A method and system for on-line monitoring of a sodium-cooled fast reactor steam generator

Abstract

This application discloses an online monitoring method and system for a sodium-cooled fast reactor steam generator. The method employs mode order reduction technology to construct a low-dimensional modal space that accurately characterizes the dominant features of the two-dimensional transient thermal-hydraulic field of the steam generator. Within this space, a physically constrained neural network model is used to describe the temporal evolution of modal coefficients under various transient operating conditions. The neural network incorporates residuals of heat transfer conservation on both sides, boundary temperature consistency, physical property parameter consistency, and heat transfer coefficient consistency into its loss function, thereby ensuring the physical consistency of each physical quantity in the model during the prediction process. During online monitoring, the system receives real-time operating parameters from the power plant's operation control system, obtains transient modal coefficients through the physically constrained neural network, and reconstructs the two-dimensional temperature field, pressure field, and heat transfer coefficient field of the steam generator by combining them with a pre-established POD modal basis, thus achieving timely assessment of the thermal-hydraulic characteristics.

Description

Technical Field

[0001] This application belongs to the field of online monitoring technology of nuclear engineering and thermal hydraulics, and particularly relates to an online monitoring method and system for a sodium-cooled fast reactor steam generator. Background Technology

[0002] Sodium-cooled fast reactor steam generators are subjected to coupled thermal-hydraulic effects from the primary sodium side and the secondary steam side during operation. Internally, they contain a layered tube bundle structure, complex two-phase flow, and high-temperature heat transfer processes. Furthermore, during typical transient events such as start-up, shutdown, flow disturbances, sudden changes in steam pressure, and feedwater loss or LOCA (Loss of Flow and Response) events, their temperature, pressure, and two-phase flow fields exhibit strong nonlinearity, high dimensionality, and rapid evolution. Traditional thermal-hydraulic calculation tools, such as one-dimensional or two-dimensional transient analysis programs, while possessing high physical fidelity, typically rely on dense control volume partitioning and step-by-step time progression in their numerical solution structure, making the computation time insufficient for real-time online monitoring requirements.

[0003] To reduce computational costs, some scholars have attempted to replace traditional numerical solutions with reduced-order models or neural network models. However, existing reduction-order techniques generally suffer from the following shortcomings: (1) It cannot take into account physical constraints such as energy conservation and mass conservation, and the prediction results lack physical interpretation, making it difficult to meet the requirements of nuclear safety supervision.

[0004] (2) It lacks the ability to express the transient coupling characteristics of complex structures of steam generators (such as multi-layer tube bundles and secondary two-phase flow), and its accuracy is unstable.

[0005] (3) It lacks generalization ability under transient disturbance conditions and is difficult to apply to the online monitoring of actual power plants.

[0006] Therefore, there is an urgent need for a method and system that can significantly reduce the computational scale and achieve rapid and stable prediction of the transient thermal-hydraulic characteristics of steam generators while maintaining the key physical properties and two-dimensional field structure representation. Summary of the Invention

[0007] The purpose of this application is to overcome the problems of the prior art by disclosing an online monitoring method and system for a sodium-cooled fast reactor steam generator. This application constructs a modal reduction model and a physical constraint neural network, which enables the transient temperature, pressure and heat flow distribution of the steam generator to be accurately reconstructed in a time scale much faster than that of traditional numerical solutions, thereby meeting the engineering needs of online monitoring, structural life assessment and operation auxiliary decision-making.

[0008] The objective of this application is achieved through the following technical solution: A method for online monitoring of a sodium-cooled fast reactor steam generator, the method comprising: S1: Sample library construction, constructing a thermal-hydraulic sample library covering steady-state and various transient operating conditions; S2: POD mode reduction, which performs POD mode reduction on the two-dimensional field quantities in the sample library to obtain the modal basis and modal coefficients; S3: Neural network construction, constructing a neural network model with physical constraints, and using the corresponding model to predict the evolution of modal coefficients over time; S4: Online monitoring and transient field reconstruction. The real-time operating parameters of the power plant are used as input, and the current mode coefficients are obtained through the neural network. The mode coefficients are inversely transformed by combining the preset mode basis to reconstruct the two-dimensional temperature field, pressure field and heat transfer coefficient field of the steam generator. The online monitoring and structural life assessment of the sodium-cooled fast reactor steam generator are completed and output.

[0009] According to a preferred embodiment, in step S1, for the envelope of steady-state operating conditions, steady-state boundary conditions are generated by orthogonal experimental design and Latin hypercube sampling, and based on the steady-state boundary conditions, a complete steady-state sample is generated for each set of steady-state inputs by a transient thermal-hydraulic analysis program. For each transient condition, Lagrange / spline boundary condition interpolation is used to construct transient boundary conditions with different rates of change. Based on the transient boundary conditions, a complete transient sample is generated for each set of transient inputs using a transient thermal-hydraulic analysis program.

[0010] According to a preferred embodiment, in step S2, after obtaining a preset number of samples, the dominant mode features of the key physical quantities of the steam generator are obtained by digitizing the data of each field quantity sample and performing singular value decomposition. In the POD modal order reduction process, the modal truncation order is determined by a combination of the cumulative energy ratio method, the error-complexity balance method, and cross-validation. Furthermore, the temperature field, pressure field, enthalpy field, and heat transfer coefficient field in the sample library are each constructed into a sample matrix and POD order reduction is performed independently.

[0011] According to a preferred embodiment, in step S2, the mode reduction is achieved by singular value decomposition or eigenorthogonal decomposition.

[0012] According to a preferred embodiment, in step S3, the physical constraints of the neural network model include the heat transfer conservation residual on both sides, the boundary temperature consistency residual, the physical property parameter consistency residual, and the heat transfer coefficient consistency residual. Among them, the heat transfer conservation residual on both sides is obtained by calculating the difference between the heat transfer measured on the first side and the heat transfer on the second side. The boundary temperature consistency residual is obtained by calculating the difference between the inlet and outlet temperatures predicted by the neural network and the actual temperature measured by the DCS. The consistency residual of physical property parameters is obtained by calculating the temperature predicted by the neural network and the temperature difference calculated by enthalpy and pressure. The heat transfer coefficient consistency residual is obtained by calculating the difference between the heat transfer coefficient predicted by the neural network and the heat transfer coefficient calculated by the empirical formula.

[0013] According to a preferred embodiment, in step S3, the steady-state prediction neural network is a BP neural network, whose input is the steady-state boundary conditions, including temperature, flow rate, and pressure; and whose output is the steady-state temperature field, pressure field, and heat transfer coefficient field.

[0014] According to a preferred embodiment, in step S3, the transient prediction neural network is a multi-step operator learning network, whose input includes the initial mode coefficients and the time-varying sequence of boundary conditions, and whose output is the transient time-series temperature field, pressure field and heat transfer coefficient field.

[0015] According to a preferred embodiment, in step S3, the predicted mode coefficients are back-calculated to the two-dimensional field space during the neural network training phase and used to construct the physical loss term.

[0016] On the other hand, this application also discloses: An online monitoring system for a sodium-cooled fast reactor steam generator is provided, wherein the system employs the aforementioned method for online monitoring of the sodium-cooled fast reactor steam generator. The online monitoring system for the sodium-cooled fast reactor steam generator includes: A data acquisition module, which is used to receive DCS data in real time; A reduced-order mode library, which stores the POD mode basis, eigenvalues, and mean field; A physically constrained neural network prediction module, which is used to perform mode coefficient prediction; The POD reconstruction module reconstructs a two-dimensional field distribution based on POD for structural stress analysis and life assessment. A visualization output module is used to output monitoring results.

[0017] According to a preferred embodiment, the online monitoring system for the sodium-cooled fast reactor steam generator further includes: The adaptive update module is used to perform transfer learning or incremental learning on the neural network model based on historical monitoring data of the power plant.

[0018] The aforementioned main solution and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed in this application. Those skilled in the art, after understanding the solution of this application, will realize that there are many combinations based on the prior art and common general knowledge, all of which are technical solutions to be protected in this application, and will not be exhaustively listed here.

[0019] The beneficial effects of this application are: (1) The reduced-order model can effectively reduce the computational burden of high-dimensional numerical solutions, shortening the transient field prediction from the second or even minute level to the sub-second or second level, thus meeting the needs of online monitoring; (2) Physically constrained neural networks effectively improve the stability and reliability of the model under large disturbance conditions by explicitly adding physical conservation conditions during the training phase; (3) The modal basis maintains the dominant structural characteristics of the two-dimensional field of the steam generator in the spatial dimension, making the reconstructed field interpretable in engineering. (4) The system is compatible with a variety of operating conditions and accident scenarios and has a high model generalization ability; (5) It can be directly coupled with the life assessment module to realize real-time creep-fatigue analysis and equipment remaining life assessment. Attached Figure Description

[0020] Figure 1 This is the overall process flowchart of this application; Figure 2 This is a schematic cross-sectional view of the steam generator structure of this application; Figure 3 This is a schematic diagram of a steady-state BP neural network model; Figure 4 This is a schematic diagram of a transient multi-step operator neural network model; Figure 5 This is a schematic diagram showing the energy percentage of different orders of POD. Detailed Implementation

[0021] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0022] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0023] Furthermore, it should be noted that unless otherwise specified in this application, the specific structures, connections, positions, power sources, etc. involved are all things that a person skilled in the art can know without creative effort based on the prior art.

[0024] refer to Figures 1 to 4 As shown, this application discloses an online monitoring method for a sodium-cooled fast reactor steam generator. This application uses POD to reduce the order of the high-dimensional transient thermal-hydraulic field, mapping the PDE problem to the ODE problem of modal coefficients; then uses a physical constraint neural network to learn the evolution law of the modal coefficients over time, and finally reconstructs the transient field in real time through the POD modal basis.

[0025] During online monitoring, real-time operating parameters from the power plant's operation control system are received. Transient mode coefficients are obtained through a physical constraint neural network. Combined with a pre-established POD mode basis, the two-dimensional temperature field, pressure field, and heat transfer coefficient field of the steam generator are reconstructed to achieve timely assessment of the thermal-hydraulic characteristics.

[0026] This application fundamentally solves the problems of slow traditional transient calculation speed and unsuitability for real-time monitoring, loss of physicality and insufficient generalization ability of traditional order reduction and neural network methods, and difficulty in simplifying the strongly coupled two-phase flow field of steam generator. It is an innovative solution that deeply integrates physical model and data-driven model.

[0027] The online monitoring method for sodium-cooled fast reactor steam generators in this application specifically includes the following steps.

[0028] Step S1: Sample Library Construction To cover the main steady-state and transient operating conditions that the steam generator may experience throughout its entire operating range, a multi-dimensional sample library was first constructed based on a high-fidelity transient thermal-hydraulic analysis program.

[0029] (1) Steady-state sample library The input variables to be calculated include: Sodium side inlet temperature, flow rate, and outlet pressure; water side inlet temperature, flow rate, and outlet pressure.

[0030] Based on the above input parameters, a complete temperature field, pressure field, and enthalpy field are generated through a high-fidelity transient thermal-hydraulic analysis program.

[0031] To ensure the comprehensiveness and coverage of the samples, orthogonal experimental design and Latin hypercube sampling techniques were used to generate combinations of operating parameters. Each steady-state sample contains two-dimensional unfolded field data, with a typical dimension being a 13-layer heat transfer tube bundle × 120 height directional control volume.

[0032] (2) Transient sample library The transient operating conditions encompass all operating transients of the steam generator, including at least the typical transients such as heating / cooling start-up and shutdown processes, sodium-side or water-side flow disturbances, outlet pressure disturbances, feedwater changes with large rates of change, feedwater loss, LOCA and random fluctuations.

[0033] The input variables to be calculated include: The sodium-side inlet temperature, flow rate, and outlet pressure vary with time, as do the water-side inlet temperature, flow rate, and outlet pressure. The system's initial steady-state temperature field, pressure field, and enthalpy field are also considered.

[0034] For each transient condition, transient boundary conditions with different rates of change are constructed using boundary condition interpolation (Lagrange / spline). Based on the above input parameters, a high-fidelity transient thermo-hydraulic analysis program generates complete time-series temperature, pressure, and enthalpy fields for each set of transient inputs.

[0035] (3) Data formatting All two-dimensional fields are uniformly meshed and unfolded to form a matrix. .

[0036] A separate sample library was constructed for each physical quantity, including: sodium-side temperature, enthalpy, pressure, and heat transfer coefficient; water-side temperature, enthalpy, pressure, and heat transfer coefficient; and wall temperature.

[0037] Standardization, noise reduction, and temporal alignment are performed.

[0038] Step S2: POD Mode Reduction After obtaining sufficient samples, the dominant modal characteristics of key physical quantities of the steam generator were obtained by digitizing the data of each field quantity sample and performing singular value decomposition. To ensure that the dimensionality-reduced modal space can accurately characterize the main changing structure of the high-dimensional transient field, the modal cutoff order was determined by combining the cumulative energy proportion method, the error-complexity balance method, and cross-validation. The resulting modal basis can significantly reduce the data dimensionality while maintaining the core spatial characteristics of the temperature field, pressure field, enthalpy field, and heat transfer coefficient field.

[0039] (1) POD Mathematical Method Execute POD on the processed matrix:

[0040]

[0041] in, Represents the original data matrix. Represents a centralized data matrix. Represents the mean field matrix. Orthogonal basis in spatial directions Singular value diagonal matrix, corresponding to energy contribution. : The modal coefficient basis in the time direction.

[0042] (2) Modal truncation order Three criteria are used to determine the required modal cutoff order for each physical quantity data characteristic: Cumulative energy percentage ≥ 98%; finding the balance point using the error-complexity curve; K-fold cross-validation.

[0043] (3) POD results The final dimensionality reduction compresses the original two-dimensional mesh field with dimensions of 1500–3000 into k=8~20 spatial modes (depending on physical quantities and scene), with a dimensionality reduction ratio of over 100 times.

[0044] Step S3: Physically constrained neural network predicts modal coefficients This application constructs a neural network model that combines a low-dimensional space after modal order reduction with physical constraints. The network takes the transient boundary condition sequence of the steam generator and the initial modal coefficients as input, and the evolution results of the modal coefficients in future time intervals as output.

[0045] During training, the field quantities obtained by back-calculating the modal coefficients are used to calculate the residuals of heat transfer conservation on both sides, boundary temperature consistency, physical property parameter consistency, and heat transfer coefficient consistency. These residuals, along with the prediction error, are incorporated into the loss function to suppress physical biases, thereby ensuring the physical consistency of each physical quantity in the model during the prediction process. This mechanism enables the model to maintain data fitting accuracy while adhering to the fundamental physical laws of thermal-hydraulic processes.

[0046] (1) Network structure Two types of network collaboration: 1) The steady-state agent network adopts a multi-layer fully connected BP neural network. Input: Boundary conditions (temperature, flow rate, pressure); Output: Steady-state modal coefficients; Purpose: To provide initial values ​​for transient states and to construct initial fields.

[0047] 2) The transient agent network adopts a multi-step operator network. Input: Steady-state modal coefficients, boundary condition sequence within the time window; Output: A sequence of modal coefficients for multiple future time steps.

[0048] (2) Physical constraints Loss function:

[0049] Indicates the mean square error loss. This represents the heat transfer conservation penalty coefficient. This indicates the constraint of heat transfer conservation on both sides. This represents the boundary temperature uniformity penalty coefficient. This indicates a boundary temperature consistency constraint. This represents the penalty coefficient for consistency of physical property parameters. This indicates a constraint on the consistency of physical property parameters. This represents the penalty coefficient for consistency in heat transfer coefficients. This indicates a constraint on the consistency of the heat transfer coefficient.

[0050] ①Conservation constraint of heat transfer on both sides:

[0051] Q1 and Q2 represent the primary heat transfer and secondary heat transfer, respectively. This term is used to constrain the conservation of heat transfer on both sides.

[0052] ② Boundary temperature uniformity constraint:

[0053] T pre and T DCS These represent the inlet and outlet temperatures predicted by the neural network and the actual temperatures measured by the DCS, respectively. This item is used to match the DCS measurements to ensure that the predicted inlet and outlet temperatures match the measured data.

[0054] ③ Consistency constraints of physical property parameters

[0055] T pre and T p,h These represent the temperature predicted by the neural network and the temperature calculated using enthalpy and pressure, respectively. This term is used to ensure consistency between the temperature, enthalpy, and pressure of the working fluids on both sides.

[0056] ④ Consistency constraint of heat transfer coefficient

[0057] h pre and h cal These represent the heat transfer coefficients predicted by the neural network and the heat transfer coefficients calculated using empirical formulas, respectively. This term is used to ensure that the predicted convective heat transfer coefficient is consistent with the heat transfer coefficients calculated using temperature and pressure.

[0058] Step S4: Online monitoring and transient field reconstruction During online monitoring, the system receives operating parameters from the control system in real time and inputs them into a physical constraint neural network to obtain the modal coefficients at the current time. Subsequently, it reconstructs the corresponding temperature, pressure, enthalpy, and heat transfer coefficient fields using a pre-established POD modal basis, ultimately outputting the data in a two-dimensional or three-dimensional distribution format, which can be directly supplied to equipment condition monitoring, stress analysis, and life assessment modules. Because the modal coefficient prediction and field reconstruction process has low computational complexity, the entire online inference process can be completed within seconds.

[0059] The specific steps are as follows: (1) Real-time input signals to the power plant DCS include: Sodium side inlet temperature, flow rate, and outlet pressure; Water-side inlet temperature, flow rate, and outlet pressure; (2) Predicting modes using real-time DCS data .

[0060] (3) Reconstruction via POD basis:

[0061] (4) The output includes a complete time-series temperature field, pressure field, and enthalpy field, and the reconstruction speed can reach 0.1–1 seconds.

[0062] This application also discloses an online monitoring system for a sodium-cooled fast reactor steam generator, which employs the aforementioned method for online monitoring of the sodium-cooled fast reactor steam generator. This system can be deployed on a digital twin platform, an online monitoring server, or a control room analysis host.

[0063] Preferably, the online monitoring system for the sodium-cooled fast reactor steam generator includes the following modules.

[0064] A data acquisition module, which is used to receive DCS data in real time; A reduced-order mode library, which stores the POD mode basis, eigenvalues, and mean field; A physically constrained neural network prediction module, which is used to perform mode coefficient prediction; The POD reconstruction module reconstructs a two-dimensional field distribution based on POD for structural stress analysis and life assessment. A visualization output module, which is used to output monitoring results; The adaptive update module is used to perform transfer learning or incremental learning on the neural network model based on historical monitoring data of the power plant.

[0065] Example This embodiment further illustrates the online monitoring method for the sodium-cooled fast reactor steam generator of this application, the method comprising:

[0066] Step S1: Construction of Steady-State Sample Library This embodiment uses a transient thermal-hydraulic analysis program for sodium-cooled fast reactor steam generators to perform steady-state simulations within a range of multi-dimensional input parameters, including sodium-side inlet temperature, sodium-side flow rate, water-side flow rate, and steam pressure, generating over 150 sets of steady-state samples. The data is then processed through unified interpolation, denoising, gridding, and normalization to form a POD input matrix.

[0067] Determine the input boundary thresholds for the dataset based on the actual operating conditions of the power plant: Sodium side inlet flow rate: (170, 400) kg / s; Sodium side inlet temperature: (350, 550) ℃; Sodium side outlet pressure: (0.2, 0.5) MPa; Water side inlet flow rate: (1, 40) kg / s; Water side inlet temperature: (150, 250) ℃; Water side outlet pressure: (12, 14) MPa.

[0068] Therefore, the level of each factor is determined based on the threshold of the input boundary (either by equal division or by selecting representative points), as shown in Table 1: Table 1. Levels of each factor in orthogonal experimental design.

[0069] Step S2: POD mode basis generation Singular value decomposition (SVD) is used to reduce the order of the sample matrices for temperature, pressure, enthalpy, and heat transfer coefficients. Taking the temperature field as an example, ... Figure 5 As shown, the modal cutoff order is determined to be 10 through the energy percentage curve, which can retain approximately 98% of the dominant energy. Finally, the modal basis Φ is constructed and its corresponding modal coefficients a(t) are calculated for all time points.

[0070] Step S3: Training the Physically Constrained Neural Network This embodiment uses a multi-layer fully connected BP neural network as the prediction structure. It takes the initial mode, boundary condition sequence and physical property information as input, and obtains the mode coefficient sequence in the future time period through multi-node nonlinear mapping.

[0071] During the training phase, the predicted modal coefficients are back-calculated to the physical solution through the modal basis, and the heat transfer conservation residuals on both sides, the boundary temperature consistency residuals, the physical property parameter consistency residuals, and the heat transfer coefficient consistency residuals are calculated accordingly, so that the network must satisfy the corresponding physical constraints in addition to numerical fitting.

[0072] The neural network architecture is a 4-layer backpropagation (BP) neural network with 30 hidden layers. During training, the Adam optimizer, mean squared error loss function, and ExponentialLR learning rate function are used. After training convergence, the network prediction error is controlled within the range of 1–2%.

[0073] Step S4: Online Prediction and Field Reconstruction The online monitoring system receives real-time data on sodium-side temperature, pressure, flow rate, and water-side parameters, and inputs these data into a trained neural network. The network outputs the modal coefficients for the current moment. Subsequently, based on the POD modal basis, the corresponding two-dimensional temperature distribution, pressure distribution, and heat transfer coefficient distribution are reconstructed. The reconstructed results can be used in the steam generator wall temperature calculation and life assessment module to achieve real-time (second-level) online assessment of the equipment status.

[0074] When the power plant's DCS provides real-time data, the model calculates the current transient mode coefficients within 0.5–1 seconds. And through POD base The two-dimensional temperature field, pressure field, and other distributions were obtained, and the error was relatively high, with the results within the acceptable range for engineering.

[0075] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for online monitoring of a sodium-cooled fast reactor steam generator, characterized in that, The online monitoring method for the sodium-cooled fast reactor steam generator includes: S1: Sample library construction, constructing a thermal-hydraulic sample library covering steady-state and various transient operating conditions; S2: POD mode reduction, which performs POD mode reduction on the two-dimensional field quantities in the sample library to obtain the modal basis and modal coefficients; S3: Neural network construction, constructing a neural network model with physical constraints, and using the corresponding model to predict the evolution of modal coefficients over time; S4: Online monitoring and transient field reconstruction. The real-time operating parameters of the power plant are used as input, and the current mode coefficients are obtained through the neural network. The mode coefficients are inversely transformed by combining the preset mode basis to reconstruct the two-dimensional temperature field, pressure field and heat transfer coefficient field of the steam generator. The online monitoring and structural life assessment of the sodium-cooled fast reactor steam generator are completed and output.

2. The online monitoring method for a sodium-cooled fast reactor steam generator as described in claim 1, characterized in that, Step S1: For the steady-state operating condition envelope, steady-state boundary conditions are generated through orthogonal experimental design and Latin hypercube sampling. Based on the steady-state boundary conditions, a complete steady-state sample is generated for each set of steady-state inputs through a transient thermo-hydraulic analysis program. For each transient condition, Lagrange / spline boundary condition interpolation is used to construct transient boundary conditions with different rates of change. Based on the transient boundary conditions, a complete transient sample is generated for each set of transient inputs using a transient thermal-hydraulic analysis program.

3. The online monitoring method for a sodium-cooled fast reactor steam generator as described in claim 1, characterized in that, In step S2, after obtaining a preset number of samples, the dominant mode features of the key physical quantities of the steam generator are obtained by digitizing the data of each field quantity sample and performing singular value decomposition. In the POD modal order reduction process, the modal truncation order is determined by a combination of the cumulative energy ratio method, the error-complexity balance method, and cross-validation. Furthermore, the temperature field, pressure field, enthalpy field, and heat transfer coefficient field in the sample library are used to construct sample matrices and perform POD order reduction independently.

4. The online monitoring method for a sodium-cooled fast reactor steam generator as described in claim 3, characterized in that, In step S2, the mode reduction is achieved using singular value decomposition or eigenorthogonal decomposition.

5. The online monitoring method for a sodium-cooled fast reactor steam generator as described in claim 1, characterized in that, In step S3, the physical constraints of the neural network model include the residuals of heat transfer conservation on both sides, the residuals of boundary temperature consistency, the residuals of physical property parameters consistency, and the residuals of heat transfer coefficient consistency. Among them, the heat transfer conservation residual on both sides is obtained by calculating the difference between the heat transfer measured on the first side and the heat transfer on the second side. The boundary temperature consistency residual is obtained by calculating the difference between the inlet and outlet temperatures predicted by the neural network and the actual temperature measured by the DCS. The consistency residual of physical property parameters is obtained by calculating the temperature predicted by the neural network and the temperature difference calculated by enthalpy and pressure. The heat transfer coefficient consistency residual is obtained by calculating the difference between the heat transfer coefficient predicted by the neural network and the heat transfer coefficient calculated by the empirical formula.

6. The online monitoring method for a sodium-cooled fast reactor steam generator as described in claim 5, characterized in that, In step S3, the steady-state prediction neural network is a BP neural network. Its input is the steady-state boundary conditions, including temperature, flow rate, and pressure; and its output is the steady-state temperature field, pressure field, and heat transfer coefficient field.

7. The online monitoring method for a sodium-cooled fast reactor steam generator as described in claim 5, characterized in that, In step S3, the transient prediction neural network is a multi-step operator learning network. Its input includes the initial mode coefficients and the time-varying sequence of boundary conditions, and its output is the transient time-series temperature field, pressure field, and heat transfer coefficient field.

8. The online monitoring method for a sodium-cooled fast reactor steam generator as described in claim 5, characterized in that, In step S3, during the neural network training phase, the predicted mode coefficients are back-calculated to the two-dimensional field space and used to construct the physical loss term.

9. An online monitoring system for a sodium-cooled fast reactor steam generator, characterized in that, The online monitoring system for the sodium-cooled fast reactor steam generator employs the method described in any one of claims 1 to 8 for online monitoring of the sodium-cooled fast reactor steam generator. The online monitoring system for the sodium-cooled fast reactor steam generator includes: A data acquisition module, which is used to receive DCS data in real time; A reduced-order mode library, which stores the POD mode basis, eigenvalues, and mean field; A physically constrained neural network prediction module, which is used to perform mode coefficient prediction; The POD reconstruction module reconstructs a two-dimensional field distribution based on POD for structural stress analysis and life assessment. A visualization output module is used to output monitoring results.

10. The online monitoring system for a sodium-cooled fast reactor steam generator as described in claim 9, characterized in that, The online monitoring system for the sodium-cooled fast reactor steam generator also includes: The adaptive update module is used to perform transfer learning or incremental learning on the neural network model based on historical monitoring data of the power plant.

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