A Machine Learning-Based Method and System for Nuclear Fuel Reactivity Optimization and Safety Verification

Abstract

This invention belongs to the field of machine learning technology and discloses a method and system for optimizing and verifying the reactivity of nuclear fuel based on machine learning. Using machine learning, a linear regression model is trained on existing data of plate-shaped and rod-shaped dispersed fuels. New data is then used for prediction to derive the corresponding similarity ratio. Burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis are performed using the OpenMC program. Data results show that the reactivity equivalent physical conversion method based on the linear regression model not only significantly improves computational efficiency but also ensures very high accuracy, meeting practical application requirements.

Description

Technical Field

[0001] This invention belongs to the field of machine learning technology, and in particular relates to a method and system for optimizing and verifying the reactivity of nuclear fuel based on machine learning. Background Technology

[0002] Dispersed fuels can withstand higher temperatures under extreme accident conditions, maintain fuel integrity, and prevent the release of fission products into the environment, exhibiting excellent inherent safety. Due to these superior characteristics, they have gradually gained attention and application. Particulate dispersed systems, in addition to the inhomogeneity at the conventional grid level, also exhibit microscopic inhomogeneity between dispersed particles and the matrix, thus possessing dual inhomogeneity. Traditional neutronics computational software can only describe and handle grid-level inhomogeneity, and cannot handle the self-shielding effect of particles in dual inhomogeneous systems. To address the dual inhomogeneity problem, reactor physicists have proposed numerous methods, among which the RPT method has gradually become a research hotspot due to its simplicity and efficiency.

[0003] In 2005, Kim Y. of South Korea proposed the RPT method to handle the problem of dispersed particulate fuel. This method compresses the dispersed particulate region into a smaller area by maintaining system reactivity at the beginning of the system's lifespan and then homogenizing the volume, thus converting a doubly non-uniform system into a single-uniform system. This method does not require changes to the algorithm; only geometric modifications are needed to obtain relatively accurate results. The advantages of the RPT method are its simplicity and effectiveness, leading to its widespread research. Tsinghua University proposed an improved IRPT method, and Lou Lei of the China Nuclear Power Research and Design Institute proposed numerous improvements to the RPT method. First, it was found that the traditional RPT method was difficult to accurately describe the dual-particulate system with added toxic substances, leading to the proposal of the toroidal RPT method, which better simulates the stratification effect of combustible poisons and offers wider applicability and higher accuracy compared to the traditional RPT method. Further research revealed that the toroidal RPT method is well-suited for cylindrical and spherical elements. Subsequently, IRPT, TRRPT, and HRPT methods were proposed, solving the problem of calculating the dual non-uniformity of dispersed particulate fuel and combustible poisons in plate, rod, and spherical geometries. Meanwhile, Li Peijun of Harbin Engineering University, in his research on methods for handling plate-like dual inhomogeneities, proposed a reactive physical equivalent conversion method based on particle diameter by comparing the toroidal RPT method, IRPT method, and hybrid RPT method. This method demonstrates good computational accuracy for plate-like inhomogeneities, is simple to operate, has better performance, and a wide range of applications. S. Golesorkhi of Canadian Nuclear Laboratories used the OpenMC program to compare the accuracy and computation time differences between the volume homogenization method (VHM) and the RPT method in modular high-temperature gas-cooled reactors. He also proposed a method for rapidly fitting the RPT radius, quantitatively demonstrating that the RPT method outperforms the VHM method in both accuracy and speed by calculating multi-group macroscopic cross sections, neutron energy spectra, and neutron flux distribution. In 2020, Zhang Yunfei analyzed the influencing parameters of the equivalent radius in reactive equivalent methods and proposed the FRPT method based on FCM parameter fitting to directly obtain the equivalent radius, avoiding 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 sensitivity analysis of the parameters of plate fuel elements and derived a method for rapidly obtaining the RPT model of plate fuel elements. Verification showed that this model has high fitting accuracy and practical engineering application value. Combining the achievements of these two scholars, it can be concluded that methods for rapidly obtaining RPT models using corresponding fitting methods already exist; however, these methods require a large amount of data for fitting and are more time-consuming compared to new intelligent algorithms. Therefore, this invention decides to apply machine learning, an intelligent algorithm, to the application of rapidly obtaining RPT models.

[0004] With the continuous evolution of technology, machine learning has now expanded into the field of reactor analysis, becoming a key tool for constructing alternative models for complex, large-scale numerical computation programs. These alternative models not only significantly improve computational efficiency but also make large-scale sampling of large numerical programs feasible and achievable within an acceptable timeframe, thus promoting further development in nuclear engineering research and applications. In 2021, Vicente-Valdez and Pedro proposed using machine learning (ML) and artificial intelligence (AI) to support the complex tasks of evaluators. They developed two proof-of-concept ML models, a decision tree model and a K-nearest neighbor model, to fit nuclear data in the EXFOR database with high accuracy. In 2022, Wang Heming et al. from Harbin Institute of Technology conducted research on predicting nuclides and burnup in fuel rods based on machine learning. This research established different regression models between average burnup and nuclide content using various methods. The analysis results showed that the three machine learning methods employed demonstrated extremely high accuracy in predicting nuclide content and average burnup. Also in 2022, Suubi Racheal proposed a novel machine learning model training method using an augmented dataset reflecting sensor states. This study developed, trained, and compared three machine learning models: Support Vector Machine (SVM), Decision Tree (DT), and Multilayer Perceptron (MLP). The study found that for certain accident scenarios, SVM and DT models outperformed MLP models. In 2023, Liu Zhenhai et al. from the China Nuclear Power Research and Design Institute conducted research on a machine learning-based surrogate model construction method for fuel rod temperature distribution. This research aimed to improve the computational efficiency of large-scale fuel rod performance simulation. Using fuel rod temperature prediction as a case study, the construction strategy for the surrogate model for fuel rod temperature distribution prediction was discussed and analyzed in detail. The analysis results showed that the constructed surrogate model was approximately 204 times faster than the COPERNIC program, while also possessing high accuracy. Also in 2023, Guanghu described five DDML algorithms, including Linear Regression (LR), Principal Component Analysis (PCA), and Artificial Neural Networks (ANN). DDML has good applicability in multi-scale and multi-physics simulations. Finally, physics-based DDML can improve the performance of all algorithms. In 2024, HaoWu developed a tree-based automated machine learning method for nuclear sphere beds in high-temperature gas-cooled reactors (HTGRs) to explore complex thermal radiation behavior. Numerical results show that the AutoML model is approximately 5 × 10 times faster than traditional methods. The mean squared error of the Pareto positive representation of the AutoML model decreases as the model complexity decreases until the optimal solution is reached.Currently, the application of machine learning and artificial intelligence in the field of nuclear engineering is still superficial, and there is no obvious advantage compared with traditional methods or experience. For example, to calculate the effective multiplication factor keff of a reactor, the deterministic whole-reactor calculation under the two-step framework takes only about ten minutes, and the result is accurate enough. Although machine learning is fast for prediction, it requires a large amount of simulation data for training in the early stage, and the trained system cannot be used for other different reactor types.

[0005] A review of current research both domestically and internationally reveals numerous studies and analyses of the RPT method and the use of machine learning for measuring various kernel parameters. However, effective computation and analysis of RPT parameters using machine learning is scarce. While the RPT method is an effective approach for addressing the double non-uniformity problem, its computational process is complex, requiring numerous Monte Carlo calculations, and the vast majority of parameter determinations rely on empirical evidence, lacking a sound theoretical basis. Machine learning algorithms have demonstrated significant potential in kernel parameter calculation, but current research largely focuses on using empirical parameters for subsequent analysis.

[0006] Based on the above analysis, the existing technology faces the following main technical problems in industrial applications:

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

[0008] While the Reaction Rate Perturbation (RPT) method can effectively solve the problem of dual non-uniformity, its computational process is complex, especially in the field of nuclear engineering, where it typically requires calling numerous Monte Carlo calculation programs. The Monte Carlo method itself is a computationally intensive and time-consuming numerical simulation method, resulting in low overall computational efficiency. This high computational complexity hinders the widespread adoption of the RPT method in practical industrial applications.

[0009] 2) Relies on empirical parameters and lacks scientific theoretical basis:

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

[0011] 3) Insufficient generalization ability of machine learning models:

[0012] The application of existing machine learning models in nuclear parameter calculations typically requires extensive training with simulated data. However, well-trained models are often only applicable to specific reactor types or specific nuclear parameter calculation tasks. This lack of generalization ability means that the model's predictive power significantly decreases when applied to different reactor types or different computational tasks, thus limiting its application in practical engineering.

[0013] 4) High initial data requirements and costs:

[0014] The application of machine learning methods in nuclear engineering typically requires a large amount of simulation data for training. Acquiring this data often consumes significant time and resources, especially with the support of Monte Carlo simulations and other complex numerical calculations. This high data requirement not only increases upfront development costs but also limits the adoption of machine learning technologies in nuclear engineering by small and medium-sized enterprises.

[0015] 5) Lack of ability to handle complex multiphysics problems:

[0016] Nuclear engineering often involves complex problems involving multi-scale and multi-physics coupling. Existing machine learning methods are typically limited to analyzing problems at a single physics field or scale, and cannot effectively handle complex coupled problems. This limitation makes it difficult for current technologies to meet the needs of global optimization and multi-objective optimization of complex systems in practical industrial applications.

[0017] In summary, the main technical challenges of existing technologies in industrial applications include high computational complexity, over-reliance on empirical parameters, insufficient model generalization ability, large initial data requirements, lack of significant advantages over traditional methods, and a lack of ability to handle complex multiphysics problems. These issues hinder the widespread application and industrialization of machine learning technologies in the field of nuclear engineering. Summary of the Invention

[0018] To address the problems existing in the prior art, this invention provides a method for optimizing and verifying the reactivity of nuclear fuel based on machine learning.

[0019] This invention is implemented as follows: A machine learning-based method for optimizing and verifying the reactivity of nuclear fuel includes:

[0020] Step 1: Using machine learning methods, the existing plate-shaped and rod-shaped dispersed fuel data are trained based on a linear regression model.

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

[0022] Furthermore, the method for learning and training existing plate-shaped 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] Furthermore, the data loading and preprocessing method:

[0028] The training data is loaded from the training set file using the loadtxt function of the NumPy library, with spaces as the delimiter. After loading, the data needs to be preprocessed by extracting features f, R, S and the target variable SR through slicing operations.

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

[0030] After data preprocessing, import the LinearRegression class from the sklearn.linear_model module, instantiate a LinearRegression object, and create a linear regression model. Then, call the model's fit method, passing the feature matrix X and the target variable y as parameters to 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 is as follows:

[0032] After training the model, use the model to predict new data; load the test data from the test set file, extract the features f, R, S and the target variable SR, and then call the model's predict method to obtain the predicted values.

[0033] Furthermore, the new data prediction method:

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

[0035] Another objective of this invention is to provide a machine learning-based nuclear fuel reactivity optimization and safety verification system, comprising:

[0036] The learning and training module is used to learn and train on existing plate-shaped and rod-shaped dispersed fuel data using machine learning methods based on a linear regression model.

[0037] The prediction module is used to make predictions using new data, obtain the corresponding similarity ratio, and verify it through the OpenMC program, including burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis.

[0038] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the machine learning-based nuclear fuel reactivity optimization and safety verification method.

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

[0040] Another objective of this invention is to provide an information data processing terminal for implementing the machine learning-based nuclear fuel reactivity optimization and safety verification system.

[0041] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

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

[0043] 1) Improved computational efficiency and accuracy:

[0044] By introducing machine learning models, particularly linear regression models, this invention significantly improves the computational efficiency for the reactive equivalent physical conversion of plate-shaped and rod-shaped dispersed fuels. Traditional methods often rely on complex numerical simulations and large amounts of experimental data for prediction and verification, resulting in long computation times and limited accuracy. In contrast, this invention utilizes machine learning models, trained on a large amount of historical data, to achieve fast and accurate predictions, reducing the consumption of computational resources and time costs.

[0045] 2) Improvement in automation and intelligence levels:

[0046] This invention automates the data processing and prediction process by automating data loading, preprocessing, and model training, reducing the complexity and error rate of manual operations. Simultaneously, the machine learning model can dynamically adjust based on new data, automatically optimizing prediction results, thereby enhancing the overall system's intelligence and adaptability.

[0047] 3) Highly scalable and adaptable to different fuel types:

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

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

[0050] By using the OpenMC program to perform burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis, this invention ensures that the predicted results of reactive equivalent physical transformations are highly reliable and safe. These verification steps provide a scientific basis for the design and management of nuclear fuel, reduce 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 reactive equivalent physical conversion methods mostly rely on physical models and empirical formulas, while this invention, by introducing machine learning technology, pioneers a completely new data-driven approach. This technological innovation not only provides new tools and methods for computation 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, this invention significantly improves computational efficiency and accuracy, enhances automation and intelligence, strengthens safety, and provides strong support for technological innovation in the field of nuclear engineering in industrial applications. These technological advancements 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] Secondly, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

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

[0056] This invention pioneers the application of machine learning algorithms in RPT model predictions within nuclear reactor physics calculations, significantly improving the ease of handling dual non-uniformities. For the dual non-uniformities caused by various commercial reactors containing dispersed particles, this method is even simpler and more efficient, possessing practical engineering significance.

[0057] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0058] The RPT method is simple and efficient for solving double non-uniformity, but most current RPT model fitting relies on experience and traditional fitting methods, which are complex and time-consuming. This invention proposes using machine learning to predict RPT models, filling the technological gap of combining widely used machine learning algorithms with the simple and efficient RPT method, and greatly improving computational efficiency.

[0059] (3) Whether the technical solution of the present invention solves the technical problem that people have long wanted to solve but have never been able to solve successfully:

[0060] This invention is the first to combine machine learning with the RPT model, solving the complexity of obtaining the RPT model through traditional empirical methods. It enables the use of intelligent algorithms to handle dual non-uniformity, which can greatly improve computational efficiency and has practical engineering value.

[0061] Third, the technical solution of this invention addresses the limitations of existing reactive equivalent physical conversion methods by proposing an improved method based on machine learning. Traditional reactive equivalent physical conversion methods mainly rely on empirical formulas and manual parameter tuning, typically requiring substantial computational resources and exhibiting low accuracy and efficiency when dealing with complex fuel geometries and material properties. Furthermore, existing technologies often lack flexibility and robustness in predicting the similarity ratio of new fuels, making it difficult to meet diverse fuel design requirements.

[0062] This invention significantly improves the accuracy and efficiency of reactive equivalent physical transformation by introducing machine learning techniques, particularly linear regression models. First, a data-driven approach is used to train existing plate- and rod-shaped dispersed fuel data, establishing a mathematical model capable of accurately predicting similarity ratios. Compared to traditional methods, this data-based model better captures the underlying relationships between fuel characteristics, thus exhibiting higher accuracy and reliability in predicting the similarity ratio of new fuels.

[0063] Secondly, the technical solution of this invention demonstrates significant technological advancements in handling complex fuel geometries and material properties. By leveraging the predictive capabilities of machine learning models, this invention can rapidly generate high-quality similarity ratio prediction results, and these results are validated in multiple dimensions using the OpenMC program, including burnup, density, fission rate, and neutron energy spectrum analysis, ensuring the physical feasibility of the results. This method not only reduces computation time but also lowers the demand for computational resources, thereby improving overall computational efficiency.

[0064] Furthermore, the model provided by this invention has excellent generalization ability, capable of adapting to different types of fuel design requirements, and providing strong support for the rapid evaluation and optimization of new fuels. By applying machine learning techniques to reactive equivalent physical transformations, this invention achieves significant technological advancements in flexibility, efficiency, and accuracy, solving many technical problems inherent in traditional methods and promoting further development in fuel design and nuclear reactor safety. Attached Figure Description

[0065] Figure 1 This is a flowchart of a machine learning-based method for optimizing and verifying the reactivity of nuclear fuel, provided in an embodiment of the present invention.

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

[0067] Figure 3 This is a flowchart of the RPT method provided in an embodiment of the present invention.

[0068] Figure 4 This is a basic schematic diagram of the plate-shaped element RPT method provided in the embodiments of the present invention.

[0069] Figure 5 This is a graph showing the predicted and actual similarity ratio values ​​of the plate-shaped RPT model provided in this embodiment of the invention.

[0070] Figure 6 This is a graph showing the predicted and actual similarity ratio values ​​of the rod-shaped RPT model provided in this embodiment of the invention.

[0071] Figure 7 This is a graph showing the change in fuel consumption when the kinf deviation is at its minimum, as provided in an embodiment of the present invention.

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

[0073] Figure 9 This is a graph showing the change in 235U density with fuel consumption when the kinf deviation is minimal, provided by an embodiment of the present invention.

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

[0075] Figure 11 This is a graph showing the change in 235U fission rate with fuel consumption when the Kinf deviation is minimized, as provided in an embodiment of the present invention.

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

[0077] Figure 13 This is a graph showing the change of neutron flux with neutron energy when the Kinf deviation is minimized, provided by an embodiment of the present invention.

[0078] Figure 14 This is a graph showing the change in neutron flux with neutron energy when the Kinf deviation is at its maximum, provided in an embodiment of the present invention.

[0079] Figure 15 This is a graph showing the change in fuel consumption when the kinf deviation is at its minimum, as provided in an embodiment of the present invention.

[0080] Figure 16 This is a graph showing the change in fuel consumption when the kinf deviation is at its maximum, provided in an embodiment of the present invention.

[0081] Figure 17 When the KIF deviation is minimized as provided in the embodiments of the present invention 235 U density as a function of fuel consumption.

[0082] Figure 18 When the KIF deviation is at its maximum as provided in the embodiments of the present invention. 235 U density as a function of fuel consumption.

[0083] Figure 19 When the KIF deviation is minimized as provided in the embodiments of the present invention 239 Graph showing the change in Pu density with fuel consumption.

[0084] Figure 20 When the KIF deviation is at its maximum as provided in the embodiments of the present invention. 239 Graph showing the change in Pu density with fuel consumption.

[0085] Figure 21 This is a graph showing the change in neutron flux with energy when the Kinf deviation is minimized, provided in an embodiment of the present invention.

[0086] Figure 22 This is a graph showing the change in neutron flux with energy when the Kinf deviation is at its maximum, provided in an embodiment of the present invention. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0088] like Figure 1 As shown in the figure, the method for optimizing and verifying nuclear fuel reactivity based on machine learning provided in this embodiment of the invention includes the following steps:

[0089] S101 uses machine learning methods to learn and train existing plate-shaped and rod-shaped dispersed fuel data based on a linear regression model.

[0090] S102 uses new data to make predictions and obtain the corresponding similarity ratio. It is then verified by the OpenMC program, including burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis.

[0091] The method for learning and training existing plate-shaped and rod-shaped dispersed fuel data based on a linear regression model provided in this embodiment of the 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 this invention is based on machine learning technology, aiming to achieve reactive equivalence conversion between plate-shaped and rod-shaped dispersed fuels. First, existing plate-shaped and rod-shaped dispersed fuel data are loaded and preprocessed to ensure data integrity and consistency. This step includes cleaning, normalizing, and extracting features from the dataset to provide high-quality input data for subsequent model training.

[0097] Next, a linear regression model is created and trained. Linear regression was chosen because it can simply and effectively capture the linear relationship between fuel characteristics. During model training, preprocessed fuel data is used as the training set, and the model parameters are optimized by minimizing the loss function, enabling the model to accurately fit the relationship between fuel characteristics and similarity ratios.

[0098] The third step involves using the trained model to predict the new input data and obtain the corresponding similarity ratio. The core of this step is leveraging the model's linear predictive power to map the new fuel data to the similarity ratio space. Subsequently, the prediction results are validated using the OpenMC program, including burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis, to ensure the predicted similarity ratio is physically feasible and accurate.

[0099] Finally, after validation, the model can be used for rapid prediction and analysis of new fuel data. This approach not only improves the efficiency of reactive equivalent physical conversions 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 in this embodiment of the invention:

[0101] The training data is loaded from the training set file using the loadtxt function of the NumPy library, with spaces as the delimiter. After loading, the data needs to be preprocessed by extracting features f, R, S and the target variable SR through slicing operations.

[0102] The creation and training of the linear regression model provided in this embodiment of the invention:

[0103] After data preprocessing, import the LinearRegression class from the sklearn.linear_model module, instantiate a LinearRegression object, and create a linear regression model. Then, call the model's fit method, passing the feature matrix X and the target variable y as parameters to 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 in this embodiment of the invention:

[0105] After training the model, use the model to predict new data; load the test data from the test set file, extract the features f, R, S and the target variable SR, and then call the model's predict method to obtain the predicted values.

[0106] The novel data prediction method provided by this invention:

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

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

[0109] The learning and training module is used to learn and train on existing plate-shaped and rod-shaped dispersed fuel data using machine learning methods based on a linear regression model.

[0110] The prediction module is used to make predictions using new data, obtain the corresponding similarity ratio, and verify it through the OpenMC program, including burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis.

[0111] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the machine learning-based nuclear fuel reactivity optimization and safety verification method.

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

[0113] Another objective of this invention is to provide an information data processing terminal for implementing the machine learning-based nuclear fuel reactivity optimization and safety verification system.

[0114] Specific implementation of the present invention:

[0115] 1. This invention utilizes machine learning methods, employing a linear regression model to train existing data on plate-shaped and rod-shaped dispersed fuels. New data is then used for prediction to derive the corresponding similarity ratio. This is then verified using the OpenMC program, including burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis. Data results demonstrate that the reactive equivalent physical conversion method based on the linear regression model not only significantly improves computational efficiency but also ensures very high accuracy, meeting practical application requirements.

[0116] 2. Materials and Methods

[0117] This chapter introduces the Reactive Physical Equivalent Transformation (RPT) method and machine learning, and delves into the RPT method based on machine learning. Through machine learning, efficient computational analysis of dispersed particulate fuels is achieved.

[0118] 2.1 Traditional Reactive Physical Equivalent Conversion Method

[0119] RPT stands for Reactivity-equivalent Physical Transformation. This method primarily works by altering physical parameters to reduce the self-shielding effect caused by the geometric distribution of fuel and matrix, thereby obtaining a more accurate and effective multiplication factor. The RPT method was initially applied to rod-shaped fuel elements, such as... Figure 1 First, the concept of an equivalent model was proposed, which is to use an equivalent simplified model 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 region. Once the equivalent radius is obtained, the RPT model can maintain high 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 initial fuel region radius, and the internal volume is homogenized for fuel and matrix. The lower limit is the minimum equivalent radius obtained by compressing all fuel particles to the center of the fuel region. The accurate RPT radius is generally located between the upper and lower limits.

[0120] For fuel distribution in cylindrical and spherical geometries, the conceptual illustration of the traditional reactive equivalent physical transformation method can be shown as follows: Figure 3 Explain it as described:

[0121] (1) All the dispersed fuel particles that were originally distributed throughout the fuel region are concentrated into a smaller, specific region. The purpose of this step is to simplify the model so that subsequent calculations can be performed.

[0122] (2) The reduced fuel region is volume-homogenized. This step simplifies the original dual inhomogeneity (i.e., the inhomogeneity between fuel particles and the matrix, and the inhomogeneity of the grid structure, cladding, and moderator) into a single inhomogeneity model. This simplification enables conventional 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 double non-uniformity model into a single non-uniformity model that is easier to handle, thereby reducing computational costs while ensuring computational accuracy and providing an efficient computational method for fuel distribution in cylindrical and spherical geometries.

[0124] 2.2 Plate-shaped element RPT method

[0125] For plate geometry, referencing the implementation of the cylindrical RPT, we propose an implementation of the traditional RPT method for plate geometry, as illustrated in the diagram below. Figure 4As shown. Similarly, the RPT method works similarly for plate-shaped elements. The difference is that plate-shaped elements, due to the rectangular shape of their fuel region, are limited by both length and width. Here, for fuel plates containing dispersed particles, an equivalent side length concept is proposed. The equivalent side length is the length and width of the reduced fuel region, where the reduction ratio of length and width is the same. Like rod-shaped elements, the equivalent side length is also limited by upper and lower thresholds. The upper limit should not exceed the side length of the original fuel region, which is the initial fuel region length and width, and the internal volume is homogenized between the fuel and the matrix. The lower limit is the minimum length and width obtained by compressing all fuel particles to the center of the fuel region. The accurate equivalent side length generally lies between the upper and lower limits.

[0126] Here we provide a simple calculation explanation of the application of the RPT method on fuel plates containing dispersed particles, such as... Figure 4 As shown in the middle, assuming the length of the fuel region of the plate-shaped element is a, the width is b, the height is H, and the particle packing ratio is f:

[0127] 1. First, the range of fuel particle compression within a certain region needs to be determined, where the length and width are compressed proportionally, and a and b are simultaneously reduced by a factor of s. The new fuel region's length and width then become the original as and bs. Here, s is referred to as the similarity ratio of the fuel plate model containing dispersed particles in the RPT method. As mentioned above, the upper limit of s is 1. Based on the principle of maintaining consistent dispersed particle volume, formula (1.1) is derived, thus yielding the lower limit of s.

[0128] 2. Then, keeping the number of nucleons of each nuclide unchanged in the fuel and matrix within the reduced fuel region, homogenization is performed according to volume weights to obtain a new material, mixedfuel. Meanwhile, the matrix between the original fuel region and the new fuel region remains unchanged, ultimately yielding an RPT model of a fuel plate containing dispersed particles under this similarity ratio.

[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, which is the ratio of the side length of the reduced dispersed fuel region to the side length of the original dispersed fuel region. The principle of obtaining the similarity ratio is that the effective multiplication factor of the equivalent model is equal to the effective multiplication factor under the direct explicit particle modeling condition. Direct explicit particle modeling calculation generally requires the use of the Monte Carlo program and multiple side length searches. Once the similarity ratio is obtained, the equivalent model can still maintain high accuracy in fuel consumption calculation. According to the relevant paper

[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, this invention first establishes a regular arrangement model of fuel particles, and uses the calculation result of the Monte Carlo program particle model (Grain Model, abbreviated as GM) as the benchmark value. Then, it establishes RPT models with different equivalent side lengths, obtains the effective multiplication factor corresponding to the fuel region with different side lengths, and draws a scatter plot. The calculated results are fitted, and then interpolation is performed according to the effective multiplication factor of the particle model. After multiple such interpolations, 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 models is a common supervised learning method used to predict the output of a continuous value. In linear regression, it is assumed that there is a linear relationship between the dependent variable (output) and the independent variables (features). The model describes the relationship between the features and the output by fitting the best straight line, minimizing the error between the model's predicted output and the actual observed value. The basic form of a 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 model parameters (weights), and x1, x2, ..., xn are the input features. The essence of a linear regression model is to estimate the mean of the explained variable using the least squares method, that is, to minimize the sum of squared residuals between the observed values ​​and the model's predicted values, in order to find the best-fitting line. By extracting independent variables, creating and fitting a linear regression model, and making predictions, the predicted values ​​are obtained. To evaluate the model's performance, various metrics can be used for validation, such as mean squared error or coefficient of determination. These metrics measure the model's fit to the observed data and its predictive ability. Finally, by optimizing the parameters, the desired optimal predicted values ​​are obtained.

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

[0138] This model uses the LinearRegression model from the sklearn library to train and predict linear regression models on a given dataset.

[0139] 1) Data loading and preprocessing

[0140] First, the training data is loaded from the training set file using the `loadtxt` function from the NumPy library, with spaces as the delimiter. After loading, we need to preprocess the data by extracting features f, R, S, and the target variable SR through slicing operations.

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

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

[0143] 3) Model prediction and evaluation

[0144] After training the model, it can be used to predict new data. First, the test data from the test set file is loaded, and the features f, R, S, and the target variable SR are extracted. Then, the model's predict method is called to obtain the predicted values. To evaluate the model's performance, error calculation is added, and the matplotlib library is used to plot the true target values ​​and predicted values ​​to more intuitively compare the differences between them.

[0145] 4) New data prediction

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

[0147] 3. Results

[0148] This chapter investigates the RPT method for rod-shaped and plate-shaped fuel elements based on machine learning. For plate-shaped fuel elements, three RPT parameters are analyzed and calculated: fuel particle size, particle phase volume, and fuel region area (see Table 3.1). For rod-shaped fuel elements, six RPT parameters are analyzed and calculated: particle fuel core radius Rpf, particle outer radius Rpar, grid fuel region radius Rcf, grid length L, moderator density ρmod, and phase volume f (see Table 3.2). Numerical verification and analysis are then performed compared with traditional Monte Carlo calculations.

[0149] Table 3.1 Parameters of Plate Components

[0150]

[0151] Table 3.2 Parameters of Rod-shaped Elements

[0152]

[0153] §3.1 Calculation of RPT for Plate-like Elements Based on Linear Regression Model

[0154] Based on the sensitivity analysis of the parameters in the previous section, among the three parameters RPT of the selected plate-shaped element, 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 through these three parameters. Finally, 19 sets of three parameters R, S, and f, and their corresponding similarity ratios SR were selected from the existing data (see Table 3.2) for model training. The trained model was used to predict the 5 sets of new data in Table 3.3, all of which were taken within the above parameter ranges. The prediction results are as follows: Figure 5 As shown in Table 3.4.

[0155] Table 3.2 RPT Parameters for Plate-like Elements (Training)

[0156]

[0157]

[0158] pass Figure 5 It can be seen that the linear regression model has a good fit, with the training data curves almost completely overlapping, and the absolute error accurate to the thousandths place. The predicted data curves also almost overlap. This indicates that the machine learning method has high accuracy in processing plate-shaped RPT components and can meet practical needs.

[0159]

[0160] Table 3.3 RPT Parameters (Predicted) for Plate Elements

[0161] Table 3.4 Errors between predicted and actual similarity ratios of RPT parameters for plate-shaped elements

[0162]

[0163] §3.2 Calculation of RPT for Rod-shaped Elements Based on Linear Regression Model

[0164] Based on the RPT parameter selection for rod-shaped elements in the previous section, six parameters—Rpf, Rpar, Rcf, L, ρmod, and f—and their corresponding similarity ratios SR, totaling 21 groups (see Table 4.2), were selected for model training. The trained model was then used to predict the results of the five new data sets (Table 4.3). Figure 6 As shown in Table 4.4, among the six selected parameters, Rpf ranges from 0.027 to 0.038, Rpar from 0.049 to 0.055, Rcf from 0.55 to 0.61, f from 0.34 to 0.53, L from 1.597 to 1.762, ρmod from 0.52 to 0.98, and SR is the actual similarity ratio obtained from these six parameters.

[0165] Table 4.2 RPT parameters for rod-shaped elements (training)

[0166]

[0167] Table 4.3 RPT parameters (predicted) for rod-shaped elements

[0168]

[0169]

[0170] Table 4.4 Errors between predicted and actual similarity ratios of RPT parameters for rod-shaped elements.

[0171]

[0172] The final results showed that the absolute errors remained after the thousandths, and the relative errors remained within 1%. Figure 6 It can be seen that the linear regression model has a good fit, with the training data curves almost completely overlapping and the predicted data curves also nearly overlapping. This indicates that the machine learning method has high accuracy in processing rod-shaped elements (RPTs) and can meet practical needs.

[0173] 3.3 Numerical Verification and Analysis

[0174] 3.3.1 Verification Analysis of Plate-Shaped Fuel Elements

[0175] This section will use the OpenMC program to verify the similarity ratio of the RPT parameters of the plate-like elements predicted above, including the effective multiplication factor calculated from the actual similarity ratio. Effective proliferation factor calculated from predicted similarity ratio The Kinf deviation and PCM of the two are shown in Table 3.5. The Kinf deviation is given by formula (3.2).

[0176] Table 3.5 Deviations between actual and predicted Kinf and PCM for plate fuel

[0177]

[0178]

[0179] Table 3.5 shows the similarity ratio of the RPT parameters of the plate-shaped element predicted by the linear regression model, calculated using OpenMC. With the actual value of the guarantee system The deviations are small, all within 200 pcm, which meets the actual accuracy requirements.

[0180] 3.3.1.1 Fuel Consumption Verification

[0181] Case 3, with the smallest kinf bias, and Case 5, with the largest kinf bias, were selected from Table 3.5 to verify the fuel consumption of the GM model and the RPT model, respectively. Figure 7-8 Showing k infGM With k infRPT Changes with fuel consumption.

[0182] For both the minimum and maximum Kinf deviation cases, the overall trend is consistent, decreasing with increasing burnup depth. In the case of minimum Kinf deviation, the RPT model curve and the GM model curve essentially overlap, with the maximum deviation not exceeding 200 pcm and remaining generally within 100 pcm. At a burnup depth of 1.037 MWd / t, the maximum error is 168.62 pcm, and at a burnup depth of 4.666 MWd / t, the minimum deviation is 13.384 pcm. In the case of maximum Kinf deviation, the RPT model curve and the GM model curve essentially overlap. At a burnup depth of 4.66575 MWd / t, the maximum deviation is 108.85 pcm, and at a burnup depth of 2.592 MWd / t, the minimum deviation is 13.357 pcm. This indicates that the RPT model maintains high accuracy throughout its entire burnup lifespan.

[0183] 3.3.1.2235U Density Verification

[0184] Case 3, with the smallest kinf bias, and Case 5, with the largest kinf bias, were selected from Table 3.5 to perform 235U density validation on the GM model and RPT model, respectively. Figure 9-10 The diagram shows how the density of 235U changes with fuel consumption.

[0185] For both the minimum and maximum kinf deviations, the overall trend remains consistent, decreasing with increasing burnup depth. The two graphs clearly show that the GM model curve and the RPT model curve completely overlap, with the relative error showing an increasing trend but remaining at a very small order of magnitude. At a burnup depth of 5.869 MWd / t, the maximum error is 0.00284%, which is negligible. This indicates that the 235U density of the RPT model has virtually no impact on the fitting throughout the entire burnup lifespan, meeting practical accuracy requirements.

[0186] 3.3.1. Verification of 3235U fission rate

[0187] Case 3, with the smallest kinf bias, and Case 5, with the largest kinf bias, were selected from Table 3.5 to verify the 235U fission rate of the GM model and the RPT model, respectively. Figure 11-12 The study demonstrates how the fission rate of 235U changes with fuel consumption.

[0188] For both the minimum and maximum Kinf deviation cases, the overall trend remains consistent, decreasing with increasing burnup depth. In the case of minimum Kinf deviation, the maximum error is 0.021% at a burnup depth of 2.592 MWd / t. In the case of maximum Kinf deviation, the maximum error is 0.011% at a burnup depth of 6.221 MWd / t. This indicates that the 235U fission rate of the RPT model has virtually no impact on the fit throughout the entire burnup lifespan, meeting the actual accuracy requirements.

[0189] 3.3.1.4 Neutron Energy Spectrum Analysis

[0190] Neutron energy spectrum represents the energy distribution of neutrons within the reactor. Case 3 (with the smallest kinf deviation) and Case 5 (with the largest kinf deviation) from Table 3.5 were selected for neutron energy spectrum analysis of the GM model and 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 errors between the GM model and the RPT model are relatively large. For the case with the smallest kinf deviation, the relative error is 6.55% at an energy of 1.23E-03eV. For the case with the largest kinf deviation, the relative error is 5.10% at an energy of 1.23E-03eV. In the medium-energy and high-energy regions, the energy spectrum trends of the GM model and the RPT model are basically consistent. Due to the partial loss caused by the self-shielding effect, the deviations of the RPT models in both cases fluctuate significantly in the resonance region, but the deviations are within 2%.

[0192] In summary, the relative error in the low-energy region is relatively large, but remains within 7%. The resonance regions in the medium-energy and high-energy regions show significant fluctuations, but the relative errors are all within 2%, meeting the actual accuracy requirements.

[0193] 3.3.2 Verification Analysis of Rod-shaped Fuel Elements

[0194] This section will use the effective multiplication factor calculated from the six parameters in the previous section and the similarity ratio of the predicted RPT parameters of the rod-shaped element in the previous section to verify the calculation. It is divided into three parts: the first part calculates the corresponding effective multiplication factor using the original rod-shaped dispersed fuel particles; the second part calculates the corresponding effective multiplication factor, 235U density, 239Pu density, burnup depth, and neutron spectrum using the rod-shaped dispersed fuel particles after the RPT method; the third part calculates the similarity ratio predicted by machine learning and compares the effective multiplication factors in the second and third parts, selecting 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 and predicted Kinf values ​​and deviations for rod-shaped fuels

[0196]

[0197] Table 4.5 shows the similarity ratio of the RPT parameters of the rod-shaped element predicted by the linear regression model, calculated using ALPHA. Compared to the actual value of rod fuel The deviations are small, all remaining within 100 pcm, indicating that the linear regression model has a good fit and meets the actual accuracy requirements.

[0198] 3.3.2.1 Fuel Consumption Verification

[0199] Case 3, with the smallest kinf bias, and Case 1, with the largest kinf bias, were selected from Table 4.5 to verify the fuel consumption of the GM model and the RPT model, respectively. Figure 15-16 Showing and Changes with fuel consumption.

[0200] For k inf In both the minimum and maximum deviation cases, the overall trend remains consistent: the deviation decreases with increasing burn depth. At k... inf In the case of minimal deviation, the RPT model curve and the GM model curve essentially coincide, with pcm showing a monotonically increasing trend, and the maximum deviation not exceeding 50 pcm. At a burnup depth of 19.25 MWd / t, the maximum error is 48.7 pcm, and at a burnup depth of 1.75 MWd / t, the minimum error is 45.7 pcm. In the case of maximum Kinf deviation, the RPT model curve and the GM model curve essentially coincide, with pcm showing a monotonically increasing trend, and the maximum deviation not exceeding 100 pcm. At a burnup depth of 19.25 MWd / t, the maximum error is 98.7 pcm, and at a burnup depth of 1 MWd / t, the minimum error is 93.6 pcm. This indicates that the RPT model has a very stable fitting effect; although pcm increases with increasing burnup depth, the increase is small, and it maintains high accuracy throughout the burnup life.

[0201] 3.3.2.2 235 U、 239 Pu density verification

[0202] Select k from Table 4.5 inf The smallest bias was found in Case 3, and the largest bias was found in Case 5, which were used to evaluate the GM model and the RPT model, respectively. 235 U and 239 Pu density verification, Figure 17-18 Showing 235 How U-density changes with fuel consumption Figures 19-20 Showing 239 How Pu density changes with fuel consumption.

[0203] pass 235 The graph showing the change in U density with fuel consumption yields results for k. inf In both the minimum and maximum deviation scenarios, the overall trend of the two models is consistent, decreasing with increasing burn depth. It is evident from the two graphs that the GM model curve and the RPT model curve are essentially parallel and nearly coincident, with the relative error gradually decreasing. At k inf In the case of minimal deviation, when the burnup depth reaches 0.25 MWd / t, the maximum error is 0.0001965%; at k inf In the case of the largest deviation, when the burn depth is at the initial value, the maximum error is 0.0002216%, which can be ignored. This indicates that the RPT model... 235 The U-density has virtually no impact on the fitting within the fuel consumption lifespan, meeting the actual accuracy requirements.

[0204] pass 239 The graph showing the change in Pu density with fuel consumption yields results for k. inf In both the minimum and maximum deviation scenarios, the overall trend of the two models remains consistent, increasing with increasing burn depth. It is evident from the two graphs that the GM model curve and the RPT model curve largely overlap, with the relative error gradually increasing. At k... inf In the case of minimal deviation, when the burnup depth reaches 19.25 MWd / t, the maximum error is 0.00000643%; at k inf In the case of the largest deviation, when the burnup depth reaches 19.25 MWd / t, the maximum error is 0.00000823%, which can be ignored. This indicates that the RPT model... 239 The Pu density has virtually no impact on the fitting process during the fuel lifespan, meeting the actual accuracy requirements.

[0205] 3.3.2.3 Neutron Energy Spectrum Analysis

[0206] Neutron energy spectrum represents the energy distribution of neutrons within the reactor. Case 3 (with the smallest kinf deviation) and Case 1 (with the largest kinf deviation) from Table 4.5 were selected for neutron energy spectrum analysis of the GM model and 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, almost zero. In the high energy region, for the case with the smallest Kinf deviation at the highest energy point, the relative error is 0.445%, while for the case with the largest Kinf deviation 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, essentially zero. The resonance region in the high-energy region exhibits significant fluctuations, but the relative errors are all within 0.445%, which can be ignored and meet the actual accuracy requirements.

[0209] in conclusion

[0210] This invention focuses on a machine learning-based method for optimizing and verifying the reactivity of nuclear fuel. It calculates and predicts the reactive physical transformation (RPT) parameters of plate-shaped and rod-shaped particulate fuels using a linear regression model, ultimately deriving the similarity ratio of the corresponding parameters. The equivalent radius or equivalent side length of the RPT model is calculated using this similarity ratio, and then verified through OpenMC (Open Reactivity Model) for burnup, density, fission rate, and neutron spectrum analysis. The data results demonstrate that the reactivity equivalent physical transformation method based on the linear regression model not only significantly improves computational efficiency but also ensures very high accuracy, meeting practical application requirements.

[0211] I. Specific application areas or related products of this invention.

[0212] In nuclear reactor physics calculations, this invention tightly integrates machine learning algorithms with the RPT model, then transforms double non-uniformity into single non-uniformity, which can then be calculated using traditional neutron physics programs.

[0213] II. Evidence related to the technical effects obtained by the embodiments of the present invention.

[0214] As shown in the figure, in terms of numerical verification of plate fuel elements, the steady-state verification deviation remained within 200 pcm. The overall trend of both methods in fuel consumption verification was consistent, decreasing with increasing burn depth, with the maximum deviation not exceeding 200 pcm and generally remaining within 100 pcm. 235 Regarding U-density verification, the overall trend of both is consistent, decreasing with increasing burn depth, with a maximum error of 0.00284%. 235 U fission rate verification, at k inf In the case of minimal deviation, the maximum error is 0.021% when the burnup depth reaches 2.592 MWd / t. At k infIn the case of the largest deviation, when the burnup depth reaches 6.221 MWd / t, the maximum error is 0.011%. Neutron energy spectrum analysis shows that the relative error in the low-energy region is relatively large, but all remain within 7%. The resonance regions in the medium-energy and high-energy regions show significant fluctuations, but the relative errors are all within 2%.

[0215] For rod-shaped fuel elements, the deviation remained within 100 pcm during steady-state verification. In burnup verification, both showed a consistent overall trend, decreasing with increasing burnup depth, with a maximum error not exceeding 100 pcm. 235 U、 239 Pu density verification shows that both exhibit consistent overall trends, decreasing with increasing burnup depth. In neutron spectroscopy analysis, the relative errors in the low and medium energy regions are small, essentially zero. While the resonance region in the high energy region shows significant fluctuations, the relative errors are all within 0.445%, which can be ignored.

[0216] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0217] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing and verifying the reactivity of nuclear fuel based on machine learning, characterized in that, Includes the following steps: Step 1: Using machine learning methods, the existing plate-shaped and rod-shaped dispersed fuel data are trained based on a linear regression model. Step 2: Use the new data to make predictions and obtain the corresponding similarity ratio. Then, use the OpenMC program to verify the burnup, density, fission rate, and neutron energy spectrum. The method for learning and training existing plate-shaped and rod-shaped dispersed fuel data based on a 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; The data loading and preprocessing method: The training data is loaded from the training set file using the loadtxt function of the NumPy library, with spaces as the delimiter. After loading, the data needs to be preprocessed by extracting features f, R, S and the target variable SR through slicing operations. The creation and training of the linear regression model: After data preprocessing, import the LinearRegression class from the sklearn.linear_model module, instantiate a LinearRegression object, and create a linear regression model; then call the model's fit method, passing the feature matrix X and the target variable y as parameters to the model for training and fitting; observe the model parameters by printing the model's coefficients coef_ and intercept_. The model prediction and evaluation method is as follows: After training the model, use the model to predict new data; load the test data from the test set file, extract the features f, R, S and the target variable SR, and then call the model's predict method to obtain the predicted values; The new data prediction method: Use a trained model to make predictions on unseen data by creating a pandas DataFrame object containing new feature values, applying the model to the new dataset, and obtaining the prediction results.

2. A machine learning-based nuclear fuel reactivity optimization and safety verification system implementing the method as described in claim 1, characterized in that, The machine learning-based nuclear fuel reactivity optimization and safety verification system includes: The learning and training module is used to learn and train on existing plate-shaped and rod-shaped dispersed fuel data using machine learning methods based on a linear regression model. The prediction module is used to make predictions using new data, obtain the corresponding similarity ratio, and verify it through the OpenMC program, including burnup verification, density verification, fission rate verification, and neutron energy spectrum analysis.

3. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the machine learning-based nuclear fuel reactivity optimization and safety verification method as described in claim 1.

4. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the machine learning-based nuclear fuel reactivity optimization and safety verification method as described in claim 1.

5. 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 2.

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