2. The residual term corresponding to the continuity equation is expressed as: e 3: In the formula, U Represents the resultant velocity vector. U = ( u , v ), u Indicates the velocity component in the mainstream direction. v Represents the velocity component perpendicular to the mainstream direction; ▽ represents the gradient operator in spatial coordinates. U•▽ It is a vector differential operator representing the convection term in the Navier-Stokes equations. , Indicates the sign of the partial derivative. Indicates to x Find the partial derivative in the direction. Indicates to y Find the partial derivative in the direction. Represents velocity components u about x The first-order partial derivative of the function in the direction describes the change of the function with respect to the direction of ... x Rate of change of direction Represents velocity components v about y The first-order partial derivative of the function in the direction describes the change of the function with respect to the direction of ... y Rate of change of direction; Re The Reynolds number represents the flow; u t for u Components versus time t The derivative; u x for u Component pairs x The derivative of a component; v t for v Components versus time t The derivative; v y for v Component pairs y The derivative of a component; p t Pressure component p Regarding time t The derivative; p x for p Component pairs x The derivative of a component; p y for p Component pairs y The derivative of a component; It's the Laplacian operator, it's the gradient. ▽ The divergence is expressed as ; Multiplying by the velocity component represents the viscous term in the Navier-Stokes equations; , Represents velocity components u about x The second partial derivative in the direction measures the... x The rate of change of velocity in the direction, Represents velocity components u about y The second partial derivative in the direction measures the... y The rate of change of velocity in a direction; , Represents velocity components v about x The second partial derivative in the direction measures the... x The rate of change of velocity in the direction, Represents velocity components v about y The second partial derivative in the direction measures the... y The rate of change of velocity in a direction; and For partial derivative terms in neural networks and Calculated using an automatic difference method based on the chain rule; The decision to retrain is made based on the convergence value of the preset loss function; if the convergence value is reached, it indicates that the weights of the neural network conform to the prediction characteristics of the flow field.

2. The three-dimensional sparse velocity field encryption method according to claim 1, characterized in that, Scale factor n Set to 10, β The initial value is set to 0.

1.

3. The three-dimensional sparse velocity field encryption method according to claim 1, characterized in that, Before performing encrypted prediction, the existing flow field should be preprocessed, including: Extract the three-dimensional flow field obtained from cross-correlation calculation ( t , x , y , u , v ) as training data for the neural network, and the corresponding ( t , x , y () as known data for calculating the residuals of the Navier-Stokes equations; The optical field PIV collects flow field information on the same plane sequentially at different depths; The velocity field obtained by reconstructing and cross-correlating the light field image can be independently divided into two-dimensional flow field information of different planes according to depth, and the two-dimensional flow fields corresponding to all depths can be predicted in sequence.

4. The three-dimensional sparse velocity field encryption method according to claim 3, characterized in that, The entire training process involves changing the slice depth four times, sequentially predicting and integrating the output for each slice, including: Suppose that the cross-correlation calculation yields... u , v and w The dimensions of the components are all m×k×n; First, the three-dimensional experimental data were sorted according to depth. z Perform slicing to obtain the corresponding x - y Using a planar flow field as a two-dimensional training set, prediction u’ and v’ The components, with an integrated encryption dimension of 2m×2k×n; where, in x - y In the plane, x The positional component in the mainstream direction, y The position component is perpendicular to the mainstream direction. u’ for x - y The velocity components in the mainstream direction within the plane, v’ for x - y The velocity component perpendicular to the mainstream direction in the plane; Then x Slice the image using depth to obtain the corresponding depth. y - z Planar flow field prediction v’ and w’ The components are encrypted with a dimension of 2m×k×2n; where, in y - z In the plane, y The positional component in the mainstream direction, z The position component is perpendicular to the mainstream direction. v’ for y - z The velocity components in the mainstream direction within the plane, w’ for y - z The velocity component perpendicular to the mainstream direction in the plane; Then, from the encrypted velocity components, according to 2m... y Depth in x - z In-plane encryption u’’ and w’’ The components, when integrated, yield an encryption dimension of 2m×2k×2n; where, in x - z In the plane, x The positional component in the mainstream direction, z The position component is perpendicular to the mainstream direction. u’’ for x - z The velocity components in the mainstream direction within the plane, w’’ for x - z The velocity component perpendicular to the mainstream direction in the plane; Finally, from the velocity components obtained through encryption, according to 2n... z Depth in x - y In-plane encryption u’’ and v’’ The components, integrating the three predicted velocity components, yield a new encryption dimension of 2m×2k×2n; where, in x - y In the plane, x The positional component in the mainstream direction, y The position component is perpendicular to the mainstream direction. u’’ for x - y The velocity components in the mainstream direction within the plane, y’’ for x - y The velocity component perpendicular to the mainstream direction in the plane.

5. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; The one or more programs are executed by the one or more processors, causing the one or more processors to implement the steps of a three-dimensional sparse velocity field encryption method as described in any one of claims 1-4.

6. A storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of a three-dimensional sparse velocity field encryption method as described in any one of claims 1 to 4.

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