Nuclear fuel reactivity optimization and safety verification method and system based on machine learning

Abstract

The invention belongs to the technical field of machine learning, and discloses a nuclear fuel reactivity optimization and safety verification method and system based on machine learning, and the method comprises the steps: carrying out the learning training of existing plate-shaped dispersion fuel and rod-shaped dispersion fuel data based on a linear regression model through a machine learning method, and carrying out the prediction through new data, a corresponding similarity ratio is obtained, and burnup verification, density verification, fission rate verification and neutron energy spectrum analysis are carried out on the similarity ratio through an OpenMC program. Data results show that the reactivity equivalent physical conversion method based on the linear regression model not only greatly improves the calculation efficiency, but also ensures very high accuracy, and meets the actual use requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning, and in particular relates to a method and system for nuclear fuel reactivity optimization and safety verification based on machine learning. Background Art

[0002] Dispersed fuel can withstand higher temperatures under some extreme accident conditions, maintain fuel integrity, and block the release of fission products into the environment, and has excellent inherent safety. Due to its above-mentioned excellent characteristics, it has gradually gained attention and application. Based on the inhomogeneity of the conventional grid level, the particle-type dispersion system adds the inhomogeneity of the dispersed particles and the matrix at the microscopic level, so it has double inhomogeneity. Traditional neutronics calculation software can only describe and deal with the inhomogeneity at the grid level, and cannot deal with the self-screening effect of particles in the double inhomogeneity system. In order to solve the problem of double inhomogeneity, reactor physicists have proposed many methods. Among the many methods, the RPT method has gradually become one of the research hotspots because of its simplicity and efficiency.

[0003] In 2005, Kim Y. of South Korea proposed the RPT method to deal with the problem of dispersed particle fuel. By maintaining the system reactivity equivalence at the beginning of the life cycle, the dispersed particle area is compressed to a smaller area and then the volume is homogenized, thereby converting the double inhomogeneous system into a single inhomogeneous system. This method does not require changing the program algorithm, and only changes the geometry to obtain more accurate results. The advantage of the RPT method is that it is simple and effective, so it has been widely studied in the future. Tsinghua University proposed an improved IRPT method. Lou Lei of the China Nuclear Power Research and Design Institute proposed a large number of improved methods for the RPT method. First, it was found that the traditional RPT method of the double particle system with poison added was difficult to describe the accuracy. The annular RPT method that can better simulate the stratification effect of combustible poisons was proposed. Compared with the traditional RPT method, it has a wider range of usage methods and accuracy. Further research found that the annular RPT method has good applicability in cylindrical and spherical elements. Subsequently, the IRPT, TRRPT, and HRPT methods were proposed to solve the problem of double inhomogeneity calculation of dispersed particle fuel and combustible poisons in plate, rod, and spherical geometries. At the same time, Li Peijun of Harbin Engineering University studied the method of processing plate-like double inhomogeneity systems. By comparing the annular RPT method, IRPT method and hybrid RPT method, he proposed a reactive physical equivalent conversion method based on particle diameter. This method has good calculation accuracy for the processing of plate-like inhomogeneity systems, and its operation is simple, the effect is better and the scope of application is wide. S. Golesorkhi of Canadian Nuclear Laboratories used the openmc program to compare the differences in accuracy and calculation time between the volume homogenization method (VHM) and the RPT method in modular high-temperature gas-cooled reactors, and proposed a method for fast fitting of the RPT radius. By calculating the characteristics of multi-group macroscopic cross-sections, neutron energy spectra and neutron flux distribution, it is quantitatively shown that the RPT method is superior to the VHM method in both accuracy and speed. In 2020, Zhang Yunfei analyzed the influencing parameters of the equivalent radius in the reactive equivalent method, and proposed the FRPT method based on FCM parameter fitting to directly obtain the equivalent radius and avoid the radius search process of the Monte Carlo program. The FRPT method can use traditional component programs to calculate the burnup of FCM fuel. In 2024, Li Jiannan conducted a parameter sensitivity analysis on the plate-shaped fuel element and derived a method to quickly obtain the RPT model of the plate-shaped fuel element. It was verified that the model has high fitting accuracy and practical engineering application value. Combining the results of these two scholars, it can be concluded that there is already a method to use the corresponding fitting method to quickly obtain the RPT model, but this fitting method requires a large amount of data fitting, which is more time-consuming than the new intelligent algorithm. Therefore, the present invention decides to apply machine learning, an intelligent algorithm, to the application of quickly obtaining the RPT model.

[0004] With the continuous evolution of technology, machine learning has now expanded to the field of reactor analysis and has become a key tool for building alternative models for complex large-scale numerical calculation programs. This alternative model can not only significantly improve computational efficiency, but also make large-scale sampling of large numerical programs feasible and can be completed within an acceptable time frame, thereby promoting the further development of research and application in the field of nuclear engineering. In 2021, Vicente-Valdez, Pedro. proposed the use of machine learning (ML) and artificial intelligence (AI) to support the complex tasks of evaluators. Two proof-of-concept ML models, a decision tree model and a K-nearest neighbor model, were developed to fit nuclear data in the EXFOR database with high accuracy. In 2022, Wang Heming and others from Harbin Institute of Technology carried out machine learning-based prediction of fuel rod nuclides and burnup. The study established different regression models between average burnup and nuclide content by using a variety of methods. The analysis results showed that the three machine learning methods used showed extremely high accuracy in predicting nuclide content and average burnup. In 2022, Suubi Racheal proposed a novel machine learning model training method using an enhanced data set reflecting the sensor status. This study developed, trained and compared three machine learning models: support vector machine (SVM), decision tree (DT) and multi-layer perceptron (MLP). Through this study, it was found that for some accident scenarios, SVM and DT models performed better than MLP model. In 2023, Liu Zhenhai and others from China Nuclear Power Research Institute conducted a study on the construction method of fuel rod temperature distribution proxy model based on machine learning. The study aims to improve the computational efficiency of large-scale fuel rod performance simulation. Taking fuel rod temperature prediction as a research example, the construction strategy of fuel rod temperature distribution prediction proxy model was discussed and analyzed in detail. The analysis results show that the constructed proxy model is about 204 times faster than the COPERNIC program in calculation speed and has high accuracy. In 2023, Guanghu described five DDML algorithms, including linear regression (LR), principal component analysis (PCA) and artificial neural network (ANN). DDML has good applicability in multi-scale and multi-physics simulation. Finally, physics-based DDML can improve the performance of all algorithms. In 2024, HaoWu developed a tree-based automated machine learning method for the nuclear pebble bed of a high-temperature gas-cooled reactor (HTGR) to explore the complex thermal radiation behavior. Numerical results show that the AutoML model is about 5 times × 10 times faster than the traditional method. The Pareto positive of the AutoML model indicates that the mean square error decreases as the model complexity decreases until the optimal solution is reached.At present, the application of machine learning and artificial intelligence in the field of nuclear engineering is still at a shallow level, and has no obvious advantages compared with traditional methods or experience: for example, to calculate the effective proliferation factor keff of a reactor, the deterministic full-reactor calculation under the two-step framework only takes ten minutes, and the result is accurate enough; although machine learning is used for prediction, it is very fast, but a large amount of simulation data is required for training in the early stage, and the trained system cannot be used for other different reactor types.

[0005] Based on the current research status at home and abroad, it can be found that there have been many studies and analyses on the RPT method and the measurement and calculation of various nuclear parameters using machine learning methods, but there are few effective calculations and analyses of RPT parameters using machine learning methods. The RPT method is an effective method to solve the problem of double non-uniformity, but the calculation process is complicated, requiring the call of a large number of Monte Carlo calculation programs, and most of them rely on daily experience to determine parameters, lacking a scientific theoretical basis. Machine learning algorithms have shown great potential in the calculation of nuclear parameters, but most of the current research is based on empirical parameters for subsequent research and analysis.

[0006] According to the above analysis, the existing technology has the following major technical problems in industrial application:

[0007] 1) High computational complexity and low efficiency:

[0008] Although the RPT (Reaction Rate Perturbation) method can effectively solve the dual inhomogeneity problem, its calculation process is complicated, especially in the field of nuclear engineering. This method usually requires calling a large number of Monte Carlo calculation programs. The Monte Carlo method itself is a numerical simulation method with high computational complexity and high time cost, resulting in low overall computational efficiency. This high computational complexity hinders the widespread promotion of the RPT method in actual industrial applications.

[0009] 2) Reliance on empirical parameters and lack of scientific theoretical basis:

[0010] In the process of calculating nuclear parameters, traditional methods mostly rely on expert experience to determine parameter settings. This experience-based approach lacks a scientific theoretical basis and easily leads to insufficient reliability and stability of the calculation results, especially when faced with new or unconventional reactor designs. This dependence limits the versatility and accuracy of existing technologies in different application scenarios.

[0011] 3) The generalization ability of machine learning models is insufficient:

[0012] The application of existing machine learning models in nuclear parameter calculation usually requires a large amount of simulation data for training. However, the trained models are often only applicable to specific reactor types or specific nuclear parameter calculation tasks. This defect of insufficient model generalization ability means that once it is switched to a different reactor type or a different calculation task, the model's predictive ability will be significantly reduced, thus limiting its application in actual engineering.

[0013] 4) Large amount of data required in the early stage and high cost:

[0014] The application of machine learning methods in the field of nuclear engineering usually requires a large amount of simulation data for training. The acquisition of this data often requires a lot of time and resources, especially with the support of Monte Carlo simulations and other complex numerical calculations. This high data demand not only increases the initial development costs, but also limits the feasibility of small and medium-sized enterprises to adopt machine learning technology in the field of nuclear engineering.

[0015] 5) Lack of ability to handle complex multi-physics problems:

[0016] The field of nuclear engineering often involves complex problems of multi-scale and multi-physics coupling. Existing machine learning methods are usually limited to the analysis of problems in a single physical field or a single scale and cannot effectively handle complex coupling problems. This limitation makes it difficult for existing technologies to meet the needs of global optimization and multi-objective optimization of complex systems in actual industrial applications.

[0017] In summary, the main technical problems of existing technologies in industrial applications include high computational complexity, over-reliance on empirical parameters, insufficient model generalization, large amount of initial data requirements, lack of obvious advantages over traditional methods, and lack of ability to handle complex multi-physics field problems. These problems restrict the widespread application and industrial promotion of machine learning technology in the field of nuclear engineering. Summary of the invention

[0018] In response to the problems existing in the prior art, the present invention provides a nuclear fuel reactivity optimization and safety verification method based on machine learning.

[0019] The present invention is implemented as follows: a method for optimizing nuclear fuel reactivity and safety verification based on machine learning comprises:

[0020] Step 1, using a machine learning method, based on a linear regression model, the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data are trained;

[0021] Step 2: Use the new data to make predictions and obtain the corresponding similarity ratio, and then use the OpenMC program to perform burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis.

[0022] Furthermore, the method for learning and training the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data based on the linear regression model is as follows:

[0023] 1) Data loading and preprocessing;

[0024] 2) Creation and training of linear regression models;

[0025] 3) Model prediction and evaluation;

[0026] 4) New data prediction.

[0027] Further, the data loading and preprocessing method:

[0028] Use the loadtxt function of the numpy library to load the training data from the training set file and use spaces as delimiters. After loading, the data needs to be preprocessed to extract features f, R, S and target variable SR through slicing operations.

[0029] Further, the creation and training of the linear regression model:

[0030] After data preprocessing, import the LinearRegression class in the sklearn.linear_model module, instantiate the LinearRegression object, and create a linear regression model; then call the model's fit method, pass the feature matrix X and target variable y as parameters into the model for training and fitting; observe the model parameters by printing the model's coefficients coef_ and intercept_.

[0031] Furthermore, the model prediction and evaluation method:

[0032] After the model is trained, use the model to predict new data; load the test data in the test set file, extract the features f, R, S and the target variable SR, and then call the model's predict method to get the predicted value.

[0033] Furthermore, the new data prediction method:

[0034] Use the trained model to make predictions on unseen data by creating a pandas DataFrame object containing the new feature values, using the model to make predictions, applying the model to the new dataset, and getting the predictions.

[0035] Another object of the present invention is to provide a nuclear fuel reactivity optimization and safety verification system based on machine learning, comprising:

[0036] A learning and training module is used to perform learning and training on the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data based on a linear regression model by machine learning method;

[0037] The prediction module is used to use new data for prediction and obtain the corresponding similarity ratio, and perform burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis on it through the OpenMC program.

[0038] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the nuclear fuel reactivity optimization and safety verification method based on machine learning.

[0039] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the nuclear fuel reactivity optimization and safety verification method based on machine learning.

[0040] Another object of the present invention is to provide an information data processing terminal, which is used to implement the nuclear fuel reactivity optimization and safety verification system based on machine learning.

[0041] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0042] First, the nuclear fuel reactivity optimization and safety verification method based on machine learning provided by the present invention has brought significant technological progress in industrial applications, which is specifically manifested in the following aspects:

[0043] 1) Improved computational efficiency and accuracy:

[0044] By introducing machine learning models, especially linear regression models, the present invention greatly improves the computational efficiency of the equivalent physical conversion of the reactivity of plate-shaped dispersed fuel and rod-shaped dispersed fuel. Traditional methods often rely on complex numerical simulations and a large amount of experimental data for prediction and verification, which takes a long time to calculate and has limited accuracy. The present invention uses machine learning models to achieve fast and accurate predictions through learning and training of a large amount of historical data, reducing the consumption of computing resources and time costs.

[0045] 2) Improvement of automation and intelligence level:

[0046] The present invention realizes the automation process of data processing and prediction through automated data loading, preprocessing and model training, reducing the complexity and error rate of manual operation. At the same time, the machine learning model can dynamically adjust according to new data and automatically optimize the prediction results, thereby improving the intelligence level of the entire system and making it more adaptable.

[0047] 3) Strong scalability and adaptability to different fuel types:

[0048] This method is not limited to the data processing of plate-shaped dispersed fuel and rod-shaped dispersed fuel, but also has strong scalability. By adjusting the training data and model parameters, the present invention can be adapted to other types of nuclear fuels and further extended to different reactor designs and fuel management schemes, which has a wide range of industrial application prospects.

[0049] 4) Enhanced safety of fuel design and management:

[0050] By using the OpenMC program to perform burnup verification, density verification, fission rate verification and neutron spectrum analysis, the present invention ensures that the prediction results of the equivalent physical conversion of reactivity are highly reliable and safe. These verification steps provide a scientific basis for the design and management of nuclear fuel, reduce the risks in the design and operation process, and improve the safety and reliability of nuclear engineering projects.

[0051] 5) Promoted technological innovation in the field of nuclear engineering:

[0052] Traditional methods of equivalent physical conversion of reactivity mostly rely on physical models and empirical formulas, while this invention has pioneered a new data-driven path by introducing machine learning technology. This technological innovation not only provides new tools and methods for calculation and design in the current nuclear engineering field, but also promotes the development of nuclear engineering technology towards a more intelligent and digital direction.

[0053] In summary, the present invention significantly improves computing efficiency and accuracy, enhances automation and intelligence, and enhances safety in industrial applications, and provides strong support for technological innovation in the field of nuclear engineering. These technological advances not only help promote the efficient and safe implementation of nuclear engineering projects, but also lay a solid foundation for the future development of nuclear technology.

[0054] Second, as auxiliary evidence of the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0055] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0056] The present invention opens up the application of machine learning algorithms in the prediction of RPT models in nuclear reactor physics calculations, which greatly improves the simplicity of handling double inhomogeneities. For the double inhomogeneities caused by various commercial reactors containing dispersed particles, this method is simpler and more efficient, and has practical engineering significance.

[0057] (2) The technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0058] The RPT method is simple and efficient for solving dual non-uniformity, but most of the current RPT model fitting mainly relies on experience and traditional fitting methods, and the process is relatively complicated and time-consuming. The present invention proposes to use machine learning to predict the RPT model, filling the technical gap of combining the currently widely used machine learning algorithm with the simple and efficient RPT method, greatly improving the calculation efficiency.

[0059] (3) Whether the technical solution of the present invention solves the technical problems that people have been eager to solve but have not been able to solve successfully:

[0060] The present invention combines machine learning with the RPT model for the first time, solving the complexity of obtaining the RPT model through traditional empirical methods and realizing the use of intelligent algorithms to deal with dual non-uniformity. The invention can greatly improve its computing efficiency and has practical engineering value.

[0061] Third, the technical solution of the present invention aims at the limitations of the reactivity equivalent physical conversion method in the prior art and proposes an improved method based on machine learning. The traditional reactivity equivalent physical conversion method mainly relies on empirical formulas and manual parameter adjustment, which usually requires a lot of computing resources and has low accuracy and efficiency when dealing with complex fuel geometries and material properties. In addition, the existing technology often lacks flexibility and robustness when predicting the similarity ratio of new fuels, making it difficult to cope with diverse fuel design requirements.

[0062] The present invention significantly improves the accuracy and efficiency of the equivalent physical conversion of reactivity by introducing machine learning technology, especially the linear regression model. First, through a data-driven approach, the existing plate-shaped and rod-shaped dispersed fuel data are trained to establish a mathematical model that can accurately predict the similarity ratio. Compared with traditional methods, this data-based model can better capture the potential relationship between fuel properties, thereby showing higher accuracy and reliability in predicting the similarity ratio of new fuels.

[0063] Secondly, the technical solution of the present invention shows significant technical progress in dealing with complex fuel geometry and material properties. By leveraging the predictive power of machine learning models, the present invention can quickly generate high-quality similarity ratio prediction results, and perform multi-dimensional verification through the OpenMC program, including burnup, density, fission rate and neutron spectrum analysis, to ensure the physical feasibility of the results. This method not only reduces the calculation time, but also reduces the demand for computing resources, improving the overall computing efficiency.

[0064] In addition, the model provided by the present invention has good generalization ability and can adapt to the design requirements of different types of fuels, providing strong support for the rapid evaluation and optimization of new fuels. By applying machine learning technology to reactive equivalent physical conversion, the present invention has achieved significant technical progress in flexibility, efficiency and accuracy, solved many technical problems existing in traditional methods, and promoted the further development of fuel design and nuclear reactor safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a flow chart of a method for nuclear fuel reactivity optimization and safety verification based on machine learning provided in an embodiment of the present invention.

[0066] Figure 2 It is a structural block diagram of a nuclear fuel reactivity optimization and safety verification system based on machine learning provided in an embodiment of the present invention.

[0067] Figure 3 It is a flow chart of the RPT method provided by an embodiment of the present invention.

[0068] Figure 4 It is a basic principle diagram of the plate element RPT method provided by an embodiment of the present invention.

[0069] Figure 5 It is a graph of predicted values ​​and actual values ​​of similarity ratios predicted by the plate RPT model provided in an embodiment of the present invention.

[0070] Figure 6 It is a graph of predicted values ​​and actual values ​​of similarity ratios predicted by the rod-shaped RPT model provided in an embodiment of the present invention.

[0071] Figure 7 This is a graph showing the change of kinf with fuel consumption when the deviation is minimum provided by an embodiment of the present invention.

[0072] Figure 8 This is a graph showing the change of kinf with fuel consumption when the deviation is maximum, provided by an embodiment of the present invention.

[0073] Fig. 9 This is a graph showing changes in 235U density with fuel consumption when the kinf deviation is minimum provided in an embodiment of the present invention.

[0074] Fig.10 This is a graph showing changes in 235U density with fuel consumption when the kinf deviation is maximum, provided in an embodiment of the present invention.

[0075] Fig.11 This is a graph showing the variation of 235U fission rate with fuel consumption when the kinf deviation is minimum provided in an embodiment of the present invention.

[0076] Fig.12 This is a graph showing the variation of 235U fission rate with fuel consumption when the kinf deviation is maximum, provided in an embodiment of the present invention.

[0077] Fig.13 This is a graph showing the variation of neutron flux with neutron energy when the kinf deviation is minimum provided in an embodiment of the present invention.

[0078] Fig.14 This is a graph showing the variation of neutron flux with neutron energy when the kinf deviation is maximum, provided in an embodiment of the present invention.

[0079] Fig.15 This is a graph showing the change of kinf with fuel consumption when the deviation is minimum provided by an embodiment of the present invention.

[0080] Fig.16 This is a graph showing the change of kinf with fuel consumption when the deviation is maximum, provided by an embodiment of the present invention.

[0081] Fig.17 The kinf deviation provided by the embodiment of the present invention is the minimum 235 U density as a function of burnup.

[0082] Fig.18 The maximum kinf deviation provided by the embodiment of the present invention is 235 U density as a function of burnup.

[0083] Fig.19 The kinf deviation provided by the embodiment of the present invention is the minimum 239 Pu density versus burnup.

[0084] Fig. 20 The maximum kinf deviation provided by the embodiment of the present invention is 239 Pu density versus burnup.

[0085] Fig.21 This is a graph showing the variation of neutron flux with energy when the kinf deviation is minimum provided in an embodiment of the present invention.

[0086] Fig. 22 This is a diagram showing the variation of neutron flux with energy when the kinf deviation is maximum, provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0087] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0088] like Figure 1 As shown, a method for optimizing nuclear fuel reactivity and safety verification based on machine learning provided by an embodiment of the present invention comprises the following steps:

[0089] S101, using a machine learning method, based on a linear regression model, the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data are trained;

[0090] S102, use the new data to make predictions and obtain the corresponding similarity ratio, and perform burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis on it through the OpenMC program.

[0091] The method for learning and training the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data based on the linear regression model provided in the embodiment of the present invention is as follows:

[0092] 1) Data loading and preprocessing;

[0093] 2) Creation and training of linear regression models;

[0094] 3) Model prediction and evaluation;

[0095] 4) New data prediction.

[0096] The working principle of the present invention is based on machine learning technology, aiming to achieve equivalent conversion of reactivity between plate-shaped and rod-shaped dispersed fuels. First, the integrity and consistency of the data are ensured by loading and preprocessing the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data. This step includes cleaning, normalizing and feature extraction of the data set to provide high-quality input data for subsequent model training.

[0097] Next, a linear regression model is created and trained. The linear regression model is chosen because it can capture the linear relationship between fuel properties in a simple and effective way. During the model training process, the preprocessed fuel data is used as the training set, and the model parameters are optimized by minimizing the loss function so that the model can accurately fit the relationship between fuel properties and similarity ratios.

[0098] The third step is to use the trained model to predict the new input data and obtain the corresponding similarity ratio. The core of this step is to use the linear prediction ability of the model to map the new fuel data into the similarity ratio space. Subsequently, the prediction results are verified by a series of verifications through the OpenMC program, including burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis, to ensure that the predicted similarity ratio is physically feasible and accurate.

[0099] Finally, after the verification is completed, the model can be used to quickly predict and analyze new fuel data. This method not only improves the efficiency of the equivalent physical conversion of reactivity, but also ensures the reliability of the conversion results, providing an efficient tool for fuel design and optimization.

[0100] The data loading and preprocessing method provided by the embodiment of the present invention:

[0101] Use the loadtxt function of the numpy library to load the training data from the training set file and use spaces as delimiters. After loading, the data needs to be preprocessed to extract features f, R, S and target variable SR through slicing operations.

[0102] Creation and training of the linear regression model provided by the embodiment of the present invention:

[0103] After data preprocessing, import the LinearRegression class in the sklearn.linear_model module, instantiate the LinearRegression object, and create a linear regression model; then call the model's fit method, pass the feature matrix X and target variable y as parameters into the model for training and fitting; observe the model parameters by printing the model's coefficients coef_ and intercept_.

[0104] The model prediction and evaluation method provided by the embodiment of the present invention:

[0105] After the model is trained, use the model to predict new data; load the test data in the test set file, extract the features f, R, S and the target variable SR, and then call the model's predict method to get the predicted value.

[0106] The new data prediction method provided by the embodiment of the present invention:

[0107] Use the trained model to make predictions on unseen data by creating a pandas DataFrame object containing the new feature values, using the model to make predictions, applying the model to the new dataset, and getting the predictions.

[0108] like Figure 2As shown, a nuclear fuel reactivity optimization and safety verification system based on machine learning provided by an embodiment of the present invention includes:

[0109] A learning and training module is used to perform learning and training on the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data based on a linear regression model by machine learning method;

[0110] The prediction module is used to use new data for prediction and obtain the corresponding similarity ratio, and perform burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis on it through the OpenMC program.

[0111] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the nuclear fuel reactivity optimization and safety verification method based on machine learning.

[0112] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the nuclear fuel reactivity optimization and safety verification method based on machine learning.

[0113] Another object of the present invention is to provide an information data processing terminal, which is used to implement the nuclear fuel reactivity optimization and safety verification system based on machine learning.

[0114] The present invention is specifically implemented:

[0115] 1. The present invention uses a machine learning method to train the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data based on a linear regression model, and then uses new data for prediction to obtain the corresponding similarity ratio, and performs burnup verification, density verification, fission rate verification, and neutron spectrum analysis on it through the OpenMC program. The data results show that the reactivity equivalent physical conversion method based on the linear regression model not only greatly improves the calculation efficiency, but also ensures a very high accuracy, meeting the actual use needs.

[0116] 2. Materials and Methods

[0117] This chapter introduces the Reactive Physical Equivalent Transformation (RPT) method and machine learning, and further studies the RPT method based on machine learning. Through the machine learning method, efficient computational analysis of dispersed particle fuels can be achieved.

[0118] 2.1 Traditional reactivity physical equivalent conversion method

[0119] RPT stands for Reactivity-equivalent Physical Transformation. The principle of this method is to reduce the influence of the self-screening effect caused by the geometric distribution of fuel and matrix by changing physical parameters, so as to finally obtain a more accurate effective proliferation factor. The RPT method was originally applied to rod-shaped fuel elements, such as Figure 1 First, the concept of an equivalent model was proposed, that is, an equivalent simplified model was used to restore and replace the particle model. This equivalent model is the RPT model, and the equivalent radius refers to the radius of the reduced fuel area. Once the equivalent radius is obtained, the RPT model can maintain a high degree of accuracy in traditional physical calculation programs

[26] . At the same time, the equivalent radius is limited by upper and lower thresholds. The upper limit is the radius of the initial fuel area, and the volume of the fuel and matrix is ​​homogenized inside. The lower limit is the minimum equivalent radius obtained by compressing all fuel particles to the center of the fuel area. The accurate RPT radius is generally between the upper and lower limits.

[0120] For fuel distribution in cylindrical and spherical geometries, the traditional reactivity equivalent physical transformation method can be conceptually illustrated as follows: Figure 3 Explained as depicted:

[0121] (1) All the dispersed fuel particles originally distributed in the entire fuel area are concentrated into a smaller specific area. The purpose of this step is to simplify the model for subsequent calculation processing.

[0122] (2) Perform volume homogenization on the reduced specific fuel region. Through this step, the original double inhomogeneity (i.e., the inhomogeneity of the fuel particles and the matrix and the inhomogeneity of the grid structure, cladding, and moderator) is simplified to a single inhomogeneity model. This simplification enables traditional pressurized water reactor calculation programs to handle this type of problem.

[0123] Through these two steps, the traditional RPT method can effectively transform the complex dual inhomogeneity model into a single inhomogeneity model that is easier to handle, thereby reducing the computational cost while ensuring the computational accuracy, and providing an efficient calculation method for the fuel distribution of cylindrical and spherical geometries.

[0124] 2.2 RPT method for plate elements

[0125] For plate geometry, referring to the implementation form of cylindrical RPT, the implementation form of the traditional RPT method for plate geometry is proposed, as shown in the schematic diagram Figure 4As shown. Similarly, the RPT method is similar to the principle of plate-like elements. The difference is that the fuel area of ​​the plate-like element is rectangular and is restricted in length and width. Here, a concept of equivalent side length is proposed for the fuel plate containing dispersed particles. The equivalent side length is the length and width of the reduced fuel area, and the reduction ratio of the length and width is the same. Like the rod-like element, the equivalent side length is also limited by the upper and lower thresholds. The upper limit should not exceed the side length of the original fuel area, that is, the length and width of the initial fuel area. The volume of the fuel and the matrix is ​​homogenized inside. The lower limit is the minimum length and width obtained by compressing all the fuel particles to the center of the fuel area. The accurate equivalent side length is generally between the upper and lower limits.

[0126] Here we make a simple calculation to illustrate the application of the RPT method on a fuel plate containing dispersed particles. Figure 4 As shown in the middle, assuming that the fuel area of ​​the plate element is a long, b wide, H high, and the dispersed particle filling rate is f:

[0127] 1. First, we need to determine the range of fuel particle compression in a certain area, where the length and width are compressed in equal proportions, and a and b are reduced by s times at the same time. Then the length and width of the new fuel area become as and bs. Here, s is referred to as the similarity ratio of the fuel plate model containing dispersed particles in the RPT method. From the above, we know that the upper limit of s is 1. According to the principle that the volume of dispersed particles remains consistent, we can get formula (1.1), which gives the lower limit of s as

[0128] 2. Then, the fuel and matrix in the reduced fuel area are homogenized according to the volume weight to obtain a new material mixed fuel, while the matrix between the original fuel area and the new fuel area remains unchanged, and finally the RPT model of the fuel plate containing dispersed particles under this similarity ratio is obtained.

[0129] f×a×b×H=a×b×H×S 2 (1.1)

[0130]

[0131] The range of similarity ratio is

[0132] The core of this method is to obtain the similarity ratio, that is, the ratio of the side length of the reduced diffuse fuel area to the original diffuse fuel area. The principle of obtaining the similarity ratio is that the effective proliferation factor of the equivalent model is equal to the effective proliferation factor under the direct explicit particle modeling condition. However, direct explicit particle modeling calculation generally requires the use of a Monte Carlo program, and multiple side length searches are required. Once the similarity ratio is obtained, the equivalent model can still maintain a high degree of accuracy in the fuel consumption calculation. According to relevant papers

[25] , the eigenvalue is a monotonic function of the equivalent radius, and the curve is approximately linear. Therefore, for the determination of the equivalent side length of the RPT model, the present invention first establishes a fuel particle regular arrangement model, and uses the calculation results of the Monte Carlo program grain model (Grain Model, GM for short) as the reference value, and then establishes RPT models with different equivalent side lengths to obtain the effective proliferation factors corresponding to fuel areas with different side lengths, and draws a scatter plot, fits the calculated results, and then interpolates according to the effective proliferation factor of the particle model. After multiple times, the equivalent side length of the fuel ball RPT model can be determined.

[0133] 2.3 Introduction to the Machine Learning RPT Method Based on Linear Regression Model

[0134] Machine learning based on linear regression model is a common supervised learning method used to predict a continuous value output. In linear regression, it is assumed that there is a linear relationship between the dependent variable (output) and the independent variable (feature). The model describes the relationship between the feature and the output by fitting the best straight line, so that the error between the output predicted by the model and the actual observed value is minimized. The basic form of the linear regression model can be expressed as:

[0135] y=w0+w1x1+w2x2+……+wnxn

[0136] Where y is the predicted value, w0, w1, w2, …, wn are the parameters (weights) of the model, and x1, x2, …, xn are the input features. The essence of the linear regression model is to estimate the mean value of the explained variable through the least squares method, that is, to minimize the sum of squared residuals between the observed value and the model predicted value to find the best fitting line. By extracting independent variables, creating and fitting a linear regression model, and predicting the model, the predicted value is obtained. In order to evaluate the performance of the model, various indicators can be used to verify, such as mean square error or determination coefficient, etc. These indicators can measure the degree of fit and predictive ability of the model to the observed data, and finally optimize the parameters to obtain the desired optimal prediction value.

[0137] In the RPT method, the equivalent radius of the compressed fuel is determined by ensuring that the kinf of the system is equal to the reference solution, and the reference solution is obtained through a high-fidelity deterministic program or Monte Carlo program. However, at present, the corresponding kinf is obtained through experience and repeated experiments that take a lot of time. Therefore, the present invention is based on a machine learning method, which can quickly obtain the similarity ratio of the corresponding dispersed fuel particles, that is, the radius ratio of the reduced dispersed fuel area to the original dispersed fuel area, so as to obtain the equivalent radius or equivalent variable length. The principle of obtaining the similarity ratio is that the effective proliferation factor of the equivalent model is equal to the effective proliferation factor under the direct explicit particle modeling conditions. Through the linear regression model, taking the plate-like element as an example, the three most important parameters affecting the RPT model of the plate-like element (which will be introduced in detail in the next chapter), namely the fuel particle size R, the particle phase volume f, and the fuel area S, are calculated and predicted to obtain the corresponding similarity ratio. The model establishment process is described below:

[0138] This model uses the LinearRegression model of the sklearn library to train and predict the linear regression model for a given data set.

[0139] 1) Data loading and preprocessing

[0140] First, load the training data from the training set file using the loadtxt function of the numpy library, using spaces as delimiters. After loading, we need to preprocess the data and extract features f, R, S and the target variable SR through slicing operations.

[0141] 2) Creation and training of linear regression model

[0142] After data preprocessing, import the LinearRegression class in the sklearn.linear_model module, instantiate the LinearRegression object, and create a linear regression model. Then call the model's fit method, pass the feature matrix X and the target variable y as parameters into the model for training and fitting. Observe the model parameters by printing the model's coefficients coef_ and intercept_.

[0143] 3) Model prediction and evaluation

[0144] After the model is trained, it can be used to predict new data. First, load the test data in the test set file, extract the features f, R, S and the target variable SR, and then call the model's predict method to get the predicted value. In order to evaluate the performance of the model, error calculation is added. In addition, the matplotlib library is used to draw a chart of the true target value and the predicted value to more intuitively compare the difference between the two.

[0145] 4) New data prediction

[0146] In addition to predicting the test data, we can also use the trained model to predict unseen data. By creating a pandas DataFrame object containing the new feature values ​​and using the model for prediction, we can quickly apply the model to the new data set and obtain the prediction results. In the next chapter, we will perform predictive analysis on the new rod and plate component parameters.

[0147] 3.Results

[0148] Based on machine learning, this chapter studies the RPT method for rod-shaped fuel elements and plate-shaped fuel elements. For plate-shaped fuel elements, three RPT parameters will be analyzed and calculated, namely, fuel particle size, particle phase volume, and fuel region area, as shown in Table 3.1. For rod-shaped fuel elements, six RPT parameters will be analyzed and calculated, namely, particle fuel core radius Rpf, particle outer radius Rpar, grid element fuel region radius Rcf, grid length L, moderator density ρmod, and phase volume f, as shown in Table 3.2. Numerical verification and analysis are also performed with traditional Monte Carlo calculations.

[0149] Table 3.1 Plate element parameters

[0150]

[0151] Table 3.2 Parameters of rod-shaped elements

[0152]

[0153] §3.1 Calculation of RPT of plate elements based on linear regression model

[0154] According to the analysis of parameter sensitivity in the previous section, among the three parameters of the selected plate element RPT, the value range of R is 0.015-0.04, the value range of S is 0.72-0.72×1.52, and the value range of f is 0.1-0.3. SR is the actual similarity ratio obtained by these three parameters. Finally, three parameters R, S, f and the corresponding similarity ratio SR were selected from the existing data, a total of 19 groups, see Table 3.2, for model training. The trained model was used to predict the 5 groups of new data in Table 3.3, all of which were taken from the above parameter range. The prediction results are as follows Figure 5 As shown in Table 3.4.

[0155] Table 3.2 Plate element RPT parameters (training)

[0156]

[0157]

[0158] pass Figure 5 It can be seen that the linear regression model has a good fitting effect, the training data curves are basically completely overlapped, the absolute error is accurate to the thousandth, and the predicted data curves are also basically close to overlap. This shows that the machine learning method has a high accuracy in processing the RPT of plate components and can meet actual needs.

[0159]

[0160] Table 3.3 Plate element RPT parameters (prediction)

[0161] Table 3.4 Error between predicted and actual values ​​of similarity ratio of RPT parameters of plate elements

[0162]

[0163] §3.2 Calculation of RPT of rod-shaped elements based on linear regression model

[0164] According to the previous section, six parameters Rpf, Rpar, Rcf, L, ρmod, f and the corresponding similarity ratio SR were selected, a total of 21 groups, as shown in Table 4.2, for model training. The trained model was used to predict the 5 groups of new data in Table 4.3. The prediction results are as follows Figure 6 As shown in Table 4.4. Among the six selected parameters, the value range of Rpf is 0.027-0.038, the value range of Rpar is 0.049-0.055, the value range of Rcf is 0.55-0.61, the value range of f is 0.34-0.53, the value range of L is 1.597-1.762, the value range of ρmod is 0.52-0.98, and SR is the actual similarity ratio obtained by these six parameters.

[0165] Table 4.2 Rod-shaped element RPT parameters (training)

[0166]

[0167] Table 4.3 Rod-shaped element RPT parameters (prediction)

[0168]

[0169]

[0170] Table 4.4 Error between the predicted and actual values ​​of the similarity ratio of the RPT parameters of the rod-shaped element

[0171]

[0172] The final results show that the absolute error is within the thousandth place and the relative error is within 1%. Figure 6 It can be seen that the linear regression model has a good fitting effect, the training data curves are almost completely overlapped, and the predicted data curves are also almost overlapped. This shows that the machine learning method has a high accuracy in processing the RPT of rod-shaped elements and can meet practical needs.

[0173] 3.3 Numerical verification and analysis

[0174] 3.3.1 Verification and analysis of plate-shaped fuel elements

[0175] In this section, the OpenMC program will be used to verify the similarity ratio of the RPT parameters of the plate element predicted above, including the effective multiplication factor calculated from the actual similarity ratio. Effective multiplication factor calculated from predicted similarity ratio The kinf deviation and pcm of the two. The verification results are shown in Table 3.5, where the kinf deviation is shown in formula (3.2).

[0176] Table 3.5 Deviations between actual kinf and predicted kinf and pcm of plate fuel

[0177]

[0178]

[0179] It can be concluded from Table 3.5 that the similarity ratio of the RPT parameters of the plate element predicted by the linear regression model is The actual value of the system is guaranteed The deviation is not large, and the deviation is kept within 200pcm, meeting the actual accuracy requirements.

[0180] 3.3.1.1 Fuel consumption verification

[0181] Select Case 3 with the smallest kinf deviation and Case 5 with the largest kinf deviation in Table 3.5 to verify the fuel consumption of the GM model and the RPT model respectively. Figure 7-8 Shows k infGM With k infRPT Variations with fuel consumption.

[0182] For the cases with the smallest and largest kinf deviations, the overall trends of the two are consistent, both decreasing with the increase of burnup depth. In the case of the smallest kinf deviation, the RPT model curve basically coincides with the GM model curve, and the maximum deviation does not exceed 200pcm, and the overall deviation is maintained within 100pcm. When the burnup depth is 1.037MWd / t, the maximum error is 168.62pcm, and when the burnup depth is 4.666MWd / t, the minimum deviation is 13.384pcm. In the case of the largest kinf deviation, the RPT model curve basically coincides with the GM model curve, and when the burnup depth is 4.66575MWd / t, the maximum deviation is 108.85pcm, and when the burnup depth is 2.592MWd / t, the minimum deviation is 13.357pcm. This shows that the RPT model can maintain a high degree of accuracy throughout the entire life of burnup.

[0183] 3.3.1.2235U Density Verification

[0184] Case 3 with the smallest kinf deviation and Case 5 with the largest kinf deviation in Table 3.5 are selected to perform 235U density verification on the GM model and RPT model respectively. Figure 9-10 The variation of 235U density with fuel consumption is shown.

[0185] For the cases with the smallest and largest kinf deviations, the overall trends of the two are consistent, both decreasing with the increase of burnup depth. It can be clearly seen in the two figures that the GM model curve completely overlaps with the RPT model curve, and the relative error shows an upward trend but the order of magnitude is very small. When the burnup depth reaches 5.869MWd / t, the maximum error is 0.00284%, which can be ignored. This shows that the 235U density of the RPT model has basically no effect on the fitting during the entire life of the burnup, and meets the actual accuracy requirements.

[0186] 3.3.1.3235U fission rate verification

[0187] Case 3 with the smallest kinf deviation and Case 5 with the largest kinf deviation in Table 3.5 are selected to verify the 235U fission rate of the GM model and the RPT model respectively. Figure 11-12 The variation of 235U fission rate with fuel consumption is shown.

[0188] For the cases with the smallest and largest kinf deviations, the overall trends of the two are consistent, both decreasing with the increase of burnup depth. In the case of the smallest kinf deviation, the maximum error is 0.021% when the burnup depth reaches 2.592MWd / t. In the case of the largest kinf deviation, the maximum error is 0.011% when the burnup depth reaches 6.221MWd / t. This shows that the 235U fission rate of the RPT model has basically no effect on the fitting during the full life of the burnup, and meets the actual accuracy requirements.

[0189] 3.3.1.4 Neutron spectrum analysis

[0190] The neutron spectrum represents the distribution of neutrons in the reactor according to energy. Case 3 with the smallest kinf deviation and Case 5 with the largest kinf deviation in Table 3.5 are selected to perform neutron spectrum analysis on the GM model and the RPT model respectively. Figure 13-14 The variation of neutron flux with neutron energy and the relative error are shown.

[0191] In the low energy region, the relative error between the GM model and the RPT model is relatively large. For the case with the smallest kinf deviation, when the energy is 1.23E-03eV, the relative error is 6.55%. For the case with the largest kinf deviation, when the energy is 1.23E-03eV, the relative error is 5.10%. In the middle and high energy regions, the energy spectrum trends of the GM model and the RPT model are basically consistent. Due to the partial loss of the self-screening effect, the deviations of the RPT models in the resonance region in both cases fluctuate significantly, but the deviations are within 2%.

[0192] In summary, the relative error in the low energy zone is relatively large, but it is kept within 7%. The resonance zones in the medium and high energy zones fluctuate significantly, but the relative errors are all within 2%, meeting the actual accuracy requirements.

[0193] 3.3.2 Verification and analysis of rod-shaped fuel elements

[0194] This section will use the calculation of the six parameters in the previous section to obtain the effective multiplication factor and the similarity ratio of the RPT parameters of the rod-shaped element predicted in the previous section for verification. It is divided into three parts. The first part is to use the original rod-shaped dispersed fuel particles to calculate and obtain the corresponding effective multiplication factor; the second part is to use the rod-shaped dispersed fuel particles after the RPT method to calculate and obtain the corresponding effective multiplication factor, 235U density, 239Pu density, burnup depth, and neutron energy spectrum; the third part is to use the similarity ratio predicted by machine learning to calculate and compare the effective multiplication factors of the second and third parts, and select the two cases with the largest and smallest errors for numerical verification and analysis. The verification results of the effective multiplication factor are shown in Table 4.5.

[0195] Table 4.5 Actual kinf and predicted kinf of rod fuel and their deviations

[0196]

[0197] It can be concluded from Table 4.5 that the similarity ratios of the RPT parameters of rod-shaped elements predicted by the linear regression model and those calculated by ALPHA are The actual value of the fuel rod The deviations are not large and are all kept within 100 pcm, which indicates that the linear regression model has a good fitting effect and meets the actual accuracy requirements.

[0198] 3.3.2.1 Fuel consumption verification

[0199] Select Case 3 with the smallest kinf deviation and Case 1 with the largest kinf deviation in Table 4.5 to verify the fuel consumption of the GM model and the RPT model respectively. Figure 15-16 Shown and Variations with fuel consumption.

[0200] For k inf The overall trends of the cases with the smallest and largest deviations are consistent, both decreasing with the increase of burnup depth. inf In the case of the smallest deviation, the RPT model curve basically coincides with the GM model curve, pcm shows a monotonically increasing trend, and the maximum deviation does not exceed 50pcm. When the burnup depth is 19.25MWd / t, the maximum error is 48.7pcm, and when the burnup depth is 1.75MWd / t, the minimum error is 45.7pcm. In the case of the largest Kinf deviation, the RPT model curve basically coincides with the GM model curve, pcm shows a monotonically increasing trend, and the maximum deviation does not exceed 100pcm. When the burnup depth is 19.25MWd / t, the maximum error is 98.7pcm, and when the burnup depth is 1MWd / t, the minimum error is 93.6pcm. This shows that the fitting effect of the RPT model is very stable. Although pcm increases with the increase of burnup depth, the increase is very small, and a high degree of accuracy can be maintained during the burnup life.

[0201] 3.3.2.2 235 U. 239 Pu Density Verification

[0202] Select k from Table 4.5 inf Case 3 with the smallest deviation and Case 5 with the largest deviation are used to analyze the GM model and RPT model respectively. 235 U and 239 Pu density verification, Figure 17-18 Shown 235 The variation of U density with burnup, Figure 19-20 Shown 239 Variation of Pu density with burnup.

[0203] pass 235 The graph of U density changing with burnup shows that for k inf In the cases of minimum and maximum deviation, the overall trends of the two are consistent, both decreasing with the increase of burnup depth. It can be clearly seen from the two figures that the GM model curve is basically parallel to the RPT model curve, almost overlapping, and the relative error gradually decreases. inf In the case of the smallest deviation, when the burnup depth reaches 0.25MWd / t, the maximum error is 0.0001965%; inf In the case of the largest deviation, when the burnup depth is at the initial value, the maximum error is 0.0002216%, which can be ignored. 235 The U density has little effect on the fitting during the burnup life, which meets the actual accuracy requirements.

[0204] pass 239 Pu density changes with burnup. inf In the cases with the smallest and largest deviations, the overall trends of the two are consistent, both increasing with the increase of burnup depth. It can be clearly seen from the two figures that the GM model curve and the RPT model curve basically overlap, and the relative error gradually increases. inf In the case of the smallest deviation, when the burnup depth reaches 19.25MWd / t, the maximum error is 0.00000643%; inf In the case of the largest deviation, when the burnup depth reaches 19.25MWd / t, the maximum error is 0.00000823%, which can be ignored. 239 The Pu density has little effect on the fitting during the burnup life, which meets the actual accuracy requirements.

[0205] 3.3.2.3 Neutron spectrum analysis

[0206] The neutron spectrum represents the distribution of neutrons in the reactor according to energy. Case 3 with the smallest kinf deviation and Case 1 with the largest kinf deviation in Table 4.5 are selected to perform neutron spectrum analysis on the GM model and the RPT model respectively. Figure 21-22 The variation of neutron flux with neutron energy and the relative error of flux are shown.

[0207] In the low and medium energy regions, the relative error between the GM model and the RPT model is small and almost zero. In the high energy region, for the case where the kinf deviation is the smallest, at the highest energy point, the relative error is 0.445%, and for the case where the kinf deviation is the largest, at the highest energy point, the relative error is 0.243%. The energy spectrum trends of the GM model and the RPT model are completely consistent.

[0208] In summary, the relative errors in the low-energy and medium-energy regions are small, basically zero, and the resonance region in the high-energy region fluctuates significantly, but the relative errors are all within 0.445%, which can be ignored and meet the actual accuracy requirements.

[0209] in conclusion

[0210] The present invention takes the nuclear fuel reactivity optimization and safety verification method based on machine learning as the research object, calculates and predicts the RPT parameters of plate-shaped dispersed particle fuel and rod-shaped dispersed particle fuel through a linear regression model, and finally obtains the similarity ratio of the corresponding parameters. The equivalent radius or equivalent side length of the RPT model is calculated using the similarity ratio, and then burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis are performed on it through OpenMC. The data results show that the reactivity equivalent physical conversion method based on the linear regression model not only greatly improves the calculation efficiency, but also ensures a very high accuracy, meeting the actual use needs.

[0211] 1. Specific application fields or related products of the present invention.

[0212] In nuclear reactor physics calculations, the present invention closely combines machine learning algorithms with RPT models, and then transforms double inhomogeneities into single inhomogeneities, which can then be calculated using traditional neutron physics programs.

[0213] 2. Relevant evidence of the technical effects obtained by the embodiments of the present invention.

[0214] It can be seen from the figure that in terms of the numerical verification of plate-shaped fuel elements, the steady-state verification deviation is kept within 200pcm, and the overall trend of the burnup verification is consistent, both decreasing with the increase of burnup depth, the maximum deviation does not exceed 200pcm, and the overall deviation is maintained within 100pcm. 235 In terms of U density verification, the overall trends of the two are consistent, both decreasing with the increase of burnup depth, with the maximum error being 0.00284%. 235 U fission rate verification, in k inf In the case of the smallest deviation, when the burnup depth reaches 2.592MWd / t, the maximum error is 0.021%. infIn the case of the largest deviation, when the burnup depth reaches 6.221MWd / t, the maximum error is 0.011%. Neutron spectrum analysis shows that the relative error in the low energy zone is large, but it is kept within 7%. The resonance zone in the medium and high energy zones fluctuates significantly, but the relative error is within 2%.

[0215] For rod-shaped fuel elements, the deviations were kept within 100 pcm in steady-state verification. The overall trends of the two in burnup verification were consistent, both decreasing with increasing burnup depth, with the maximum error not exceeding 100 pcm. 235 U. 239 Pu density verification shows that the overall trends of the two are consistent, both decreasing with the increase of burnup depth. In neutron spectrum analysis, the relative errors in the low-energy and medium-energy regions are small, basically zero, and the resonance region in the high-energy region fluctuates significantly, but the relative errors are all within 0.445%, which can be ignored.

[0216] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0217] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for nuclear fuel reactivity optimization and safety verification based on machine learning, characterized in that: The following steps are involved: Step 1, using a machine learning method, based on a linear regression model, the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data are trained; Step 2: Use the new data to make predictions and obtain the corresponding similarity ratio, and then use the OpenMC program to perform burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis.

2. The method for optimizing nuclear fuel reactivity and verifying safety based on machine learning as claimed in claim 1, characterized in that: The method for learning and training the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data based on the linear regression model is as follows: 1) Data loading and preprocessing; 2) Creation and training of linear regression models; 3) Model prediction and evaluation; 4) New data prediction.

3. The method for optimizing nuclear fuel reactivity and verifying safety based on machine learning as claimed in claim 2, characterized in that: The data loading and preprocessing method: Use the loadtxt function of the numpy library to load the training data from the training set file and use spaces as delimiters. After loading, the data needs to be preprocessed to extract features f, R, S and target variable SR through slicing operations.

4. The method for optimizing nuclear fuel reactivity and verifying safety based on machine learning as claimed in claim 2, characterized in that: Creation and training of the linear regression model: After data preprocessing, import the LinearRegression class in the sklearn.linear_model module, instantiate the LinearRegression object, and create a linear regression model; then call the model's fit method, pass the feature matrix X and target variable y as parameters into the model for training and fitting; observe the model parameters by printing the model's coefficients coef_ and intercept_.

5. The method for optimizing nuclear fuel reactivity and verifying safety based on machine learning as claimed in claim 2, characterized in that: The model prediction and evaluation method: After the model is trained, use the model to predict new data; load the test data in the test set file, extract the features f, R, S and the target variable SR, and then call the model's predict method to get the predicted value.

6. The method for optimizing nuclear fuel reactivity and verifying safety based on machine learning as claimed in claim 2, characterized in that: The new data prediction method: Use the trained model to make predictions on unseen data by creating a pandas DataFrame object containing the new feature values, using the model to make predictions, applying the model to the new dataset, and getting the predictions.

7. A nuclear fuel reactivity optimization and safety verification system based on machine learning that implements the method according to any one of claims 1 to 6, characterized in that: The nuclear fuel reactivity optimization and safety verification system based on machine learning includes: A learning and training module is used to perform learning and training on the existing plate-shaped dispersed fuel and rod-shaped dispersed fuel data based on a linear regression model by machine learning method; The prediction module is used to use new data for prediction and obtain the corresponding similarity ratio, and perform burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis on it through the OpenMC program.

8. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the nuclear fuel reactivity optimization and safety verification method based on machine learning as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the nuclear fuel reactivity optimization and safety verification method based on machine learning as described in any one of claims 1 to 6.

10. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the nuclear fuel reactivity optimization and safety verification system based on machine learning as described in claim 7.

Images