A reactor thermal-hydraulic state prediction method based on order reduction and data assimilation

Abstract

The application discloses a reactor thermal-hydraulic state prediction method based on order reduction and data assimilation, and belongs to the technical field of nuclear reactor thermal-hydraulic characteristic analysis and digital twinning. In order to solve the problem that the prediction error of the existing reactor thermal-hydraulic state prediction model accumulates with time and it is difficult to maintain stable accuracy for a long time, the application first obtains the prediction value of a POD coefficient by using a machine learning model based on the operating parameters of a reactor system, linearly combines the POD mode to reconstruct a reduced snapshot, and restores the reduced snapshot to a complete snapshot through SVD orthogonal projection to obtain an observation snapshot; then, in each data assimilation cycle, the set Kalman filter is used to update the prediction state, the POD coefficient predicted by the machine learning model and the POD coefficient corrected through observation are weighted and fused based on optimal weights, and inverse mapping operation is performed to restore to a physical quantity space, so that the corrected reactor thermal-hydraulic prediction result is obtained.

Description

Technical Field

[0001] This invention belongs to the field of nuclear reactor thermal-hydraulic characteristic analysis and digital twin technology, and relates to a method for predicting the thermal-hydraulic state of a reactor. Background Technology

[0002] The thermal-hydraulic characteristics of a reactor are key factors in its safety and performance assessment. Traditional analysis methods mainly rely on mechanistic simulation programs (such as RELAP5 or CFD). These methods have advantages in accuracy, but their computational cost is extremely high, making it difficult to meet the needs of digital twins and real-time monitoring.

[0003] To improve computational efficiency, a research direction combining Model Reduction (MOR) and Machine Learning (ML) has emerged in recent years. Through techniques such as Singular Value Decomposition (SVD) or Dynamic Mode Decomposition (DMD), model reduction maps the state of a high-dimensional system to a low-dimensional space, thereby accelerating computation. Meanwhile, machine learning methods, especially algorithms such as Recurrent Neural Networks (RNNs) and Long Short-Term Memory Networks (LSTMs), have demonstrated powerful capabilities in capturing nonlinear dynamics. However, traditional MOR-ML models have an "open-loop" structure, and their prediction errors accumulate over time, making it difficult to maintain stable accuracy over the long term. Summary of the Invention

[0004] The present invention aims to address the problem that existing reactor thermal-hydraulic state prediction models suffer from prediction errors that accumulate over time, making it difficult to maintain stable accuracy over the long term.

[0005] A reactor thermal-hydraulic state prediction method based on order reduction and data assimilation includes:

[0006] Step 1: Obtain snapshot data of the reactor's thermal-hydraulic parameters under different operating conditions. The reactor's thermal-hydraulic parameters include temperature, pressure, and flow rate.

[0007] Step 2: Use singular value decomposition and intrinsic orthogonal decomposition to reduce the dimension of the snapshot to obtain a reduced snapshot, and extract the dominant mode from the data. Thus, the reduced snapshot is represented as a linear combination of the dominant mode and the mode coefficients, and the POD reconstructed snapshot is obtained; the dominant mode is the POD mode, and the mode coefficients are the POD coefficients.

[0008] Step 3: In the actual process of predicting the thermal-hydraulic state of the reactor, based on the operating parameters of the reactor system, the predicted value of the POD coefficient is obtained by using a machine learning model. Then, it is reconstructed by linearly combining it with the POD mode and the reduced snapshot is then restored to the complete snapshot by SVD orthogonal projection. The machine learning is obtained by training with the data obtained in Step 1 and Step 2.

[0009] Step 4: In the online phase, use ensemble Kalman filtering to correct the predictions of the machine learning model in real time.

[0010] S401. Unify the observation time step of the observation data with the prediction output time step of the machine learning model.

[0011] S402, Noise Modeling: Random perturbation terms are superimposed on the observation data to construct the observation error covariance matrix;

[0012] S403. Using the observation data processed by noise modeling in S402, replace the "parameters with the same physical meaning" in the complete snapshot predicted in step 3 to obtain the observation snapshot. Transform it using the same order reduction mapping operator as the machine learning model so that the observation snapshot obtains the same representation as the POD coefficients, and finally obtains the observation vector, which is the POD coefficient form of the observation snapshot.

[0013] S404. Normalize the observation vector:

[0014] S405. In each data assimilation period, the predicted state is updated using ensemble Kalman filtering; the prior state of the POD coefficients is predicted based on the machine learning model, and the deviation between the prior state and the observation vector processed in S403 is calculated.

[0015] During the filtering update phase, dynamic confidence weight coefficients are used. Corrected prediction covariance matrix: , To predict the covariance matrix, This is the corrected prediction covariance matrix;

[0016] S406, Model Fusion Index By solving Minimize the weight coefficients and , as the optimal weight; , satisfy , For the error of the machine learning model, The error is after assimilation correction; the POD coefficient is predicted by the machine learning model based on the optimal weights. and the observed corrected POD coefficient Perform weighted fusion ;

[0017] Step 5: The weighted fused POD coefficients are restored to the physical quantity space through an inverse mapping operation to obtain the corrected reactor thermal-hydraulic prediction results.

[0018] Furthermore, the process of obtaining the reactor's thermal-hydraulic parameters under different operating conditions includes:

[0019] The preset range of values ​​for reactor system operating parameters is selected, and N is chosen within the parameter space. sample Group operating conditions; for each group operating condition, transient calculations are performed using a refined simulation model, and time-series data of thermal-hydraulic parameters are collected.

[0020] Furthermore, when stitching together multiple snapshots acquired under different operating conditions in a horizontal stacking manner, the number of rows in the matrix is ​​kept consistent with the number of rows in a single snapshot data, and the integration of snapshots under multiple operating conditions is achieved only by accumulating the number of columns.

[0021] Furthermore, the specific process of obtaining the POD reconstruction snapshot includes:

[0022] First, multiple snapshots acquired under different working conditions are stitched together in a horizontal stacking manner to obtain a stitched matrix; singular value decomposition is performed on the stitched matrix, the singular value energy ratio and SVD reconstruction error are calculated, and the truncation rank is selected to obtain the dimensionality reduction mode obtained by SVD truncation;

[0023] Then, through orthogonal projection, the snapshot data under different operating conditions are projected onto the dimensionality-reduced modes obtained by SVD truncation to obtain the low-dimensional representation of the snapshot data, i.e., the reduced snapshot. Based on the reduced snapshot, the dominant mode in the data is extracted by the intrinsic orthogonal decomposition method, so that the reduced snapshot is represented as a linear combination of the dominant mode and the mode coefficients, and the POD reconstructed snapshot is obtained. The dominant mode is the POD mode, and the mode coefficients are the POD coefficients.

[0024] Furthermore, the process of training a machine learning model using the data obtained in steps 1 and 2 includes:

[0025] A machine learning model is constructed using the reactor system's operating parameters as input and the POD coefficient prediction value as output. A training set is determined based on the dataset consisting of the reactor system's operating parameters and the POD coefficient. The training data is normalized to the [-1,1] interval, and then the machine learning model is trained to obtain the trained machine learning model.

[0026] Furthermore, during the normalization process of the observation vector, S404 calls the normalization matrix corresponding to the POD coefficients during the training of the machine learning model and applies the normalization parameters of the matrix.

[0027] Furthermore, the observation data described in S401 is obtained in a different manner than the thermal-hydraulic parameters obtained in step 1, including experimental monitoring or numerical simulation results from simulation programs.

[0028] Furthermore, dynamic confidence weight coefficients in, Let p be the root mean square error of the observed parameters at time step t. For the first The observed values ​​of each observation parameter at this time step. For the first Machine learning model predictions for each observation parameter; Adjust the parameters.

[0029] Furthermore, the error of the machine learning model , For the truncated rank of POD, The POD coefficient predicted by the machine learning model, and For the observation vector, the subscript... This represents the POD coefficient at time step i.

[0030] Error after assimilation correction , This is the POD coefficient after observation correction.

[0031] Beneficial effects:

[0032] 1. By organically combining model reduction, machine learning, and data assimilation, a multi-layered fusion system of low-dimensional modeling, nonlinear prediction, and real-time correction is realized. The data assimilation module can dynamically update the prediction state based on online observation, thereby effectively suppressing the propagation of open-loop errors and effectively solving the problem of prediction errors accumulating over time, thus maintaining stable accuracy over a long period of time.

[0033] 2. The reduced-order model reduces the computational dimension of complex reactor systems by 2 to 3 orders of magnitude, significantly improving computational speed while ensuring accuracy, and can meet the requirements of near real-time analysis.

[0034] 3. The framework can embed experimental measurement data or multiphysics simulation data to achieve rapid digital twin modeling of different reactor types (pressurized water reactor, lead-bismuth reactor, space reactor, etc.). Attached Figure Description

[0035] Figure 1 This is a schematic diagram illustrating the implementation process of a reactor thermal-hydraulic state prediction method based on order reduction and data assimilation.

[0036] Figure 2 This is a schematic diagram of the snapshot sampling results based on the Latin hypercube.

[0037] Figure 3 This is a schematic diagram of the singular value decomposition results during the dimensionality reduction process.

[0038] Figure 4 This is a comparison chart of the predicted POD coefficients before and after EnKF data assimilation correction.

[0039] Figure 5 This is a comparison between the predicted results and the refined simulation results of the key thermal-hydraulic parameters of the reactor (core coolant temperature).

[0040] Figure 6 This is a comparison between the predicted results and the refined simulation results of the key parameters of reactor thermal-hydraulic (primary coolant flow rate). Detailed Implementation

[0041] To address the problems in the background technology, this invention introduces data assimilation (DA) technology, utilizing ensemble Kalman filtering (EnKF) to dynamically correct model prediction results, forming a reduction-data assimilation framework. This framework integrates the efficiency of reduction-data assimilation modeling, the nonlinear modeling capability of machine learning, and the self-correcting characteristics of data assimilation, achieving rapid, stable, and high-precision prediction of reactor thermal-hydraulic characteristics.

[0042] This implementation proposes a reactor thermal-hydraulic state prediction method based on order reduction and data assimilation. The overall process is as follows: Figure 1 As shown. The method includes the following steps:

[0043] Step 1, Snapshot Acquisition and Construction:

[0044] The reactor's thermal-hydraulic parameters, including temperature, pressure, and flow rate, are obtained under different operating conditions using mechanistic simulation programs (such as RELAP5). More specifically,

[0045] The range of values ​​for the reactor system operating parameters is preset, and N is selected within the above parameter space using methods such as random sampling and Latin hypercube sampling. sample Group operating conditions; for each group operating condition, transient calculations are performed using a refined simulation model, and time-series data of thermal-hydraulic parameters such as coolant temperature, primary loop system pressure, coolant flow rate, secondary working fluid temperature of steam generator, and steam flow rate are collected, thereby constructing a high-fidelity database;

[0046] The spatiotemporal data (at different times and spatial locations / nodes) of the thermal-hydraulic parameters used for subsequent dimensionality reduction and other processing are called snapshot data. Noise-reduced multi-resolution snapshot data is obtained through smoothing filtering and temporal resampling. Multi-resolution refers to data obtained at different time sampling intervals, such as 0.2 seconds, 1.0 seconds, and 2.0 seconds. Sensitivity analysis of temporal resolution is conducted for the time series corresponding to the snapshots to clarify the sampling time interval, simultaneously satisfying: 1) supporting the target reconstruction accuracy for dimensionality reduction modeling and the target prediction performance for time series prediction modeling; 2) ensuring that the complexity of both types of models is within a reasonable range that is engineering-feasible and efficient, ultimately achieving the optimal balance between reconstruction accuracy, prediction performance, and model complexity.

[0047] The model reduction and machine learning model training may use data with different time steps. For example, the original high-fidelity data is obtained based on a 0.2-second sampling interval, while the data used for reduction is based on a 1.0-second time step, and the data used for machine learning training is based on a 2.0-second time step. This processing is to balance model accuracy and training complexity at different stages.

[0048] Step 2, Snapshot Reduction and Feature Extraction:

[0049] Dimensionality reduction of snapshots is performed using singular value decomposition (SVD) and orthogonal eigenvalue decomposition (POD) to determine the dominant characteristic modes. Modal features and dynamic evolution laws under different operating parameters are extracted, and parameterized low-dimensional linear operators are established to represent the evolution of the thermal-hydraulic field.

[0050] Specifically, the process of reducing the dimensionality of the snapshot matrix based on singular value decomposition and eigenorthogonal decomposition includes:

[0051] First, multiple snapshots acquired under different operating conditions are stitched together horizontally (i.e., expanded along the column dimensions of the matrix) to form a large matrix. During the stitching process, it is strictly ensured that the number of rows in the large matrix matches the number of rows in a single snapshot; integration of snapshots from multiple operating conditions is achieved solely through column addition.

[0052] Singular value decomposition (SVD) is performed on the spliced ​​large matrix. The singular value energy ratio and SVD reconstruction error (measured by Frobenius norm) are calculated. The truncation rank is selected to obtain the dimensionality-reduced mode obtained by SVD truncation.

[0053] Then, through orthogonal projection, the snapshot data under different operating conditions are projected onto the dimensionality-reduced modes obtained by SVD truncation, resulting in the reduced snapshot (i.e., low-dimensional representation) corresponding to the snapshot data. Based on this reduced snapshot, the intrinsic orthogonal decomposition (POD) method is used to extract the dominant modes in the data, thereby representing the reduced snapshot as a linear combination of the dominant modes (POD modes) and mode coefficients (POD coefficients), thus realizing the reconstruction of the reduced snapshot and obtaining the POD reconstructed snapshot.

[0054] Calculate the relative error between the POD reconstruction snapshot and the reduced snapshot:

[0055]

[0056] In the formula, the subscript F represents the Frobenius norm. For the sake of a simplified snapshot, Reconstruct a snapshot for POD.

[0057] Step 3, Time Series Forecasting Modeling:

[0058] To overcome the extrapolation limitations of data-driven, non-intrusive model reduction methods such as singular value decomposition and intrinsic orthogonal decomposition in the nonlinear region, machine learning methods such as Long Short-Term Memory (LSTM) networks or Multilayer Perceptrons (MLPs) are employed to learn the nonlinear mapping relationship between operating parameters and reduced-order modal coefficients. This module enables rapid prediction of the thermal-hydraulic state under different operating conditions by training a mapping model in a compressed subspace.

[0059] The specific steps include:

[0060] S301. A machine learning model is used to fit the evolution of the POD coefficient over time. The input is the operating parameters of the reactor system, and the output is the predicted value of the POD coefficient under the full time series.

[0061] The dataset, based on the running parameters and POD coefficients, is divided into an inner region, a transition region, and a boundary region according to the parameter space in a ratio (e.g., 8:1:1), which serve as the training set, validation set, and test set, respectively.

[0062] S302. Normalize the training data to the [-1,1] interval, select the loss function and training optimizer of the algorithm, and adjust the hyperparameters of the algorithm through the model performance on the validation set. Once the model meets the accuracy requirements, the training is completed and the results are output.

[0063] S303. In the actual process of predicting the thermal-hydraulic state of a reactor, based on the operating parameters of the reactor system, the predicted value of the POD coefficient is obtained by using a trained machine learning model. Then, it is reconstructed by linearly combining the POD mode and the reduced snapshot. The reduced snapshot is then restored to the complete snapshot by SVD orthogonal projection.

[0064] Step 4: Data assimilation and dynamic correction based on ensemble Kalman filtering:

[0065] During the online phase, the predictions of the machine learning model are corrected in real time using ensemble Kalman filtering (EnKF). When observation data becomes available, the data assimilation module updates the reduction coefficients and system state based on the deviation between the measurements and model predictions, achieving model correction and uncertainty control. In principle, any parameter that makes up the snapshot can be used as observation data; the actual selection depends on the feasibility of experimental measurement or high-fidelity calculation of the parameter.

[0066] The specific process includes the following steps:

[0067] S401, Time Step Alignment: Since the observation data (experimental monitoring or numerical simulation results of another simulation program) may have different sampling frequencies and noise levels, the observation time step is aligned with the time step predicted by the machine learning model.

[0068] It should be noted that the high-fidelity database in step 1 and the high-fidelity database used by the data assimilation module cannot be the same data source, or at least different software. For example, in the embodiment, the high-fidelity database in step 1 is obtained based on a one-dimensional thermal-hydraulic program simulation, while the assimilated high-fidelity data is obtained based on CFD.

[0069] S402. Noise Modeling: Based on the typical measurement errors of sensors or simulation programs, random disturbance terms are superimposed on the observation data to construct the observation error covariance matrix R.

[0070] S403, Low-dimensional mapping and observation vector construction:

[0071] First, the observation data processed by S402 noise modeling (i.e., the observation values ​​after superimposed random perturbations) is used to replace the "parameters with the same physical meaning" (same parameters) in the complete snapshot predicted by S303. Specifically, S303 predicts a complete snapshot covering all key parameters of the system based on the operating parameters, while the observation data only contains some measurable parameters. Therefore, only the parameters in the snapshot corresponding to the observation data are replaced, and the parameters without observation data are retained by the prediction results of S303. Subsequently, the observation snapshot composed of the prediction results and the observation data is transformed by the same order reduction mapping operator as the machine learning model (i.e., SVD projection matrix and POD projection matrix) so that the observation snapshot obtains the same representation as the POD coefficients, and finally the observation vector (i.e., the POD coefficient form of the observation snapshot) is obtained.

[0072] S404, Normalization Process:

[0073] Call the normalization matrix corresponding to the POD coefficients in S302, and map the above observation vector (the POD coefficient form of the observation data) to the interval [-1, 1] according to the normalization parameters of the matrix to maintain scale consistency.

[0074] S405 and EnKF assimilation and prediction correction:

[0075] Within each data assimilation period, the predicted state is updated using ensemble Kalman filtering. The prior state of the POD coefficients is predicted based on a machine learning model, and the deviation between the prior state and the observed vector processed by S403 is calculated.

[0076] The prior state of the POD coefficient (here, the prior state is the "prior state" in the EnKF process) refers to the POD coefficient at the current moment predicted by the machine learning model based solely on "historical correction state + current operating parameters" when "current observation data has not been introduced". It is the "initial prediction value to be corrected" in the EnKF assimilation and is completely equivalent to the "POD coefficient prediction value" output by the model. It only adapts to the "prior-posterior" expression system of EnKF in terms of terminology.

[0077] To improve the adaptability of the data assimilation process to prediction uncertainty, this invention introduces a dynamic confidence weight coefficient (…). This coefficient is used to characterize the reliability of the machine learning prediction model at each time step, and adaptively adjusts the update strength of EnKF based on the instantaneous prediction error. Its definition is as follows:

[0078]

[0079] in, For the first The root mean square error of the observed parameters at each time step (assuming there are p observed parameters in total). For the first The observed values ​​of each observation parameter at this time step. For the first The predicted values ​​of the machine learning model for each observation parameter. Adjust the parameters. When the prediction error is large... This reduces the confidence level in the current predicted state; when the error is small, Keep the weight close to 1 and maintain the standard update weight.

[0080] During the filtering update phase, the predicted covariance matrix is ​​corrected using this coefficient:

[0081] (3)

[0082] in, To predict the covariance matrix, This is the corrected prediction covariance matrix.

[0083] This enables a dynamic adjustment mechanism for the assimilation weights, making the filter's response to prediction errors adaptive, thereby effectively suppressing the accumulation of errors in the model during non-steady-state phases.

[0084] S406. State Reconstruction and Prediction Output: To further integrate the prediction advantages of models at different levels, this invention proposes a model fusion index. It is used to solve for the optimal weights and to perform weighted fusion of the POD coefficient state vectors output by the two types of models.

[0085] The model fusion index is as follows:

[0086] (4)

[0087] in, , The weighting coefficients are satisfied. .

[0088] The error of the machine learning model is calculated using the following formula: (5)

[0089] in, For the truncated rank of POD, The POD coefficient predicted by the machine learning model (obtained from S303), and The observation vector (result after S404 processing) is represented by the subscript i, which indicates the POD coefficient at the i-th time step (each order of POD coefficient is a time vector).

[0090] The error after assimilation correction is calculated using the following formula:

[0091]

[0092] in, The POD coefficients are the observation-corrected values ​​(which include a fusion of model predictions and observations).

[0093] During the state reconstruction process, by solving... Minimized and The optimal weights are obtained; the predictions of the machine learning model are then based on these optimal weights. and assimilation value Weighted fusion is performed, resulting in:

[0094]

[0095] in, The weighted fusion coefficients are the POD coefficients.

[0096] This indicator achieves the optimal combination of multi-source predictions through weight adjustment, so that the final prediction results have both physical consistency and temporal stability under different operating conditions.

[0097] Step 5, State Reconstruction and Predicted Output:

[0098] The POD coefficients obtained from formula (7) are restored to the physical quantity space through an inverse mapping operation (i.e., multiplying by the POD basis matrix), thereby obtaining the corrected reactor thermal-hydraulic prediction results.

[0099] Example

[0100] like Figure 1As shown, this invention provides a reactor thermal-hydraulic state prediction method based on order reduction and data assimilation, comprising five main steps: snapshot acquisition and construction, snapshot order reduction and feature extraction, time series prediction modeling, data assimilation and dynamic correction, and state reconstruction and prediction output. This method can be widely applied to the rapid prediction of thermal-hydraulic state and the construction of digital twin models for reactor systems such as pressurized water reactors, lead-bismuth reactors, and space reactors.

[0101] Snapshot Acquisition and Construction: First, the operating parameter space of the reactor system is determined, including the mean core coolant temperature, steam pressure, and reactor power. Specifically, in this example, steam flow rate and mean core coolant temperature are selected as operating parameters, and their value ranges are shown in Table 1. N is generated within the set parameter range using Latin hypercube sampling. sample =400 operating conditions, such as Figure 2 As shown.

[0102] Table 1. Range settings for running parameters in simulation calculations

[0103]

[0104] It should be noted that: in this embodiment, steam flow rate and average core coolant temperature are selected as operating parameters, but other operating parameters can also be selected in other embodiments.

[0105] Each set of operating conditions was input into a mechanistic simulation program (such as RELAP5 or other system-level thermal-hydraulic analysis programs) for transient simulation. The total simulation duration was set to 500 s, and the core coolant temperature and flow rate, primary loop pressure and coolant density, secondary steam temperature and flow rate of the steam generator (OTSG), and temperature fields of key nodes in the pressure vessel and piping were collected.

[0106] The original data was obtained with a time step of 0.2 s, forming a high-fidelity dataset. Subsequently, Savitzky-Golay smoothing filtering was used to suppress noise, and the dataset was resampled every 1.0 s to generate snapshot sequences. This process ensures that data dimensionality and storage costs are reduced while preserving key dynamic features.

[0107] Snapshot Reduction and Feature Extraction: Perform singular value decomposition on the above snapshot matrix X:

[0108]

[0109] Where U is the spatial mode matrix, and Σ is the singular value diagonal matrix. This is the time coefficient matrix. The truncation rank is determined by calculating the singular value energy percentage and the reconstruction error (measured by the Frobenius norm). .

[0110] The singular value decomposition results during dimensionality reduction are as follows: Figure 3 As shown.

[0111] In this embodiment of the invention, when When the reconstruction error is ,and Or an error difference of 20 within 10 -7 Within the order of magnitude, they are negligible, indicating that the first five modes are sufficient to characterize the main system features. Therefore, [the following is selected]. To balance computational accuracy and efficiency.

[0112] Furthermore, intrinsic orthogonal decomposition was employed to perform mode decomposition on the dimensionality-reduced snapshot, extracting the dominant spatiotemporal feature modes. The results show that the first three POD modes account for approximately 99% of the energy, effectively capturing the dominant dynamics during the transition from forced cycling to natural cycling. The remaining modes only describe high-frequency perturbations and can be neglected.

[0113] Time series forecasting modeling: This involves using machine learning methods to learn the nonlinear dynamic mapping relationship between operating parameters and reduced-order mode coefficients. In this example, a Long Short-Term Memory (LSTM) network is chosen to construct the time series forecasting model.

[0114] First, the 400 samples were partitioned based on the physical range of the original operating parameters: the inner region corresponds to the core operating range of the original parameters (later normalized and mapped to [-0.8, 0.8]², where the superscript 2 indicates that the parameter domain is a 2D plane), and the transition region corresponds to the edge operating range of the original parameters (later normalized and mapped to...). The outer domain is the extended operating range of the original parameters excluding the inner domain and the transition zone; the target partitioning ratio is: inner domain samples are used as the training set (accounting for 80% of the total samples), transition zone samples are used as the validation set (accounting for 10% of the total samples), and outer domain samples are used for extrapolation performance verification.

[0115] In actual partitioning, since the number of original samples in the inner region is less than 80% of the total samples, some samples are selected from the transition region to supplement the inner region, together forming a training set that accounts for 80% of the total samples; the remaining samples in the transition region are merged with some samples selected in the outer region to form a validation set that accounts for 10% of the total samples; the remaining samples in the outer region that were not selected into the validation set are used as the final test set for extrapolation performance verification.

[0116] Furthermore, the outputs (POD coefficients) of both the training and validation sets are normalized to the interval [-1, 1], and resampling is performed at 2.0 s intervals to reduce time-dependent noise in the POD coefficients and accelerate network convergence. The LSTM network contains two memory layers with 128 units per layer, an activation function of tanh, and a linear mapping layer as the output layer. Mean squared error (MSE) is used as the loss function, and the Adam optimizer is used for training. After 5000 training epochs, the average RMSE of both the training and validation sets remains below 0.02 of the normalized magnitude, and the prediction determination coefficient R0 is [value missing]. 2 A value >0.97 indicates that the model can effectively capture the main dynamic trends.

[0117] Data assimilation and dynamic correction: When experimental measurements or high-fidelity simulation data are available, key monitoring parameters (such as core outlet temperature, primary loop flow rate, and secondary side steam temperature) are selected as the observation input. In this example, high-fidelity simulation results from computational fluid dynamics (CFD) are used as the data source for data assimilation.

[0118] Based on the calculated observation data, the time step is unified to 1.0 s, and the measurement accuracy of the corresponding instrument is determined according to the parameters (e.g., ...). Construct the observation error covariance matrix. Simultaneously, map it to [-1, 1] according to the normalization parameters of the training phase.

[0119] By using a reduction operator consistent with the prediction model, the observed data are projected onto the POD coefficient space to obtain the observation vector. According to the EnKF algorithm, the system state (i.e., the POD coefficient) is updated once every assimilation period (1.0 s in this embodiment):

[0120]

[0121] in, This is the POD coefficient vector after EnKF assimilation correction. The results are the predictions from the LSTM model, where K is the Kalman gain and Y is the value of the Kalman Array. obs For high-fidelity simulation data of CFD models, To predict the covariance matrix, The observation operator—in this embodiment, it is taken as the identity matrix of the same order as the truncated rank of POD. , Let be the observation error covariance matrix.

[0122] To enhance the adaptive response of data assimilation to prediction uncertainty, this embodiment introduces a dynamic confidence weight coefficient. The predicted covariance matrix is ​​modified to make the filter's response to the error time-adaptive. Based on this dynamic adjustment mechanism, the updated system state value after assimilation is:

[0123]

[0124] in, To introduce a Kalman gain corrected by a dynamic confidence weight coefficient.

[0125] Parameter scanning analysis shows that when the set size is 500, The model exhibits the lowest RMSE, approximately 0.044. Compared to the uncorrected LSTM, the EnKF-corrected model shows an average RMSE reduction of 27.5%, significantly improving prediction stability and temporal consistency.

[0126] State Reconstruction and Predicted Output: The POD coefficients, corrected by EnKF, are inversely mapped back to the physical quantity space to obtain the time evolution of core coolant temperature, flow rate, pressure, and steam generator outlet parameters. In this example, the model fusion index... Used for comprehensive evaluation and weighted output of prediction results from ROM, LSTM, and EnKF; POD truncated rank Therefore:

[0127]

[0128] The fusion index of the model is calculated based on the above formula. The optimal POD coefficient for the fusion state is obtained through dynamic optimization. For example... Figure 4 As shown, the POD coefficients after EnKF dynamic data assimilation show a significant improvement in prediction accuracy compared to the LSTM model. The physical quantity field is recovered through inverse mapping. Assimilation results show that the maximum deviation of coolant temperature decreased from 40 K to 8.4 K, steam temperature deviation decreased from 30 K to 8.9 K, and the average relative error decreased from 0.0021 to 0.0016. This framework enables real-time reconstruction and dynamic prediction of the reactor's thermal-hydraulic state, providing a feasible technical path for online calibration of reactor digital twin systems.

[0129] Comparison of predicted results and refined simulation results of key reactor thermal-hydraulic parameters, for example Figure 5 and Figure 6 As shown.

[0130] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for predicting the thermal-hydraulic state of a reactor based on order reduction and data assimilation, characterized in that, include: Step 1: Obtain snapshot data of the reactor's thermal-hydraulic parameters under different operating conditions. The reactor's thermal-hydraulic parameters include temperature, pressure, and flow rate. Step 2: Use singular value decomposition and intrinsic orthogonal decomposition to reduce the dimension of the snapshot to obtain a reduced snapshot, and extract the dominant mode from the data. Thus, the reduced snapshot is represented as a linear combination of the dominant mode and the mode coefficients, and the POD reconstructed snapshot is obtained; the dominant mode is the POD mode, and the mode coefficients are the POD coefficients. Step 3: In the actual process of predicting the thermal-hydraulic state of the reactor, based on the operating parameters of the reactor system, the predicted value of the POD coefficient is obtained by using a machine learning model. Then, it is reconstructed by linearly combining it with the POD mode and the reduced snapshot is then restored to the complete snapshot by SVD orthogonal projection. The machine learning is obtained by training with the data obtained in Step 1 and Step 2. Step 4: In the online phase, use ensemble Kalman filtering to correct the predictions of the machine learning model in real time. S401. Unify the observation time step of the observation data with the prediction output time step of the machine learning model. S402, Noise Modeling: Random perturbation terms are superimposed on the observation data to construct the observation error covariance matrix; S403. Using the observation data processed by noise modeling in S402, replace the "parameters with the same physical meaning" in the complete snapshot predicted in step 3 to obtain the observation snapshot. Transform it using the same order reduction mapping operator as the machine learning model so that the observation snapshot obtains the same representation as the POD coefficients, and finally obtains the observation vector, which is the POD coefficient form of the observation snapshot. S404. Normalize the observation vector; S405. During each data assimilation period, the predicted state is updated using ensemble Kalman filtering. The prior state of the POD coefficient is predicted based on the machine learning model, and the deviation between the prior state and the observation vector after S403 processing is calculated. During the filtering update phase, dynamic confidence weight coefficients are used. Corrected prediction covariance matrix: , To predict the covariance matrix, This is the corrected prediction covariance matrix; S406, Model Fusion Index By solving Minimize the weight coefficients and , as the optimal weight; , satisfy , For the error of the machine learning model, The error is after assimilation correction; the POD coefficient is predicted by the machine learning model based on the optimal weights. and the observed corrected POD coefficient Perform weighted fusion of POD coefficients ; Step 5: The weighted fused POD coefficients are restored to the physical quantity space through an inverse mapping operation to obtain the corrected reactor thermal-hydraulic prediction results.

2. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 1, characterized in that, The process of obtaining the reactor's thermal-hydraulic parameters under different operating conditions includes: The preset range of values ​​for reactor system operating parameters is selected, and N is chosen within the parameter space. sample Group operating conditions; for each group operating condition, a refined simulation model is used to perform transient calculations and collect time-series data of thermal and hydraulic parameters.

3. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 1, characterized in that, For multiple snapshots acquired under different operating conditions, during the process of stitching them together in a horizontal stacking manner, the number of rows in the matrix is ​​kept consistent with the number of rows in a single snapshot data, and the integration of snapshots under multiple operating conditions is achieved only by accumulating the number of columns.

4. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 1, characterized in that, The specific process of obtaining the POD reconstruction snapshot includes: First, multiple snapshots acquired under different working conditions are stitched together in a horizontal stacking manner to obtain a stitched matrix; singular value decomposition is performed on the stitched matrix, the singular value energy ratio and SVD reconstruction error are calculated, and the truncation rank is selected to obtain the dimensionality reduction mode obtained by SVD truncation; Then, through orthogonal projection, the snapshot data under different operating conditions are projected onto the dimensionality-reduced modes obtained by SVD truncation to obtain the low-dimensional representation of the snapshot data, i.e., the reduced snapshot. Based on the reduced snapshot, the dominant mode in the data is extracted by the intrinsic orthogonal decomposition method, so that the reduced snapshot is represented as a linear combination of the dominant mode and the mode coefficients, and the POD reconstructed snapshot is obtained. The dominant mode is the POD mode, and the mode coefficients are the POD coefficients.

5. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 1, characterized in that, The process of training a machine learning model using the data obtained in steps 1 and 2 includes: A machine learning model is constructed using the reactor system's operating parameters as input and the POD coefficient prediction value as output. A training set is determined based on the dataset consisting of the reactor system's operating parameters and the POD coefficient. The training data is normalized to the [-1,1] interval, and then the machine learning model is trained to obtain the trained machine learning model.

6. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 5, characterized in that, During the normalization process of the observation vector, S404 calls the normalization matrix corresponding to the POD coefficients during the training of the machine learning model and performs normalization according to the normalization parameters of the matrix.

7. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 1, characterized in that, The observation data described in S401 is obtained in a different way than the thermal-hydraulic parameters obtained in step 1, including experimental monitoring or numerical simulation results from simulation programs.

8. A reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to any one of claims 1 to 7, characterized in that, Dynamic confidence weight coefficient in, For the first The root mean square error of p observed parameters at each time step For the first The observed values ​​of each observation parameter at this time step. For the first The machine learning model predicts the values ​​of the observed parameters; α is the adjustment parameter.

9. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 8, characterized in that, Error of machine learning models , For the truncated rank of POD, The first prediction of the machine learning model POD coefficient at time step This is the observation vector predicted by the machine learning model at time step i.

10. The reactor thermal-hydraulic state prediction method based on order reduction and data assimilation according to claim 9, characterized in that, Error after assimilation correction , is the POD coefficient at the i-th time step after observation correction.

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