Pump station flow channel flow field prediction and optimization method based on transfer learning enhanced physical information neural network

Abstract

The invention provides a pump station flow channel flow field prediction and optimization method based on a transfer learning enhanced physical information neural network. The method comprises the following steps: constructing a training data set; constructing a loss function based on the control equation, the initial runner condition and the inlet and outlet boundary; a physical information neural network is constructed, hydraulic design parameters, space coordinates and time data are input into the physical information neural network, and pump station flow channel flow field data are output into the physical information neural network; intensively training the physical information neural network through time slice transfer learning by using the training data set based on the loss function to obtain a target physical information neural network model; determining a plurality of candidate hydraulic design parameters, and inputting each candidate hydraulic design parameter into the target physical information neural network model to obtain corresponding candidate pump station flow channel flow field data so as to obtain candidate performance parameters; and an objective function is constructed based on the performance parameters, the objective function is solved to obtain optimal performance parameters, and the candidate hydraulic design parameters corresponding to the optimal performance parameters are the optimal candidate hydraulic design parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of predicting and optimizing the flow field of pump station channels, and particularly to a method for predicting and optimizing the flow field of pump station channels based on a physics-informed neural network enhanced by transfer learning. Background Art

[0002] The existing technologies for predicting and analyzing the flow field of pump station channels mainly rely on traditional computational fluid dynamics (CFD) simulation methods and experience-based design optimization techniques. These techniques generally include steps such as establishing a hydrodynamic model, meshing, setting boundary conditions, running a solver, and post-processing analysis. In terms of selecting an optimization scheme, the existing technologies may adopt single-objective or simple multi-objective optimization algorithms to iteratively find the optimal solution of design parameters.

[0003] However, these existing technologies face certain limitations in application scenarios with sparse data or high data acquisition costs, especially when direct measurement data is insufficient to fully reflect the complexity of the flow channel design performance. In addition, when facing multi-objective optimization problems, traditional methods usually have low computational efficiency, are difficult to handle large-scale parameter spaces, and are difficult to capture the complex relationships between multiple performance indicators. The existing optimization methods may also not be able to provide a global optimal solution and sometimes can only find a local optimum. Summary of the Invention

[0004] The present invention aims to solve at least one of the technical problems in the related technologies to some extent.

[0005] To this end, the first object of the present invention is to propose a method for predicting and optimizing the flow field of pump station channels based on a physics-informed neural network enhanced by transfer learning to solve the problems of low prediction accuracy and optimization problems under sparse data conditions.

[0006] The second object of the present invention is to propose a system for predicting and optimizing the flow field of pump station channels based on a physics-informed neural network enhanced by transfer learning.

[0007] The third object of the present invention is to propose an electronic device.

[0008] The fourth object of the present invention is to propose a computer-readable storage medium.

[0009] To achieve the above object, the first aspect of the present invention proposes a method for predicting and optimizing the flow field of pump station channels based on a physics-informed neural network enhanced by transfer learning, including:

[0010] Constructing a training data set, which is composed of hydraulic design parameters, spatial coordinates, time data of the pump station channel, and pump station channel flow field data;

[0011] Construct a loss function based on the governing equations, the initial conditions of the flow channel, and the inlet and outlet boundaries, and determine the performance parameters;

[0012] Construct a physics-informed neural network, where the input of the physics-informed neural network is the hydraulic design parameters, spatial coordinates, and time data, and the output is the flow field data of the pump station flow channel;

[0013] Based on the loss function, use the training dataset to strengthen the training of the physics-informed neural network through time-slice transfer learning to obtain the target physics-informed neural network model;

[0014] Determine multiple candidate hydraulic design parameters, and based on each candidate hydraulic design parameter, use the target physics-informed neural network model to obtain the corresponding candidate pump station flow channel flow field data, and calculate the corresponding candidate performance parameters using each candidate pump station flow channel flow field data;

[0015] Construct an objective function based on the performance parameters, and solve the objective function to obtain the optimal performance parameter from all candidate performance parameters. The candidate pump station flow channel flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameter are the optimal flow field data and the optimal hydraulic design parameters.

[0016] In the method of the first aspect of the present invention, the construction of the training dataset includes: collecting the flow field data of the pump station flow channel and the hydraulic design parameters, and performing three-dimensional hydrodynamic numerical simulations on the flow channels under different hydraulic design parameters using the orthogonal experimental design method to obtain the training dataset.

[0017] In the method of the first aspect of the present invention, the governing equation uses the N-S equation.

[0018] In the method of the first aspect of the present invention, the construction of the loss function based on the governing equations, the initial conditions of the flow channel, and the inlet and outlet boundaries includes: obtaining the control equation loss function component based on the governing equation; obtaining the initial condition loss function component based on the initial conditions of the flow channel; obtaining an extended function based on the inlet and outlet boundary coupling distance function, and then obtaining the boundary loss function component; correcting the control equation loss function component, the initial condition loss function component, and the boundary loss function component based on the extended function to obtain the finally required loss function.

[0019] In the method of the first aspect of the present invention, the strengthening of the training of the physics-informed neural network based on the loss function using the training dataset through time-slice transfer learning to obtain the target physics-informed neural network model includes: dividing the training dataset into a source domain dataset and a target domain dataset according to time; training the physics-informed neural network using the source domain dataset to obtain a source model; training the source model using the target domain dataset to obtain the target physics-informed neural network model.

[0020] In the method of the first aspect of the present invention, when solving the objective function, a multi-island genetic algorithm is used for solving.

[0021] In the method of the first aspect of the present invention, the performance parameters include the head loss of the cross-section, the axial flow velocity distribution uniformity, the comprehensive flow velocity distribution uniformity, and the calculation efficiency.

[0022] To achieve the above object, the second aspect of the present invention proposes a pumping station runner flow field prediction and optimization system based on a transfer learning enhanced physics-informed neural network, including:

[0023] A training dataset construction module for constructing a training dataset, which is composed of the hydraulic design parameters, spatial coordinates, time data, and pumping station runner flow field data of the pumping station runner;

[0024] A loss function determination module for constructing a loss function based on the control equation, the initial conditions of the runner, and the inlet and outlet boundaries, and determining the performance parameters;

[0025] A modeling module for constructing a physics-informed neural network, where the input of the physics-informed neural network is the hydraulic design parameters, spatial coordinates, and time data, and the output is the pumping station runner flow field data; based on the loss function, using the training dataset to strengthen the training of the physics-informed neural network through time-slice transfer learning to obtain a target physics-informed neural network model;

[0026] A candidate solution determination module for determining a plurality of candidate hydraulic design parameters, obtaining corresponding candidate pumping station runner flow field data based on each candidate hydraulic design parameter, and calculating corresponding candidate performance parameters using each candidate pumping station runner flow field data;

[0027] A prediction and optimization module for constructing an objective function based on the performance parameters, solving the objective function to obtain the optimal performance parameters from all candidate performance parameters, and the candidate pumping station runner flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameters are the optimal flow field data and the optimal hydraulic design parameters.

[0028] To achieve the above object, the third aspect of the present invention proposes an electronic device, including: a processor, and a memory communicatively connected to the processor; the memory stores computer execution instructions; the processor executes the computer execution instructions stored in the memory to implement the method proposed in the first aspect of the present invention.

[0029] To achieve the above object, the fourth aspect of the present invention proposes a computer-readable storage medium, in which computer execution instructions are stored, and when the computer execution instructions are executed by a processor, they are used to implement the method proposed in the first aspect of the present invention.

[0030] The pump station runner flow field prediction and optimization method, system, electronic device and storage medium based on the physics-informed neural network enhanced by transfer learning provided by the present invention construct a training data set, which consists of the hydraulic design parameters, spatial coordinates, time data and pump station runner flow field data of the pump station runner; construct a loss function based on the control equation, the initial conditions of the runner and the inlet and outlet boundaries, and determine the performance parameters; construct a physics-informed neural network, the input of the physics-informed neural network is the hydraulic design parameters, spatial coordinates and time data, and the output is the pump station runner flow field data; based on the loss function, use the training data set to strengthen the training of the physics-informed neural network through time-slice transfer learning to obtain the target physics-informed neural network model; determine a plurality of candidate hydraulic design parameters, based on each candidate hydraulic design parameter, use the input target physics-informed neural network model to obtain the corresponding candidate pump station runner flow field data, and calculate the corresponding candidate performance parameters by using each candidate pump station runner flow field data; construct an objective function based on the performance parameters, and solve the objective function to obtain the optimal performance parameter from all the candidate performance parameters. The candidate pump station runner flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameter are the optimal flow field data and optimal hydraulic design parameters. In this case, based on the loss function, use the training data set to strengthen the training of the physics-informed neural network through time-slice transfer learning to obtain the target physics-informed neural network model, which improves the accuracy of the model under sparse data conditions. Integrate the pump station runner based on the physics-informed neural network enhanced by transfer learning and the solution of the objective function to obtain the optimal flow field data, where the candidate hydraulic design parameter corresponding to the optimal performance parameter is the optimal hydraulic design parameter, realizing the efficient and accurate prediction result and runner design optimization result, thus solving the problems of low prediction accuracy and optimization problems under sparse data conditions.

[0031] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0032] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of the embodiments in conjunction with the drawings, where:

[0033] Figure 1 is a schematic flowchart of a pump station runner flow field prediction and optimization method based on a physics-informed neural network enhanced by transfer learning provided by an embodiment of the present invention;

[0034] Figure 2 is a specific schematic flowchart of a pump station runner flow field prediction and optimization method based on a physics-informed neural network enhanced by transfer learning provided by an embodiment of the present invention;

[0035] Figure 3 It is the framework diagram of the physics-informed neural network model provided by the embodiments of the present invention;

[0036] Figure 4 It is the training process diagram of the physics-informed neural network model enhanced by time slice transfer learning provided by the embodiments of the present invention;

[0037] Figure 5 It is the flow chart of the multi-island genetic optimization algorithm provided by the embodiments of the present invention;

[0038] Figure 6 It is the block diagram of a pump station runner flow field prediction and optimization system based on a physics-informed neural network enhanced by transfer learning provided by the embodiments of the present invention. Detailed implementation manners

[0039] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present invention, and should not be construed as limiting the present invention.

[0040] The following refers to the accompanying drawings to describe the pump station runner flow field prediction and optimization method and system based on a physics-informed neural network enhanced by transfer learning according to the embodiments of the present invention.

[0041] The embodiments of the present invention provide a pump station runner flow field prediction and optimization method based on a physics-informed neural network enhanced by transfer learning to solve the problems of low prediction accuracy and optimization problems under sparse data conditions.

[0042] Figure 1 It is the schematic flow diagram of a pump station runner flow field prediction and optimization method based on a physics-informed neural network enhanced by transfer learning provided by the embodiments of the present invention.

[0043] As Figure 1 shown, the pump station runner flow field prediction and optimization method based on a physics-informed neural network enhanced by transfer learning includes the following steps:

[0044] Step S101, construct a training data set, which is composed of hydraulic design parameters, spatial coordinates, time data and pump station runner flow field data of the pump station runner.

[0045] In step S101, constructing a training data set includes: collecting pump station runner flow field data and hydraulic design parameters, and performing three-dimensional hydrodynamic numerical simulation on the runner under different hydraulic design parameters by using the orthogonal experimental design method, and combining spatial coordinates and time data to obtain the training data set.

[0046] Step S102: Construct a loss function based on the governing equations, initial conditions of the flow channel, and inlet and outlet boundaries, and determine the performance parameters.

[0047] In step S102, the governing equations are the Navier-Stokes equations.

[0048] In step S102, constructing the loss function based on the governing equations, initial conditions of the flow channel, and inlet and outlet boundaries includes: obtaining the loss function component of the governing equations based on the governing equations; obtaining the loss function component of the initial conditions based on the initial conditions of the flow channel; obtaining an extended function based on the coupling distance function of the inlet and outlet boundaries, and then obtaining the loss function component of the boundaries; and correcting the loss function component of the governing equations, the loss function component of the initial conditions, and the loss function component of the boundaries based on the extended function to obtain the final required loss function.

[0049] In the embodiments of the present invention, the performance parameters include the head loss of the cross-section, the axial velocity distribution uniformity, the comprehensive velocity distribution uniformity, and the calculation efficiency.

[0050] Step S103: Construct a physics-informed neural network. The input of the physics-informed neural network is the hydraulic design parameters, spatial coordinates, and time data, and the output is the flow field data of the pump station flow channel.

[0051] In step S103, the physics-informed neural network (PINN) is the physics-informed neural network model.

[0052] Step S104: Based on the loss function, use the training dataset to intensively train the physics-informed neural network through time-slice transfer learning to obtain the target physics-informed neural network model.

[0053] In step S104, intensively training the physics-informed neural network based on the loss function using the training dataset through time-slice transfer learning to obtain the target physics-informed neural network model includes: dividing the training dataset into a source domain dataset and a target domain dataset according to time; training the physics-informed neural network using the source domain dataset to obtain a source model; and training the source model using the target domain dataset to obtain the target physics-informed neural network model.

[0054] In step S104, the target physics-informed neural network model is the physics-informed neural network enhanced by time-slice transfer learning (TL-PINN).

[0055] Step S105: Determine multiple candidate hydraulic design parameters. Based on each candidate hydraulic design parameter, use the target physics-informed neural network model to obtain the corresponding candidate pump station flow channel flow field data, and calculate the corresponding candidate performance parameters using each candidate pump station flow channel flow field data.

[0056] In step S105, each candidate hydraulic design parameter, the corresponding time data, and the spatial coordinates are input into the target physics-informed neural network model to obtain the corresponding candidate pump station runner flow field data, and the corresponding candidate performance parameters are calculated using the candidate pump station runner flow field data. All the candidate performance parameters serve as candidate solutions for the subsequent objective function.

[0057] Step S106: Construct an objective function based on the performance parameters, and solve the objective function to obtain the optimal performance parameters from all the candidate performance parameters. The candidate pump station runner flow field data and the candidate hydraulic design parameters corresponding to the optimal performance parameters are the optimal flow field data and the optimal hydraulic design parameters.

[0058] In step S106, when solving the objective function, a multi-island genetic algorithm (MIGA) is used for the solution.

[0059] In some embodiments, Figure 2 is a schematic flowchart of the specific process of the pump station runner flow field prediction and optimization method based on the physics-informed neural network enhanced by transfer learning provided by the embodiments of the present invention. Figure 3 is a framework diagram of the physics-informed neural network model provided by the embodiments of the present invention. Figure 4 is a training process diagram of the physics-informed neural network model enhanced by time-slice transfer learning provided by the embodiments of the present invention. Figure 5 is a flowchart of the multi-island genetic optimization algorithm provided by the embodiments of the present invention.

[0060] As Figure 2 shown, the specific process of the pump station runner flow field prediction and optimization method based on the physics-informed neural network enhanced by transfer learning is as follows:

[0061] S1. Perform data collection and verification: Collect the flow velocity, pressure data of the pump station inlet and outlet runners and the runner hydraulic design parameters, and use the orthogonal experimental design method to perform three-dimensional hydrodynamic numerical simulations on the runners under different hydraulic design parameters to obtain the training dataset.

[0062] Specifically, S1 includes the following steps:

[0063] S11: Determine the hydraulic design parameters of the pump station inlet runner: It is necessary to collect the hydraulic design parameters of the pump station inlet runner according to the design documents or on-site measurements. The hydraulic design parameters include length, width, cross-sectional shape, bottom longitudinal slope, diffusion angle, submerged depth of the suction pipe, suspended height, distance from the rear wall, etc.;

[0064] S12: Determine the simulation initial conditions of the pump station inlet runner, including the simulation inlet and outlet boundary conditions, and record the pressure and flow velocity at the inlet (i.e., the inlet) and outlet (i.e., the outlet) of the inlet runner; the wall conditions, and determine whether to use the no-slip boundary condition or the slip boundary condition;

[0065] S13: Measure the hydrodynamic parameters of the actual intake channel: Use sensors and other measurement tools to collect pressure and flow velocity parameters in the channel, including time series data covering different spatial coordinates and different time points, as well as pressure and flow velocity data under different operating conditions (such as different flow rates), etc.;

[0066] S14: Construct a three-dimensional model of the intake channel of the pumping station using 3D modeling software such as UG and SolidWorks according to the determined hydraulic design parameters. Set simulation parameters in ANSYS Fluent software according to the measured boundary conditions and hydrodynamic parameters, and conduct three-dimensional hydrodynamic numerical simulations under multiple operating condition points to obtain velocity field and pressure field data of the intake channel;

[0067] S15: Statistically analyze and verify the consistency of results: Use statistical analysis methods, such as root mean square error and correlation coefficient method, to compare the consistency of the measured pressure field, flow velocity field data and numerical simulation results;

[0068] S16: Adjust the numerical simulation model and parameters: Judge whether it is necessary to adjust the model and parameter settings of the numerical simulation according to the consistency of the comparison results. For example, improve the simulation accuracy by improving mesh generation, adjusting the turbulence model, etc.;

[0069] S17: Determine the key hydraulic parameters (referring to other parameters in the hydraulic design parameters except length and width) that affect the flow field characteristics of the intake channel of the pumping station, and determine the allowable value range of each key hydraulic parameter with reference to the current "Code for Design of Pumping Stations";

[0070] S18: Set several reasonable value levels for the key hydraulic parameters of the intake channel, use the orthogonal experimental design method to determine the experimental factor table of the numerical simulation orthogonal scheme. At the same time, additional value levels can be set for sensitive parameters (i.e., some of the key hydraulic parameters) to expand the orthogonal table. Conduct CFD (Computational Fluid Dynamics) three-dimensional hydrodynamic numerical simulations according to the parameter combinations designed in the orthogonal table, and record the flow field data of each group (i.e., velocity field and pressure field data of the intake channel);

[0071] S19: Preprocess the collected flow field data of each group. The preprocessing includes data cleaning, removing outliers in the data, and filling in missing data using interpolation; Standardize the data using the Z-score standardization method; Divide the data into a training set and a test set according to a set ratio, such as a ratio of 4:1, to form the training data set of the subsequent PINN (Physics-Informed Neural Networks) model. The Z-score standardization formula is as follows:

[0072]

[0073] Where: x is the original data point; μ is the mean of the data set; s is the standard deviation of the data set; x' is the data point after standardization.

[0074] S2. Establish a mathematical model: Determine the governing equations and give the initial conditions of the flow channel, the inlet and outlet boundaries. Construct the loss function of the physics-informed neural network according to the governing equations, including the residuals of the boundary conditions, initial conditions, and governing equations (such as the N - S equations). Each residual is corrected using an extended function, and select the performance parameters that can reflect the flow field characteristics of the inlet flow channel of the pump station as the quantitative evaluation parameters of the flow field.

[0075] Specifically, S2 includes the following steps:

[0076] S21: Construct the mathematical model followed by the velocity field and pressure field in the inlet flow channel of the pump station, that is, the partial differential governing equations reflecting physical laws in the physics-informed neural network (PINN). The partial differential governing equations include the Navier–Stokes (N - S) equations for incompressible flow, initial conditions, and boundary conditions.

[0077] Specifically, S21 includes the following steps:

[0078] S211: First, construct the partial differential governing equations that the inlet flow channel of the pump station conforms to. That is, the unsteady incompressible flow in the inlet flow channel of the pump station can be described by the Navier–Stokes equations:

[0079]

[0080] Specifically, Equation (2) contains the following formulas:

[0081]

[0082] Where: u is the velocity vector, p is the pressure, t is the time, ρ represents the density of the fluid; v s represents the kinematic viscosity; b f is the body force; in this step, x, t ∈ Ω f,t , where x is the spatial coordinate (x, y, z), represents the fluid boundary region; T is the total duration; the velocity values u and pressure p are both functions of time t, spatial coordinate x, and variable parameter θ; θ is a d - dimensional parameter vector, including input or operation parameters, such as fluid properties (including density, kinematic viscosity, fluid pressure, flow velocity, etc.), the geometry of the inlet (i.e., the entrance) / exit region, and hydraulic design parameters; u is the velocity value in the x - axis direction, v is the velocity value in the y - axis direction, w is the velocity value in the z - axis direction; T represents the transpose.

[0083] S212: Given appropriate initial conditions and boundary conditions to constrain the governing equations so that the solutions of the velocity \(u\) and pressure \(p\) can be uniquely determined. The constraint conditions are shown as follows:

[0084]

[0085]

[0086] Among them: Equation (6) is the initial condition constraint, is the generalized differential operator, is the differential operator defining the initial conditions; Equation (7) is the boundary condition constraint, \(B\) is the generalized differential operator, represents the boundary region;

[0087] Specifically, the boundaries mentioned in S212 include Dirichlet boundaries and Neumann boundaries. The Dirichlet boundary and Neumann boundary are represented by the following formulas respectively:

[0088]

[0089] Among them: The domain of Equation (8) is \(\Gamma\) D , that is, the Dirichlet boundary; The domain of Equation (9) is \(\Gamma\) N , that is, the Neumann boundary; represents the normal vector (unit vector) of the boundary, perpendicular to the boundary surface.

[0090] S22: According to the partial differential control equation set of the physics-informed neural network, construct a loss function for training the parameters of the physics-informed neural network to obtain the solutions of the equation set, which consists of the Navier–Stokes equation loss, boundary condition loss, and initial condition loss, as shown in the following equations respectively:

[0091] \(L = L\) e +\(\alpha L\) b +\(\beta L\) i (10)

[0092]

[0093]

[0094]

[0095] Among them: \(L\) e , \(L\) b , \(L\) irespectively represent the control equation loss function component corresponding to the Navier-Stokes equation, the boundary loss function component corresponding to the boundary conditions, and the initial condition loss function component corresponding to the initial conditions; α and β are penalty (weight) coefficients used to balance different residual terms in the loss function and accelerate convergence during training; represents the velocity field predicted by PINN; represents the pressure field predicted by PINN; N b 、N e 、N i respectively represent the number of training data for different terms; is the predicted velocity at the nth data point; is the velocity at the nth data point given on the boundary; is the velocity at the nth data point at the initial time; the initial condition residual for any data point can be expressed as For any data point, the boundary condition residual can be expressed as represents the control equation residual of the ith equation at the nth data point, where the residuals of the four control equations for any data point are respectively:

[0096]

[0097] S23: Since the optimization performance of the soft constraint (initial / boundary condition) loss function depends on the magnitude of each term, it is difficult to allocate the weights of each term. Therefore, for the Dirichlet boundary and Neumann boundary mentioned in S21, a mixed forced initial / boundary condition constraint application method is adopted. Among them, the Neumann boundary condition is expressed as the loss of the equation shown in S22, that is, added in the form of a soft constraint. While the Navier–Stokes equation, initial conditions, and Dirichlet boundary conditions are applied in the form of hard constraints, adding a specific solution (expansion function) that separately satisfies the initial / boundary conditions to make it automatically satisfy the condition constraints, so as to reduce the optimization pressure of the boundary conditions on the loss function and accelerate the convergence of the neural network. While satisfying the condition that the solution result automatically satisfies the specific solution, it can accelerate the convergence of the physics-informed neural network in the reasonable gradient direction. The specific solution is constructed as follows:

[0098]

[0099] where: is the original output of the PINN neural network constructs a velocity field that satisfies certain physical constraints (initial conditions and boundary conditions), which is one of the final outputs of the model, is the original output of the PINN neural network The constructed pressure field that satisfies certain physical constraints (initial conditions and boundary conditions), which is one of the final outputs of the model. W is the weight matrix of the neural network, b is the bias term of the neural network, and u par is a particular solution of the velocity that exactly satisfies the initial / boundary conditions and is directly embedded in the solution of the neural network to ensure that the solution satisfies the Dirichlet and initial conditions. u par (x, 0) = u 0 (x), p par (x, 0) = p 0 (x), u 0 (x) is the initial velocity at t = 0; p 0 (x) is the initial pressure at t = 0; u b (x) is the boundary velocity; p b (x) is the boundary pressure; D(t, x, θ) is the distance function, which is a smooth function related to the minimum distance from the internal point to the boundary, that is, D is 0 on the boundary and Ω f ×{0} and increases away from the boundary. It is used to embed the initial / boundary conditions into the solution; on the boundary, D(t, x, θ) = 0, ensuring that the solution is completely controlled by u par and p par The farther away from the boundary, the larger D(t, x, θ) is, making the influence of the offset function gradually increase. p par is a particular solution of the pressure that exactly satisfies the initial / boundary conditions. Substitute equations (14) and (15) into equations (11) - (13) to correct the loss function components of the control equation, the initial condition loss function component, and the boundary loss function component, thereby obtaining the final required loss function.

[0100] S24: Determine the performance parameters of the flow field characteristics of the intake channel: In order to finally evaluate and optimize the intake channel structure, it is necessary to quantitatively evaluate the flow field characteristics of the intake structure. Select the following flow field characteristic performance parameters to comprehensively reflect the flow field characteristic parameters of the pump station intake structure, including the head loss H f from the inlet section to the inlet section of the intake pond, the uniformity of the mean axial velocity distribution of multiple sections of the intake structure the comprehensive uniformity of the axial velocity distribution of the suction pipes of multiple units based on flow rate weighting and the calculation efficiency η, which are respectively expressed by the following formulas:

[0101]

[0102] Where: H f is the section head loss, P in , P out are the total pressures at the inlet and outlet respectively, and ρ lis the density of the water-sediment two-phase flow, and g is the acceleration due to gravity;

[0103]

[0104] Where: is the axial velocity distribution uniformity of the cross-section of the water flow channel, is the average axial velocity of the cross-section, and u ai is the axial velocity of each unit of the cross-section, and m is the number of units divided by the cross-section;

[0105]

[0106] Where: is the average velocity distribution uniformity of the cross-section of the pump station intake structure, are the velocity distribution uniformities of the cross-sections at the 1 / 2 and 3 / 4 positions in the intake direction respectively, is the velocity distribution uniformity of the cross-section at the inlet of the intake sump;

[0107]

[0108] Where: is the comprehensive velocity distribution uniformity of the suction pipes of the pump station units based on flow weighting, is the velocity distribution uniformity of the characteristic cross-section of the suction pipe of the Nth unit, and Q n is the flow rate of the Nth unit;

[0109]

[0110] Where: η is the calculated efficiency of the pump station, is the average flow rate of the units, is the average head of the units, is the average power of the units.

[0111] S3: Construct a fully connected physics-informed neural network with 5 hidden layers and 30 neurons in each layer. The input layer is the spatio-temporal sampling data of each term of the control equation, and the output layer is the flow field data and performance parameters. The automatic differentiation algorithm is used to calculate the partial differential equation to approximate the exact solution of the partial differential equation. The hyperbolic tangent activation function tanh is used as the non-linear activation function, and the Adam and L-BFGS optimizer combination is used as the optimizer. The training parameters of the physics-informed neural network are randomly initialized using the Xavier initialization scheme.

[0112] Specifically, S3 includes the following steps:

[0113] S31: Construct a physics-informed neural network for solving the control equation (Navier-Stokes equation) of the pump station intake channel, and determine that its input layer parameters are spatio-temporal sampling data, which, for example, includes the time, spatial coordinates, and hydraulic design parameters of the flow field of the pump station intake channel structure. See Figure 3 The input layer parameters can be represented by (t, x, y, z, θ)), the output layer is the flow field data (i.e., the velocity field (i.e., the flow velocity field) and pressure field corresponding to the predicted intake channel flow field), and the flow field data can be represented by (u, v, w, p)), as well as performance parameters (i.e., the flow field characteristic parameters H f , and η);

[0114] S32: The physics-informed neural network consists of a fully connected neural network and a residual network. Construct 5 hidden layers, and add 30 neurons to each layer to the fully connected neural network;

[0115] S33: The derivative in the PDE (partial differential equation) is approximated by the derivative of the output with respect to the input of the physics-informed neural network. The activation function needs to be differentiable. Select the hyperbolic tangent activation function tanh with continuous derivative as the non-linear activation function; as Figure 3 shown, σ in the physics-informed neural network represents the mapping function of the activation function;

[0116] S34: According to the loss function mathematical model established in S22 and S23, construct the residual network of the physics-informed neural network (see Figure 3 the initial conditions, boundary conditions, and control equation residuals), including the control equation residuals, boundary condition residuals, and extended function parameters coupling the boundary function and distance function. Take the initial conditions and boundary conditions as the supervised data-driven part, and take the residuals of the Navier-Stokes equation as the unsupervised physics information part in the loss function. Use the automatic differentiation (AD) algorithm to calculate the partial differential operator to approximate the exact solution. The general idea of the AD algorithm is to use the chain rule to backpropagate the derivative from the output layer to the input layer;

[0117] S35: In order to balance the contributions of different terms in the equation, adopt a dynamic weight strategy to select the weight coefficients α and β, and adaptively update the coefficients using the gradient statistics of backpropagation during network training. At each training step, for example, the (k + 1)-th iteration, the estimated values of α and β can be calculated by the following formula:

[0118]

[0119] where: is the estimated value of α in the (k + 1)-th iteration, is the estimated value of β in the (k + 1)-th iteration, is the gradient operator under the d-dimensional parameter vector, is obtained from the maximum value, and respectively represent and the mean values of, and the initial value of the dynamic weight needs to be provided;

[0120] S36: Calculate the gradient of the parameters of the physics-informed neural network through the AD algorithm, and update the weighted coefficients for the next iteration using the moving average form:

[0121]

[0122]

[0123] where: α (k+1) is the α value of the (k + 1)-th iteration, α (k) is the α value of the k-th iteration, β (k+1) is the β value of the (k + 1)-th iteration, β (k) is the β value of the k-th iteration, and the coefficient λ is a hyperparameter used to determine the decay rate of the contribution of the dynamic weight of the previous step. Select λ = 0.1. A smaller λ makes the contribution of the previous value to the current dynamic weight greater, ensuring the stability of the adjustment during training;

[0124] S37: Use the Sobol sequence algorithm to perform random spatio-temporal sampling on the residual points within the computational domain. Given that the numbers of the boundary condition dataset, the initial condition dataset, and the equation residual point set are N b , N i , N e ;

[0125] S38: Adopt the optimization strategy of the adaptive optimization algorithm Adam and the L-BFGS optimizer to minimize the loss function in the equation, where the Admin optimization algorithm can achieve global fast convergence, and then obtain a high-precision solution by connecting to the L-BFGS optimization;

[0126] S39: The trainable parameters in the neural network are randomly initialized using the Xavier initialization scheme. When the physics-informed neural network training converges, that is, when the total loss function is less than the preset value, the solution is obtained.

[0127] S4: On the basis of the physics-informed neural network constructed in S1, S2, and S3, introduce a physics-informed neural network with time-slice transfer learning for enhanced training; among them, in the pre-training stage, preprocess based on the source domain dataset; in the retraining stage, use the target domain dataset to train the model;

[0128] Specifically, S4 includes the following steps:

[0129] S41: Use time-slice transfer learning to enhance the training of the physics-informed neural network to obtain TL-PINN (i.e., the physics-informed neural network enhanced by time-slice transfer learning) to overcome the problem of sparsity of measured data such as flow velocity and pressure in the pump station inlet channel flow field; the task of the source domain Ds is to use the flow field dataset obtained in S1, according to the time-sliced training dataset (which can be called the training time series dataset at this time), extract the coordinates of each spatio-temporal sampling point in the flow field area and the flow field data corresponding to the first half (0-T / 2) of the entire time series (i.e., the sampling point data in the first half of the training time series dataset), and use it as the source domain training data to train the established physics-informed neural network to obtain the source model (i.e., the pre-trained model); the target domain D T The task is to use the second half (T / 2-T) data of the entire time series as the target domain dataset (i.e., the sampling point data in the second half of the training time series dataset);

[0130] S42: In the pre-training stage, under the constraints of the N-S equation, initial conditions, and boundary conditions (i.e., under the constraints of the loss function obtained in S2), train the physics-informed neural network based on the dataset of the source domain Ds, so that the neural network model learns the basic laws of fluid dynamics and the general characteristics of the pump station inlet channel, and obtain the learned model structure and related network parameters. The model at this time is the pre-trained model (see Figure 4 );

[0131] S43: In the retraining stage, under the constraints of the N-S equation, initial conditions, and boundary conditions (i.e., under the constraints of the loss function obtained in S2), use the model training parameters (weights and biases) obtained from the source domain training as the initialization parameters for training the target model (i.e., the target physics-informed neural network model). Specifically, freeze the structure and parameters of the first L layers of the source model and transplant them into the target model, and fine-tune the source model on the target domain dataset to accurately capture the physical conditions of the channel (see Figure 4 );

[0132] S44: Evaluate the performance of the model optimized by transfer learning, pay attention to the accuracy and generalization ability of the model in predicting the characteristics of the pump station channel, and perform tuning according to the evaluation results.

[0133] S5: Construct an objective function with the selected performance parameters, and use the value range of the key hydraulic parameters of the inlet channel as the constraint conditions. Use the flow field data and performance parameters predicted by the model, and adopt the multi-objective optimization algorithm MIGA to obtain the optimal solution of the performance design parameters, and input it into the PINN model to obtain the flow field data of the optimal design parameters.

[0134] Specifically, S5 includes the following steps:

[0135] S51: First, construct an objective function for the performance parameters of the pump station intake channel predicted by the physics-informed neural network using the linear weighting method. The optimization objective is to minimize the objective function to minimize the section head loss as much as possible, improve the uniformity of the average axial velocity distribution at multiple sections, the comprehensive axial velocity distribution uniformity of the suction pipes of multiple units, and the calculation efficiency. The constraint condition is the value range of the key hydraulic parameters of the pump station intake channel determined in step S17. Determine the weights of the performance parameters and perform normalization processing on each performance parameter (normalization by the ratio relative to the reference value of each performance parameter), and then perform linear weighting to obtain the objective function f for multi-objective optimization:

[0136]

[0137] Where: is the weight coefficient of H f w MV is w CV is w η is the weight coefficient of η, η i is the reference value set for each performance parameter.

[0138] S52: Integrate the physics-informed neural network enhanced by time-slice transfer learning (TL-PINN) with the multi-island genetic algorithm (MIGA) so that MIGA can effectively use the results predicted by the physics-informed neural network to evaluate the performance of different hydraulic design parameters; that is, determine multiple candidate hydraulic design parameters, input each candidate hydraulic design parameter, the corresponding time data, and spatial coordinates into the target physics-informed neural network model to obtain the corresponding candidate pump station channel flow field data, and calculate the corresponding candidate performance parameters using the candidate pump station channel flow field data. All candidate performance parameters are used as candidate solutions for the subsequent objective function, and then the multi-island genetic algorithm (MIGA) is used to find the optimal solution.

[0139] Among them, the multi-island genetic algorithm (MIGA) is an improved genetic algorithm. As Figure 5 shown, in the t 1 -th generation population and the t 1 +1-th generation population, MIGA divides the population into multiple (for example, n 1 ) sub-populations (islands), and each sub-population independently performs genetic operations (selection, crossover, mutation) to explore local solutions. When a certain number of generations are reached or the migration condition is met, excellent individuals are migrated and gene exchange occurs between sub-populations to enhance the global search ability and population diversity. Repeat the iterative optimization until the termination condition (such as the maximum number of generations or fitness convergence) is met, and finally integrate all sub-populations to obtain the global optimal solution.

[0140] S53: Run the integrated optimization algorithm to perform multi-objective global search and optimization on all candidate performance parameters of the intake channel of the pumping station. Through multiple iterative optimizations, obtain the optimal performance parameters that meet the objective function and constraints. These performance parameters correspond to the hydraulic design parameters, which are the optimal solutions for the intake channel design parameters.

[0141] S54: The candidate pumping station channel flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameters are the optimal flow field data and optimal hydraulic design parameters. Numerical simulation can also be used to verify the optimal solution.

[0142] To implement the above embodiments, the present invention also proposes a pumping station channel flow field prediction and optimization system based on a physics-informed neural network enhanced by transfer learning.

[0143] Figure 6 It is a block diagram of a pumping station channel flow field prediction and optimization system based on a physics-informed neural network enhanced by transfer learning provided by an embodiment of the present invention.

[0144] As Figure 6 shown, the pumping station channel flow field prediction and optimization system based on a physics-informed neural network enhanced by transfer learning includes a training dataset construction module 11, a loss function determination module 12, a modeling module 13, a candidate solution determination module 14, and a prediction and optimization module 15, where:

[0145] The training dataset construction module 11 is used to construct a training dataset, which consists of hydraulic design parameters, spatial coordinates, time data, and pumping station channel flow field data of the pumping station channel.

[0146] The loss function determination module 12 is used to construct a loss function based on the control equation, initial conditions of the channel, and inlet and outlet boundaries, and determine the performance parameters.

[0147] The modeling module 13 is used to construct a physics-informed neural network. The input of the physics-informed neural network is hydraulic design parameters, spatial coordinates, and time data, and the output is the pumping station channel flow field data. Based on the loss function, use the training dataset to strengthen the training of the physics-informed neural network through time-slice transfer learning to obtain the target physics-informed neural network model.

[0148] The candidate solution determination module 14 is used to determine multiple candidate hydraulic design parameters. Based on each candidate hydraulic design parameter, use the target physics-informed neural network model to obtain the corresponding candidate pumping station channel flow field data, and calculate the corresponding candidate performance parameters using each candidate pumping station channel flow field data.

[0149] The prediction optimization module 15 is used to construct an objective function based on performance parameters, solve the objective function to obtain optimal performance parameters from all candidate performance parameters, and the candidate pump station runner flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameters are the optimal flow field data and optimal hydraulic design parameters.

[0150] Furthermore, in a possible implementation manner of the embodiment of the present invention, the training dataset construction module 11 is specifically used for: collecting pump station runner flow field data and hydraulic design parameters, and performing three-dimensional hydrodynamic numerical simulation on the runners under different hydraulic design parameters by using the orthogonal experimental design method to obtain a training dataset.

[0151] Furthermore, in a possible implementation manner of the embodiment of the present invention, the performance parameters include the head loss of the section, the axial velocity distribution uniformity, the comprehensive velocity distribution uniformity, and the calculation efficiency.

[0152] Furthermore, in a possible implementation manner of the embodiment of the present invention, the control equation in the loss function determination module 12 adopts the N-S equation.

[0153] Furthermore, in a possible implementation manner of the embodiment of the present invention, the loss function determination module 12 is specifically used for: obtaining the loss function component of the control equation based on the control equation; obtaining the loss function component of the initial condition based on the initial conditions of the runner; obtaining an extended function based on the inlet and outlet boundary coupling distance function, and further obtaining the boundary loss function component; correcting the loss function component of the control equation, the loss function component of the initial condition, and the boundary loss function component based on the extended function to obtain the finally required loss function.

[0154] Furthermore, in a possible implementation manner of the embodiment of the present invention, in the modeling module 13, based on the loss function, the training dataset is used to strengthen the training of the physics-informed neural network through time-slice transfer learning to obtain the target physics-informed neural network model, including: dividing the training dataset into a source domain dataset and a target domain dataset according to time; training the physics-informed neural network with the source domain dataset to obtain a source model; training the source model with the target domain dataset to obtain the target physics-informed neural network model.

[0155] Furthermore, in a possible implementation manner of the embodiment of the present invention, in the prediction optimization module 15, the multi-island genetic algorithm is used to solve the objective function.

[0156] It should be noted that the foregoing explanation of the embodiment of the pump station runner flow field prediction and optimization method based on the transfer learning-enhanced physics-informed neural network is also applicable to the pump station runner flow field prediction and optimization system based on the transfer learning-enhanced physics-informed neural network of this embodiment, which will not be elaborated here.

[0157] In an embodiment of the present invention, a training data set is constructed, which consists of hydraulic design parameters, spatial coordinates, time data, and pump station runner flow field data of a pump station runner; a loss function is constructed based on control equations, initial conditions of the runner, and inlet and outlet boundaries, and performance parameters are determined; a physics-informed neural network is constructed, the input of the physics-informed neural network is hydraulic design parameters, spatial coordinates, and time data, and the output is pump station runner flow field data; the physics-informed neural network is intensively trained based on the loss function using the training data set through time-slice transfer learning to obtain a target physics-informed neural network model; multiple candidate hydraulic design parameters are determined, corresponding candidate pump station runner flow field data are obtained by using each candidate hydraulic design parameter as the input to the target physics-informed neural network model, and corresponding candidate performance parameters are calculated by using each candidate pump station runner flow field data; a target function is constructed based on the performance parameters, and the target function is solved to obtain the optimal performance parameter from all candidate performance parameters. The candidate pump station runner flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameter are the optimal flow field data and the optimal hydraulic design parameters. In this case, the physics-informed neural network is intensively trained based on the loss function using the training data set through time-slice transfer learning to obtain a target physics-informed neural network model, which improves the accuracy of the model under sparse data conditions. By comprehensively considering the pump station runner based on the transfer learning-enhanced physics-informed neural network and the solution of the target function, the optimal flow field data is obtained, where the candidate hydraulic design parameter corresponding to the optimal performance parameter is the optimal hydraulic design parameter, realizing the efficient and accurate acquisition of prediction results and runner design optimization results, thus solving the problems of low prediction accuracy and optimization problems under sparse data conditions.

[0158] The transfer learning strategy adopted in the method and system of the present invention significantly improves the training efficiency and prediction accuracy of the physics-informed neural network model under sparse data. Meanwhile, the introduced multi-island genetic algorithm (MIGA) provides efficient global search capabilities for multi-objective optimization problems, ensuring the finding of optimal or near-optimal solutions in complex multi-parameter spaces. Therefore, the present invention has the potential to improve the existing pump station runner design to make it more economical, efficient, and reliable. The present invention aims to provide a high-precision and high-efficiency method for simulating and optimizing pump station runners. By integrating a physics-informed neural network (PINN) model enhanced by transfer learning, the present invention solves the optimization problem of the design of the intake runner of a pump station under data sparsity conditions. It improves the prediction accuracy of the model under sparse data conditions and enables fast and accurate solution space search in multi-objective optimization scenarios. That is, the present invention achieves accurate and efficient prediction results and is applicable to problems with few data samples. The present invention can be applied to the design and optimization of water conservancy projects, especially applicable to pump station design, runner optimization of hydropower stations, urban water service system upgrading projects, etc. In these projects, accurately simulating and optimizing the runner can significantly improve hydraulic efficiency, extend equipment life, and optimize energy consumption.

[0159] In some embodiments, the flow field prediction and optimization of pump station runners can be carried out by using enhanced CFD simulation, machine learning optimization, multidisciplinary optimization (MDO), surrogate model optimization. However, usually more data support is required, or it may not be as flexible and efficient as the solution of the present invention in terms of multi-objective optimization, computational efficiency, and user-defined requirements. Therefore, these alternative solutions may be used in specific scenarios, but the comprehensive optimization solution provided by the present invention has more advantages in a wide range of applications. The beneficial effects of the method and system of the present invention specifically include:

[0160] 1) Enhanced prediction accuracy: By integrating a physics-informed neural network (PINN) with transfer learning, the present invention can achieve high-precision flow field simulation using limited data, which is particularly crucial for projects with high data acquisition costs or conditional limitations.

[0161] 2) Improved design efficiency: Compared with traditional CFD simulation methods, the present invention significantly reduces the dependence on high-performance computing resources and at the same time reduces the running time of simulations, thus accelerating the design iteration cycle.

[0162] 3) Multi-objective optimization ability: The adoption of the advanced multi-island genetic algorithm (MIGA) makes it possible to optimize multiple performance parameters simultaneously, exceeding the limitations of single-objective or simple multi-objective common in traditional optimization algorithms.

[0163] 4) Competitive advantage: An enterprise adopting the present invention will be able to provide a more economical and efficient pump station runner design solution, and will have stronger market competitiveness compared with competitors. While saving more costs for customers, it can also provide products with better performance.

[0164] 5) Dual environmental and economic benefits: The optimized runner design not only reduces energy consumption but also lowers maintenance costs, bringing economic benefits to users while promoting environmental sustainability.

[0165] To implement the above embodiments, the present invention also provides an electronic device, including: a processor, and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the method provided in the foregoing embodiments.

[0166] To implement the above embodiments, the present invention also provides a computer-readable storage medium storing computer-executable instructions, which are used to implement the method provided in the foregoing embodiments when executed by a processor.

[0167] To implement the above embodiments, the present invention also provides a computer program product including a computer program, which implements the method provided in the foregoing embodiments when executed by a processor.

[0168] In the description of the foregoing embodiments, the descriptions with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0169] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, "a plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0170] Any process or method description represented in a flowchart or otherwise described herein can be understood to represent a module, segment, or portion of code including one or more executable instructions for implementing a customized logical function or process. The scope of the preferred embodiments of the present invention includes additional implementations where functions may be executed not in the order shown or discussed, including in a substantially simultaneous manner according to the functions involved or in a reverse order, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

[0171] The logic and / or steps represented in a flowchart or otherwise described herein, for example, can be considered a sequenced list of executable instructions for implementing a logical function, and can be embodied specifically in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device. As used in this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium include the following: an electrical connection having one or more wires (electronic device), a portable computer diskette (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable medium on which the program can be printed, as the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpretation, or other suitable processing as necessary, and then stored in a computer memory.

[0172] It should be understood that various parts of the present invention can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one of the following techniques known in the art or a combination thereof can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0173] Those of ordinary skill in the art can understand that all or part of the steps carried out in implementing the above-described embodiment methods can be completed by a program instructing relevant hardware. The program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0174] In addition, in each of the embodiments of the present invention, the functional units can be integrated into one processing module, or each unit can exist physically alone, or two or more units can be integrated into one module. The above-mentioned integrated module can be implemented in the form of hardware or in the form of a software functional module. When the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0175] The above-mentioned storage medium can be a read-only memory, a magnetic disk, an optical disc, etc. Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for predicting and optimizing flow field in pump station flow channel based on physical information neural network enhanced by transfer learning, characterized in that: include: Constructing a training data set, wherein the training data set consists of hydraulic design parameters, spatial coordinates, time data and flow field data of the pump station flow channel; Construct loss functions based on the governing equations, initial flow conditions, and inlet and outlet boundaries, and determine performance parameters; Constructing a physical information neural network, wherein the input of the physical information neural network is hydraulic design parameters, spatial coordinates and time data, and the output is flow field data of the pump station flow channel; Based on the loss function, the training data set is used to strengthen the training of the physical information neural network through time slice transfer learning to obtain a target physical information neural network model; Determine a plurality of candidate hydraulic design parameters, obtain corresponding candidate pump station flow field data based on each candidate hydraulic design parameter using the target physical information neural network model, and calculate corresponding candidate performance parameters using the flow field data of each candidate pump station flow field; An objective function is constructed based on the performance parameters, and the objective function is solved to obtain the optimal performance parameters from all candidate performance parameters. The candidate pump station flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameters are the optimal flow field data and the optimal hydraulic design parameters.

2. The method for predicting and optimizing flow field of pump station flow channel based on transfer learning enhanced physical information neural network according to claim 1 is characterized in that: The constructing of the training data set comprises: The flow field data and hydraulic design parameters of the pump station flow channel are collected, and the orthogonal experimental design method is used to perform three-dimensional hydrodynamic numerical simulation of the flow channel under different hydraulic design parameters to obtain a training data set.

3. The method for predicting and optimizing flow field of pump station flow channel based on transfer learning enhanced physical information neural network according to claim 1 is characterized in that: The control equation adopts NS equation.

4. The method for predicting and optimizing flow field of pump station flow channel based on transfer learning enhanced physical information neural network according to claim 1 is characterized in that: The loss function is constructed based on the control equation, the initial condition of the flow channel and the inlet and outlet boundaries, including: Obtaining a control equation loss function component based on the control equation; Obtaining an initial condition loss function component based on the initial condition of the flow channel; Based on the import and export boundary coupling distance function, the expansion function is obtained, and then the boundary loss function component is obtained; Based on the extended function, the control equation loss function component, the initial condition loss function component and the boundary loss function component are corrected to obtain the final required loss function.

5. The method for predicting and optimizing flow field of pump station flow channel based on transfer learning enhanced physical information neural network according to claim 1, characterized in that: The step of strengthening the training of the physical information neural network by using the training data set through time slice transfer learning based on the loss function to obtain a target physical information neural network model includes: Dividing the training data set into a source domain data set and a target domain data set according to time; Using the source domain data set to train the physical information neural network to obtain a source model; The source model is trained using a target domain data set to obtain a target physical information neural network model.

6. The method for predicting and optimizing flow field of pump station flow channel based on transfer learning enhanced physical information neural network according to claim 1, characterized in that: The multi-island genetic algorithm is used to solve the objective function.

7. The method for predicting and optimizing flow field of pump station flow channel based on transfer learning enhanced physical information neural network according to claim 1, characterized in that: The performance parameters include head loss of the cross section, axial velocity distribution uniformity, comprehensive velocity distribution uniformity and calculation efficiency.

8. A pump station flow field prediction and optimization system based on a physical information neural network enhanced by transfer learning, characterized in that: include: A training data set construction module is used to construct a training data set, wherein the training data set consists of hydraulic design parameters, spatial coordinates, time data and flow field data of the pump station flow channel; A loss function determination module is used to construct a loss function based on the control equation, the initial conditions of the flow channel and the inlet and outlet boundaries, and determine the performance parameters; A modeling module is used to construct a physical information neural network, the input of which is hydraulic design parameters, spatial coordinates and time data, and the output is flow field data of the pump station flow channel; based on the loss function, the training data set is used to strengthen the training of the physical information neural network through time slice transfer learning to obtain a target physical information neural network model; A candidate solution determination module is used to determine a plurality of candidate hydraulic design parameters, obtain corresponding candidate pump station flow field data based on each candidate hydraulic design parameter using the target physical information neural network model, and calculate corresponding candidate performance parameters using the flow field data of each candidate pump station flow field; The prediction and optimization module is used to construct an objective function based on the performance parameters, and solve the objective function to obtain the optimal performance parameters from all candidate performance parameters. The candidate pump station flow field data and candidate hydraulic design parameters corresponding to the optimal performance parameters are the optimal flow field data and the optimal hydraulic design parameters.

9. An electronic device, characterized in that: include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executable instructions; The processor executes the computer-executable instructions stored in the memory to implement the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, which are used to implement the method according to any one of claims 1 to 7 when executed by a processor.

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