Sand mill dynamic separator flow field reconstruction method and system based on PINN

Abstract

This invention relates to the field of flow field reconstruction technology, specifically to a method and system for reconstructing the flow field of a dynamic separator in a sand mill based on PINN. The method includes: simulating the flow field of the dynamic separator in the sand mill using CFD to obtain CFD simulation results; embedding the Navier-Stokes equations into PINN to construct an initial PINN model; acquiring experimental flow field data of the sand mill; using the CFD simulation results and experimental flow field data as input data to the initial PINN model, and generating a final PINN joint model through supervised learning; using the PINN joint model to predict the leakage of the grinding media and measuring the accuracy of the prediction results. This invention combines PINN with CFD, achieving computational lightweighting and higher computational efficiency and flexibility by shortening computation time; and reducing dependence on computational resources while achieving accurate simulation calculations by adjusting various parameters and network structure in the neural network.

Description

Technical Field

[0001] This invention relates to the field of flow field reconstruction technology, specifically to a method and system for reconstructing the flow field of a dynamic separator in a sand mill based on PINN. Background Technology

[0002] PINN (Physical Informed Neural Network) is a model that combines physical laws with deep learning. It aims to use physical equations to guide the training process of a neural network, thereby solving problems involving physical modeling. Its core idea is to embed physical laws (such as partial differential equations) into the training process of the neural network, allowing the network to simultaneously learn the characteristics of the data and the physical laws during training. This method not only improves the accuracy of predictions but also enhances the interpretability of the model. In the field of fluid mechanics, flow field reconstruction is an important and complex problem. PINN can achieve high-precision reconstruction of complex flow fields by combining partial observation data with physical governing equations (such as the Navier-Stokes equations).

[0003] Sand mills are primarily used for grinding granular materials in a liquid medium. Their internal components typically consist of a multiphase flow, including solid particles, liquid media, and gases (if bubble dispersion is involved). The dynamic separator, a crucial component of the sand mill, is responsible for separating the abrasive and the raw material from the grinding media, ensuring the stability of the desired particle size. The flow field in a sand mill is complex; due to the presence of multiphase flow, its flow characteristics differ significantly from single-phase flow. Grinding media leakage refers to the quantity or mass of grinding media (such as steel balls or sand particles) that flows out of the mill through the dynamic separator during operation. Grinding media leakage not only reduces grinding efficiency but can also cause equipment damage and increased operating costs. Therefore, controlling grinding media leakage is of paramount importance.

[0004] Because traditional computational fluid dynamics (CFD) is time-consuming when simulating multiphase flow fields, reconstructing the multiphase flow field in the dynamic separator of a sand mill and predicting the leakage of grinding media have always been difficult problems to solve. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for reconstructing the flow field of a dynamic separator in a sand mill based on PINN, which aims to solve the problem of long time consumption when simulating the multiphase flow field in a dynamic separator of a sand mill using traditional computational fluid dynamics. This invention can generate high-precision multiphase flow field results in real time and quickly, and predict the leakage of grinding media in the dynamic separator of the sand mill.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] In a first aspect, embodiments of the present invention provide a method for reconstructing the flow field of a dynamic separator in a sand mill based on PINN, the method comprising the following steps:

[0008] The flow field of the dynamic separator in the sand mill was simulated using CFD, and the CFD simulation results were obtained. The CFD simulation results are the preliminary flow field data of the dynamic separator, including flow velocity, rotational speed, turbulence intensity and pressure distribution.

[0009] The N-S equations of CFD are embedded in the neural network of PINN to construct the initial PINN model;

[0010] Experimental flow field data accumulated by the sand mill under actual working conditions were obtained using experimental methods.

[0011] The CFD simulation results and the experimental flow field data are used as input data for the initial PINN model, and the final PINN joint model is generated through supervised learning.

[0012] The PINN joint model was used to predict the leakage of grinding media, and the mean absolute percentage error was used to measure the accuracy of the prediction results.

[0013] Optionally, the initial PINN model includes an encoding layer, a convolutional layer, a deconvolutional layer, and a differential operator; the initial PINN model uses the ReLU function as the activation function; the initial PINN model uses convolutional kernels to perform convolution processing on the input data, and the convolutional blocks and the deconvolutional blocks in the decoder adopt the ResNet architecture; wherein, the convolutional kernels include 1*1 convolutional kernels and 3*1 convolutional kernels, the 1*1 convolutional kernels are used to reduce the number of channels, and the 3*1 convolutional kernels are used to extract local features in the spatial dimension.

[0014] Optionally, the initial PINN model sets up a max-pooling layer to downsample the data to reduce the feature map size and inputs the feature map extracted by the encoder into the parallel decoder.

[0015] Optionally, embedding the N_S equation of CFD in the neural network of PINN specifically involves discretizing the N_S equation and discretizing the Euler multiphase flow.

[0016] Optionally, the N_S equations can be discretized, specifically as follows:

[0017] Discretization of the convection term is performed using an upwind scheme, including:

[0018] In a two-dimensional Cartesian coordinate system, the continuity equation is discretized using the central difference method, and expressed as:

[0019] The continuity equation is expressed as:

[0020] Discretizing the momentum equation in the x-direction yields the discretized momentum equation in the x-direction, expressed as:

[0021]

[0022] Specifically:

[0023] Discretize the convection term using the upwind scheme, and represent it as follows:

[0024] Discretize the diffusion term using the central difference method, and express it as follows:

[0025]

[0026] Discretizing the pressure gradient, we can express it as follows:

[0027] The discretized convection term, diffusion term and pressure gradient are combined to obtain the discretized momentum equation in the x-direction;

[0028] Discretizing the momentum equation in the y-direction yields the discretized momentum equation in the y-direction, expressed as:

[0029]

[0030] Specifically:

[0031] Discretize the convection term using the upwind scheme, and represent it as follows:

[0032] Discretize the diffusion term using the central difference method, and express it as follows:

[0033]

[0034] Discretizing the pressure gradient, we can express it as follows:

[0035] By combining the discretized convection term, diffusion term, and pressure gradient, we obtain the discretized momentum equation in the y-direction.

[0036] The momentum equation in the x-direction is expressed as: The momentum equation in the y-direction is expressed as:

[0037] Where u and v are fluid velocity components, and the subscripts i and j correspond to the node numbers on the x-axis and y-axis, respectively; Δx is the difference between the node corresponding to the i-th row of the x-axis and the j-th column of the y-axis and the node corresponding to the (i-1)-th row of the x-axis and the j-th column of the y-axis in the mesh; Δy is the difference between the node corresponding to the i-th row of the x-axis and the j-th column of the y-axis and the node corresponding to the i-th row of the x-axis and the (j-1)-th column of the y-axis in the mesh; ρ represents density, p is pressure, and υ is the kinematic viscosity coefficient.

[0038] Optionally, using the mean absolute percentage error to measure the accuracy of the prediction results includes:

[0039] Normalized mean absolute error and normalized root mean square error are used as prediction evaluation indicators.

[0040] The normalized mean absolute error is expressed as:

[0041]

[0042] The normalized root mean square error is expressed as:

[0043]

[0044] Where mean(H) represents the average value of the data; Hj,m represents the predicted value of the neural network in the grid node; and Hi,m represents the value of the grid node after CFD calculation.

[0045] Optionally, using the mean absolute percentage error to measure the accuracy of the prediction results further includes:

[0046] The regression coefficient R² is introduced to comprehensively evaluate the goodness of fit of the PINN joint model, expressed as:

[0047]

[0048] in, This represents the average value of multiple sets of data in the current grid node.

[0049] Secondly, embodiments of the present invention provide a flow field reconstruction system for a dynamic separator in a sand mill based on PINN, the system comprising:

[0050] At least one processor;

[0051] At least one memory for storing at least one program;

[0052] When the at least one program is executed by the at least one processor, the at least one processor implements the PINN-based flow field reconstruction method for dynamic separators in sand mills as described in any of the preceding claims.

[0053] The beneficial effects of this invention are as follows: This invention discloses a method and system for reconstructing the flow field of a dynamic separator in a sand mill based on PINN. This invention solves the problem of long processing times in traditional computational fluid dynamics (CFD) simulations of multiphase flow fields in dynamic separators of sand mills. It can generate high-precision multiphase flow field results in real time and quickly, and predict the leakage of grinding media in the dynamic separator of the sand mill. This invention not only provides a powerful tool for studying the flow field laws of dynamic separators in sand mills, but also provides methodological support for the design of parameter spectrums of dynamic separators with various structures, demonstrating the strong potential of PINN in the simulation and prediction of complex flow fields.

[0054] This invention addresses the shortcomings of traditional CFD methods in reconstructing dynamic and complex flow fields by combining PINN with CFD. It achieves computational lightweighting by shortening computation time, resulting in higher computational efficiency and flexibility. By adjusting various parameters in the neural network and network structures such as convolutional and deconvolutional layers, it enables the learning and prediction of flow field data, thereby achieving accurate simulation calculations while reducing dependence on computing resources. Furthermore, it can perform real-time online analysis to achieve full lifecycle management of equipment. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a schematic flowchart of the flow field reconstruction method for the dynamic separator of a sand mill based on PINN in an embodiment of the present invention;

[0057] Figure 2 This is a computational fluid dynamics distribution diagram using CFD technology.

[0058] Figure 3 This is a fluid flow field distribution map predicted by the trained model in an embodiment of the present invention;

[0059] Figure 4 This is a structural diagram of the flow field reconstruction system of the dynamic separator for a sand mill based on PINN in an embodiment of the present invention. Detailed Implementation

[0060] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present invention can be combined with each other.

[0061] See Figure 1 , Figure 1 This invention provides a method for reconstructing the flow field of a dynamic separator in a sand mill based on PINN. The method includes the following steps:

[0062] The flow field of the dynamic separator in the sand mill was simulated using CFD, and the CFD simulation results were obtained.

[0063] The N-S equations of CFD are embedded in the neural network of PINN to construct the initial PINN model;

[0064] Experimental flow field data accumulated by the sand mill under actual working conditions were obtained using experimental methods.

[0065] The CFD simulation results and the experimental flow field data are used as input data for the initial PINN model, and the final PINN joint model is generated through supervised learning.

[0066] The PINN joint model was used to predict the leakage of grinding media, and the mean absolute percentage error was used to measure the accuracy of the prediction results.

[0067] Specifically, since the flow field inside the separator directly affects the distribution, particle size, and processing efficiency of abrasive particles, accurate simulation of its internal flow field is crucial for optimizing the performance of the sand mill. However, due to the complexity of the flow inside the sand mill (such as turbulence, nonlinear boundary effects, and dynamic changes), using traditional computational fluid dynamics (CFD) methods to fully describe this process faces high computational costs, long processing times, and complex mesh generation problems. Therefore, this application proposes a neural network method based on PINN (Physical Information Neural Network) to address the problems of multiphase flow field reconstruction and grinding media leakage prediction in the dynamic separator of a sand mill. This method aims to solve the problem of long processing times in traditional CFD simulation of multiphase flow fields by combining a joint model of CFD and PINN to generate high-precision multiphase flow field results in real time and quickly. This PINN joint model not only provides a powerful tool for studying the flow field laws of dynamic separators but also provides methodological support for the design of parameter spectrums of dynamic separators with various structures, demonstrating the powerful potential of PINN neural networks in the simulation and prediction of complex flow fields.

[0068] Understandably, this application addresses the shortcomings of traditional CFD methods in reconstructing dynamic and complex flow fields by combining PINN with CFD. It achieves computational lightweighting by shortening computation time, resulting in higher computational efficiency and flexibility. By adjusting various parameters in the neural network and network structures such as convolutional and deconvolutional layers, it enables the learning and prediction of flow field data, thereby achieving accurate simulation calculations while reducing dependence on computing resources. Furthermore, it can perform real-time online analysis to achieve full lifecycle management of the equipment.

[0069] In one embodiment provided in this application, the CFD simulation results are preliminary flow field data of the dynamic separator, including flow velocity, rotational speed, turbulence intensity, and pressure distribution.

[0070] Specifically, the CFD simulation results obtained by simulating the flow field of the dynamic separator in the sand mill are preliminary flow field data, including but not limited to flow velocity, rotational speed, turbulence intensity, and pressure distribution. CFD is used as prior knowledge to generate preliminary flow field solutions, which are then optimized and corrected using PINN. For example, the flow field simulated by CFD can be used as input to PINN, and PINN can be used to further refine and reconstruct the flow field.

[0071] In one embodiment provided in this application, the initial PINN model includes an encoding layer, a convolutional layer, a deconvolutional layer, and a differential operator.

[0072] Specifically, this embodiment uses a PINN neural network, including encoding layers, convolutional layers, deconvolutional layers, and differential operators. Velocity, pressure, rotational speed, and other parameters such as their proportions and time are used as inputs to train the neural network. The neural network can be constructed using, but is not limited to, convolutional and deconvolutional layers. Then, data calculated using CFD is used to verify the results of the partial differential equations to form the MSE. R The value is determined, and the final MSE value is used as the basis for stopping the iterative calculation. If the corresponding value is not reached, the iterative calculation continues until it is less than that value.

[0073] In one embodiment provided in this application, the initial PINN model uses the ReLU function as the activation function.

[0074] Specifically, this embodiment uses, but is not limited to, the ReLU function as the activation function, in order to effectively avoid gradient vanishing caused by negative outliers.

[0075] In one embodiment provided in this application, the initial PINN model uses convolution kernels to perform convolution processing on the input data, and the convolutional blocks and the deconvolutional blocks in the decoder adopt the ResNet architecture; wherein, the convolutional kernels include 1*1 convolutional kernels and 3*1 convolutional kernels, the 1*1 convolutional kernels are used to reduce the number of channels, and the 3*1 convolutional kernels are used to extract local features in the spatial dimension.

[0076] Specifically, in this embodiment, convolutional kernels are used to perform convolution processing on the input data. The convolutional blocks and the deconvolutional blocks in the decoder adopt the ResNet architecture, which allows the model to learn more detailed information while avoiding gradient vanishing and gradient exploding. The convolutional kernel settings adopt the network-in-network configuration of the Inception Net structure. The 1*1 convolutional kernel is responsible for reducing the number of channels and is mainly used for feature combination between channels; while the 3*1 convolutional kernel is responsible for extracting local features in the spatial dimension, thereby deepening and widening the network while keeping the parameters unchanged, which reduces the amount of computation.

[0077] It's important to clarify that convolutional kernels and convolutional blocks are not the same concept. A convolutional kernel is a small matrix, typically with a small size (e.g., 3×3, 5×5), used to slide across the input data and perform local weighted summation operations. The role of a convolutional kernel is to extract local features from the input data, such as edges and textures. Each convolutional kernel learns specific feature patterns, thus different kernels can extract different features. A convolutional block, on the other hand, usually refers to a module containing multiple layers. It typically includes convolutional layers, activation layers (such as ReLU), pooling layers (such as max pooling), etc. A convolutional block is a structural unit in a convolutional neural network, designed to progressively extract and learn high-level features of the data through multiple layers of operations.

[0078] In one embodiment provided in this application, the initial PINN model sets a max pooling layer to downsample the data to reduce the feature map size, and inputs the feature map extracted by the encoder into the parallel decoder.

[0079] Specifically, in this embodiment, the initial PINN model further reduces the feature map size and improves the abstraction level of the feature map by setting a max pooling layer to downsample the data, and then inputs the feature map extracted by the encoder into the parallel decoder.

[0080] In one embodiment provided in this application, embedding the N_S equation of CFD in the neural network of PINN specifically involves discretizing the N_S equation and discretizing the Euler multiphase flow.

[0081] Specifically, by discretizing the Navier-Stokes equations and the Euler multiphase flow, the neural network optimizes not only its own loss function during training iterations, but also the difference in the physical equations at each iteration, ensuring that the final trained initial PINN model satisfies a certain set physical law. It should be noted that the aforementioned Navier-Stokes equations are the Navier-Stokes equations.

[0082] Understandably, the discretization of the Navier-Stokes equations is primarily for subsequent calculations of the physical equations. The PINN neural network essentially uses powerful computing capabilities to guess a series of results. The "P" in PINN stands for "physical," meaning the guessed values ​​are substituted into the physical equations to verify their correctness. By setting the error term, this verification process is repeated until the error is acceptable. For the meshing of this dynamic separator's two-dimensional model, the predicted values ​​of the neural model are compared with sample values ​​for the data values ​​in each mesh node, such as the velocity component and zirconium bead (grinding medium) leakage, as shown in this application. This trains the neural network by training the physical quantities of each node in the mesh. The network is then validated using test data.

[0083] In one embodiment provided in this application, the N_S equation is discretized, specifically by discretizing the convection term using an upwind scheme, including:

[0084] In a two-dimensional Cartesian coordinate system, the continuity equation is discretized using the central difference method, and expressed as:

[0085] The continuity equation is expressed as:

[0086] Discretizing the momentum equation in the x-direction yields the discretized momentum equation in the x-direction, expressed as:

[0087]

[0088] Specifically, the convection term is discretized using the upwind scheme, and expressed as:

[0089]

[0090] Discretize the diffusion term using the central difference method, and express it as follows:

[0091]

[0092] Discretizing the pressure gradient, we can express it as follows:

[0093]

[0094] The discretized convection term, diffusion term and pressure gradient are combined to obtain the discretized momentum equation in the x-direction;

[0095] Where u and v are fluid velocity components, and the subscripts i and j correspond to the node numbers on the x-axis and y-axis, respectively; u i,j v represents the velocity in the x-direction at the node corresponding to the i-th row of the x-axis and the j-th column of the y-axis in the mesh. i,j Δx represents the velocity in the y-direction at the node corresponding to the i-th row of the x-axis and the j-th column of the y-axis in the mesh; i and j correspond to the node numbers on the x-axis and y-axis, respectively; Δx is the difference between the node corresponding to the i-th row of the x-axis and the j-th column of the y-axis and the node corresponding to the (i-1)-th row of the x-axis and the j-th column of the y-axis in the mesh; Δy is the difference between the node corresponding to the i-th row of the x-axis and the j-th column of the y-axis and the node corresponding to the (j-1)-th row of the x-axis and the j-th column of the y-axis in the mesh; ρ represents density, in kg / m³. 3 , p is pressure, υ is kinematic viscosity coefficient.

[0096] Discretizing the momentum equation in the y-direction yields the discretized momentum equation in the y-direction, expressed as:

[0097]

[0098] Specifically:

[0099] Discretize the convection term using the upwind scheme, and represent it as follows:

[0100]

[0101] Discretize the diffusion term using the central difference method, and express it as follows:

[0102]

[0103] Discretizing the pressure gradient, we can express it as follows:

[0104]

[0105] By combining the discretized convection term, diffusion term, and pressure gradient, we obtain the discretized momentum equation in the y-direction.

[0106] The momentum equation in the x-direction is expressed as:

[0107]

[0108] The momentum equation in the y-direction is expressed as:

[0109]

[0110] In one embodiment provided in this application, using the mean absolute percentage error to measure the accuracy of the prediction result includes:

[0111] Normalized mean absolute error and normalized root mean square error are used as prediction evaluation indicators.

[0112] The normalized mean absolute error is expressed as:

[0113]

[0114] The normalized root mean square error is expressed as:

[0115]

[0116] Where mean(H) represents the average value of the data; H j,m H represents the predicted value of the neural network in the grid node; i,m This represents the value of a grid node after CFD calculation.

[0117] Specifically, the Mean Absolute Percentage Error (MAPE) is typically used to measure the accuracy of model predictions. However, in flow field prediction, the component content may be small data points between (0,1), which makes the MAPE very large or infinite. Therefore, this application uses Normalized Mean Absolute Error (MAPE) and Normalized Root Mean Square Error (RMSE) as prediction evaluation metrics.

[0118] This embodiment shows the predicted value of each node in the grid generated by the neural network and the value calculated by CFD software. The purpose is to compare the difference between the two in order to measure the prediction effect of the model.

[0119] In one embodiment provided in this application, the method of using the mean absolute percentage error to measure the accuracy of the prediction result further includes:

[0120] Introducing regression coefficient R 2 The overall evaluation of the goodness of fit of the PINN joint model is expressed as follows:

[0121]

[0122] in, This represents the average value of multiple sets of data in the current grid node.

[0123] Specifically, this application introduces a regression coefficient R. 2 This is used to comprehensively evaluate the model's fit. The smaller the MAPE and RMSE, the better the regression coefficient R. 2 The closer the value is to 1, the higher the model's prediction accuracy and the better the fit.

[0124] Using a 400L sand mill dynamic separation as an example, the distribution of various substances in the two-dimensional plane within the dynamic separator was calculated, and the leakage of the grinding media was predicted. CFD calculation results were used as the results of the discretized Navier-Stokes equations. Data was calculated under low-speed, normal-speed, and high-speed conditions (specifically, these three types of data served as the calibration standard for training and the verification data for testing, respectively). The sample sizes were 20, 20, and 20, for a total of 60 samples. The parameterized flow field dataset was divided into two parts: a training set, which was used as input data for supervised learning to train the neural network to minimize the loss function; and a test set, which simulated unknown operating conditions and fed back to the neural network. Two-thirds of the 60 samples obtained through the CFD method were used as the training set, and one-third as the test set.

[0125] In one embodiment provided in this application, the error results of the velocity portion of the flow field predicted by the model are shown in the table below:

[0126] Low speed (0.5 times) Normal speed (1x) High speed (1.5 times) MAPE 0.49 0.92 0.2 RMSE 0.29 0.88 0.25 <![CDATA[R 2 ]]> 0.975 0.996 0.985

[0127] For normal operating speeds, the model's prediction accuracy is good. For both low and high operating speeds, the R-value for high operating speeds is relatively higher, indicating that the model's prediction results at high operating speeds are better than those at low operating speeds.

[0128] In another embodiment provided in this application, the error results of the model predicting the leakage of the abrasive medium in the flow field are shown in the table below:

[0129] Low speed (0.5 times) Normal speed (1x) High speed (1.5 times) MAPE 0.52 0.95 0.26 RMSE 0.39 0.98 0.20 R2 0.975 0.996 0.985

[0130] For normal operating speeds, the model's prediction accuracy is good. For both low and high operating speeds, the R-value for high operating speeds is relatively higher, indicating that the model's prediction results at high operating speeds are better than those at low operating speeds.

[0131] Figure 2 The fluid flow field velocity distribution calculated by CFD and the velocity distribution predicted by the model are shown in the following diagrams. Based on the model prediction data, the rotational speed was adjusted on-site, and the actual project test showed the effect after installing the separator. Figure 3 As shown.

[0132] Compared with existing technologies, this invention can lightweight the computational model, achieve accurate simulation calculations while reducing dependence on computing resources and shortening computation time.

[0133] and Figure 1 The corresponding method is referenced. Figure 4This invention provides a PINN-based dynamic separator flow field reconstruction system for sand mills, comprising:

[0134] At least one processor;

[0135] At least one memory for storing at least one program;

[0136] When the at least one program is executed by the at least one processor, the at least one processor performs the method described above.

[0137] It is evident that the content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0138] It will be understood by those skilled in the art that all or some of the methods and systems disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0139] The above is a detailed description of the preferred embodiments of this disclosure. However, this disclosure is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this disclosure. All such equivalent modifications or substitutions are included within the scope defined by the claims of this disclosure.

Claims

1. A method for reconstructing the flow field of a dynamic separator in a sand mill based on PINN, characterized in that, The method includes the following steps: The flow field of the dynamic separator in the sand mill was simulated using CFD, and the CFD simulation results were obtained. The CFD simulation results are the preliminary flow field data of the dynamic separator, including flow velocity, rotational speed, turbulence intensity and pressure distribution. The N_S equations of CFD and the Euler multiphase flow equations are embedded in the neural network of PINN to construct the initial PINN model. The N_S equations are discretized by using an upwind scheme for the convection term and by using the central difference method for the diffusion term. Experimental flow field data accumulated by the sand mill under actual working conditions were obtained using experimental methods. The CFD simulation results and the experimental flow field data are used as input data for the initial PINN model, and the final PINN joint model is generated through supervised learning. The leakage of the grinding medium is predicted using the PINN joint model, wherein the initial PINN model includes a coding layer, a convolutional layer, a deconvolutional layer and a differential operator, the ReLU function is used as the activation function, the input data is convolved using a convolutional kernel, and the convolutional block and the deconvolutional block in the decoder adopt the ResNet architecture. The accuracy of the prediction results is measured using the mean absolute percentage error.

2. The method for reconstructing the flow field of a dynamic separator in a sand mill based on PINN according to claim 1, characterized in that, The initial PINN model sets up a max-pooling layer to downsample the data, thereby reducing the feature map size, and inputs the feature map extracted by the encoder into the parallel decoder.

3. The method for reconstructing the flow field of a dynamic separator in a sand mill based on PINN according to claim 1, characterized in that, The discretization of the N_S equations is specifically performed as follows: Discretizing the momentum equation in the x-direction yields the discretized momentum equation in the x-direction, expressed as: ； Discretizing the momentum equation in the y-direction yields the discretized momentum equation in the y-direction, expressed as: ； in, , These represent the fluid velocity components, with subscripts i and j corresponding to node numbers on the x-axis and y-axis, respectively; Δx is the difference between the node in the i-th row of the x-axis and the j-th column of the y-axis and the node in the (i-1)-th row of the x-axis and the j-th column of the y-axis; Δy is the difference between the node in the i-th row of the x-axis and the j-th column of the y-axis and the node in the (j-1)-th row of the x-axis and the j-th column of the y-axis; ρ represents density, and p is pressure. It is the kinematic viscosity coefficient.

4. The method for reconstructing the flow field of a dynamic separator in a sand mill based on PINN according to claim 1, characterized in that, The use of mean absolute percentage error to measure the accuracy of prediction results includes: Normalized mean absolute error and normalized root mean square error are used as prediction evaluation indicators. The normalized mean absolute error is expressed as: ； The normalized root mean square error is expressed as: ； Where mean(H) represents the average value of the data; H j,m H represents the predicted value of the neural network in the grid node; i,m This represents the value of a grid node after CFD calculation.

5. The method for reconstructing the flow field of a dynamic separator in a sand mill based on PINN according to claim 4, characterized in that, The method of using mean absolute percentage error to measure the accuracy of prediction results also includes: The regression coefficient R² is introduced to comprehensively evaluate the goodness of fit of the PINN joint model, expressed as: ； in, This represents the average value of multiple sets of data in the current grid node.

6. A flow field reconstruction system for a dynamic separator in a sand mill based on PINN, characterized in that, The system includes: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any one of claims 1 to 5.

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