Reactor thermal hydraulic characteristic rapid prediction method based on dynamic mode decomposition and deep learning

Abstract

The invention discloses a reactor thermal hydraulic characteristic rapid prediction method based on dynamic mode decomposition and deep learning, and the method comprises the steps: obtaining thermal hydraulic characteristic data of a reactor under different operation conditions, and selecting steady-state operation data to establish a snapshot; initial dimension reduction is carried out on the snapshot through singular value decomposition, and snapshot representation after dimension reduction is obtained; constructing an order reduction model based on the snapshot representation after dimension reduction; wherein the step of constructing the reduced-order model comprises the steps of performing dynamic mode decomposition on the snapshot after dimension reduction, constructing a parameterized low-dimensional linear operator, and fitting a mapping relation between the operator and an operation parameter through deep learning; verifying the reduced-order model according to a simulation result of the nuclear reactor mechanism model, and obtaining a parameterized reduced-order model when the verification is passed; and inputting the actual operation condition data into the parameterized reduced-order model to obtain a prediction result of the thermal hydraulic characteristics of the reactor. According to the method, the simulation efficiency is remarkably improved by combining the dynamic mode decomposition and the deep learning technology.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear reactor thermal-hydraulic characteristics analysis, and particularly relates to a rapid prediction method for reactor thermal-hydraulic characteristics based on dynamic mode decomposition and deep learning. Background Art

[0002] The safe and stable operation of nuclear reactors is crucial for the effective utilization of nuclear energy. The thermal-hydraulic characteristics of reactors are one of the key factors affecting their operating states. Accurately and rapidly predicting these characteristics is of great significance for reactor design optimization, operation monitoring, and accident prevention.

[0003] Traditional methods for analyzing reactor thermal-hydraulic characteristics mainly rely on complex physical models and numerical simulations, such as simulation models based on the RELAP5 program or computational fluid dynamics (CFD). Although these methods can relatively accurately describe the thermal-hydraulic characteristics of reactors, they have the problems of large computational amount and long time consumption, and are difficult to meet the requirements of rapidity and immediacy. Especially in multi-query scenarios that require a large number of repeated calculations, such as sensitivity analysis, optimization design, uncertainty analysis, and digital twins, the application cost is too high.

[0004] In recent years, model reduction techniques have gradually received attention. It can significantly improve the computational efficiency on the premise of ensuring a certain accuracy. Among them, dynamic mode decomposition (DMD), as a data-driven reduction method, is favored because of its simplicity and easy implementation and applicability to various scenarios. However, the standard DMD method cannot directly handle parametric problems, that is, it cannot simultaneously consider the influence of time and parameters on system dynamics, which limits its application in complex systems. Summary of the Invention

[0005] The present invention proposes a rapid prediction method for reactor thermal-hydraulic characteristics based on dynamic mode decomposition and deep learning to solve the problems of long time consumption and high cost existing in the above-mentioned prior art.

[0006] To achieve the above object, the present invention provides a rapid prediction method for reactor thermal-hydraulic characteristics based on dynamic mode decomposition and deep learning, including the following steps:

[0007] Obtain the thermal-hydraulic characteristic data of the reactor under different operating conditions, and select the steady-state operating data to form snapshots;

[0008] Perform initial dimensionality reduction on the snapshots through singular value decomposition to obtain the reduced-dimensional snapshot representation;

[0009] Construct a reduced-order model based on the snapshot representation after dimensionality reduction; wherein constructing the reduced-order model includes: performing dynamic mode decomposition on the snapshots after dimensionality reduction, constructing a parameterized low-dimensional linear operator, and fitting the mapping relationship between the operator and the operating parameters through deep learning;

[0010] Verify the reduced-order model through the simulation results of the nuclear reactor mechanism model, and obtain a parameterized reduced-order model when the verification is passed;

[0011] Input the actual operating condition data into the parameterized reduced-order model to obtain the prediction results of the reactor thermal-hydraulic characteristics.

[0012] Preferably, obtaining the thermal-hydraulic characteristic data includes:

[0013] Performing simulation calculations through the numerical simulation model of the nuclear reactor;

[0014] Obtain the thermal-hydraulic characteristic data of the nuclear reactor under different operating conditions through its actual operating model;

[0015] The thermal-hydraulic characteristic data includes the core coolant temperature, the primary loop system pressure, the coolant flow rate, the secondary side working fluid temperature and the gas content rate of the steam generator heat transfer tubes.

[0016] Preferably, the selection of steady-state operation data to form snapshots includes:

[0017] Determine the value range of the operating parameters of the reactor system, and select several operating conditions through the sampling method;

[0018] Perform simulation calculations under each condition to obtain the simulation data of the thermal-hydraulic parameters;

[0019] Take the average value of the data within the stable operation period of the reactor system to construct the snapshot.

[0020] Preferably, the initial dimensionality reduction of the snapshots includes:

[0021] Assemble the snapshots under different conditions into a two-dimensional matrix and perform singular value decomposition;

[0022] Normalize the singular values and determine the truncation rank according to the threshold condition;

[0023] Calculate the approximation error under different truncation ranks and select a suitable truncation rank;

[0024] Project the full-order snapshots into the low-dimensional space to obtain the snapshot representation after dimensionality reduction.

[0025] Preferably, the fitting of the mapping relationship between the operator and the operating parameters includes:

[0026] Perform DMD calculation on the snapshots after dimensionality reduction under each condition to obtain the DMD linear operator;

[0027] Flatten the DMD operator and assemble it into a parameterized operator matrix, perform SVD decomposition on the parameterized operator matrix, and extract the dominant structure of the parameterized DMD operator;

[0028] Extract the singular values and their vectors of the dominant structure to obtain a reduced parameterized operator snapshot;

[0029] Fit the mapping relationship between the operating parameters and the reduced operator through a deep learning method.

[0030] Preferably, the deep learning method includes a multi-layer perceptron and a convolutional neural network.

[0031] Preferably, when the verification of the reduced-order model fails, the reduced-order model is optimized by increasing the number of snapshots.

[0032] Preferably, the obtaining of the predicted results of the reactor thermal-hydraulic characteristics includes:

[0033] Input the actual operating condition data into the parameterized reduced-order model to generate a corresponding DMD parameterized operator;

[0034] Update the low-dimensional representation through the DMD parameterized operator, and restore the updated low-dimensional representation through inverse operation to obtain the predicted results of the reactor thermal-hydraulic characteristics.

[0035] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory, and the processor executes the computer program to implement the steps of the method.

[0036] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method are implemented.

[0037] Compared with the prior art, the present invention has the following advantages and technical effects:

[0038] The traditional DMD method is usually only applicable to the analysis of system dynamic characteristics under a single parameter or fixed operating conditions. By expanding the DMD method, the present invention can more accurately describe the thermal-hydraulic characteristics of the reactor under different operating conditions;

[0039] By combining the deep learning method, the influence of multiple operating parameters (such as reactor power, flow rate, etc.) on the reactor thermal-hydraulic characteristics is incorporated into the reduced-order model, improving the generalization ability of the DMD model;

[0040] Using the parameterized DMD model obtained through training, in the online prediction stage, it can quickly generate prediction results of the reactor thermal-hydraulic characteristics under different operating conditions, significantly improving the calculation efficiency of thermal-hydraulic analysis. It can be used to replace the mechanism model for digital twin, optimization design, and uncertainty analysis of nuclear reactor systems to save calculation costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which form a part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0042] Figure 1 It is a process diagram of the parameterized DMD model training in the embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of the sampling results of the operating parameters in the embodiment of the present invention;

[0044] Figure 3 It is a diagram of the singular value decomposition results in the snapshot dimensionality reduction process in the embodiment of the present invention;

[0045] Figure 4 1]]It is a diagram of the SVD approximation error corresponding to different truncation ranks in the embodiment of the present invention;

[0046] Figure 5 It is a comparison diagram of the predicted results and the true values of the reactor thermal-hydraulic characteristics in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the accompanying drawings and combine with the embodiments to detail this application.

[0048] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0049] Embodiment 1

[0050] In this embodiment, a rapid prediction method for reactor thermal-hydraulic characteristics based on dynamic mode decomposition and deep learning is provided, including the following steps:

[0051] Obtain the thermal-hydraulic characteristic data of the reactor under different operating conditions, and select the steady-state operating data to form snapshots;

[0052] Perform initial dimensionality reduction on the snapshots through singular value decomposition to obtain the reduced-dimensional snapshot representation;

[0053] Construct a reduced - order model based on the snapshot representation after dimensionality reduction (the construction and training processes are as Figure 1 shown); the construction of the reduced - order model includes: performing dynamic mode decomposition on the snapshots after dimensionality reduction, constructing a parameterized low - dimensional linear operator, and fitting the mapping relationship between the operator and the operating parameters through deep learning;

[0054] Verify the reduced - order model through the simulation results of the nuclear reactor mechanism model, and obtain a parameterized reduced - order model when the verification is passed;

[0055] Input the actual operating condition data into the parameterized reduced - order model to obtain the prediction results of the reactor thermohydraulic characteristics.

[0056] Specifically, it includes the following steps:

[0057] Step 1 Snapshot acquisition: Obtain the thermohydraulic characteristic data of the reactor under different operating conditions through a simulator or a nuclear reactor mechanism model, including parameters such as the core coolant temperature, the primary loop system pressure, the coolant flow rate, the secondary - side working fluid temperature and gas - void fraction of the steam generator heat transfer tubes, etc. Select the steady - state operation results of the above - mentioned parameters to form snapshots.

[0058] Step 2 Snapshot dimensionality reduction: Use singular value decomposition (SVD) to perform initial dimensionality reduction on the snapshots. Determine the rank of the low - dimensional space through singular value analysis and approximate error calculation results, and project the snapshots under different operating conditions onto this low - dimensional space respectively to obtain the snapshot representation after dimensionality reduction.

[0059] Step 3 Parameterized dynamic mode decomposition: Perform DMD analysis on the snapshots after dimensionality reduction for each operating condition, incorporate the influence of different operating parameters (such as reactor power, feed - water flow rate, etc.) on the system dynamic characteristics into the model, and construct a parameterized low - dimensional linear operator; then assemble these DMD operators into an operator matrix, perform SVD decomposition again, and extract the dominant structure of the parameterized DMD operator; finally, use deep - learning tools such as multi - layer feed - forward neural networks and convolutional neural networks to fit the mapping relationship between the parameterized DMD operator and the operating parameters.

[0060] Step 4 Model verification and optimization: Verify the constructed reduced - order model using the simulation results of the mechanism model, evaluate the reconstruction error of the model. If the requirements are not met, improve the calculation accuracy by increasing the number of snapshots until the conditions are satisfied.

[0061] Step 5 Online prediction of reactor thermohydraulic characteristics: Based on the parameterized reduced - order model obtained in Step 4, for new operating conditions in the online stage, the operating parameters are first input into the deep - learning model to construct its corresponding DMD parameterized operator. Through inverse operation, the low - dimensional representation obtained from the DMD model can be restored to obtain the prediction results of the reactor thermohydraulic characteristics under this condition.

[0062] Furthermore, the steps of snapshot acquisition include:

[0063] 1. According to the requirements of reactor thermal-hydraulic analysis, first determine the value range of reactor system operation parameters: including reactor power Pr, feedwater flow rate Gw, main pump speed Mp, etc., and select Nsample operating conditions in the above parameter sample space by using methods such as random sampling and Latin hypercube sampling;

[0064] 2. Conduct simulation calculations under each operating condition to obtain simulation data of thermal-hydraulic parameters such as coolant temperature in the core, primary loop system pressure, coolant flow rate, secondary side working fluid temperature and gas content rate of steam generator heat transfer tubes under this condition;

[0065] 3. By observing the time-varying characteristics of main operating parameters such as core power Pr, judge whether the reactor system is in a stable operating state, and take the average value of the simulation data within 1000 s of stable operation as the steady-state value of the thermal-hydraulic parameters to construct a snapshot.

[0066] Furthermore, the steps of the snapshot dimensionality reduction method based on singular value decomposition include:

[0067] 1. Assemble the snapshots collected under different conditions into a two-dimensional matrix X with Nm rows and Nsample columns, where Nm is the product of the number of thermal-hydraulic parameters and the number of simulation model nodes, and perform singular value decomposition on this two-dimensional matrix to obtain U, Σ, and V matrices, where U and V are orthogonal matrices, and the diagonal elements of Σ are the singular values of X.

[0068] 2. Normalize the decomposed singular values σ, and there is Find the smallest serial number of the singular value (i.e., the truncation rank r) that satisfies specific threshold conditions (1e-4, 1e-6, 1e-8);

[0069] 3. Calculate the approximation error corresponding to different truncation ranks of SVD. The formula is as follows:

[0070]

[0071] In the formula, the subscript F is the Frobenius norm, X is the full-order snapshot, and X′ is the SVD reconstructed snapshot;

[0072] 4. By analyzing the change trend of the approximation error with the truncation rank, select an appropriate SVD truncation rank r1;

[0073] 5. Calculate the low-dimensional approximation of U under the setting of the truncation rank r1, and project the full-order snapshot under each condition to obtain its low-dimensional representation.

[0074] Furthermore, the steps of the parametric dynamic mode decomposition method include:

[0075] 1. Perform DMD calculation on the snapshot after dimension reduction for each operating condition, and the DMD linear operator A under different operating parameter conditions can be obtained;

[0076] 2. Flatten each DMD linear operator A into N A ×1 column vector (A is a square matrix of r1×r1, and is assembled into N A Snapshot of parameterized operators with Nsample rows and columns;

[0077] 3. Perform SVD calculation on the parameterized operator matrix again. Through singular value analysis and approximate error calculation results, extract the first r2 singular values and their vectors in the parameterized operator to obtain a simplified parameterized operator snapshot.

[0078] 4. Use deep learning tools such as multi-layer perceptrons (MLPs) and convolutional neural networks (CNNs) to fit the mapping relationship between the simplified parameterized DMD operator and the operating parameters. The operating parameters are used as the input of the deep learning model, and the simplified parameterized DMD operator is used as the output. The mean square error (MSE) and root mean square error (RMSE) are selected as the loss function for deep neural network model training. The specific hyperparameter settings are determined by actual needs and model training results.

[0079] 5. If the loss value and determination coefficient of the deep learning training results do not meet the target requirements, the model architecture selection and model structure configuration will be reselected until the model meets the requirements.

[0080] This example was verified as follows:

[0081] Step 1: Snapshot collection: Use a simulator or nuclear reactor mechanism model to obtain the thermal-hydraulic characteristic data of the reactor under different operating conditions, including parameters such as core coolant temperature, primary circuit system pressure, coolant flow rate, secondary side working fluid temperature of the steam generator heat transfer tubes, and gas fraction. Select the steady-state operating results of the above parameters to form a snapshot.

[0082] Specifically, in this example, steam flow rate and average core coolant temperature are selected as operating parameters, and their value ranges are shown in Table 1. Random sampling is used to select Nsample=400 operating conditions in this parameter space, as shown in Table 1. Figure 2 As shown in the figure, simulation calculations were performed under each operating condition, with a total simulation duration of 5000 seconds. Simulation data for the core coolant temperature, primary circuit system pressure, coolant flow rate, steam generator heat transfer tube secondary side working medium temperature, and gas fraction were collected from the 4000th to 5000th second period, and their average value was taken as the steady-state result to construct a snapshot.

[0083] Table 1

[0084]

[0085] Step 2 Snapshot dimensionality reduction: Assemble the snapshots collected under different working conditions into a two-dimensional matrix \(X\) with \(N_m\) rows and \(N_{sample}\) columns, where \(N_m\) is the product of the number of thermohydraulic parameters and the number of nodes in the simulation model. In this example, the dimension of matrix \(X\) is \(102\times400\);

[0086] Perform singular value decomposition on this two-dimensional matrix. According to The singular value results after normalization are as shown in Figure 3 Shown, satisfying \(1e\) -4 、\(1e\) -5 、\(1e\) -6 The minimum serial numbers of the singular values that meet the threshold conditions are 14, 28, and 43 respectively;

[0087] Calculate the SVD approximation error under different truncation rank settings. Its change trend with the truncation rank is as shown in Figure 4 Shown. It can be found that the SVD approximation error is lower than 0.0001 when the truncation rank is 30. In order to balance the SVD calculation accuracy and the snapshot dimensionality reduction effect, take the truncation rank \(r_1 = 30\);

[0088] Calculate the low-dimensional approximation of \(U\) under the setting of truncation rank \(r_1\), and project the full-order snapshots under each working condition to obtain their low-dimensional representations. In this example, the dimension of the reduced snapshots is \(30\times400\);

[0089] Step 3 Parametric dynamic mode decomposition: Perform DMD calculation on the reduced snapshots under each working condition, then a total of 400 groups of DMD linear operators \(A\) under different operating parameter conditions can be obtained;

[0090] Flatten each DMD linear operator \(A\) into a column vector of \(N\) A \(\times1\), and assemble it into a parametric operator snapshot with \(N\) A rows and \(N_{sample}\) columns. In this example, \(N\) A \(= r_1\) 2 \(= 900\), and the dimension of the newly assembled parametric operator snapshot is \(900\times400\);

[0091] Perform SVD calculation on the parametric operator matrix again. The selection of its singular value truncation rank is the same as that in Step 2. In this example, extract the first 10 singular values and their vectors in the parametric operator to obtain a reduced parametric operator snapshot;

[0092] A multi-layer feedforward neural network is selected to approximate the mapping relationship between the parameterized DMD operator and the operating parameters. In the construction of the neural network model, the operating parameters - steam flow rate and average coolant temperature in the core are used as the input of the deep learning model, and the reduced parameterized DMD operator is used as the output. The Levenberg-Marquardt (LM) algorithm is used to minimize the loss function (mean square error loss, MSE) by iteratively updating the weights and biases of the network. The definition of the loss function is as follows:

[0093]

[0094] where \(x\) i is the true value, is the predicted value of the model, and \(n\) is the number of samples.

[0095] Step 4 Model verification and optimization: Use the simulation results of the mechanism model to verify the constructed reduced-order model. In this example, the root mean square error RMSE and the coefficient of determination \(R\) 2 are used as evaluation criteria. If the requirements are not met, the calculation accuracy is improved by increasing the number of snapshots until the conditions are satisfied.

[0096] Step 5 Online prediction of reactor thermal-hydraulic characteristics: Based on the parameterized reduced-order model obtained in Step 4, for new operating conditions in the online stage, the operating parameters are first input into the deep learning model to construct its corresponding DMD parameterized operator. The low-dimensional representation obtained from the DMD model can be restored through inverse operation to obtain the prediction results of the reactor thermal-hydraulic characteristics under this condition, as shown in Figure 5 .

[0097] It can be seen from Figure 5 that the prediction results are highly consistent with the true values, indicating that the reduced-order model of this application can accurately predict the thermal-hydraulic characteristics of the reactor under different operating conditions.

[0098] Figure 5 The data in cover a variety of operating conditions, which indicates that the model of this application is not only applicable to a single condition, but also can maintain high-precision prediction ability within a wide range of operating parameters.

[0099] This embodiment also provides a computer device, including a memory, a processor, and a computer program stored on the memory. The processor executes the computer program to implement the steps of the method.

[0100] This embodiment also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method are implemented.

[0101] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A rapid prediction method for the thermal-hydraulic characteristics of a reactor based on dynamic mode decomposition and deep learning, characterized in that, It includes the following steps: Obtain the thermohydraulic characteristic data of the reactor under different operating conditions, and select the steady-state operating data to form a snapshot; Perform initial dimensionality reduction on the snapshot through singular value decomposition to obtain the reduced-dimensional snapshot representation; Construct a reduced-order model based on the reduced-dimensional snapshot representation; Among them, constructing the reduced-order model includes: performing dynamic mode decomposition on the reduced-dimensional snapshot, constructing a parameterized low-dimensional linear operator, and fitting the mapping relationship between the operator and the operating parameters through deep learning; Verify the reduced-order model through the simulation results of the nuclear reactor mechanism model, and obtain a parameterized reduced-order model when the verification is passed; Input the actual operating condition data into the parameterized reduced-order model to obtain the prediction results of the reactor thermohydraulic characteristics.

2. The method according to claim 1, wherein Obtaining the thermohydraulic characteristic data includes: Carry out simulation calculations through the numerical simulation model of the nuclear reactor; Through the actual operating model of the nuclear reactor, obtain its thermohydraulic characteristic data under different conditions; The thermohydraulic characteristic data includes the coolant temperature in the core, the pressure of the primary loop system, the coolant flow rate, the temperature of the secondary-side working fluid in the steam generator heat transfer tubes, and the gas content rate.

3. The method according to claim 1, characterized in that, The selection of steady-state operating data to form a snapshot includes: Determine the value range of the operating parameters of the reactor system, and select several operating conditions through the sampling method; Perform simulation calculations under each condition to obtain the simulation data of the thermohydraulic parameters; Take the average value of the data within the stable operating period of the reactor system to construct a snapshot.

4. The method according to claim 1, characterized in that The initial dimensionality reduction of the snapshot includes: Assemble the snapshots under different conditions into a two-dimensional matrix and perform singular value decomposition; Normalize the singular values, and determine the truncation rank according to the threshold condition; Calculate the approximation error under different truncation ranks and select a suitable truncation rank; Project the full-order snapshot into the low-dimensional space to obtain the reduced-dimensional snapshot representation.

5. The method according to claim 1, wherein The fitting of the mapping relationship between the operator and the operating parameters includes: Perform DMD calculation on the reduced-dimensional snapshot under each condition to obtain the DMD linear operator; Flatten and assemble the DMD operator into a parameterized operator matrix, perform SVD decomposition on the parameterized operator matrix, and extract the dominant structure of the parameterized DMD operator; Extract the singular values and their vectors of the dominant structure to obtain the reduced parameterized operator snapshot; Fit the mapping relationship between the operating parameters and the reduced operator through the deep learning method.

6. The method according to claim 5, characterized in that, The deep learning method includes a multi-layer perceptron and a convolutional neural network.

7. The method according to claim 1, characterized in that When the verification of the reduced-order model fails, optimize the reduced-order model by increasing the number of snapshots.

8. The method according to claim 1, wherein The obtaining of the prediction results of the reactor thermohydraulic characteristics includes: Input the actual operating condition data into the parameterized reduced-order model to generate the corresponding DMD parameterized operator; Update the low-dimensional representation through the DMD parameterized operator, and restore the updated low-dimensional representation through inverse operation to obtain the prediction results of the reactor thermohydraulic characteristics.

9. A computer device, comprising a memory, a processor, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-8.

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