Data reconstruction method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention provides a data reconstruction method and device, electronic equipment and a storage medium, and belongs to the technical field of data processing. The method comprises the following steps: acquiring a measurement data set of a nuclear power system; determining a constraint equation set according to at least one of the law of conservation of mass and the law of conservation of energy; the constraint equation comprises at least one second parameter and at least one first parameter in the measurement data set, and the second parameter refers to an unmeasured parameter not included in the measurement data set; for each first parameter, calculating according to a parameter value of the first parameter to obtain a relative residual error of the first parameter; constructing a data reconstruction model of the nuclear power system according to the constraint equation set and the relative residual error of each first parameter; the data reconstruction model is solved, reconstruction data are obtained, and the reconstruction data comprise the reconstruction value of each first parameter and the estimation value of each second parameter. According to the embodiment of the invention, the accuracy of the measured data can be improved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a data reconstruction method, apparatus, electronic device and storage medium. Background Technology

[0002] In industrial systems (especially those relying on data-driven digital twin models), the accuracy of measurement data directly impacts the reliability of system state assessment, performance analysis, and optimized control. Measurement data fault-tolerant reconstruction, a proven technique, corrects and estimates measurement data to reduce random errors and suppress the impact of significant errors. This ensures the processed data meets system process constraints (such as mass and energy conservation constraints), thereby improving data consistency, reliability, and the accuracy and stability of data-driven models. Particularly in high-safety-requirement fields like nuclear power, the quality of measurement data directly affects the reliability of fault-tolerant control, state monitoring, and operational decision-making. However, due to sensor accuracy limitations, environmental interference, and equipment aging, actual measurement data often contains random and significant errors, increasing data uncertainty and making it difficult to meet the demands of high-precision control. Summary of the Invention

[0003] The main objective of this application is to provide a data reconstruction method, apparatus, electronic device, and storage medium, which aims to solve the problem of large errors in actual measurement data, thereby improving data accuracy.

[0004] To achieve the above objectives, a first aspect of this application proposes a data reconstruction method, the method comprising:

[0005] Acquire a measurement dataset of a nuclear power system, the measurement dataset including multiple data points, the data points including parameter values ​​of at least one first parameter collected during the operation of the nuclear power system;

[0006] A set of constraint equations is determined based on at least one of the laws of conservation of mass and conservation of energy; the set of constraint equations includes multiple constraint equations, each constraint equation including at least one second parameter and / or at least one first parameter from the measurement dataset, wherein the second parameter refers to an unmeasured parameter not included in the measurement dataset, and the parameter from the measurement dataset is included in at least one of the constraint equations;

[0007] For each of the first parameters, the relative residual of the first parameter is calculated based on the parameter value of the first parameter.

[0008] Based on the set of constraint equations and the relative residuals of each of the first parameters, a data reconstruction model of the nuclear power system is constructed.

[0009] Solving the data reconstruction model yields reconstructed data, which includes the reconstructed value of each of the first parameters and the estimated value of each of the second parameters.

[0010] In some embodiments, prior to acquiring the measurement data set of the nuclear power system, the method further includes:

[0011] Determine whether the nuclear power system is in a steady state.

[0012] When the nuclear power system is in a steady state, the operating data of the nuclear power system under steady state is acquired, and the operating data is used as the measurement dataset.

[0013] In some embodiments, determining whether the operating state of the nuclear power system is in a steady state includes:

[0014] Obtain the operating parameters of the nuclear power system within a preset time period;

[0015] Calculate the fluctuation range of the operating parameters within the preset time period;

[0016] If the fluctuation amplitude is less than the steady-state threshold, then the nuclear power system is determined to be in a steady state within a preset time period.

[0017] In some embodiments, determining the set of constraint equations based on at least one of the laws of conservation of mass and conservation of energy includes:

[0018] Based on the laws of conservation of mass and energy, multiple constraint equations are constructed according to the correlation between the second parameter of the nuclear power system and the first parameter in the measurement dataset.

[0019] If the number of the second parameter in the nuclear power system exceeds the number of constraint equations, all constraint equations containing unpredictable second parameters are removed from the multiple constraint equations to obtain the constraint equation set.

[0020] The removal of all constraint equations containing unpredictable second parameters from multiple constraint equations includes:

[0021] Construct the coefficient matrix of the unmeasured variables corresponding to the constraint equation system;

[0022] Calculate the null space basis vectors of the coefficient matrix of the unmeasured variables;

[0023] Based on the position of the zero element in the null space basis vector, the corresponding unpredictable second parameter is identified;

[0024] Remove the constraint equations that contain the unpredictable second parameter.

[0025] In some embodiments, the step of calculating the relative residual of the first parameter based on the parameter value of the first parameter includes:

[0026] The parameter value, correction value, and standard deviation of the first parameter are determined based on the measurement dataset.

[0027] The relative residual of the first parameter is calculated based on the difference between the correction value of the first parameter and the parameter value of the first parameter, as well as the standard deviation of the first parameter.

[0028] In some embodiments, constructing a data reconstruction model of the nuclear power system based on the constraint equations and the relative residuals of each of the first parameters includes:

[0029] An influence function is determined based on the relative residual. The influence function is used to evaluate the degree of influence of the relative residual of each first parameter on the final estimation result. The influence function is a piecewise function. When the relative residual is less than a first preset threshold, the degree of influence increases with the increase of the relative residual. When the relative residual is greater than the first preset threshold, the degree of influence tends to saturate or decrease with the increase of the relative residual.

[0030] Integrating the influence function yields the data reconstruction model of the nuclear power system.

[0031] In some embodiments, solving the data reconstruction model to obtain reconstructed data includes:

[0032] The data reconstruction model is iteratively solved using a sequential quadratic programming method until the change in the solution of the data reconstruction model is less than a second preset threshold.

[0033] The reconstructed value of the first parameter and the estimated value of the second parameter obtained from the last iteration are used as the reconstructed data.

[0034] In some embodiments, the step of iteratively solving the data reconstruction model using a sequential quadratic programming method until the change in the solution of the data reconstruction model is less than a second preset threshold includes:

[0035] Obtain the initial iteration values ​​of the data reconstruction model;

[0036] Based on the initial iteration value, the data reconstruction model is expanded to a second-order Taylor series, and the constraints are linearized to construct a quadratic programming subproblem.

[0037] Solve the quadratic programming subproblem to obtain the search direction and Lagrange multipliers;

[0038] If the search direction is a non-zero vector, the step size is determined by a one-dimensional search, and a new iteration value is calculated based on the search direction and the step size.

[0039] If the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, then the new iteration value is used as the initial iteration value, and the process jumps to the step of performing a second-order Taylor expansion of the data reconstruction model based on the initial iteration value, linearizing the constraints, and constructing a quadratic programming subproblem, until the change in the solution of the data reconstruction model is less than the second preset threshold.

[0040] In some embodiments, after solving the quadratic programming subproblem to obtain the search direction and Lagrange multipliers, the method further includes:

[0041] If the search direction is the zero vector, then calculate the change in the solution of the data reconstruction model between the current iteration value and the previous iteration value;

[0042] If the change in the solution of the data reconstruction model is less than the second preset threshold, the iteration is terminated and the current iteration value is used as the reconstructed data.

[0043] If the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, the construction parameters of the quadratic programming subproblem are adjusted, the quadratic programming subproblem is reconstructed, and the process jumps to the step of solving the quadratic programming subproblem to obtain the search direction and Lagrange multipliers, until the change in the solution of the data reconstruction model is less than the second preset threshold.

[0044] To achieve the above objectives, a second aspect of this application provides a data reconstruction apparatus, the apparatus comprising:

[0045] An acquisition module is used to acquire a measurement dataset of a nuclear power system, the measurement dataset including multiple data points, the data points including parameter values ​​of at least one first parameter collected during the operation of the nuclear power system;

[0046] A determination module is used to determine a set of constraint equations based on at least one of the laws of conservation of mass and conservation of energy; the set of constraint equations includes multiple constraint equations, each constraint equation including at least one second parameter and at least one first parameter from the measurement dataset, wherein the second parameter refers to an unmeasured parameter not included in the measurement dataset, and the parameter in the measurement dataset is included in at least one of the constraint equations;

[0047] The calculation module is used to calculate the relative residual of each of the first parameters based on the parameter value of the first parameter.

[0048] A construction module is used to construct a data reconstruction model of the nuclear power system based on the constraint equation set and the relative residual of each of the first parameters;

[0049] The solution module is used to solve the data reconstruction model to obtain reconstructed data, which includes the reconstructed value of each first parameter and the estimated value of each second parameter.

[0050] To achieve the above objectives, a third aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described in the first aspect.

[0051] To achieve the above objectives, a fourth aspect of the present application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in the first aspect.

[0052] The data reconstruction method, apparatus, electronic device, and storage medium proposed in this application first acquire the measurement dataset (containing measured values ​​of multiple first parameters) collected during the operation of the nuclear power system, and construct a set of constraint equations containing the first parameters and unmeasured second parameters based on the laws of mass conservation and / or energy conservation; then calculate the relative residual for each first parameter, and establish a data reconstruction model in combination with the set of constraint equations; finally, output the reconstructed values ​​of all first parameters and the estimated values ​​of the second parameters through model solving, thereby realizing the physical constraint-driven correction and unknown parameter inference of nuclear power system data. This application's embodiments construct constraint equations using the law of conservation of mass / energy, ensuring that the reconstructed data strictly conforms to the physical laws of nuclear power systems, eliminating physical contradictions caused by measurement errors (such as material imbalance and energy non-conservation), and significantly improving data reliability. Based on the relative residual optimization model of the first parameter, it dynamically suppresses interference from abnormal data, making the reconstruction results closer to real operating conditions. By simultaneously solving the second parameter not included in the measurement data through the constraint equation set, it overcomes sensor deployment limitations, fills in key monitoring blind spots, and provides complete data support for system status assessment. The reconstructed high-precision data can accurately reflect the operating status of the nuclear power system, supporting equipment health diagnosis and safety margin analysis. It provides a reliable basis for system efficiency assessment and parameter calibration, reducing misjudgments caused by data distortion, lowering maintenance costs, and extending equipment life. The method can be extended to industrial systems requiring physical constraints, such as chemical and power industries, solving common problems of data loss and noise interference. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the data reconstruction method provided in an embodiment of this application;

[0054] Figure 2This is a flowchart illustrating the principle of the data reconstruction method provided in the embodiments of this application;

[0055] Figure 3 This is a schematic diagram of steady-state data filtering provided in an embodiment of this application;

[0056] Figure 4 This is a schematic diagram of redundancy determination provided in the embodiments of this application;

[0057] Figure 5 This is a schematic diagram of the SQP method solution steps provided in the embodiments of this application;

[0058] Figure 6 This is a schematic diagram of the first set of simulation sequences provided in the embodiments of this application;

[0059] Figure 7 This is a schematic diagram of the second set of simulation sequences provided in the embodiments of this application;

[0060] Figure 8 This is a schematic diagram of the third set of simulation sequences provided in the embodiments of this application;

[0061] Figure 9 This is a schematic diagram of the fourth set of simulation sequences provided in the embodiments of this application;

[0062] Figure 10 This is a schematic diagram of the relative error when the first group of errors is 1σ, provided in the embodiments of this application;

[0063] Figure 11 This is a schematic diagram of the relative error when the second set of errors is 1σ, provided in the embodiments of this application;

[0064] Figure 12 This is a schematic diagram of the relative error when the third group of errors is 1σ, provided in the embodiments of this application;

[0065] Figure 13 This is a schematic diagram of the relative error when the fourth group of errors is 1σ, provided in the embodiments of this application;

[0066] Figure 14 This is a schematic diagram of the absolute uncertainty of a set of traffic flows provided in the embodiments of this application;

[0067] Figure 15 This is a schematic diagram illustrating the absolute uncertainty of a set of enthalpy values ​​provided in the embodiments of this application;

[0068] Figure 16 This is a schematic diagram of the probability density of a set of traffic flows provided in an embodiment of this application;

[0069] Figure 17 This is a schematic diagram of the data reconstruction apparatus provided in the embodiments of this application;

[0070] Figure 18 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0072] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0073] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0074] In industrial process control and monitoring, the accuracy and reliability of measurement data are crucial for the safe operation and performance optimization of the system. Especially in fields with high safety requirements, such as nuclear power, the quality of measurement data directly impacts the reliability of fault-tolerant control, condition monitoring, and operational decisions. However, due to factors such as sensor accuracy limitations, environmental interference, and equipment aging, actual measurement data often contains random and significant errors, leading to increased data uncertainty and making it difficult to meet the demands of high-precision control.

[0075] To address the aforementioned issues, data fault-tolerant reconstruction techniques have emerged. These techniques improve data consistency and reliability by correcting and estimating measurement data, reducing random errors, and suppressing the impact of significant errors. Traditional data fault-tolerant reconstruction methods are typically based on least squares estimation (LSE) or maximum likelihood estimation (MLE), assuming that measurement errors follow a normal distribution with a mean of zero. These methods are effective for linear systems or when the error distribution is known, but their applicability and accuracy are significantly limited when dealing with complex nonlinear systems (such as nuclear power thermal systems).

[0076] With the development of technology, robust estimation methods have been introduced into the field of data fault-tolerant reconstruction to enhance robustness to significant errors. Although existing robust data reconstruction techniques have advantages in handling data with significant errors, in practical applications (especially complex nonlinear thermal systems such as nuclear power units), the models are often complex to build and have low solution efficiency, making it difficult to meet the requirements of modularity, lightweight design, and real-time reconstruction.

[0077] Existing robust estimation functions suffer from unclear parameter definitions and struggle to meet reconstruction accuracy requirements in specific scenarios with high noise and complex error distributions. More critically, there is a lack of robust estimation functions that can be directly used as the objective function for reconstructing secondary loop data in nuclear power units, failing to adapt to the highly nonlinear and constrained characteristics of nuclear power systems. The selection of parameters for existing robust estimation functions lacks uniformity, leading to significant differences in reconstruction results due to varying parameter settings. In complex systems like nuclear power units, parameter adjustment is difficult, and improper parameter selection can easily affect the final reconstruction outcome. Some robust data reconstruction methods rely on genetic algorithms and complex optimization algorithms, resulting in high computational costs. When processing large-scale measurement data from nuclear power units, their computational efficiency is low, failing to meet the data processing speed requirements of real-time monitoring and control. Existing robust estimation methods are mostly designed for specific error types or specific systems (such as bilinear chemical systems and conventional thermal systems), lacking a data reconstruction scheme widely applicable to different error types and industrial systems, thus exhibiting insufficient adaptability when facing the differences between nuclear power units and other industrial systems. Most robust estimation methods assume that the error distribution conforms to specific statistical models such as normal or Cauchy distributions. However, in actual industrial scenarios (especially nuclear power systems), measurement errors are affected by multiple factors such as equipment operating conditions and environmental interference, resulting in complex distributions that are difficult to predict accurately. This limits the reconstruction effectiveness of existing methods. The nonlinear characteristics of nuclear power units are significantly stronger than those of chemical processes and conventional thermal processes. Existing reconstruction methods require listing all mass and energy constraints of the nuclear power system, leading to large-scale reconstruction models that are difficult to solve and cannot meet the practical needs of modular and lightweight intelligent reconstruction models for nuclear energy systems.

[0078] Based on this, embodiments of this application provide a data reconstruction method, apparatus, electronic device, and storage medium, aiming to address the problem that existing measurement data fault-tolerant reconstruction technologies cannot fully adapt to the actual needs of complex nonlinear systems such as nuclear power units. Embodiments of this application, based on a robust data fault-tolerant reconstruction model, present a novel design for fault-tolerant reconstruction methods in thermal processes. Combining the statistical characteristics of the measurement system with the mechanistic characteristics of the thermal system, a smart measurement data reconstruction method suitable for complex nonlinear environments such as nuclear power systems is proposed. This method effectively suppresses significant errors while improving reconstruction accuracy and computational efficiency, providing a high-quality data foundation for fault-tolerant control.

[0079] The data reconstruction method, apparatus, electronic device, and storage medium provided in this application are specifically described through the following embodiments. First, the data reconstruction method in this application is described.

[0080] The data reconstruction method provided in this application relates to the field of data processing technology. The data reconstruction method provided in this application can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, etc.; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms; the software can be an application implementing the data reconstruction method, but is not limited to the above forms.

[0081] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0082] It should be noted that in all specific embodiments of this application, when processing data related to user identity or characteristics, such as user information, user behavior data, user historical data, and user location information, user permission or consent is obtained first. Furthermore, the collection, use, and processing of this data comply with relevant laws, regulations, and standards. In addition, when embodiments of this application require access to sensitive personal information of users, separate permission or consent from the user is obtained through pop-ups or redirection to confirmation pages. Only after obtaining the user's separate permission or consent is the necessary user-related data required for the proper functioning of these embodiments acquired.

[0083] Figure 1This is an optional flowchart of the data reconstruction method provided in the embodiments of this application. Figure 1 The method may include, but is not limited to, steps S100 to S500.

[0084] Step S100: Obtain a measurement dataset of the nuclear power system. The measurement dataset includes multiple data points, and the data points include parameter values ​​of at least one first parameter collected during the operation of the nuclear power system.

[0085] In this embodiment, firstly, key measurement parameters during the operation of the nuclear power unit are collected to form a measurement dataset. The measurement dataset consists of multiple data points, each corresponding to a set of measurement parameter values ​​at a certain moment (or steady-state operation period). The first parameter refers to the key operating parameters that can be directly collected by sensors, such as: the inlet and outlet fluid flow rates of the heaters / heat exchangers in the secondary loop of the nuclear power unit, the enthalpy of steam / feedwater, and the inlet and outlet pressures of the equipment.

[0086] Step S200: Determine a set of constraint equations based on at least one of the laws of conservation of mass and conservation of energy; the set of constraint equations includes multiple constraint equations, each constraint equation including at least one second parameter and / or at least one first parameter from the measurement dataset, wherein the second parameter refers to an unmeasured parameter not included in the measurement dataset, and the parameter in the measurement dataset is included in at least one of the constraint equations.

[0087] In this embodiment, based on the physical operating mechanism of the nuclear power system, a set of constraint equations is constructed using at least one of the laws of conservation of mass and energy. The core of this approach is to transform the physical laws of the system into mathematical relationships between first and second parameters, ensuring that the reconstruction results conform to objective physical logic. The set of constraint equations consists of multiple constraint equations, each corresponding to the conservation relationship of a specific device (such as a heater or pipe) or subsystem (such as a series heater group). The second parameter refers to unmeasured parameters not included in the measurement dataset, such as: the shell-side outlet flow rate of a heat exchanger that cannot be directly measured, the unknown enthalpy of the medium inside a pipe, or the branch flow rate of a flow channel inside the device. The construction of the constraint equations must satisfy parameter correlation; that is, each constraint equation must contain at least one first parameter and / or one second parameter, and all first parameters must be included in at least one constraint equation.

[0088] Step S300: For each of the first parameters, calculate the relative residual of the first parameter based on the parameter value of the first parameter.

[0089] In this embodiment, for each first parameter in the measurement dataset, a relative residual is calculated based on its measured value and error characteristics. The core of this calculation is to quantify the degree of measurement error of the first parameter, providing a basis for error suppression in the subsequent reconstruction model. The relative residual reflects the degree to which the measured value of the first parameter deviates from a reliable reference value. The historical steady-state correction value, design value, or multi-sensor fusion reference value of the first parameter can be selected as the reference value. The relative residual is calculated by combining its measured value and the standard deviation of the sensor calibration (reflecting measurement accuracy). The smaller the relative residual, the more reliable the measured value of the first parameter, and more original information should be retained in the reconstruction. The larger the relative residual, the more likely the measured value contains significant errors, and its interference with the results needs to be reduced in the reconstruction.

[0090] Step S400: Construct a data reconstruction model of the nuclear power system based on the constraint equation set and the relative residual of each of the first parameters.

[0091] In this embodiment, a nuclear power system data reconstruction model is constructed to satisfy system physical constraints and aim to suppress measurement errors and optimize parameter accuracy. This model integrates physical constraints and error quantification into a unified optimization problem. The data reconstruction model uses a set of constraint equations as constraints to ensure that the reconstruction results satisfy mass / energy conservation and avoid physical logic contradictions. An objective function is constructed based on relative residuals, prioritizing robust estimation functions (such as robust estimation functions corresponding to piecewise influence functions). By dynamically adjusting the weights of different relative residuals (high weight for reliable data, low weight for error data), the overall error impact is minimized. Since the energy conservation equations of nuclear power systems are typically nonlinear (such as the product of enthalpy and flow rate), this data reconstruction model is an optimization model with nonlinear constraints, adapting to the complex characteristics of nuclear power systems.

[0092] Step S500: Solve the data reconstruction model to obtain reconstructed data, which includes the reconstructed value of each first parameter and the estimated value of each second parameter.

[0093] In this embodiment, an adaptive nonlinear constraint optimization problem solution method (such as the Sequential Quadratic Programming (SQP) method) is used to solve the data reconstruction model, ultimately outputting reconstructed data. Through iterative optimization, the values ​​of the first parameter (reconstructed value) and the second parameter (estimated value) are gradually adjusted until both the objective function minimization (minimum error) and all constraint conditions (physical conservation) are simultaneously satisfied. The reconstructed value of the first parameter is a correction of the original measured value, eliminating random and significant errors and satisfying physical constraints; the estimated value of the second parameter is calculated based on the constraint relationships and the reconstructed value of the first parameter, filling in the gaps of unmeasured parameters. Preferably, this embodiment uses the Sequential Quadratic Programming (SQP) method because of its strong convergence, high computational efficiency, and ability to effectively handle the nonlinear constraints of nuclear power systems, avoiding getting trapped in local optima. SQP is an iterative algorithm that approximates the optimal solution of the original problem by locally approximating the objective function and constraints at the current iteration point and repeatedly solving quadratic programming subproblems. The final output is a set of optimal solutions, including the reconstructed values ​​of all first parameters and the estimated values ​​of all second parameters. This reconstructed data can be stored in a database for unit status monitoring, performance analysis, and operation optimization.

[0094] like Figure 2 As shown in the flowchart, this embodiment provides a robust data reconstruction method applicable to the secondary loop of a nuclear power unit. First, the measurement dataset (including the measured value of the first parameter) under steady-state operation of the nuclear power system is obtained. Based on the laws of mass conservation and energy conservation, a set of constraint equations containing the first parameter and the unmeasured second parameter is constructed, and equations containing unpredictable parameters are optimized and removed. Then, the relative residuals of each first parameter are calculated, and the piecewise influence function is used to suppress outlier interference. A reconstruction model is established by integrating the influence function and the set of constraint equations. Finally, the model is iteratively solved using a sequential quadratic programming method, and the reconstructed value of the first parameter and the estimated value of the second parameter are output, realizing the physical constraint-driven and robust correction of nuclear power system data.

[0095] This embodiment ensures that the reconstructed data strictly conforms to the physical operating laws of the nuclear power system by using the law of conservation of mass / energy. It quantifies measurement errors through relative residuals and constructs the objective function using a robust estimation function, effectively suppressing significant errors without pre-removing outlier data, thus preserving data integrity while improving reconstruction accuracy. The model supports nonlinear constraints, and the solution method is adaptable to complex optimization problems, capable of handling the strong nonlinearity and multivariate coupling characteristics of the secondary loop of nuclear power units, and can be directly applied to actual nuclear power units. The reconstructed data provides a high-quality data foundation for nuclear power unit condition monitoring (such as equipment efficiency calculation), fault early warning (such as abnormal parameter deviation identification), and operation optimization (such as load adjustment strategies), indirectly improving the safety and economy of the unit.

[0096] In some embodiments, steps prior to step S100 may include, but are not limited to, the following steps:

[0097] Determine whether the nuclear power system is in a steady state.

[0098] When the nuclear power system is in a steady state, the operating data of the nuclear power system under steady state is acquired, and the operating data is used as the measurement dataset.

[0099] Specifically, determining whether the nuclear power system is in a steady state may include, but is not limited to, the following steps:

[0100] Obtain the operating parameters of the nuclear power system within a preset time period;

[0101] Calculate the fluctuation range of the operating parameters within the preset time period;

[0102] If the fluctuation amplitude is less than the steady-state threshold, then the nuclear power system is determined to be in a steady state within a preset time period.

[0103] In this embodiment, before obtaining the raw measurement data from the data source, it is first necessary to determine the operating state of the nuclear power system to identify whether it is in a steady-state operating condition. Since the operating state of a nuclear power system is dynamically changing—for example, during unit load increases, decreases, or equipment start-ups and shutdowns—process parameters undergo drastic transient changes. Data collected during such transient processes has its inherent physical laws obscured by strong dynamic effects, failing to meet the requirements of data reconstruction methods based on steady-state assumptions. Therefore, it is essential to ensure that the data used in subsequent reconstruction calculations originates from the system's steady-state operating period.

[0104] In this embodiment, steady-state operation identification is achieved by using a state identification algorithm to determine whether the unit is in a steady state and to filter out valid data during the steady-state process for subsequent reconfiguration. Specifically, this can be implemented through a time window function.

[0105] Specifically, operating parameters are collected in real time through the sensor network of the nuclear power system. The selection of operating parameters and the setting of the time window directly affect the accuracy of the judgment and must be designed in conjunction with the characteristics of the nuclear power system. Key operating parameters that reflect the system's energy balance and mass balance are selected, which may include, but are not limited to: thermodynamic parameters (main steam temperature and pressure, primary / secondary loop water temperature, heater inlet and outlet temperatures, etc.), flow parameters (primary loop coolant flow rate, secondary loop feedwater flow rate, steam flow rate, etc.), and power parameters (core power, turbine power, etc.). The selected key operating parameters must directly participate in subsequent data reconstruction (such as the first parameter in the constraint equation set). A preset time period (e.g., 30 minutes to 2 hours) is set, and this time window must cover at least one complete system response cycle to capture the dynamic characteristics of the parameters. The collected parameters are stored as a dataset in time series, with each parameter corresponding to a set of continuous sampled values, and the sampling frequency is not less than 1Hz to ensure data integrity.

[0106] For the time series data of each operating parameter, calculate its statistical fluctuation characteristics within a preset time period; the fluctuation amplitude can be quantified by calculating the difference between the maximum and minimum values ​​of the parameter within the time window, reflecting the instantaneous fluctuation range of the parameter; or it can be quantified by calculating the standard deviation of the parameter, characterizing the degree of dispersion of the parameter around the mean.

[0107] The steady-state threshold is a critical value for determining whether a parameter is stable. It needs to be dynamically set in conjunction with the physical meaning of the parameter and engineering standards. It can be set based on the parameter's engineering tolerance and with reference to industry standards. For the same parameter, the threshold can also be adjusted according to the unit's operating load segment. The fluctuation amplitude of each parameter is compared with its corresponding threshold. If the fluctuation amplitude of all parameters is less than its steady-state threshold, the nuclear power system is determined to be in a steady state within the preset time period. If the fluctuation amplitude of any parameter exceeds its steady-state threshold, the system is determined to be in a transient or disturbed state, requiring data to be re-collected or the time period adjusted.

[0108] For example, such as Figure 3 As shown, a steady-state screening of samples from a power plant between 12:00 noon on a certain day and 12:00 noon on the following day is performed using the time window method. In this embodiment, the actual generated power is selected as the judgment variable, the sampling frequency is recorded once every 60 seconds, the time window width is selected as 5 minutes, and the threshold is selected as 0.01 according to recommendations. The sample standard deviation of the actual generated power is calculated and compared with the threshold.

[0109] Figure 3 The blue curve at the top represents the actual generated power, the orange curve below represents its sample standard deviation, and the gray dashed line represents the threshold. Samples with a standard deviation less than the threshold are considered to be in steady-state operation and are marked with a red rectangle. Figure 3As can be seen, relatively stable data were identified as being in a steady state, while data with large fluctuations or those undergoing load changes failed the steady-state operation screening. These results demonstrate the effectiveness of the time-window-based steady-state operation identification method, which can be used for robust data correction preprocessing to ensure that measurement data are in a steady state.

[0110] This embodiment ensures that the physical constraint equations hold under quasi-static equilibrium conditions through steady-state screening, avoiding the failure of constraint equations due to dynamic processes. The steady-state data has small parameter fluctuations and few transient disturbances. Its random errors only come from the inherent accuracy of the sensor and have no additional transient interference errors, providing an accurate error quantification basis for subsequent relative residual calculation and reducing the deviation of the reconstruction results.

[0111] In some embodiments, step S200 may include, but is not limited to, the following steps:

[0112] Based on the laws of conservation of mass and energy, multiple constraint equations are constructed according to the correlation between the second parameter of the nuclear power system and the first parameter in the measurement dataset.

[0113] If the number of the second parameter in the nuclear power system exceeds the number of constraint equations, all constraint equations containing unpredictable second parameters are removed from the multiple constraint equations to obtain the constraint equation set.

[0114] In some embodiments, removing all constraint equations containing unpredictable second parameters from a plurality of constraint equations may include, but is not limited to, the following steps:

[0115] Construct the coefficient matrix of the unmeasured variables corresponding to the constraint equation system;

[0116] Calculate the null space basis vectors of the coefficient matrix of the unmeasured variables;

[0117] Based on the position of the zero element in the null space basis vector, the corresponding unpredictable second parameter is identified;

[0118] Remove the constraint equations that contain the unpredictable second parameter.

[0119] In this implementation, based on the process flow and equipment connection structure of the nuclear power system (such as feedwater heaters, steam generators, and turbines in the secondary loop system), and combining the laws of conservation of mass and energy, constraint equations are constructed around the quantitative correlation between the first and second parameters. The core logic of mass conservation is that, under steady-state conditions, the total inflow mass flow rate of the analytical unit equals the total outflow mass flow rate; the core logic of energy conservation is that, under steady-state conditions, the total inflow energy of the analytical unit equals the total outflow energy.

[0120] Based on the constructed initial constraint equations, the redundancy of the system is assessed. This is a crucial prerequisite for ensuring that all unmeasured variables are estimable and the model is solvable. The redundancy is determined by comparing the number of unmeasured second parameters in the system with the number of independent constraint equations. If the number of unmeasured parameters is less than or equal to the number of independent equations, the system has sufficient redundancy, and all unmeasured variables are theoretically estimable. In this case, the initial constraint equations can be directly used as the final constraint equations for reconstruction. If the number of unmeasured parameters exceeds the number of independent equations, the system lacks sufficient redundancy, and there must be unpredictable second parameters. In this case, the initial constraint equations must be analyzed to identify and remove all constraint equations containing unpredictable second parameters.

[0121] The linear correlation between variables and equations can be used to determine unpredictable second parameters. If a second parameter cannot be derived from the known first parameter using any linear combination of constraint equations, then that parameter is an unpredictable second parameter.

[0122] Specifically, the constraint equations are transformed into a linear equation system, where each equation corresponds to a row vector and each unmeasured variable corresponds to a column vector, thus constructing an unmeasured variable coefficient matrix. The number of rows in the coefficient matrix equals the number of constraint equations, the number of columns equals the number of unmeasured variables, and the matrix elements represent the coefficient values ​​of the corresponding variables in the equations.

[0123] Matrix decomposition is performed on the coefficient matrix of the unmeasured variables to solve for its null space. The null space consists of a set of linearly independent basis vectors that satisfy the condition that multiplying them by the coefficient matrix results in a zero vector. Numerical methods such as singular value decomposition or Gaussian elimination are used to obtain the set of basis vectors for the null space. All basis vectors in the null space are traversed, and the distribution of zero elements in each basis vector is examined. If a certain unmeasured variable has zero elements in all corresponding column positions of all basis vectors, then the variable is determined to be unmeasurable. All unmeasured variables satisfying the above condition are marked as unmeasurable second parameters. Finally, all constraint equations containing unmeasurable second parameters are removed.

[0124] For example, such as Figure 4 As shown, a simple heater system is used as the research object to determine its redundancy. The system consists of two shell-and-tube heaters connected in series, containing a total of seven fluids, whose mass flow rates are represented by m1 to m7. Among them, m1, m2, and m3 are measured variables, and the rest are unmeasured variables. According to the law of conservation of mass, a set of constraint equations is established for the system, including four mass conservation constraints on the heater tube side and shell side.

[0125] Based on the conservation of mass on the tube side of heater No. 1, constraint equation 1 can be obtained: m1-m2=0.

[0126] Based on the conservation of mass on the shell side of heater No. 1, constraint equation 2 can be obtained: m3-m4=0.

[0127] Based on the conservation of mass on the tube side of heater No. 2, constraint equation 3 can be obtained: m2-m7=0.

[0128] Based on the conservation of mass on the shell side of heater No. 2, constraint equation 4 can be obtained: m5-m6=0.

[0129] If the constraint equations of the system are expressed in the form AU+BU=0, then we have formula (1):

[0130]

[0131] U = [m4, m5, m6, m7] T

[0132]

[0133] First, the unmeasured variables are classified, and the redundancy of the system is determined. Matrix B is divided into two submatrices, as shown in formula (2):

[0134]

[0135] In this context, columns B1 correspond to the unmeasured variables m4, m5, and m7, respectively, while column B2 corresponds to the unmeasured variable m6. Calculate B2... T The zero-degree matrix P2 T P2 can be represented as shown in formula (3):

[0136]

[0137] Multiplying matrix B on the left is shown in formula (4):

[0138]

[0139] The all-zero columns in P2B are the second and third columns, corresponding to the unmeasured variables m5 and m6. This means that among the four unmeasured variables, m5 and m6 are unpredictable unmeasured variables, while m4 and m7 are predictable unmeasured variables. The presence of unpredictable unmeasured variables in the system indicates that the system does not meet the redundancy condition for data correction. Unpredictable unmeasured variables need to be removed.

[0140] This embodiment introduces a systematic redundancy discrimination and correction process, which can automatically identify and handle situations where the system redundancy is insufficient. By eliminating unpredictable variables, a problem that originally had no solution or infinitely many solutions is transformed into a well-posed optimization problem with a unique optimal solution. The reliable constraint equation set provides physical boundaries for the subsequent data reconstruction model, ensuring that the reconstruction results satisfy both error minimization and conservation laws, avoiding invalid reconstruction results with optimal data but physical contradictions, and providing a high-quality data foundation for nuclear power unit condition monitoring.

[0141] In some embodiments, step S300 may include, but is not limited to, the following steps:

[0142] The parameter value, correction value, and standard deviation of the first parameter are determined based on the measurement dataset.

[0143] The relative residual of the first parameter is calculated based on the difference between the correction value of the first parameter and the parameter value of the first parameter, as well as the standard deviation of the first parameter.

[0144] In this implementation, for each first parameter (i.e., the measured parameter) in the measurement dataset, the parameter value, correction value, and standard deviation of the first parameter are determined. The parameter value of the first parameter is the steady-state measurement value, which is the raw data collected by the sensor under steady-state operating conditions. The correction value of the first parameter is a benchmark value reflecting the true operating level of the parameter, which can be obtained through periodic sensor calibration or laboratory calibration. The standard deviation of the first parameter is an indicator reflecting the inherent measurement accuracy of the sensor, which can be obtained based on the sensor's accuracy level or historical data statistics.

[0145] In this implementation, the absolute error of the first parameter is obtained based on the difference between the correction value and the parameter value, reflecting the degree to which the parameter value deviates from the true reference. The relative residual of the first parameter is calculated based on the ratio of the absolute error to the standard deviation. Standard deviation normalization is then applied to eliminate the influence of different parameter magnitudes, allowing the residual to be directly used to compare the error levels of different types of first parameters. The smaller the absolute value of the relative residual, the smaller the error of the parameter value relative to the inherent accuracy of the sensor, and the more reliable the data.

[0146] Specifically, the formula for calculating the relative residual is shown in formula (5):

[0147]

[0148] in, X is the correction value. i For the measured value, σ i To measure the standard deviation.

[0149] This embodiment eliminates the differences in parameter magnitudes (such as the direct comparison of residuals between flow rate and enthalpy) through the normalization logic of absolute error / standard deviation, so that the residuals can objectively reflect the degree of error of different types of first parameters, providing an accurate basis for the differentiated weight allocation of the subsequent robust estimation function.

[0150] In some embodiments, step S400 may include, but is not limited to, the following steps:

[0151] An influence function is determined based on the relative residual. The influence function is used to evaluate the degree of influence of the relative residual of each first parameter on the final estimation result. The influence function is a piecewise function. When the relative residual is less than a first preset threshold, the degree of influence increases with the increase of the relative residual. When the relative residual is greater than the first preset threshold, the degree of influence tends to saturate or decrease with the increase of the relative residual.

[0152] Integrating the influence function yields the data reconstruction model of the nuclear power system.

[0153] In this embodiment, the influence function is a core concept in robust estimation theory. It quantitatively describes the degree of influence of the relative residuals of each first parameter on the final estimation result. The output value of the influence function represents the weight of the parameter's influence on the reconstruction result. The larger the value, the more significant the influence of the parameter's residuals on the reconstruction result; the smaller the value, the weaker the influence.

[0154] Choosing an appropriate robust estimation function as the objective function involves obtaining a suitable influence function by measuring the importance of different relative residuals to the estimation function, and obtaining a suitable weight function based on the weights of different data points. Analyzing the properties of the influence function and weight function allows for the construction of robust estimation functions that meet different requirements, which can then be used as the objective function. The relative residuals affect the establishment of the objective function by acting on the influence function. Under the premise of satisfying system constraints, the robust estimation function is used as the objective function for minimizing the residuals. According to the principle of robust estimation, when the relative residuals are small, the robust estimation function should be close to the weighted least squares estimation function, thus obtaining accurate reconstruction results when there are no significant errors in the measurement data. When the relative residuals are large, the robust estimation function should grow more slowly than a quadratic function, ensuring that its influence function is bounded, thereby effectively suppressing the influence of significant errors. Based on this idea, this embodiment constructs the influence function in a piecewise form. The first half is consistent with the influence function of the weighted least squares estimation, while the second half is constructed using an exponential function, allowing the influence function to gradually decrease and eventually converge. In this way, we can ensure both the reconstruction effect of the least squares estimation and the boundedness of the influence function. Finally, we integrate the influence function to obtain the proposed estimator constructed in this embodiment.

[0155] When the absolute value of the relative residual is less than a first preset threshold, the error of the data point is small. Therefore, the influence increases linearly with the increase of the relative residual. This means that within this interval, the behavior of the influence function is consistent with that of the least squares estimation (whose influence function is linear). This ensures that, in the absence of significant errors, it maintains the highest statistical efficiency, similar to the least squares method, and fully utilizes the information from all reliable data. When the absolute value of the relative residual is greater than the first preset threshold, the data point is likely to contain significant errors (outliers). To protect the overall estimation result from being skewed by a few outliers, the influence tends to saturate or even decrease with the increase of the relative residual, eventually converging to a fixed value. This means that the influence function is bounded. The destructive power of a data point with a large error will be strictly limited to an upper limit, thus achieving strong robustness against significant errors.

[0156] Specifically, the proposed estimation function is shown in Equation (6):

[0157]

[0158] In practical applications, the first preset threshold, i.e., parameter c, can be reasonably adjusted based on the error distribution of historical data. For example, when the accuracy of historical data is high, the value of parameter c can be appropriately reduced to better suppress significant errors (the accuracy of historical data needs to be determined based on the actual field conditions; reducing the value of parameter c can be 1.5).

[0159] The core of the data reconstruction model is to minimize the sum of the influence function values ​​of all first parameters under the premise of satisfying the constraint equations. That is, the influence function of a single parameter is aggregated into a global objective function by integration (summation). At the same time, the constraint equations are incorporated into the model as constraints to form a constrained optimization problem, resulting in the data reconstruction model, as shown in formula (7):

[0160]

[0161] This embodiment designs a piecewise influence function to automatically reduce the weight of outlier data, avoiding outlier interference caused by traditional linear weights. By using a constrained optimization model, the reconstruction results are forced to satisfy the mass / energy conservation law. At the same time, the objective function maximizes the use of reliable data, solving the problem of insufficient reconstruction accuracy of traditional models.

[0162] In some embodiments, step S500 may include, but is not limited to, the following steps:

[0163] The data reconstruction model is iteratively solved using a sequential quadratic programming method until the change in the solution of the data reconstruction model is less than a second preset threshold.

[0164] The reconstructed value of the first parameter and the estimated value of the second parameter obtained from the last iteration are used as the reconstructed data.

[0165] In this embodiment, the Sequential Quadratic Programming (SQP) algorithm is used to iteratively solve the data reconstruction model. This algorithm is an iterative process, and its core idea is to approximate a complex nonlinear programming problem into a simpler quadratic programming (QP) subproblem at the current iteration point, and to approximate the optimal solution of the original problem by repeatedly solving a series of quadratic programming subproblems.

[0166] Specifically, such as Figure 5 As shown, in sequential quadratic programming, a quadratic programming subproblem is first constructed based on the current iteration point: the Hessian matrix of the objective function is approximated using a second-order Taylor expansion, and the constraints are linearized, forming a locally convex optimization problem. By solving this quadratic programming subproblem, the search direction and corresponding Lagrange multipliers for this iteration are obtained. Subsequently, a one-dimensional search is used to determine the step size along this search direction. By continuously testing the step size and calculating the improvement of the objective function and constraints, a step size that satisfies the convergence condition is finally selected, thereby updating the iteration point and entering the next iteration, gradually approaching the optimal solution of the original problem. Using the SQP method, a robust data reconstruction model with nonlinear constraints can be solved, and a set of optimal solutions can be obtained. This optimal solution includes the reconstructed values ​​of the measured variables and the estimated values ​​of the unmeasured variables.

[0167] After applying the coupling algorithm for data fault-tolerant reconstruction, the variables at the connection point between the two heat exchangers still differ. These connection point variables refer to mass, flow rate, and enthalpy. Depending on the application scenario, these can be a single value or multiple values. This is because the inlet and outlet of the virtual heat exchanger belong to two independent heat exchanger models. The initial input collected by the sensors has a significant impact on the final data fault-tolerant reconstruction result. Therefore, the variable values ​​of the virtual heat exchanger need to be iteratively calculated until the system constraints reach equilibrium under the assumption of module data fault-tolerant reconstruction. The convergence condition for the iteration is that the change in the objective function value is less than a certain threshold (a second preset threshold). This threshold can be set independently, but is typically 1e-4.

[0168] This embodiment achieves efficient solution of the data reconstruction model through sequential quadratic programming. The iteration termination condition is set at the change of the solution being less than a second preset threshold, ensuring that high-precision and high-reliability reconstruction data is obtained while satisfying the physical constraints of the nuclear power system.

[0169] In some embodiments, the iterative solution of the data reconstruction model using a sequential quadratic programming method until the change in the solution of the data reconstruction model is less than a second preset threshold may include, but is not limited to, the following steps:

[0170] Obtain the initial iteration values ​​of the data reconstruction model;

[0171] Based on the initial iteration value, the data reconstruction model is expanded to a second-order Taylor series, and the constraints are linearized to construct a quadratic programming subproblem.

[0172] Solve the quadratic programming subproblem to obtain the search direction and Lagrange multipliers;

[0173] If the search direction is a non-zero vector, the step size is determined by a one-dimensional search, and a new iteration value is calculated based on the search direction and the step size.

[0174] If the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, then the new iteration value is used as the initial iteration value, and the process jumps to the step of performing a second-order Taylor expansion of the data reconstruction model based on the initial iteration value, linearizing the constraints, and constructing a quadratic programming subproblem, until the change in the solution of the data reconstruction model is less than the second preset threshold.

[0175] After solving the quadratic programming subproblem and obtaining the search direction and Lagrange multipliers, the method may further include, but is not limited to, the following steps:

[0176] If the search direction is the zero vector, then calculate the change in the solution of the data reconstruction model between the current iteration value and the previous iteration value;

[0177] If the change in the solution of the data reconstruction model is less than the second preset threshold, the iteration is terminated and the current iteration value is used as the reconstructed data.

[0178] If the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, the construction parameters of the quadratic programming subproblem are adjusted, the quadratic programming subproblem is reconstructed, and the process jumps to the step of solving the quadratic programming subproblem to obtain the search direction and Lagrange multipliers, until the change in the solution of the data reconstruction model is less than the second preset threshold.

[0179] In this embodiment, after the data reconstruction model is constructed, iterative solutions are obtained using the Sequential Quadratic Programming (SQP) method until the change in the solution converges. First, initial iteration values ​​are set based on historical operating data or design baseline values ​​of the nuclear power system. The initial values ​​of all variables to be optimized in the data reconstruction model (including the corrected values ​​of all first parameters and the estimated values ​​of the second parameters) can be combined into an initial vector, which serves as the initial iteration values.

[0180] At the current iteration point (the first iteration uses the initial iteration value as the current iteration point), a local approximation is performed on the data reconstruction model to construct a simpler quadratic programming subproblem. Specifically, the nonlinear objective function (i.e., the sum of robust estimation functions) is expanded in second order at the current point and approximated by a quadratic function. The nonlinear constraint equations are expanded in first order at the current point (i.e., linearized), transforming them into linear constraints. Through these two approximations, the original complex nonlinear optimization problem is transformed into a quadratic programming (QP) subproblem that is easy to solve near the current point.

[0181] The quadratic programming subproblem constructed in the above steps is solved using efficient QP solving algorithms (such as the effective set method and the interior point method), yielding the search direction and Lagrange multipliers. The search direction is a vector indicating the optimal direction of movement from the current iteration point that decreases the objective function value while satisfying the linearization constraints. The Lagrange multipliers provide the degree of influence of the constraints on the gradient of the objective function at the current point; these multipliers will be used to update the Hessian matrix in the next iteration.

[0182] After solving the quadratic programming subproblem, check if the search direction is a zero vector. If the search direction is a non-zero vector, it means the optimal point has not yet been reached, and we need to move forward in this direction. Subsequently, perform a one-dimensional search (line search) along the search direction to find an optimal step size. The step size should be chosen to sufficiently reduce a new evaluation function. After determining the step size, a new set of iteration values ​​is obtained based on the initial iteration values ​​and the step size.

[0183] Calculate the change in solution between the current iteration value and the previous iteration value. This change is typically measured by calculating the Euclidean norm or infinite norm of the difference between the two. Compare the calculated change with a pre-set second threshold. If the change in solution is greater than or equal to the second threshold, it indicates that convergence has not yet occurred and the optimal solution has not been found. In this case, the new iteration value is used as the new initial iteration value, and a new round of iteration begins. If the change in solution is less than the second threshold, it indicates that the iteration process has sufficiently converged, and further iterations will bring negligible improvement. In this case, the iteration loop terminates. When the algorithm meets the convergence condition, the new iteration value calculated in the last iteration is output as the final optimal solution. This optimal solution contains the reconstructed values ​​of all first parameters and the estimated values ​​of all second parameters, which together constitute the reconstructed data.

[0184] If the search direction is the zero vector, it indicates that the current iteration point may be a local optimum, and convergence needs further verification. When the search direction is the zero vector, record the data reconstruction model solution obtained in this iteration, and extract the solution from the previous iteration from the historical iteration record. Calculate the difference between the current iteration value and the previous iteration value, i.e., the change in the solution of the data reconstruction model. This change is usually quantified by calculating the Euclidean norm (2-norm) or infinite norm of the difference between the two.

[0185] If the change in the solution is less than the second preset threshold, it indicates that although the search direction for this iteration is zero, the position of the solution has stabilized since the last iteration and hardly changes anymore. Therefore, it can be determined that the algorithm has converged. At this point, the iteration loop terminates, and the current iteration value is output as the final reconstructed data.

[0186] If the change in the solution is greater than or equal to the second preset threshold, it indicates that the current point is optimal for the locally approximated QP subproblem. However, due to factors such as inaccurate Hessian matrix approximation or linearization errors, this point is not the true optimal point of the original nonlinear problem. In this case, the algorithm will not terminate forcibly, but will actively adopt an adjustment strategy.

[0187] The core of parameter tuning is to optimize the approximation accuracy of the subproblem to the original model, breaking the deadlock of the zero vector search direction. Specifically, adjusting the construction parameters of the quadratic programming subproblem can be achieved by resetting the Hessian matrix approximation to the identity matrix or restarting the approximation using other update strategies; or by adding a regularization term to the objective function of the QP subproblem to improve the numerical stability of the problem and ensure the generation of a non-zero search direction; or by slightly relaxing the tolerance of linearization constraints to expand the feasible search range. Then, using the adjusted parameters, a new quadratic programming subproblem is reconstructed based on the current iteration point, and this new subproblem is solved. Finally, the process jumps back to solving the quadratic programming subproblem, repeating the iteration until the convergence condition that the change in the solution is less than the second preset threshold is finally met.

[0188] This embodiment uses a closed-loop feedback mechanism of "constructing sub-problems - solving - searching - judging" to ensure that the algorithm can systematically and stably approximate the optimal solution of the problem. The SQP method, through local quadratic approximation, makes full use of the local curvature information of the objective function and constraints in each iteration, and has superlinear convergence speed and high computational efficiency. The one-dimensional search process ensures that each iteration moves in the direction of true optimization, avoids oscillation, and thus reduces the total number of iterations while ensuring accuracy.

[0189] In one embodiment of this invention, the scheme was validated using a nuclear power unit reheat system. This framework is based on a robust data fault-tolerant reconstruction framework, using the system characteristic equations as additional constraints. This embodiment modularizes the data fault-tolerant reconstruction process by proposing a general model for the heat exchanger and a virtual heat exchanger model for the heat exchanger connection points. Iterative calculations reduce the residual error of the coordinated system.

[0190] like Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 and Figure 13 As shown, the data fault-tolerant reconstruction method proposed in this embodiment can improve the quality of process data and reduce measurement data uncertainty. Compared with other methods, the advantage of this method is that, under the general heat exchanger assumption, the constraint equations of the reconstructed system can be standardized. By using different thermal characteristic equations, this method provides limited flexibility, which can help operators focus more on collecting measurement data and improve the efficiency of data fault-tolerant reconstruction without considering the relationship between coordinating variables.

[0191] Meanwhile, for the nuclear power plant's secondary loop system, the constraint equations become nonlinear when energy conservation is considered. For this type of nonlinearly constrained data reconstruction problem, nonlinear programming methods can be used for solution. Sequential Quadratic Programming (SQP) has good convergence and high computational efficiency, and can handle both equality and inequality constraints. Therefore, upper and lower bound constraints can be added to the measured variables to improve the reliability of the reconstruction results. Thus, SQP is chosen as the solution method for nonlinearly constrained problems. The SQP method can solve robust data reconstruction models with nonlinear constraints and obtain a set of optimal solutions. The optimal solutions include the reconstructed values ​​of the measured variables and the estimated values ​​of the unmeasured variables.

[0192] according to Figure 14 , Figure 15 and Figure 16 It can be seen that the mean of the estimated data is very close to the design value of the variable, with relative errors all within 1%. The standard deviation of the estimated data for the unmeasured flow variable is even lower, indicating higher overall accuracy. These results demonstrate that, in nuclear power systems, the robust data reconstruction method improves the accuracy of measured data and has good estimation performance for unmeasured variables.

[0193] This application's embodiments, through pre-steady-state judgment, use only the steady-state operating data of the nuclear power system as the measurement dataset, eliminating parameter fluctuation interference under transient conditions (such as sudden load changes, equipment start-up and shutdown); based on the mass / energy conservation law (the core physical law of nuclear power systems), constraint equations are constructed, and the first parameter (measurable) and the second parameter (unmeasurable) are forced to be correlated, avoiding physical contradictions caused by the disconnect between constraints and parameters in traditional schemes; for cases where the second parameter is excessive, equations containing unpredictable parameters are eliminated (claim 3), solving the problem of insufficient equations for solution, ensuring that the constraint equation set conforms to objective physical laws and has engineering solvability, adapting to the multivariable and strongly coupled characteristics of nuclear power; when calculating the relative residual, a correction value and standard deviation are introduced instead of the single measurement value in traditional schemes, which can more realistically reflect the error degree of the first parameter; when constructing the model subsequently, a piecewise influence function is used to realize that the influence degree of small residuals varies with the residuals. Reasonable incremental increments gradually saturate or reduce the impact of large residuals, preventing anomalous data from dominating the reconstruction results. By integrating the piecewise influence function, a robust model is formed that balances residual minimization and constraint satisfaction, adhering to physical laws while maximizing the use of reliable data. The Sequential Quadratic Programming (SQP) method, compared to the traditional gradient descent method, converges faster and satisfies constraints more effectively, meeting the nuclear power plant's requirements for reconstruction accuracy while adapting to the unit's real-time data processing needs. The reconstructed data simultaneously covers the reconstructed value of the first parameter and the estimated value of the second parameter, both of which strictly satisfy conservation constraints. This directly supports subsequent core applications in nuclear power, such as calculating heater heat exchange efficiency based on reconstructed flow and enthalpy values ​​(performance analysis) and judging pipeline medium status through estimated values ​​of unmeasured parameters (fault early warning). This provides data support for unit operation optimization and status monitoring, avoiding the limitation of traditional schemes where reconstructed data can only be used for a single scenario. This application's embodiments are based on a robust data fault-tolerant reconstruction model, and a novel design for fault-tolerant reconstruction methods in thermal processes is proposed. Combining the statistical characteristics of the measurement system with the mechanistic characteristics of the thermal system, a new framework for large-scale data fault-tolerant reconstruction calculations in complex nonlinear systems is proposed. The established data fault-tolerant reconstruction framework can provide a reference for data fault-tolerant reconstruction in other industrial systems.

[0194] Please see Figure 17 This application also provides a data reconstruction apparatus 600, which can implement the above-described data reconstruction method. The apparatus includes:

[0195] The acquisition module 10 is used to acquire a measurement dataset of a nuclear power system. The measurement dataset includes multiple data points, and the data points include the parameter values ​​of at least one first parameter collected during the operation of the nuclear power system.

[0196] The determination module 20 is used to determine a set of constraint equations based on at least one of the laws of conservation of mass and conservation of energy; the set of constraint equations includes multiple constraint equations, each constraint equation including at least one second parameter and at least one first parameter from the measurement dataset, wherein the second parameter refers to an unmeasured parameter not included in the measurement dataset, and the parameter in the measurement dataset is included in at least one of the constraint equations;

[0197] The calculation module 30 is used to calculate the relative residual of each of the first parameters based on the parameter value of the first parameter.

[0198] The construction module 40 is used to construct a data reconstruction model of the nuclear power system based on the constraint equation set and the relative residual of each of the first parameters;

[0199] The solver module 50 is used to solve the data reconstruction model to obtain reconstructed data, which includes the reconstructed value of each first parameter and the estimated value of each second parameter.

[0200] In some embodiments, the apparatus may further include:

[0201] The judgment module is used to determine whether the operating state of the nuclear power system is in a steady state.

[0202] The steady-state data acquisition module is used to acquire the operating data of the nuclear power system under steady-state conditions when the operating state of the nuclear power system is in a steady state, and to use the operating data as the measurement dataset.

[0203] In some implementations, the determination module may include:

[0204] The acquisition submodule is used to acquire the operating parameters of the nuclear power system within a preset time period;

[0205] The first calculation submodule is used to calculate the fluctuation range of the operating parameters within the preset time period;

[0206] The first determining submodule is used to determine that the nuclear power system is in a steady state within a preset time period if the fluctuation amplitude is less than the steady state threshold.

[0207] In some implementations, the determining module 20 may include:

[0208] A submodule is constructed to build multiple constraint equations based on the laws of conservation of mass and energy, according to the correlation between the second parameter of the nuclear power system and the first parameter in the measurement dataset.

[0209] The deletion submodule is used to remove all constraint equations containing unpredictable second parameters from multiple constraint equations when the number of the second parameters in the nuclear power system exceeds the number of constraint equations, thereby obtaining the constraint equation set.

[0210] In some implementations, deleting a submodule may include:

[0211] The first construction unit is used to construct the coefficient matrix of the unmeasured variables corresponding to the constraint equation set;

[0212] The first calculation unit is used to calculate the null space basis vectors of the coefficient matrix of the unmeasured variables;

[0213] The identification unit is used to identify the corresponding unpredictable second parameter based on the position of the zero element in the null space basis vector;

[0214] The deletion unit is used to remove constraint equations that contain the unpredictable second parameter.

[0215] In some implementations, the computing module 30 may include:

[0216] The second determining submodule is used to determine the parameter value, correction value, and standard deviation of the first parameter based on the measurement dataset;

[0217] The second calculation submodule is used to calculate the relative residual of the first parameter based on the difference between the correction value of the first parameter and the parameter value of the first parameter, as well as the standard deviation of the first parameter.

[0218] In some implementations, the building module 40 may include:

[0219] The third determining submodule is used to determine an influence function based on the relative residual. The influence function is used to evaluate the degree of influence of the relative residual of each first parameter on the final estimation result. The influence function is a piecewise function. When the relative residual is less than a first preset threshold, the degree of influence increases with the increase of the relative residual. When the relative residual is greater than the first preset threshold, the degree of influence tends to saturate or decrease with the increase of the relative residual.

[0220] The integral submodule is used to integrate the influence function to obtain the data reconstruction model of the nuclear power system.

[0221] In some implementations, the solver module 50 may include:

[0222] The iterative submodule is used to iteratively solve the data reconstruction model using a sequential quadratic programming method until the change in the solution of the data reconstruction model is less than a second preset threshold.

[0223] The fourth determining submodule is used to take the reconstructed value of the first parameter and the estimated value of the second parameter obtained from the last iteration as the reconstructed data.

[0224] In some implementations, the iterative submodule may include:

[0225] An acquisition unit is used to acquire the initial iteration value of the data reconstruction model;

[0226] The second construction unit is used to perform a second-order Taylor expansion on the data reconstruction model based on the initial iteration value, linearize the constraints, and construct a quadratic programming subproblem.

[0227] The solving unit is used to solve the quadratic programming subproblem to obtain the search direction and Lagrange multipliers;

[0228] The second calculation unit is used to determine the step size through a one-dimensional search if the search direction is a non-zero vector, and to calculate a new iteration value based on the search direction and the step size.

[0229] The first jump unit is used to, if the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, take the new iteration value as the initial iteration value and jump to the step of performing a second-order Taylor expansion of the data reconstruction model based on the initial iteration value, linearizing the constraints, and constructing a quadratic programming subproblem, until the change in the solution of the data reconstruction model is less than the second preset threshold.

[0230] In some implementations, the iterative submodule may further include:

[0231] The third calculation unit is used to calculate the change in the solution of the data reconstruction model between the current iteration value and the previous iteration value if the search direction is a zero vector.

[0232] The termination unit is used to terminate the iteration if the change in the solution of the data reconstruction model is less than the second preset threshold, and to use the current iteration value as the reconstructed data.

[0233] The second jump unit is used to adjust the construction parameters of the quadratic programming subproblem, reconstruct the quadratic programming subproblem, and jump to the step of solving the quadratic programming subproblem to obtain the search direction and Lagrange multipliers if the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, until the change in the solution of the data reconstruction model is less than the second preset threshold.

[0234] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described data reconstruction method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0235] Please see Figure 18 , Figure 18 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes:

[0236] The processor 701 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application.

[0237] The memory 702 can be implemented as a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 702 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 702 and is called and executed by the processor 701 using the data reconstruction method of the embodiments of this application.

[0238] The input / output interface 703 is used to implement information input and output;

[0239] The communication interface 704 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0240] Bus 705 transmits information between various components of the device (e.g., processor 701, memory 702, input / output interface 703, and communication interface 704);

[0241] The processor 701, memory 702, input / output interface 703, and communication interface 704 are connected to each other within the device via bus 705.

[0242] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described data reconstruction method.

[0243] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0244] The data reconstruction method, data reconstruction device, electronic device, and storage medium provided in this application first acquire the measurement dataset (containing measured values ​​of multiple first parameters) collected during the operation of the nuclear power system, and construct a set of constraint equations containing the first parameters and unmeasured second parameters based on the laws of mass conservation and / or energy conservation; then calculate the relative residual for each first parameter, and establish a data reconstruction model in combination with the set of constraint equations; finally, output the reconstructed values ​​of all first parameters and the estimated values ​​of the second parameters through model solving, thereby realizing the physical constraint-driven correction and unknown parameter inference of nuclear power system data. This application's embodiments construct constraint equations using the law of conservation of mass / energy, ensuring that the reconstructed data strictly conforms to the physical laws of nuclear power systems, eliminating physical contradictions caused by measurement errors (such as material imbalance and energy non-conservation), and significantly improving data reliability. Based on the relative residual optimization model of the first parameter, it dynamically suppresses interference from abnormal data, making the reconstruction results closer to real operating conditions. By simultaneously solving the second parameter not included in the measurement data through the constraint equation set, it overcomes sensor deployment limitations, fills in key monitoring blind spots, and provides complete data support for system status assessment. The reconstructed high-precision data can accurately reflect the operating status of the nuclear power system, supporting equipment health diagnosis and safety margin analysis. It provides a reliable basis for system efficiency assessment and parameter calibration, reducing misjudgments caused by data distortion, lowering maintenance costs, and extending equipment life. The method can be extended to industrial systems requiring physical constraints, such as chemical and power industries, solving common problems of data loss and noise interference.

[0245] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0246] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0247] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0248] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0249] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0250] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0251] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0252] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0253] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0254] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0255] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A data reconstruction method, characterized in that, The method includes: Acquire a measurement dataset of a nuclear power system, the measurement dataset including multiple data points, the data points including parameter values ​​of at least one first parameter collected during the operation of the nuclear power system; A set of constraint equations is determined based on at least one of the laws of conservation of mass and conservation of energy; the set of constraint equations includes multiple constraint equations, each constraint equation including at least one second parameter and / or at least one first parameter from the measurement dataset, wherein the second parameter refers to an unmeasured parameter not included in the measurement dataset, and the parameter from the measurement dataset is included in at least one of the constraint equations; For each of the first parameters, the relative residual of the first parameter is calculated based on the parameter value of the first parameter. Based on the set of constraint equations and the relative residuals of each of the first parameters, a data reconstruction model of the nuclear power system is constructed. Solving the data reconstruction model yields reconstructed data, which includes the reconstructed value of each of the first parameters and the estimated value of each of the second parameters.

2. The method according to claim 1, characterized in that, Prior to acquiring the measurement data set of the nuclear power system, the method further includes: Determine whether the nuclear power system is in a steady state. When the nuclear power system is in a steady state, the operating data of the nuclear power system under steady state is acquired, and the operating data is used as the measurement dataset.

3. The method according to claim 2, characterized in that, The determination of whether the operating state of the nuclear power system is in a steady state includes: Obtain the operating parameters of the nuclear power system within a preset time period; Calculate the fluctuation range of the operating parameters within the preset time period; If the fluctuation amplitude is less than the steady-state threshold, then the nuclear power system is determined to be in a steady state within a preset time period.

4. The method according to claim 1, characterized in that, The determination of the constraint equations based on at least one of the laws of conservation of mass and conservation of energy includes: Based on the laws of conservation of mass and energy, multiple constraint equations are constructed according to the correlation between the second parameter of the nuclear power system and the first parameter in the measurement dataset. If the number of the second parameter in the nuclear power system exceeds the number of constraint equations, all constraint equations containing unpredictable second parameters are removed from the multiple constraint equations to obtain the constraint equation set.

5. The method according to claim 4, characterized in that, The removal of all constraint equations containing unpredictable second parameters from multiple constraint equations includes: Construct the coefficient matrix of the unmeasured variables corresponding to the constraint equation system; Calculate the null space basis vectors of the coefficient matrix of the unmeasured variables; Based on the position of the zero element in the null space basis vector, the corresponding unpredictable second parameter is identified; Remove the constraint equations that contain the unpredictable second parameter.

6. The method according to claim 1, characterized in that, The step of calculating the relative residual of the first parameter based on its value includes: The parameter value, correction value, and standard deviation of the first parameter are determined based on the measurement dataset. The relative residual of the first parameter is calculated based on the difference between the correction value of the first parameter and the parameter value of the first parameter, as well as the standard deviation of the first parameter.

7. The method according to claim 1, characterized in that, The step of constructing a data reconstruction model of the nuclear power system based on the constraint equations and the relative residuals of each of the first parameters includes: An influence function is determined based on the relative residual. The influence function is used to evaluate the degree of influence of the relative residual of each first parameter on the final estimation result. The influence function is a piecewise function. When the relative residual is less than a first preset threshold, the degree of influence increases with the increase of the relative residual. When the relative residual is greater than the first preset threshold, the degree of influence tends to saturate or decrease with the increase of the relative residual. Integrating the influence function yields the data reconstruction model of the nuclear power system.

8. The method according to claim 1, characterized in that, Solving the data reconstruction model to obtain reconstructed data includes: The data reconstruction model is iteratively solved using a sequential quadratic programming method until the change in the solution of the data reconstruction model is less than a second preset threshold. The reconstructed value of the first parameter and the estimated value of the second parameter obtained from the last iteration are used as the reconstructed data.

9. The method according to claim 8, characterized in that, The step of iteratively solving the data reconstruction model using a sequential quadratic programming method until the change in the solution of the data reconstruction model is less than a second preset threshold includes: Obtain the initial iteration value of the data reconstruction model, wherein the initial iteration value includes the reconstructed value of the first parameter and the estimated value of the second parameter; Based on the initial iteration value, the data reconstruction model is expanded to a second-order Taylor series, and the constraints are linearized to construct a quadratic programming subproblem. Solve the quadratic programming subproblem to obtain the search direction and Lagrange multipliers; If the search direction is a non-zero vector, the step size is determined by a one-dimensional search, and a new iteration value is calculated based on the search direction and the step size. If the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, then the new iteration value is used as the initial iteration value, and the process jumps to the step of performing a second-order Taylor expansion of the data reconstruction model based on the initial iteration value, linearizing the constraints, and constructing a quadratic programming subproblem, until the change in the solution of the data reconstruction model is less than the second preset threshold.

10. The method according to claim 9, characterized in that, After solving the quadratic programming subproblem and obtaining the search direction and Lagrange multipliers, the method further includes: If the search direction is the zero vector, then calculate the change in the solution of the data reconstruction model between the current iteration value and the previous iteration value; If the change in the solution of the data reconstruction model is less than the second preset threshold, the iteration is terminated and the current iteration value is used as the reconstructed data. If the change in the solution of the data reconstruction model is greater than or equal to the second preset threshold, the construction parameters of the quadratic programming subproblem are adjusted, the quadratic programming subproblem is reconstructed, and the process jumps to the step of solving the quadratic programming subproblem to obtain the search direction and Lagrange multipliers, until the change in the solution of the data reconstruction model is less than the second preset threshold.

11. A data reconstruction apparatus, characterized in that, The device includes: An acquisition module is used to acquire a measurement dataset of a nuclear power system, the measurement dataset including multiple data points, the data points including parameter values ​​of at least one first parameter collected during the operation of the nuclear power system; A determination module is used to determine a set of constraint equations based on at least one of the laws of conservation of mass and conservation of energy; the set of constraint equations includes multiple constraint equations, each constraint equation including at least one second parameter and at least one first parameter from the measurement dataset, wherein the second parameter refers to an unmeasured parameter not included in the measurement dataset, and the parameter in the measurement dataset is included in at least one of the constraint equations; The calculation module is used to calculate the relative residual of each of the first parameters based on the parameter value of the first parameter. A construction module is used to construct a data reconstruction model of the nuclear power system based on the constraint equation set and the relative residual of each of the first parameters; The solution module is used to solve the data reconstruction model to obtain reconstructed data, which includes the reconstructed value of each first parameter and the estimated value of each second parameter.

12. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the data reconstruction method according to any one of claims 1 to 10.

13. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the data reconstruction method according to any one of claims 1 to 10.

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