A reactor thermal-hydraulic characteristic fast prediction method based on dynamic mode decomposition and deep learning

Abstract

The application discloses a reactor thermal hydraulic characteristic fast prediction method based on dynamic mode decomposition and deep learning, and comprises the following steps: acquiring thermal hydraulic characteristic data of a reactor under different operation conditions, and selecting steady-state operation data to form snapshots; performing initial dimension reduction on the snapshots through singular value decomposition to obtain reduced snapshot representations; constructing a reduced-order model based on the reduced snapshot representations; wherein the construction of the reduced-order model comprises the following steps: performing dynamic mode decomposition on the reduced snapshots, constructing a parameterized low-dimensional linear operator, and fitting a mapping relationship between the operator and operation parameters through deep learning; verifying the reduced-order model through simulation results of a nuclear reactor mechanism model, and obtaining a parameterized reduced-order model when the verification is passed; and inputting actual operation condition data into the parameterized reduced-order model to obtain a reactor thermal hydraulic characteristic prediction result. Through the combination of dynamic mode decomposition and deep learning technology, the simulation efficiency is significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of nuclear reactor thermal-hydraulic characteristic analysis technology, and particularly relates to a rapid prediction method for reactor thermal-hydraulic characteristics based on dynamic pattern decomposition and deep learning. Background Technology

[0002] The safe and stable operation of nuclear reactors is crucial for the effective utilization of nuclear energy. The thermo-hydraulic characteristics of a reactor are one of the key factors affecting its operating status, and accurate and rapid prediction of these characteristics is of paramount importance for reactor design optimization, operation monitoring, and accident prevention.

[0003] Traditional methods for analyzing the thermal-hydraulic characteristics of reactors primarily rely on complex physical models and numerical simulations, such as simulation models based on the RELAP5 program or computational fluid dynamics (CFD). While these methods can accurately describe the thermal-hydraulic characteristics of reactors, they suffer from high computational costs and long processing times, making it difficult to meet the requirements of speed and immediacy. This is especially true in multi-query scenarios requiring numerous repetitive calculations, such as sensitivity analysis, optimization design, uncertainty analysis, and digital twins, where the application cost becomes prohibitively high.

[0004] In recent years, model order reduction techniques have gradually gained attention, as they can significantly improve computational efficiency while maintaining a certain level of accuracy. Among them, Dynamic Mode Decomposition (DMD), as a data-driven reduction method, is favored due to its simplicity, ease of implementation, and applicability to various scenarios. However, standard DMD methods cannot directly handle parameterized problems, meaning they cannot simultaneously consider the impact of time and parameters on system dynamics, which limits their application in complex systems. Summary of the Invention

[0005] This invention proposes a rapid prediction method for reactor thermal-hydraulic characteristics based on dynamic pattern decomposition and deep learning, in order to solve the problems of long time consumption and high cost of the above-mentioned existing technologies.

[0006] To achieve the above objectives, this invention provides a method for rapid prediction of reactor thermal-hydraulic characteristics based on dynamic pattern decomposition and deep learning, comprising the following steps:

[0007] Acquire thermal-hydraulic characteristic data of the reactor under different operating conditions, and select steady-state operating data to create a snapshot;

[0008] The snapshot is initially reduced in dimensionality by singular value decomposition to obtain the dimensionality-reduced snapshot representation.

[0009] A reduced-order model is constructed based on the dimensionality-reduced snapshot representation; the construction of the reduced-order model includes: performing dynamic mode decomposition on the dimensionality-reduced snapshot, constructing parameterized low-dimensional linear operators, and fitting the mapping relationship between the operators and the running parameters through deep learning;

[0010] The reduced-order model is verified by the simulation results of the nuclear reactor mechanism model. When the verification is successful, the parameterized reduced-order model is obtained.

[0011] The actual operating condition data is input into the parameterized reduced-order model to obtain the predicted results of the reactor's thermal-hydraulic characteristics.

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

[0013] Simulation calculations are performed using a numerical simulation model of a nuclear reactor;

[0014] By using actual operating models of nuclear reactors, we can obtain data on their thermal-hydraulic characteristics under different operating conditions.

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

[0016] Preferably, the step of selecting steady-state operating data to form a snapshot includes:

[0017] Determine the range of values ​​for the reactor system operating parameters and select several operating conditions by sampling.

[0018] Simulation calculations were performed under each operating condition to obtain simulation data of thermal-hydraulic parameters;

[0019] A snapshot is constructed by taking the average value of data during the stable operation period of the reactor system.

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

[0021] The snapshots under different operating conditions are assembled into a two-dimensional matrix and then singular value decomposition is performed.

[0022] The singular values ​​are normalized, and the truncation rank is determined based on the threshold condition;

[0023] Calculate the approximation error under different cutoff ranks, and select an appropriate cutoff rank;

[0024] Projecting the full-order snapshot onto a lower-dimensional space yields a dimensionality-reduced snapshot representation.

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

[0026] DMD calculations are performed on the snapshots after dimensionality reduction for each operating condition to obtain the DMD linear operator;

[0027] The DMD operators are flattened and assembled into a parameterized operator matrix. The parameterized operator matrix is ​​then decomposed by SVD to extract the dominant structure of the parameterized DMD operators.

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

[0029] The mapping relationship between the running parameters and the reduction operator is fitted using deep learning methods.

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

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

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

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

[0034] The low-dimensional representation is updated by the DMD parameterization operator, and the updated low-dimensional representation is restored by inverse operation to obtain the predicted results of reactor thermal-hydraulic characteristics.

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

[0036] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

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

[0038] Traditional DMD methods are usually only applicable to the analysis of system dynamic characteristics under a single parameter or fixed operating conditions. This invention extends the DMD method and can more accurately describe the thermal-hydraulic characteristics of the reactor under different operating conditions.

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

[0040] By utilizing the parameterized DMD model obtained through training, prediction results of reactor thermal-hydraulic characteristics under different operating conditions can be quickly generated during the online prediction phase. This significantly improves the computational efficiency of thermal-hydraulic analysis and can be used to replace mechanistic models for digital twins, optimization design, and uncertainty analysis of nuclear reactor systems to save computational costs. Attached Figure Description

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

[0042] Figure 1 This is a diagram illustrating the training process of the parameterized DMD model according to an embodiment of the present invention.

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

[0044] Figure 3 This is a diagram showing the singular value decomposition results during the snapshot dimensionality reduction process in an embodiment of the present invention.

[0045] Figure 4 The following are SVD approximation error diagrams for different truncation ranks in embodiments of the present invention;

[0046] Figure 5 This is a comparison chart of the predicted and actual values ​​of the reactor thermal-hydraulic characteristics in an embodiment of the present invention. Detailed Implementation

[0047] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

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

[0049] Example 1

[0050] This embodiment provides a method for rapid prediction of reactor thermal-hydraulic characteristics based on dynamic pattern decomposition and deep learning, including the following steps:

[0051] Acquire thermal-hydraulic characteristic data of the reactor under different operating conditions, and select steady-state operating data to create a snapshot;

[0052] The snapshot is initially reduced in dimensionality by singular value decomposition to obtain the dimensionality-reduced snapshot representation.

[0053] A reduced-order model is constructed based on the dimensionality-reduced snapshot representation (the construction and training process is as follows). Figure 1 (as shown); the construction of the reduced-order model includes: performing dynamic mode decomposition on the dimensionality-reduced snapshot, constructing parameterized low-dimensional linear operators, and fitting the mapping relationship between the operators and the running parameters through deep learning;

[0054] The reduced-order model is verified by the simulation results of the nuclear reactor mechanism model. When the verification is successful, the parameterized reduced-order model is obtained.

[0055] By inputting actual operating condition data into the parameterized reduced-order model, the predicted results of reactor thermal-hydraulic characteristics are obtained.

[0056] Specifically, the following steps are included:

[0057] Step 1: Snapshot Acquisition: Obtain thermal-hydraulic characteristic data of the reactor under different operating conditions through a simulator or nuclear reactor mechanism model, including parameters such as core coolant temperature, primary loop system pressure, coolant flow rate, secondary working fluid temperature and gas content of the steam generator heat transfer tubes, and select steady-state operating results of the above parameters to form a snapshot.

[0058] Step 2 Snapshot Dimensionality Reduction: Initial dimensionality reduction of the snapshot is performed using Singular Value Decomposition (SVD). The rank of the low-dimensional space is determined by the results of singular value analysis and approximation error calculation. Snapshots under different operating conditions are projected onto this low-dimensional space to obtain the dimensionality-reduced snapshot representation.

[0059] Step 3: Parameterized Dynamic Mode Decomposition (DMD) analysis is performed on the dimensionality-reduced snapshots under each operating condition. The influence of different operating parameters (such as reactor power, feedwater flow rate, etc.) on the dynamic characteristics of the system is incorporated into the model to construct parameterized low-dimensional linear operators. These DMD operators are then assembled into an operator matrix, and SVD decomposition is performed again to extract the dominant structure of the parameterized DMD operators. Finally, deep learning tools such as multilayer feedforward neural networks and convolutional neural networks are used to fit the mapping relationship between the parameterized DMD operators and the operating parameters.

[0060] Step 4: Model Validation and Optimization: The constructed reduced-order model is validated using the simulation results of the mechanistic model. The reconstruction error of the model is evaluated. If the target is not met, the calculation accuracy is improved by increasing the number of snapshots until the conditions are met.

[0061] 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. By inverse operation, the low-dimensional representation obtained by the DMD model is restored to obtain the prediction results of reactor thermal-hydraulic characteristics under this operating condition.

[0062] Furthermore, the snapshot acquisition steps include:

[0063] 1. Based on the requirements of reactor thermal-hydraulic analysis, first determine the range of values ​​for reactor system operating parameters, including reactor power Pr, feedwater flow rate Gw, main pump speed Mp, etc., and select N sample operating conditions in the above parameter sample space using random sampling, Latin hypercube sampling, and other methods.

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

[0065] 3. By observing the time-varying characteristics of key operating parameters such as core power Pr, determine whether the reactor system is in a stable operating state, and take the average value of the simulation data within 1000s 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 operating 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 nodes in the simulation model. Perform singular value decomposition on this two-dimensional matrix to obtain matrices U, Σ, and V, where U and V are orthogonal matrices, and the diagonal elements of Σ are the singular values ​​of X.

[0068] 2. Normalize the singular values ​​σ obtained from the decomposition. Find the smallest singular value index (i.e., the truncated rank r) that satisfies a specific threshold condition (1e-4, 1e-6, 1e-8);

[0069] 3. Calculate the approximate error of SVD corresponding to different cutoff ranks, using the following formula:

[0070]

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

[0072] 4. By analyzing the trend of approximation error with the cutoff rank, a suitable SVD cutoff rank r1 is selected;

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

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

[0075] 1. By performing DMD calculations on the snapshots after dimensionality reduction for each operating condition, the DMD linear operator A under different operating parameter conditions can be obtained;

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

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

[0078] 4. Use deep learning tools such as multilayer perceptron (MLP) and convolutional neural network (CNN) to fit the mapping relationship between the reduced parameterized DMD operator and the running parameters. The running parameters are used as the input of the deep learning model, and the reduced 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 of the deep neural network model for training. The specific hyperparameter settings are determined by the actual needs and the model training effect.

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

[0080] The following verification was performed in this embodiment:

[0081] Step 1: Snapshot Acquisition: Obtain thermal-hydraulic characteristic data of the reactor under different operating conditions through a simulator or nuclear reactor mechanism model, including parameters such as core coolant temperature, primary loop system pressure, coolant flow rate, secondary working fluid temperature and gas content of the steam generator heat transfer tubes, and select 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 within this parameter space, such as... Figure 2 As shown; simulation calculations were carried out under each operating condition, and the total simulation time was set to 5000s; simulation data of core coolant temperature, primary loop system pressure, coolant flow rate, secondary working fluid temperature and gas content of steam generator heat transfer tubes were collected in the period from 4000 to 5000s, and the 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 operating 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 nodes in the simulation model. In this example, the dimension of matrix X is 102×400.

[0086] Perform singular value decomposition on the two-dimensional matrix, according to The singular value results after normalization are as follows Figure 3 As shown, satisfying 1e -4 1e -5 1e -6 The minimum singular values ​​of the threshold conditions are 14, 28, and 43, respectively.

[0087] The SVD approximation error under different cutoff rank settings is calculated, and its trend with the cutoff rank is as follows: Figure 4 As shown, it can be found that the SVD approximation error is less than 0.0001 when the truncation rank is 30. In order to balance the SVD calculation accuracy and the snapshot dimensionality reduction effect, the truncation rank r1 = 30 is taken.

[0088] Calculate a low-dimensional approximation of U under the truncated rank r1, and project the full-order snapshot for each working condition onto it to obtain its low-dimensional representation. In this example, the dimension of the reduced snapshot is 30×400.

[0089] Step 3: Parametric Dynamic Mode Decomposition: Perform DMD calculation on the snapshot after dimensionality reduction for each operating condition, and a total of 400 sets of DMD linear operators A under different operating parameter conditions can be obtained;

[0090] Flatten each DMD linear operator A into N A A column vector of size ×1 is assembled into N. A A snapshot of the parameterized operators in rows Nsample and columns, in this example, N A =r1 2 =900, the newly assembled parameterized operator snapshot dimension is 900×400;

[0091] SVD calculation is performed again on the parameterized operator matrix, and the selection of its singular value truncation rank is the same as in step 2. In this example, the first 10 singular values ​​and their vectors in the parameterized operator are extracted to obtain a snapshot of the reduced parameterized operator.

[0092] A multilayer feedforward neural network was selected to fit the mapping relationship between the reduced parameterized DMD operator and the operating parameters. In the construction of the neural network model, the operating parameters—steam flow rate and core coolant mean temperature—were used as inputs to the deep learning model, and the reduced parameterized DMD operator was used as the output. The Levenberg-Marquardt (LM) algorithm was employed to minimize the loss function (mean squared error loss, MSE) by iteratively updating the network weights and biases. The loss function is defined as follows:

[0093]

[0094] Where, x i It is the actual value. is the model's predicted value, and n is the number of samples.

[0095] Step 4: Model Validation and Optimization: The constructed reduced-order model is validated using simulation results from the mechanistic model. In this example, the root mean square error (RMSE) and the coefficient of determination (R²) are used. 2 As an evaluation criterion, if the target requirement is not met, the calculation accuracy is improved by increasing the number of snapshots until the conditions are met.

[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 phase, the operating parameters are first input into the deep learning model to construct its corresponding DMD parameterized operator. By inverse operation, the low-dimensional representation obtained from the DMD model is restored to obtain the predicted reactor thermal-hydraulic characteristics under that operating condition, such as... Figure 5 As shown.

[0097] from Figure 5 As can be seen, the predicted results are in high agreement with the actual 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 covers a variety of operating conditions, which shows that the model in this application is not only applicable to a single operating condition, but also maintains high-precision prediction capabilities over a wide range of operating parameters.

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

[0100] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0101] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for rapid prediction of reactor thermal-hydraulic characteristics based on dynamic pattern decomposition and deep learning, characterized in that, Includes the following steps: Acquire thermal-hydraulic characteristic data of the reactor under different operating conditions, and select steady-state operating data to create a snapshot; The snapshot is initially reduced in dimensionality by singular value decomposition to obtain the dimensionality-reduced snapshot representation. Construct a reduced-order model based on the dimensionality-reduced snapshot representation; The construction of the reduced-order model includes: performing dynamic mode decomposition on the dimensionality-reduced snapshot, constructing parameterized low-dimensional linear operators, and fitting the mapping relationship between the operators and the running parameters through deep learning; The mapping relationship between the fitting operator and the running parameters includes: DMD calculations are performed on the snapshots after dimensionality reduction for each operating condition to obtain the DMD linear operator; The DMD operators are flattened and assembled into a parameterized operator matrix. The parameterized operator matrix is ​​then decomposed by SVD to extract the dominant structure of the parameterized DMD operators. Extract the singular values ​​and vectors of the dominant structure to obtain a snapshot of the reduced parameterized operators; The mapping relationship between the running parameters and the reduction operator is fitted using deep learning methods; The reduced-order model is verified by the simulation results of the nuclear reactor mechanism model. When the verification is successful, the parameterized reduced-order model is obtained. The actual operating condition data is input into the parameterized reduced-order model to obtain the predicted results of the reactor's thermal-hydraulic characteristics.

2. The method according to claim 1, characterized in that, Obtaining thermal-hydraulic characteristic data includes: Simulation calculations are performed using a numerical simulation model of a nuclear reactor; By using actual operating models of nuclear reactors, we can obtain data on their thermal-hydraulic characteristics under different operating conditions. The thermal-hydraulic characteristic data include core coolant temperature, primary loop system pressure, coolant flow rate, secondary working fluid temperature and gas content of the steam generator heat transfer tubes.

3. The method according to claim 1, characterized in that, The selection of steady-state operating data to form a snapshot includes: Determine the range of values ​​for the reactor system operating parameters and select several operating conditions by sampling. Simulation calculations were performed under each operating condition to obtain simulation data of thermal-hydraulic parameters; A snapshot is constructed by taking the average value of data during the stable operation period of the reactor system.

4. The method according to claim 1, characterized in that, The initial dimensionality reduction of the snapshot includes: The snapshots under different operating conditions are assembled into a two-dimensional matrix and then singular value decomposition is performed. The singular values ​​are normalized, and the truncation rank is determined based on the threshold condition; Calculate the approximation error under different cutoff ranks, and select an appropriate cutoff rank; Projecting the full-order snapshot onto a lower-dimensional space yields a dimensionality-reduced snapshot representation.

5. The method according to claim 4, characterized in that, The deep learning methods include multilayer perceptrons and convolutional neural networks.

6. The method according to claim 1, characterized in that, If the reduction model fails the validation, the reduction model is optimized by increasing the number of snapshots.

7. The method according to claim 1, characterized in that, The obtained reactor thermal-hydraulic characteristic prediction results include: Input actual operating condition data into the parameterized reduced-order model to generate the corresponding DMD parameterized operator; The low-dimensional representation is updated by the DMD parameterization operator, and the updated low-dimensional representation is restored by inverse operation to obtain the predicted results of reactor thermal-hydraulic characteristics.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-7.

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