A design method and system for the main pump of a lead-cooled fast reactor oriented to digital twin

Abstract

The present invention discloses a lead-cooled fast reactor main pump design method and system for digital twins, which relates to the field of pump design technology, and includes the following steps: constructing a parameterized lead-cooled fast reactor main pump flow channel geometry model; generating control equations and boundary conditions for describing the flow field inside the main pump; training a PINN proxy model through a CFD simulation data set, control equations and boundary conditions to obtain a prediction model; deploying the prediction model in a digital twin system to obtain multiple physical quantities of the lead-cooled fast reactor main pump flow field, solving the main pump design optimization problem through multiple physical quantities, and obtaining a main pump design solution. The present invention avoids the shortcoming of the PINN proxy model in the traditional CFD algorithm that requires recalculation due to changes in design and operating parameters under different application scenario requirements, and can achieve rapid simulation of its internal flow field with extremely low computing time cost and computing resource cost, greatly reducing the design cycle of the main pump.

Description

Technical Field

[0001] The present invention relates to the technical field of pump design, and in particular to a lead-cooled fast reactor main pump design method and system for digital twins. Background Art

[0002] Lead-cooled fast reactor (LFR) has good thermal hydraulic performance, stable chemical properties, and small neutron absorption cross section and other safety advantages, and is recognized as the most promising fourth-generation reactor selection. Its main pump, as a key component of the primary circuit, faces serious corrosion problems caused by the flow of high temperature, high density and high flow rate liquid metal coolant during operation, which poses a challenge to the long-term operation of the reactor without refueling. The distribution of corrosion is closely related to the flow field inside the main pump. Therefore, compared with traditional working fluid pumps, the design ideas of the main pump of lead-cooled fast reactor mainly focus on the external characteristics, and the design method needs to pay more attention to the flow field inside the pump to reduce corrosion.

[0003] Traditional pump designs are mostly based on the existing mature mother pump profiles to carry out pump parameter optimization design. As an immature design that has not yet been put into commercial use, the lead-cooled fast reactor and its main pump have not formed standardized design specifications, and it is difficult to find a reference mother pump design for specific operating requirements. At the same time, there are many design parameters in traditional pump design, which will lead to the mutual coupling influence between multiple parameters, making its design cycle long and the experimental verification cost high. Traditional pump design takes improving the pump head and efficiency as the design goal. It is difficult to carry out parameter optimization and multi-objective collaborative design for the flow field inside the pump, and it is difficult to consider the corrosion of the pump body material caused by high-temperature and high-flow liquid metal.

[0004] Digital Twins emerged in the process of traditional industry's transformation to digitalization. This structure can provide two-way communication between digital virtual assets and physical entity states. Digital Twins have two major functions: state tracking and optimization feedback. The digital system can quickly solve the state of the physical system based on the surrogate model, and can perform optimization feedback to find the optimal design parameters. If it is applied to the design of LFR main pumps, it can realize the instant solution of the flow field in the pump under different states, making it possible to apply optimization algorithms to design structures or control schemes with a small time cost, taking into account both accuracy and efficiency. In addition, digital twins have the potential to realize instant multi-physics field coupling simulation, accurately solve the main pump material stress, temperature and corrosion distribution, and then be compatible with more comprehensive optimization goals, and design LFR main pumps with better hydraulic performance and longer life. For LFR main pumps that have been designed and deployed, digital twins can also perform dynamic optimization control and fault detection and identification to reduce maintenance costs and enable the main pump to operate stably and continuously for a long period of time. Therefore, the application of digital twin technology can systematically develop the simulation, design and control functions of the LFR main pump, which is of great significance to the development of lead-cooled fast reactor technology.

[0005] The current method for calculating the flow field in the pump under different design parameters is mainly the traditional CFD numerical simulation. This method uses a semi-implicit method to solve the various parameters in the fluid domain. Its accuracy and convergence depend on the degree of grid subdivision, resulting in a contradiction between calculation accuracy and speed. For the design method of the lead-cooled fast reactor main pump, which is directly related to the optimization target and the flow field, the time cost of iterative optimization design using the traditional method is extremely high. At the same time, when solving the discrete partial differential control equation (PDE), a large amount of data will be generated at each grid point, and the space required to store this data is very large. PINN (Physics-Informed Neural Network), as a proxy model, is a method for directly solving partial differential equations with neural networks, and the results are interpretable. In the digital twin, it is used to replace the traditional iterative solution of the PDE discretized by grid. Due to the structural advantages of the neural network itself, the solution of the equation can be directly output in a short time, so it plays the role of state tracking of the spatiotemporal distribution of the physical field, and the approximate distribution of the flow field in the lead-cooled fast reactor main pump can be obtained in real time in the online deployment mode.

[0006] Under different application scenario requirements, the design of the main pump will have different structural parameters and operating parameters. However, for the control equation of the main pump, changes in the main pump structural parameters will cause changes in the shape of the solution domain and its boundary. Changes in operating parameters will cause changes in the source terms and boundary conditions in the equation. At this time, PINN needs to be retrained, and the computational time and resource costs are too high, which ultimately leads to a long design cycle for the main pump. Summary of the invention

[0007] The present invention provides a lead-cooled fast reactor main pump design method and system for digital twins, which solves the problem that the design of the main pump will have different structural parameters and operating parameters under different application scenario requirements, and different structural parameters and operating parameters will affect the control equation of the main pump, so that PINN needs to be retrained, which ultimately leads to the main pump design cycle being too long and the calculation time cost and computing resource cost being too high.

[0008] In a first aspect, the present invention provides a lead-cooled fast reactor main pump design method for digital twin, comprising the following steps:

[0009] Obtaining adjustable structural parameters of the lead-cooled fast reactor main pump, and constructing a parameterized lead-cooled fast reactor main pump flow channel geometry model according to the adjustable structural parameters;

[0010] Determine the specified structural parameters, operating parameters and control equation type of the main pump, and generate the control equations and boundary conditions for describing the flow field in the main pump in the parameterized lead-cooled fast reactor main pump flow channel geometry model according to the specified structural parameters, operating parameters and control equation type of the main pump;

[0011] Determine the number of layers, number of neurons, and activation function type of each branch and trunk of the PINN proxy model according to the actual prediction performance requirements, and build the PINN proxy model;

[0012] Obtain a CFD simulation data set, train the PINN agent model through the CFD simulation data set, control equations and boundary conditions, and obtain a prediction model;

[0013] The prediction model is deployed in the digital twin system, and the corresponding structural parameters and operating parameters are obtained according to the target operating conditions and design requirements in different application scenarios. The corresponding structural parameters and operating parameters are input into the prediction model to obtain multiple physical quantities of the flow field of the main pump of the lead-cooled fast reactor.

[0014] The main pump design optimization objective and corresponding constraint conditions are defined by multiple physical quantities to obtain the main pump design optimization problem. The main pump design optimization problem is solved to obtain the main pump design scheme.

[0015] Preferably, the adjustable structural parameters include the inner diameter of the flow channel, the inlet and outlet installation angles of each cylindrical layer of the blade, the blade profile and the impeller hub diameter.

[0016] Preferably, the control equation types include mass equation, energy equation, momentum conservation equation and turbulence model equation, and the boundary conditions include inlet and outlet conditions and no-slip boundary conditions of fluid-solid wall;

[0017] The general formula of the control equations and boundary conditions is as follows:

[0018]

[0019] In the formula, is the differential operator in the control equation, u is the physical quantity of the flow field in the main pump to be determined, x is the spatial coordinate, t is the time, α is the structural parameter, β is the operating condition parameter, f is the source term of the control equation, Ω is the control volume, is the fluid domain boundary, T is the simulation duration, S α is the value range of the structural parameters, S β is the value range of the working condition parameters, is the differential operator in the boundary condition, g s is the source term of the boundary condition.

[0020] Preferably, the construction of the PINN agent model is specifically as follows:

[0021] U(x,t,α,β;θ)=DN(IL(DN1(x,t),DN2(α),DN3(β)));

[0022] Where U is the predicted value of the physical quantity u of the flow field in the main pump to be sought by the PINN proxy model, x is the spatial coordinate, t is the time, α is the structural parameter, β is the operating condition parameter, θ is the adjustable parameter, DN, DN1, DN2 and DN3 are multi-layer fully connected feedforward neural networks, and IL is the integrated information layer;

[0023] The fully connected feedforward neural network has the following expression:

[0024]

[0025] Where: z is the input vector, d i is the dimension of the input vector, d o is the output vector dimension, n l is the first, fully connected layer, l is the number of network layers, Represents a composite operation of two functions, where the output of the former is used as the input of the latter;

[0026] The fully connected layer is defined as follows:

[0027]

[0028] In the formula, is the kth neuron in the i-th fully connected layer, η i is the number of neurons in the i-th fully connected layer;

[0029] Each neuron receives all the outputs of the previous layer, processes them linearly, and then outputs them through a nonlinear activation function:

[0030]

[0031] In the formula, For neurons To the previous layer n i-1 The weight vector of For neurons The bias of For neurons A unary nonlinear activation function.

[0032] Preferably, the training of the PINN proxy model by using the CFD simulation data set, control equations and boundary conditions comprises the following steps:

[0033] The flow field under specific structure and working parameters is solved through CFD simulation, and all points located at the boundary of the fluid domain are collected as the total set of boundary sampling points to obtain the CFD simulation data set;

[0034] Construct a discriminator, which is used to determine whether the prediction of the flow field by the PINN proxy model obeys the probability distribution of the CFD simulation data set; define an adversarial training loss function according to the output result of the discriminator;

[0035] In Ω(α)×[0,T]×S α ×S β Take the total set of internal control points;

[0036] exist Construct the total set of boundary control points;

[0037] Divide the total set of internal control points, the total set of boundary control points and the total set of boundary sampling points into small batches that do not overlap with each other to obtain a training set;

[0038] The PINN agent model is used as a generator, and the equation loss function and boundary condition loss function are defined according to the control equation and boundary conditions;

[0039] The training of the PINN proxy model is transformed into a multi-objective optimization problem for solution. The optimization goal is to minimize the adversarial training loss function and maximize the equation loss function and the boundary condition loss function.

[0040] Preferably, the adversarial training loss function is defined according to the output result of the discriminator, as shown below:

[0041]

[0042] In the formula, is the anti-training loss function, B s is the total set of boundary sampling points, B p is the total set of internal control points, θ D is the discriminator adjustable parameter, is the expected value, D(z,u;θ D ) is the discriminator, z is the input variable;

[0043] The equation loss function and the boundary condition loss function are defined according to the control equation and the boundary conditions, as shown below:

[0044]

[0045]

[0046] In the formula, is the loss function of the equation, is the boundary condition loss function, C p is the CFD simulation data set, U is the predicted value of the physical quantity u of the flow field in the main pump to be determined by the PINN proxy model;

[0047] The optimization objective is as follows:

[0048]

[0049] In the formula, min means minimization and max means maximization.

[0050] Preferably, the step of converting the training of the PINN proxy model into a multi-objective optimization problem for solving comprises the following steps:

[0051] Set the number of iterations, the training batch of the training set, and the learning rate of the generator and discriminator;

[0052] Initialize the model parameters of the generator and discriminator;

[0053] Get the discriminator gradient and update the discriminator parameters according to the discriminator gradient of this training batch;

[0054] Get multiple first gradients of the generator;

[0055] Copying multiple first gradients of the generator to obtain multiple second gradients;

[0056] Obtain the inner products of the multiple first gradients and the multiple second gradients respectively, and if the inner products are non-negative, update the parameters of the generator, otherwise perform orthogonalization processing;

[0057] Traverse all batches in the data set and repeat the above parameter update process of the discriminator and generator until the set number of iterations is reached to obtain the prediction model.

[0058] Preferably, the obtaining of the discriminator gradient is specifically as follows:

[0059]

[0060] In the formula, g is the discriminator gradient, is the gradient operator, j is the jth training batch;

[0061] The parameters of the discriminator are updated according to the discriminator gradient of this training batch, as shown below:

[0062]

[0063] Where η is the learning rate of the discriminator update;

[0064] The method of obtaining multiple first gradients of the generator is specifically as follows:

[0065]

[0066] Where g1, g2 and g3 are the first gradients in different directions;

[0067] The multiple first gradients of the copy generator are obtained to obtain multiple second gradients, as shown below:

[0068] g′1: =g1, g′2: =g2, g′3: =g3;

[0069] Where g′1, g′2 and g′3 are the second gradients in different directions;

[0070] The parameters of the generator are updated as follows:

[0071] θ j+1 : =θ j -ε(g′1+g′2+g′3);

[0072] Where ε is the learning rate of the generator update.

[0073] In a second aspect, the present invention provides a lead-cooled fast reactor main pump design method system for digital twins, comprising:

[0074] An acquisition module is used to acquire the adjustable structural parameters of the lead-cooled fast reactor main pump and to construct a parameterized lead-cooled fast reactor main pump flow channel geometry model according to the adjustable structural parameters;

[0075] A determination module is used to determine the specified structural parameters, operating parameters and control equation type of the main pump, and generate control equations and boundary conditions for describing the flow field in the main pump in the parameterized lead-cooled fast reactor main pump flow channel geometry model according to the specified structural parameters, operating parameters and control equation type of the main pump;

[0076] A construction module is used to determine the number of layers, number of neurons and activation function type of each branch and trunk of the PINN proxy model according to the actual prediction performance requirements, and to construct the PINN proxy model;

[0077] A training module is used to obtain a CFD simulation data set, train the PINN proxy model through the CFD simulation data set, control equations and boundary conditions, and obtain a prediction model;

[0078] A calculation module is used to deploy the prediction model in the digital twin system, obtain the corresponding structural parameters and operating parameters according to the target operating conditions and design requirements in different application scenarios, and input the corresponding structural parameters and operating parameters into the prediction model to obtain multiple physical quantities of the flow field of the lead-cooled fast reactor main pump;

[0079] The design module is used to define the main pump design optimization objectives and corresponding constraints through multiple physical quantities, obtain the main pump design optimization problem, solve the main pump design optimization problem, and obtain the main pump design solution.

[0080] Compared with the prior art, the present invention has the following beneficial effects:

[0081] The present invention first constructs a parameterized lead-cooled fast reactor main pump flow channel geometry model, and provides control equations and boundary conditions for describing the flow field in the main pump. A PINN proxy model is constructed, and the PINN proxy model is trained from three aspects: CFD simulation data set, control equations and boundary conditions, to obtain a prediction model. Under different application scenario requirements, the design of the main pump will have different structural parameters and operating parameters. The prediction model can be compatible with changes in the solution domain and the shape of its boundary caused by changes in different structural parameters, and can also be compatible with changes in source terms and boundary conditions in the control equation caused by changes in different operating parameters. The prediction model is then deployed in a digital twin system, and the corresponding structural parameters and operating parameters are obtained according to the target operating conditions and design requirements in different application scenarios, and the main pump flow field under different structures and operating parameters is quickly solved without retraining the PINN. The present invention solves the contradiction between design accuracy and speed in the product design process of the lead-cooled fast reactor main pump, avoids the shortcoming of the PINN proxy model in the traditional CFD algorithm that requires recalculation due to changes in design and operating parameters under different application scenario requirements, and can achieve rapid simulation of its internal flow field with extremely low computing time cost and computing resource cost, greatly reducing the design cycle of the main pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0083] Figure 1 It is a flowchart of a design method for a lead-cooled fast reactor main pump oriented to digital twins of the present invention;

[0084] Figure 2 A schematic diagram of the main pump structure and fluid domain grid of Example 1 of the present invention;

[0085] in, Figure 2 (a): Schematic diagram of the main pump structure, Figure 2 (b): Schematic diagram of the fluid domain grid;

[0086] Figure 3 This is a schematic diagram of the proxy model structure of Example 1 of the present invention;

[0087] Figure 4 Schematic diagram of the discriminator structure of embodiment 1 of the present invention;

[0088] Figure 5 This is a flow chart of agent model training according to Embodiment 1 of the present invention. DETAILED DESCRIPTION

[0089] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] The present invention provides a lead-cooled fast reactor main pump design method for digital twins. Aiming at the defects existing in the prior art, an agent model is established with the smallest possible computing cost to quickly and accurately quantitatively reflect the relationship between the flow field in the lead-cooled fast reactor main pump and various design parameters, thereby replacing the slow flow field solution process of the traditional grid CFD method, solving the contradiction between calculation accuracy and speed, and making it possible to economically apply various mature optimization algorithms to the lead-cooled fast reactor main pump design scenario for digital twins.

[0091] The following steps are involved:

[0092] Step 1: Obtain the structural parameters of the lead-cooled fast reactor main pump and construct a parameterized lead-cooled fast reactor main pump flow channel geometry model based on the structural parameters.

[0093] According to the target working conditions and design requirements, the user imports the parametric geometric model of the flow channel of the lead-cooled fast reactor main pump containing adjustable structural parameters into the system, that is, Figure 1 The parametric model import module in the . The parametric model import module can design and construct the structural parameters of the geometric model of the flow channel of the lead-cooled fast reactor main pump according to different design goals (power, size, specific speed, head and efficiency, etc.) and complex working conditions (flow, temperature and fluid properties, etc.). The structural parameters include the inner diameter of the flow channel, the inlet and outlet installation angles of each cylindrical layer of the blade, the blade profile and the impeller hub diameter.

[0094] Step 2: Determine the specified structural parameters, operating parameters and control equation type of the main pump according to the specific main pump design objectives, and generate the control equations and boundary conditions used to describe the flow field inside the main pump in the parameterized lead-cooled fast reactor main pump flow channel geometry model according to the specified structural parameters, operating parameters and control equation type of the main pump.

[0095] Based on the user-defined structural parameters and operating parameters as input variables, and the user-specified control equation type, the control equations and boundary conditions for the feedback flow field and performance of the main pump are automatically generated. The control equations include mass equations, energy equations, momentum conservation equations, and turbulence model equations, and the boundary conditions include inlet and outlet conditions and no-slip boundary conditions on the fluid-solid wall. Figure 1 The governing equations and boundary conditions module in .

[0096] The general form of the governing equations and boundary conditions is as follows:

[0097]

[0098] In the formula, is the differential operator in the control equation, u is the physical quantity of the flow field in the main pump to be determined, x is the spatial coordinate, t is the time, α is the structural parameter, β is the operating condition parameter, f is the source term of the control equation, Ω is the control volume, is the fluid domain boundary, T is the simulation duration, S α is the value range of the structural parameters, S β is the value range of the working condition parameters, is the differential operator in the boundary condition, g s is the source term of the boundary condition.

[0099] Step 3: Determine the number of layers, number of neurons, and activation function type of each branch and trunk of the PINN proxy model according to different parameter types and training results, and build the PINN proxy model. Figure 1 The model building module in .

[0100] In this embodiment, the training effect refers to the prediction performance requirement of the model for different parameter changes. For example, according to engineering needs, it is hoped that the model can predict the flow field under different parameters with higher accuracy.

[0101] Users can customize specific scales of pre-processing input channels for different parameters according to different parameter types and expected training results. Figure 1 The model building module in .

[0102] The PINN agent model is as follows:

[0103] U(x,t,α,β;θ)=DN(IL(DN1(x,t),DN2(α),DN3(β))) (2)

[0104] In the formula, U is the predicted value of the physical quantity u of the flow field in the main pump to be determined by the PINN model, θ is an adjustable parameter, DN, DN1, DN2 and DN3 are multi-layer fully connected feedforward neural networks, and IL is the integrated information layer. Define (x, t, α, β) as the input variable z.

[0105] The fully connected feedforward neural network has the following expression:

[0106]

[0107] Where z is the input vector, d i is the dimension of the input vector, d o is the output vector dimension, n iis a fully connected layer, i=1,2,...,l, l is the number of network layers, Represents a composite operation of two functions, where the output of the former serves as the input of the latter.

[0108] The fully connected layer is defined as follows:

[0109]

[0110] Where: is the kth neuron in the i-th fully connected layer, η i is the number of neurons in the i-th fully connected layer.

[0111] Each neuron receives all the outputs of the previous layer, processes them linearly, and then outputs them through a nonlinear activation function:

[0112]

[0113] In the formula, For neurons To the previous layer n i-1 The weight vector of For neurons The bias of For neurons A unary nonlinear activation function.

[0114] Step 4: Obtain CFD simulation data set, train the PINN proxy model through CFD simulation data set, control equations and boundary conditions, and obtain the prediction model. Figure 1 The model training module in .

[0115] The flow field under specific structure and working parameters is solved through CFD simulation, and all points located at the boundary of the fluid domain are collected as the total set of boundary sampling points to obtain the CFD simulation data set;

[0116] B s ={(u i , z i )|i=1,...,n s} (6)

[0117] In the formula, B s is the total set of boundary sampling points, n s is the number of boundary sampling points, u i is the physical quantity of the flow field in the main pump to be determined.

[0118] In Ω(α)×[0,T]×S α ×S β Take the total set of internal control points:

[0119] C p ={zi |i=1,...,N p} (7)

[0120] In the formula, C p is the total set of internal control points, N p is the number of internal control points, z i is the ith input variable.

[0121] exist Construct the total set of boundary control points at:

[0122] B p ={z i |i=1,...,n p} (8)

[0123] In the formula, B p is the total set of boundary control points, n p is the number of boundary control points;

[0124] Divide the total set of internal control points, the total set of boundary control points, and the total set of boundary sampling points into small batches that do not overlap with each other to prevent memory overflow, and obtain the training set:

[0125]

[0126] Where M is the batch size, is the i-th internal control point, boundary control point, and boundary sampling point batch.

[0127] Construct a discriminator, which is used to determine whether the prediction of the flow field by the PINN proxy model obeys the probability distribution of the CFD simulation data set. The discriminator is a fully connected feedforward neural network:

[0128] D(z,u;θ D )=DN D (z,u)(10)

[0129] In the formula, θ D is an adjustable parameter of the discriminator.

[0130] The output of the discriminator is a real number between 0 and 1, which is used to measure the degree to which the input data is close to the probability distribution of boundary sampling. The larger the output, the more the input data obeys the probability distribution of boundary sampling. Based on this, the loss function in adversarial training is defined (the logarithm is based on 2 if not specified):

[0131]

[0132] Where V A,B (θ,θ D ) is the adversarial loss function of the elements in the set A and B, is the expected value of all elements in set A after being acted upon by mapping f.

[0133] For the generator U, in addition to imitating the data distribution on the boundary, its training purpose should also include solving the control equation and making the solution obey the boundary conditions, so the equation loss function and the boundary condition loss function are defined:

[0134]

[0135]

[0136] In the formula, is the equation loss function of the elements in set A; is the boundary loss function of the elements in set A.

[0137] Therefore, training the proxy model is to solve the multi-objective optimization problem. While ensuring that the discriminator has the strongest ability to distinguish the generated data from the distribution of sampled data at the boundary, the generator can make the discriminator output value as close to 1 as possible, and at the same time achieve a satisfactory solution to the control equation and meet the boundary conditions:

[0138]

[0139] Each traversal of the set C is called p , B p , B s All the batches in are one training round, and the data of the j+1 batch is processed as follows:

[0140] Update the discriminator:

[0141]

[0142] is the discriminator parameter after training with the i-th batch of data, η is the learning rate of the discriminator update, which is a positive number close to 0; θ i is the generator parameter after training with the i-th batch of data.

[0143] Calculate the direction of the generator gradient descent:

[0144]

[0145] Theoretically, the directions of these three gradient descents should be the same, but since the source of the simulated boundary data is CFD simulation, it is necessary to solve discrete partial differential equations, and its accuracy depends on the quality of the grid. Therefore, there must be a certain error between the neural network method and the meshless direct solution of the control equation; in addition, if the neural network has fewer parameters, it may not be possible to satisfy both the boundary conditions and the control equation at the same time. Therefore, there may be some conflict between these three gradient descent directions when they are about to converge. In order to resolve this conflict, the following conflicting gradient method is used to determine the gradient descent direction:

[0146] Duplicate three gradients and make

[0147] g′1: =g1, g′2: =g2, g′3: =g3 (17)

[0148] Calculate inner product <g′ i , g k >; i, k = 1, 2, 3; i ≠ k, if it is non-negative, no operation is required, if it is negative, orthogonalization is performed:

[0149]

[0150] Determine the final gradient descent direction and update the generator network parameters:

[0151] θ j+1 : =θ j -ε(g′1+g′2+g′3) (19)

[0152] Where ε is the learning rate of the generator update, which is a positive number close to 0.

[0153] The model training is completed by traversing all batches in the dataset and repeating the above process for the specified number of iterations.

[0154] Step 5: Deploy the prediction model in the digital twin system, obtain the corresponding structural parameters and operating parameters according to the target operating conditions and design requirements in different application scenarios, and input the corresponding structural parameters and operating parameters into the prediction model to obtain multiple physical quantities of the main pump flow field of the lead-cooled fast reactor. Figure 1 The state tracking module in .

[0155] Step 6: Users can customize the objectives and constraints of the optimization design of the lead-cooled fast reactor main pump, construct a paradigm for multi-objective collaborative optimization problems, and select the corresponding optimization algorithm. Then, the multi-objective collaborative optimization problem is solved according to the algorithm selected by the user to obtain a collection of a series of optimization design solutions. Figure 1 The multi-objective collaborative optimization module in .

[0156] Step 7: Display the operating status of the main pump under each design scheme given in the previous step of the module. The user can export the optimized main pump structure design or control scheme design and the accompanying related information. Figure 1 The result output module in .

[0157] Example

[0158] Step 1: Construct a parametric lead-cooled fast reactor main pump flow channel geometry model and import it into the parametric model import module. Figure 2 The axial flow lead-bismuth main pump structure (left) and fluid domain grid (right) are shown in the schematic diagram, and the adjustable structural parameters include the inner diameter of the flow channel, the inlet and outlet installation angles of each cylindrical layer of the blade, the blade profile and the impeller hub diameter. In this embodiment, these parameters are fixed unchanged, and a control scheme is designed for an axial flow lead-bismuth main pump with a given structural design.

[0159] Step 2: Define all control equations and boundary conditions required to describe the flow field in the main pump in the control equation and boundary condition module. The design goal of the axial flow lead-bismuth main pump is to reduce the flow velocity near the moving blades as much as possible to reduce the impact of corrosion, while maximizing the hydraulic efficiency, when the reactor has a specific coolant flow demand (given outlet flow) and the main pump meets the head requirement. Therefore, only steady-state mass and momentum conservation equations are required in this embodiment. In addition, since the coolant is liquid metal, it is regarded as incompressible flow, so the control equation is:

[0160]

[0161] Where V is the velocity vector of the fluid micro-group in the main pump, which has components in three directions; x is the position vector of the fluid micro-group, β is the operating parameter, including the rotor speed and the outlet volume flow rate, where the rotor speed can be actively controlled and the outlet cross-sectional volume flow rate is determined by the reactor requirements; Ω(α) is the fluid domain, and F(x, β) is the acceleration caused by external force / kg·m -1 ·s -2 , ρ LBE is the density of lead-bismuth eutectic alloy (LBE) / kg·m -3 , v LBE is the kinematic viscosity of the lead-bismuth eutectic alloy / m 2 ·s -1 .

[0162] The working condition parameters are:

[0163] β=[ω,q v ](twenty one)

[0164] Where ω is the rotor blade speed (angular velocity) / rad·s -1 ;q Vis the outlet cross-sectional volume flow rate / m 3 ·s -1 .

[0165] The external force is composed of gravity, inertial centrifugal force and Coriolis force caused by the rotation of the rotor blades:

[0166]

[0167] Where: g is the acceleration due to gravity / kg·m -1 ·s-2,Ω m is the fluid domain of the flow channel where the moving blade is located;

[0168] Define the input variable z and output variable u:

[0169]

[0170] Governing equation vector:

[0171]

[0172] And the source term:

[0173]

[0174] The boundary conditions include zero total inlet pressure, a given outlet cross section, and no-slip boundary conditions at each fluid-solid wall:

[0175]

[0176] Where: n i is the normal unit vector at the inlet section, is the inlet cross section, n o is the normal unit vector at the outlet section, is the outlet cross section, A o is the outlet cross-sectional area / m 2 , For the moving blades and their hubs, are all fluid-solid walls that are stationary relative to the absolute reference system, is the fluid domain boundary.

[0177] The boundary condition vector is defined accordingly:

[0178]

[0179] and the corresponding source terms:

[0180]

[0181] Step 3: Use the model building module to build a multi-input channel PINN proxy model network structure as a generator, such as Figure 3As shown, each activation function uses the Leaky Relu function:

[0182] LReLU(·)=max(0,·)+0.05min(0,·) (29)

[0183] The input and output components of the network are z-score standardized according to the CFD data set to reduce the loss of key information. The generator is denoted as:

[0184]

[0185] Where: is the output of each component after standardization, is the input vector after the components are standardized, θ is the adjustable parameter of the generator, is the position vector after the normalization of each component, are the operating parameters of each component after standardization.

[0186] The z-score of component x1 is normalized as follows:

[0187]

[0188] Where: is the mean of the component x1 in the CFD data set, and std(x1) is the standard deviation of the component x1 in the CFD data set.

[0189] The proxy model is thus:

[0190]

[0191] Where: std(u) is the vector composed of the standard deviations of each component of u in the simulation data set, is a vector consisting of the mean values ​​of each component of u in the simulation data set.

[0192] Step 4: The model training module automatically uses the boundary adversarial method to train the proxy model. A small amount of CFD operations are performed to build a simulation data set. To ensure that the mean and standard deviation calculations are representative, the standardized proxy model prediction is as close to [-1, 1] as possible before restoration to reduce errors. Therefore, simulations need to be performed uniformly in the operating parameter space.

[0193] In Ω×S β Take the total set of internal control points:

[0194] C p ={z i |i=1,...,N p} (33)

[0195] Where: C pis the total set of internal control points; N p is the number of internal control points.

[0196] Again Construct the total set of boundary control points at:

[0197]

[0198] Where: Bp is the total set of boundary control points, For the border The set of control points.

[0199] Each set of boundary control points has the same number of control points:

[0200]

[0201] Where: n p The number of boundary control points for a single boundary area should be similar to the number of internal control points.

[0202] Collect CFD data set at the boundary The data points are taken as the total set of boundary sampling points and standardized:

[0203]

[0204] Where: B s is the total set of boundary sampling points, n s is the number of boundary sampling points.

[0205] Divide the above three point sets into small batches that do not intersect each other to prevent memory overflow and ensure that each batch in Bp contains the same number of points in four different boundary areas (the fluid-solid interface within the z-axis range of the inlet flow channel, moving blades, guide vanes, and outlet flow channel):

[0206]

[0207] Where: M is the batch size.

[0208] Construct the discriminator structure as Figure 4 As shown, it is used to determine whether the standardized output of the generator conforms to the data distribution on the boundary:

[0209]

[0210] Where: θ D is an adjustable parameter of the discriminator.

[0211] Each hidden layer is activated by the Leaky Relu function shown in formula (10), and the output layer uses the sigmoid function to map the result to the interval [0, 1]:

[0212]

[0213] Set the number of iterations E p , the learning rates ε,η of the generator and discriminator are calculated according to Figure 5 The process shown completes the training of the proxy model. The loss function includes the adversarial training loss function, the control equation loss function, and the boundary condition loss function, as shown in equations (40), (41), and (42):

[0214]

[0215] Where: V A,B (θ,θ D ) is the adversarial loss function of the elements in the set A and B, is the expected value of all elements in set A after being acted upon by mapping f, is the equation loss function of the elements in set A, is the boundary loss function of the elements in set A.

[0216] Step 5: Adoption Figure 5 After the algorithm completes model training, the proxy model is deployed online through the state tracking module. After that, the model can be used to predict the internal flow field of the axial flow lead-bismuth main pump under different operating parameters.

[0217] Step 6: Define optimization objectives and constraints in the multi-objective collaborative optimization module. The optimization objectives include:

[0218] The velocity in the moving blade area should be as small as possible, and the average velocity is:

[0219]

[0220] And ensure high hydraulic efficiency as much as possible, that is, reduce the proportion of input energy loss:

[0221]

[0222] Where: H t is the hydraulic head / m, M is the rotor torque / N·m.

[0223] The head includes the lifting of coolant and the injection of mechanical energy. In this embodiment, the total inlet pressure is set to 0, so the pressure difference is the total outlet pressure. All p(z) and V(z) are simulated and predicted by the proxy model U(z; θ) in real time, the same below:

[0224]

[0225] Where: H0 is the inlet and outlet section spacing / m.

[0226] The rotor torque is given by:

[0227]

[0228] Where: n is the unit normal vector of the rotor surface.

[0229] The constraints include an upper speed limit due to blade strength and a lower head limit determined by the reactor and pump installation method:

[0230] g1(ω,q V ):=ω M -|ω|≥0 (47)

[0231]

[0232] Where: M is the upper speed limit / rad·s -1 , It is the lower limit of lift / m.

[0233] The pump has a given outlet flow rate. The optimal speed design under the above conditions is to solve the following multi-objective optimization problem:

[0234]

[0235] Formula (49) is a general expression of multi-objective optimization problems. Such problems have been accurately solved by a large number of mature intelligent optimization algorithms, such as genetic algorithms, simulated annealing algorithms, particle swarm optimization algorithms and their corresponding variant algorithms. The proxy model constructed according to the method of the present invention has a very low prediction time cost for the flow field under different input parameters, and has great advantages in situations where large-scale iterative calculations of f1, f2, g1, g2 are required.

[0236] Step 7: Analyze the operating status of the main pump under the alternative optimization schemes visualized by the result output module, and derive the optimal speed design scheme and related information such as the flow field distribution of the main pump under the selected design scheme.

[0237] In the process of rapid design software development for the lead-cooled fast reactor main pump, the present invention combines the advantages of first principles and data-driven modeling to propose a small sample multi-channel PINN proxy model and its boundary adversarial training method. This method has the following advantages:

[0238] First: This method uses a multi-channel PINN proxy model instead of the traditional gridded CFD method to solve the flow field in the main pump of a lead-cooled fast reactor. The proxy model is trained from three aspects: fitting the boundary data distribution, satisfying the control equations and boundary conditions. The trained proxy model is then deployed to quickly solve the flow field of the main pump under different structures and operating parameters. Since this solution method directly solves partial differential equations for the basic physical laws of the flow field in the pump, it can be used to design the main pump of a lead-cooled fast reactor for digital twins without a reference mother pump and related design experience.

[0239] Second: The flow field prediction value output by this proxy model can quickly solve the objective function and constraints used in the design process without relying on gridded CFD, making it possible to economically apply traditional optimization algorithms to the design of lead-cooled fast reactor main pumps for digital twins. This solves the contradiction between design accuracy and speed in the product design process of lead-cooled fast reactor main pumps, and can achieve rapid simulation of its internal flow field at an extremely low computing cost, avoiding the shortcoming of traditional CFD algorithms that need to be recalculated due to changes in design and operating parameters.

[0240] Third: The training method based on first principles does not need to rely on a large amount of data. It can complete the training of the proxy model under small sample conditions and reduce the time and space complexity of the calculation.

[0241] Fourth: The model only needs to be trained using data at the boundary, which is convenient for the arrangement of sensors and can easily collect boundary data in the experiment to correct the model.

[0242] Fifth: The overall architecture of this method is divided into two parts: offline and online. The part involving real data is completed completely offline to ensure data security.

[0243] Based on the same concept, the present invention also provides a lead-cooled fast reactor main pump design method system for digital twins, including an acquisition module, a determination module, a construction module, a training module, a calculation module and a design module.

[0244] The acquisition module is used to obtain the adjustable structural parameters of the lead-cooled fast reactor main pump and to construct a parameterized lead-cooled fast reactor main pump flow channel geometry model according to the adjustable structural parameters.

[0245] The determination module is used to determine the specified structural parameters, operating parameters and control equation type of the main pump, and generate the control equations and boundary conditions used to describe the flow field inside the main pump in the parameterized lead-cooled fast reactor main pump flow channel geometric model according to the specified structural parameters, operating parameters and control equation type of the main pump.

[0246] The construction module is used to determine the number of layers, number of neurons and activation function type of each branch and trunk of the PINN agent model according to the actual prediction performance requirements, and to construct the PINN agent model.

[0247] The training module is used to obtain the CFD simulation data set, train the PINN proxy model through the CFD simulation data set, control equations and boundary conditions, and obtain the prediction model.

[0248] The calculation module is used to deploy the prediction model in the digital twin system, obtain the corresponding structural parameters and operating parameters according to the target operating conditions and design requirements in different application scenarios, and input the corresponding structural parameters and operating parameters into the prediction model to obtain multiple physical quantities of the flow field of the lead-cooled fast reactor main pump.

[0249] The design module is used to define the main pump design optimization objectives and corresponding constraints through multiple physical quantities, obtain the main pump design optimization problem, solve the main pump design optimization problem, and obtain the main pump design solution.

[0250] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0251] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A lead-cooled fast reactor main pump design method for digital twin, characterized in that: The following steps are involved: Obtaining adjustable structural parameters of the lead-cooled fast reactor main pump, and constructing a parameterized lead-cooled fast reactor main pump flow channel geometry model according to the adjustable structural parameters; Determine the specified structural parameters, operating parameters and control equation type of the main pump, and generate the control equations and boundary conditions for describing the flow field in the main pump in the parameterized lead-cooled fast reactor main pump flow channel geometry model according to the specified structural parameters, operating parameters and control equation type of the main pump; Determine the number of layers, number of neurons, and activation function type of each branch and trunk of the PINN proxy model according to the actual prediction performance requirements, and build the PINN proxy model; Obtain a CFD simulation data set, train the PINN agent model through the CFD simulation data set, control equations and boundary conditions, and obtain a prediction model; The prediction model is deployed in the digital twin system, and the corresponding structural parameters and operating parameters are obtained according to the target operating conditions and design requirements in different application scenarios. The corresponding structural parameters and operating parameters are input into the prediction model to obtain multiple physical quantities of the flow field of the main pump of the lead-cooled fast reactor. Define the main pump design optimization objectives and corresponding constraints through multiple physical quantities, obtain the main pump design optimization problem, solve the main pump design optimization problem, and obtain the main pump design solution; The construction of the PINN agent model is specifically as follows: U(x,t,α,β;θ)=DN(IL(DN1(x,t),DN2(α),DN3(β))); Where U is the predicted value of the physical quantity u of the flow field in the main pump to be sought by the PINN proxy model, x is the spatial coordinate, t is the time, α is the structural parameter, β is the operating condition parameter, θ is the adjustable parameter, DN, DN1, DN2 and DN3 are multi-layer fully connected feedforward neural networks, and IL is the integrated information layer; The fully connected feedforward neural network has the following expression: Where: z is the input vector, d i is the dimension of the input vector, d o is the output vector dimension, n l is the lth fully connected layer, l is the number of network layers, Represents a composite operation of two functions, where the output of the former is used as the input of the latter; The fully connected layer is defined as follows: In the formula, is the kth neuron in the i-th fully connected layer, η i is the number of neurons in the i-th fully connected layer; Each neuron receives all the outputs of the previous layer, processes them linearly, and then outputs them through a nonlinear activation function: In the formula, For neurons To the previous layer n i-1 The weight vector of For neurons The bias of For neurons A unary nonlinear activation function.

2. A lead-cooled fast reactor main pump design method for digital twinning according to claim 1, characterized in that: The adjustable structural parameters include the inner diameter of the flow channel, the inlet and outlet installation angles of each cylindrical layer of the blade, the blade profile and the impeller hub diameter.

3. A lead-cooled fast reactor main pump design method for digital twinning according to claim 1, characterized in that: The control equation types include mass equation, energy equation, momentum conservation equation and turbulence model equation, and the boundary conditions include inlet and outlet conditions and no-slip boundary conditions of fluid-solid wall; The general formula of the control equations and boundary conditions is as follows: In the formula, is the differential operator in the control equation, u is the physical quantity of the flow field in the main pump to be determined, x is the spatial coordinate, t is the time, α is the structural parameter, β is the operating condition parameter, f is the source term of the control equation, Ω is the control volume, is the fluid domain boundary, T is the simulation duration, S α is the value range of the structural parameters, S β is the value range of the working condition parameters, is the differential operator in the boundary condition, g s is the source term of the boundary condition.

4. A lead-cooled fast reactor main pump design method for digital twinning according to claim 3, characterized in that: The training of the PINN agent model by using the CFD simulation data set, control equations and boundary conditions includes the following steps: The flow field under specific structure and working parameters is solved through CFD simulation, and all points located at the boundary of the fluid domain are collected as the total set of boundary sampling points to obtain the CFD simulation data set; Construct a discriminator, which is used to determine whether the prediction of the flow field by the PINN proxy model obeys the probability distribution of the CFD simulation data set; define an adversarial training loss function according to the output result of the discriminator; In Ω(α)×[0,T]×S α ×S β Take the total set of internal control points; exist Construct the total set of boundary control points; Divide the total set of internal control points, the total set of boundary control points and the total set of boundary sampling points into small batches that do not overlap with each other to obtain a training set; The PINN agent model is used as a generator, and the equation loss function and boundary condition loss function are defined according to the control equation and boundary conditions; The training of the PINN proxy model is transformed into a multi-objective optimization problem for solution. The optimization goal is to minimize the adversarial training loss function and maximize the equation loss function and the boundary condition loss function.

5. A lead-cooled fast reactor main pump design method for digital twinning according to claim 4, characterized in that: The adversarial training loss function is defined according to the output result of the discriminator, as shown below: In the formula, is the anti-training loss function, B s is the total set of boundary sampling points, B p is the total set of internal control points, θ D is the discriminator adjustable parameter, is the expected value, D(z,u;θ D ) is the discriminator, z is the input variable; The equation loss function and the boundary condition loss function are defined according to the control equation and the boundary conditions, as shown below: In the formula, is the loss function of the equation, is the boundary condition loss function, C p is the CFD simulation data set, U is the predicted value of the physical quantity u of the flow field in the main pump to be determined by the PINN proxy model; The optimization objective is as follows: In the formula, min means minimization and max means maximization.

6. A lead-cooled fast reactor main pump design method for digital twinning according to claim 5, characterized in that: The training of the PINN proxy model is converted into a multi-objective optimization problem for solving, comprising the following steps: Set the number of iterations, the training batch of the training set, and the learning rate of the generator and discriminator; Initialize the model parameters of the generator and discriminator; Get the discriminator gradient and update the discriminator parameters according to the discriminator gradient of this training batch; Get multiple first gradients of the generator; Copying multiple first gradients of the generator to obtain multiple second gradients; Obtain the inner products of the multiple first gradients and the multiple second gradients respectively, and if the inner products are non-negative, update the parameters of the generator, otherwise perform orthogonalization processing; Traverse all batches in the data set and repeat the above parameter update process of the discriminator and generator until the set number of iterations is reached to obtain the prediction model.

7. A lead-cooled fast reactor main pump design method for digital twinning according to claim 6, characterized in that: The discriminator gradient is obtained as follows: In the formula, g is the discriminator gradient, is the gradient operator, j is the jth training batch; The parameters of the discriminator are updated according to the discriminator gradient of this training batch, as shown below: Where η is the learning rate of the discriminator update; The method of obtaining multiple first gradients of the generator is specifically as follows: Where g1, g2 and g3 are the first gradients in different directions; The multiple first gradients of the copy generator are obtained to obtain multiple second gradients, as shown below: g′1: =g1, g′2: =g2, g′3: =g3; Where g′1, g′2 and g′3 are the second gradients in different directions; The parameters of the generator are updated as follows: i j+1 :=θ j -ε(g′1+g′2+g′3); Where ε is the learning rate of the generator update.

8. A lead-cooled fast reactor main pump design method system for digital twin, characterized in that: include: An acquisition module is used to acquire the adjustable structural parameters of the lead-cooled fast reactor main pump and construct a parameterized lead-cooled fast reactor main pump flow channel geometry model according to the adjustable structural parameters; A determination module is used to determine the specified structural parameters, operating parameters and control equation type of the main pump, and generate control equations and boundary conditions for describing the flow field in the main pump in the parameterized lead-cooled fast reactor main pump flow channel geometry model according to the specified structural parameters, operating parameters and control equation type of the main pump; A construction module is used to determine the number of layers, number of neurons and activation function type of each branch and trunk of the PINN proxy model according to the actual prediction performance requirements, and to construct the PINN proxy model; A training module is used to obtain a CFD simulation data set, train the PINN proxy model through the CFD simulation data set, control equations and boundary conditions, and obtain a prediction model; A calculation module is used to deploy the prediction model in the digital twin system, obtain the corresponding structural parameters and operating parameters according to the target operating conditions and design requirements in different application scenarios, and input the corresponding structural parameters and operating parameters into the prediction model to obtain multiple physical quantities of the flow field of the lead-cooled fast reactor main pump; A design module is used to define the main pump design optimization target and corresponding constraint conditions through multiple physical quantities, obtain the main pump design optimization problem, solve the main pump design optimization problem, and obtain the main pump design solution; The construction of the PINN agent model is specifically as follows: U(x,t,α,β;θ)=DN(IL(DN1(x,t),DN2(α),DN3(β))); Where U is the predicted value of the physical quantity u of the flow field in the main pump to be sought by the PINN proxy model, x is the spatial coordinate, t is the time, α is the structural parameter, β is the operating condition parameter, θ is the adjustable parameter, DN, DN1, DN2 and DN3 are multi-layer fully connected feedforward neural networks, and IL is the integrated information layer; The fully connected feedforward neural network has the following expression: Where: z is the input vector, d i is the dimension of the input vector, d o is the output vector dimension, n l is the lth fully connected layer, l is the number of network layers, Represents a composite operation of two functions, where the output of the former is used as the input of the latter; The fully connected layer is defined as follows: In the formula, is the kth neuron in the i-th fully connected layer, η i is the number of neurons in the i-th fully connected layer; Each neuron receives all the outputs of the previous layer, processes them linearly, and then outputs them through a nonlinear activation function: In the formula, For neurons To the previous layer n i-1 The weight vector of For neurons The bias of For neurons A unary nonlinear activation function.

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