Sensitivity parameter determination method and device of nuclear reactor

Abstract

The invention relates to a method and a device for determining sensitivity parameters of a nuclear reactor. The method comprises the following steps: converting a reactor physical field sample into a space-time field data set, and projecting the space-time field data set to a manifold structure to obtain space representation and time representation of the space-time field data set on the manifold structure; determining a composite kernel matrix based on the spatial representation and the time representation; on the basis of the composite kernel matrix, diffusion coordinates of the time-space field data set on the manifold structure are determined; determining sensitivity parameters influencing space-time field distribution based on the reactor physical field sample and the diffusion coordinates; the sensitivity parameters are used for guiding design optimization or safety margin analysis of the nuclear reactor. By adopting the method, the sensitivity parameter determination accuracy can be improved.

Description

Technical Field

[0001] This application relates to the field of big data technology, and in particular to a method and apparatus for determining the sensitivity parameters of a nuclear reactor. Background Technology

[0002] In numerical reactor safety analysis, traditional sensitivity analysis methods are widely used to assess the impact of input parameter uncertainties on key output results.

[0003] However, when analyzing the three-dimensional spatiotemporal dynamic physical fields involved in strong transient and nonlinear operating conditions, the results obtained by existing methods are often insufficient to reflect that the most sensitive parameter dominating the distribution characteristics of the physical field may change at different time points. Due to the inability to capture this time-varying sensitivity feature, the accuracy of the analytical conclusions based on traditional methods in guiding the safety design and control system development under transient operating conditions is limited. Summary of the Invention

[0004] Therefore, it is necessary to provide a method and apparatus for determining the sensitivity parameters of a nuclear reactor that can improve the accuracy of sensitivity parameter determination, in order to address the above-mentioned technical problems.

[0005] In a first aspect, this application provides a method for determining the sensitivity parameters of a nuclear reactor, including:

[0006] The composite kernel matrix is ​​determined based on spatial and temporal representations;

[0007] Based on the composite kernel matrix, the diffusion coordinates of the spatiotemporal field dataset on the manifold structure are determined;

[0008] Based on reactor physics field samples and diffusion coordinates, sensitive parameters affecting the spatiotemporal field distribution are determined; these sensitive parameters are used to guide the design optimization or safety margin analysis of nuclear reactors.

[0009] Secondly, this application also provides a device for determining the sensitivity parameters of a nuclear reactor, comprising:

[0010] The projection module is used to convert reactor physics field samples into spatiotemporal field datasets and project the spatiotemporal field datasets onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field datasets on the manifold structure.

[0011] The matrix determination module is used to determine the composite kernel matrix based on spatial and temporal representations.

[0012] The coordinate determination module is used to determine the diffusion coordinates of the spatiotemporal field dataset on the manifold structure based on the composite kernel matrix;

[0013] The parameter determination module is used to determine the sensitive parameters that affect the spatiotemporal field distribution based on reactor physics field samples and diffusion coordinates; the sensitive parameters are used to guide the design optimization or safety margin analysis of nuclear reactors.

[0014] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0015] The reactor physics field samples are converted into a spatiotemporal field dataset, and the spatiotemporal field dataset is projected onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure;

[0016] The composite kernel matrix is ​​determined based on spatial and temporal representations;

[0017] Based on the composite kernel matrix, the diffusion coordinates of the spatiotemporal field dataset on the manifold structure are determined;

[0018] Based on reactor physics field samples and diffusion coordinates, sensitive parameters affecting the spatiotemporal field distribution are determined; these sensitive parameters are used to guide the design optimization or safety margin analysis of nuclear reactors.

[0019] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0020] The reactor physics field samples are converted into a spatiotemporal field dataset, and the spatiotemporal field dataset is projected onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure;

[0021] The composite kernel matrix is ​​determined based on spatial and temporal representations;

[0022] Based on the composite kernel matrix, the diffusion coordinates of the spatiotemporal field dataset on the manifold structure are determined;

[0023] Based on reactor physics field samples and diffusion coordinates, sensitive parameters affecting the spatiotemporal field distribution are determined; these sensitive parameters are used to guide the design optimization or safety margin analysis of nuclear reactors.

[0024] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0025] The reactor physics field samples are converted into a spatiotemporal field dataset, and the spatiotemporal field dataset is projected onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure;

[0026] The composite kernel matrix is ​​determined based on spatial and temporal representations;

[0027] Based on the composite kernel matrix, the diffusion coordinates of the spatiotemporal field dataset on the manifold structure are determined;

[0028] Based on reactor physics field samples and diffusion coordinates, sensitive parameters affecting the spatiotemporal field distribution are determined; these sensitive parameters are used to guide the design optimization or safety margin analysis of nuclear reactors.

[0029] Traditional methods for determining sensitivity parameters of nuclear reactors typically focus only on isolated extreme points in the spatiotemporal field, such as peak temperature or maximum stress. While computationally simple, these methods severely lose sight of the overall structure and dynamic characteristics of the physical field during its spatiotemporal evolution. Because they neglect the impact of parameter changes on the overall field distribution and its evolution, traditional methods struggle to accurately identify sensitivity parameters that have a global impact on the system's overall behavior. This application's embodiment achieves a complete capture of the global morphological characteristics of the physical field by projecting the entire spatiotemporal field dataset onto a manifold structure. Based on this, by constructing a composite kernel matrix and extracting diffusion coordinates, the complex spatiotemporal evolution process is represented as a few essential characteristic coordinates. By analyzing the influence of input parameters on these essential characteristic coordinates, this application's embodiment can accurately identify sensitivity parameters that have a global impact on the entire spatiotemporal evolution process. Compared to traditional methods, this application significantly improves the accuracy of sensitivity parameter determination by preserving complete spatiotemporal field information, capturing global morphological characteristics, and analyzing the influence of parameters on essential characteristic coordinates, providing a more reliable basis for nuclear reactor design optimization and safety margin analysis. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 A schematic diagram of the visualization representation of the three-dimensional spatiotemporal field distribution in the parameter-time space;

[0032] Figure 2 This is an internal structural diagram of a computer device in one embodiment;

[0033] Figure 3 This is a flowchart illustrating a method for determining the sensitivity parameters of a nuclear reactor in one embodiment.

[0034] Figure 4 This is a flowchart illustrating a method for determining the sensitivity parameters of a nuclear reactor in another embodiment;

[0035] Figure 5 This is a flowchart illustrating a method for determining the sensitivity parameters of a nuclear reactor in another embodiment;

[0036] Figure 6 This is a flowchart illustrating a method for determining the sensitivity parameters of a nuclear reactor in another embodiment;

[0037] Figure 7 This is a flowchart illustrating a method for determining the sensitivity parameters of a nuclear reactor in another embodiment;

[0038] Figure 8 This is a flowchart illustrating a method for determining the sensitivity parameters of a nuclear reactor in another embodiment;

[0039] Figure 9 A schematic diagram showing the distribution of sensitivity weights for different input variables across different dimensions of the manifold coordinates;

[0040] Figure 10 This is a structural block diagram of a device for determining the sensitivity parameters of a nuclear reactor in one embodiment. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0042] Traditional three-dimensional spatiotemporal numerical reactor sensitivity analysis typically relies on discretizing and numerically solving the reactor's physical model. These methods generally employ techniques such as the finite element method, finite volume method, or finite difference method to divide the reactor's spatial and temporal domains into fine meshes, thereby enabling detailed modeling of complex coupled processes such as neutron transport, thermal-hydraulic, and fluid dynamics. In practice, analysts first establish a physical-mathematical model of the reactor, clarifying the governing equations for each physical quantity, such as the neutron diffusion equation and the energy conservation equation. Subsequently, by applying small perturbations to the input parameters—including material properties, geometric configuration, and boundary conditions—the impact of these changes on key output physical quantities, such as power distribution, temperature field, and neutron flux, is assessed. This type of sensitivity analysis identifies parameters that significantly affect system performance and safety, providing a theoretical basis for reactor design and operational optimization.

[0043] like Figure 1 As shown, Figure 1 This is a visualization of the three-dimensional spatiotemporal field distribution in the parameter-time space. Its horizontal axis represents two key input variables (such as the control rod insertion depth and coolant inlet temperature), the vertical axis represents the time dimension, and the surface height represents the value of key physical quantities (such as the local line power density peak) at a specific parameter combination and time point. Figure 1 This study reveals two important characteristics of nuclear reactor system behavior under transient conditions: First, parameter sensitivity exhibits significant time-varying features, with key variables dominating the system response potentially undergoing dynamic transformations at different times; second, complex nonlinear coupling effects exist among input parameters, their interactions jointly shaping the complex topological structure of the spatiotemporal field distribution. These dynamic characteristics and cross-effects make it difficult for traditional sensitivity analysis methods based on static key points to accurately capture the true impact of parameters throughout the transient process. This highlights the necessity of employing manifold learning techniques in this application to extract essential features from spatiotemporal field data—constructing diffusion coordinates to systematically identify the sensitivity parameters that continuously dominate throughout the transient process, providing a more reliable basis for reactor safety design and margin analysis.

[0044] In reactor design, it is assumed that the main variables affecting the design results are... This indicates that these variables follow a joint probability distribution. First, a random sample is drawn from this distribution. A sample. Sampling methods can employ well-established techniques such as the Latin hypercube. These samples are denoted as: Through nuclear reactor analysis models The reactor design results are obtained and expressed as follows:

[0045] Where n represents the number of spatially discrete grid points in the reactor, and m represents the number of time discretizations.

[0046] In engineering practice, the focus is primarily on the worst-case local conditions within the spatiotemporal field distribution. For example, in reactor accident transient or operational transient analysis, particular attention is paid to the maximum local linear power density for the three-dimensional power distribution. This is because this power density can affect the heat transfer performance of the fuel and its cladding structure, and may lead to the failure of the fuel or cladding material, thereby triggering radioactive release. In this case, it is determined that:

[0047]

[0048] Next, by constructing a machine learning model (ML), we can make it possible to process each sample... It conforms to the following formula:

[0049]

[0050] Through machine learning models, different... Variables to output variables The impact of changes. Many publicly available methods exist for obtaining the first-order and global sensitivity indices of parameters based on machine learning models. Among these, the SALib library is relatively well-known. For example, by calling the SALib library's Sobol.analyze(ML, The method can be used, or the SAlib library's orris.analyze(ML, All of these methods can yield relevant sensitivity analysis results.

[0051] In addition, the Random Forest Regressor or Gradient Boosting Regressor models from the scikit-learn machine learning open-source library can be used to obtain the feature importance (first-order sensitivity index), for example by calling the model.feature_importances_ function.

[0052] However, in practical engineering problems, especially under strong transient and nonlinear scenarios such as rod ejection accidents and rod drop accidents, the assessed sensitivity indices may exhibit significant cross-effects. This means that the parameters most sensitive to the system response may change significantly at different times or under different operating conditions. Therefore, a deep understanding and effective analysis of such time-varying sensitivities are crucial for ensuring the safety and reliability of reactor design. Based on this, this application proposes a method for determining the sensitivity parameters of nuclear reactors to address the aforementioned problems.

[0053] In one exemplary embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 2 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores relevant data in the process of determining the sensitivity parameters of a nuclear reactor. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for determining the sensitivity parameters of a nuclear reactor.

[0054] Those skilled in the art will understand that Figure 2 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0055] In one exemplary embodiment, such as Figure 3 As shown, a method for determining the sensitivity parameters of a nuclear reactor is provided, which can be applied to... Figure 1 Taking the server in the example, the explanation includes the following steps 301 to 304. Wherein:

[0056] Step 301: Convert the reactor physics field samples into a spatiotemporal field dataset, and project the spatiotemporal field dataset onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure.

[0057] Among them, reactor physics field samples refer to a set of data obtained through numerical simulation or experimental measurement that reflects the physical state of a nuclear reactor under different input parameters (such as material composition, geometric dimensions, initial conditions, etc.). They typically include physical quantities such as neutron flux density, power distribution, and temperature field that change over time.

[0058] Spatiotemporal field datasets refer to the data format obtained after structuring and organizing reactor physics field samples. Each sample is a three-dimensional data field, that is, two-dimensional space and one-dimensional time or higher-dimensional data, which fully describes the continuous process of the evolution of physical quantities at various points in space over time.

[0059] A manifold structure refers to a low-dimensional nonlinear latent geometric structure embedded in a high-dimensional data space. It can be considered that all spatiotemporal field data are essentially distributed on this simple low-dimensional manifold. Projecting the data onto this manifold aims to remove redundant information from the observation data, thereby extracting its inherent physical laws and essential characteristics. One important realization of the manifold structure is the Grassmann manifold. This manifold can be represented as a set of all definite-dimensional linear subspaces, suitable for describing the spatial and temporal subspaces spanned by the left and right singular matrices obtained from the singular value decomposition of spatiotemporal field data. By projecting spatiotemporal field data onto the Grassmann manifold, the essential characteristics of its spatial patterns and temporal evolution in terms of geometric structure can be effectively characterized, laying a theoretical foundation for the subsequent construction of composite kernel matrices and diffusion coordinates.

[0060] Spatial representation and temporal representation refer to the two core components obtained after decomposing spatiotemporal field data on a manifold structure. Spatial representation mainly describes the inherent patterns of physical fields in spatial distribution (such as specific power distribution patterns), while temporal representation mainly describes the laws governing the evolution of these spatial patterns over time (such as the rate and phase of oscillation and diffusion).

[0061] In this embodiment, the server converts the reactor physics field samples into a spatiotemporal field dataset and projects the spatiotemporal field dataset onto a manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure.

[0062] In another embodiment, the server first formats multiple power distribution samples output by the full-core transient calculation software, with each sample constituting a spatiotemporal field data set containing a sequence of power changes over time at various fuel assembly locations within the core. Subsequently, singular value decomposition is performed on each spatiotemporal field data matrix. The column vectors of the resulting left singular matrix are used as the spatial representation, reflecting the spatial distribution pattern of the core power; the column vectors of the right singular matrix are used as the temporal representation, reflecting the coefficients of the aforementioned spatial pattern's evolution over time.

[0063] In another embodiment, the transformation process includes standardizing and gridding the original physics data to ensure that all samples are aligned in both spatial and temporal dimensions. When projecting onto the manifold, tensor decomposition methods can be used, for example, decomposing the spatiotemporal field data into a core tensor and factor matrices corresponding to the spatial and temporal moduli, respectively. Here, the factor matrix of the spatial moduli is the spatial representation, which extracts the spatial basis functions of the core physics; the factor matrix of the temporal moduli is the temporal representation, which describes the change in the activation weights of these spatial basis functions over time during transient processes.

[0064] Step 302: Determine the composite kernel matrix based on spatial and temporal representations.

[0065] The composite kernel matrix is ​​used to quantify the overall similarity among all spatiotemporal field data samples. It is constructed by fusing the spatial kernel matrix (quantifying spatial similarity) and the temporal kernel matrix (quantifying temporal evolution similarity), and is the foundation for subsequent manifold learning.

[0066] In this embodiment, the server determines the composite kernel matrix based on spatial and temporal representations.

[0067] In another embodiment, the server constructs kernel matrices using different kernel functions. The server uses a radial basis function kernel to calculate the similarity between spatial representations to obtain a spatial kernel matrix, and uses a linear kernel to calculate the similarity between temporal representations to obtain a temporal kernel matrix. Finally, the two kernel matrices are subjected to a Hadamard product to obtain a composite kernel matrix.

[0068] In another embodiment, the server calculates the similarity between samples based on both spatial and temporal representations. Specifically, it calculates the cosine similarity between the spatial representation vectors of all sample pairs to construct a spatial kernel matrix; simultaneously, it calculates the Gaussian radial basis function similarity between the temporal representation vectors of all sample pairs to construct a temporal kernel matrix. Finally, it performs a Hadamard product (i.e., element-wise multiplication) between the spatial and temporal kernel matrices to obtain a composite kernel matrix that comprehensively reflects the spatiotemporal similarity between samples.

[0069] In another embodiment, in addition to constructing a linear kernel matrix using inner products, more complex kernel functions can be introduced, such as a polynomial kernel for the spatial representation and a periodic kernel for the temporal representation, to capture the nonlinear characteristics of the spatial distribution and the periodic oscillations of the temporal evolution, respectively. During the fusion phase, besides using product operations, the two kernel matrices can also be weighted and summed according to specific analytical needs; for example, the temporal kernel matrix can be given a higher weight to emphasize the importance of the dynamic evolution process in sensitivity analysis.

[0070] Step 303: Based on the composite kernel matrix, determine the diffusion coordinates of the spatiotemporal field dataset on the manifold structure.

[0071] The diffusion coordinates are low-dimensional coordinates representing the essential geometry of the data manifold, calculated through the diffusion process. In this coordinate system, the geometric distances between data points more accurately reflect their essential differences in the original high-dimensional space, providing an ideal feature space for sensitivity analysis.

[0072] In this embodiment, the server determines the diffusion coordinates of the spatiotemporal field dataset on the manifold structure based on the composite kernel matrix.

[0073] In another embodiment, the server first normalizes the composite kernel matrix to obtain a transition probability matrix, which defines the probability of a data point transitioning in one step on the manifold. Then, eigenvalue decomposition is performed on this transition probability matrix to extract the eigenvectors corresponding to its largest eigenvalues. Finally, these eigenvectors are sorted by eigenvalue and combined into a new matrix, where each row represents the low-dimensional diffusion coordinates of the original spatiotemporal field data.

[0074] In another embodiment, before constructing the transition probability matrix, a graph Laplacian matrix can be constructed using a composite kernel matrix. By performing generalized eigenvalue decomposition on this Laplacian matrix, a set of eigenvectors reflecting the low-frequency vibrational modes of the data manifold can be obtained. The eigenvectors corresponding to the smallest nontrivial eigenvalues ​​constitute the data diffusion coordinates. This method can more robustly capture the connectivity and macroscopic geometric structure of the manifold.

[0075] Step 304: Based on the reactor physical field samples and diffusion coordinates, determine the sensitivity parameters that affect the spatiotemporal field distribution.

[0076] Sensitivity parameters refer to those critical parameters among the many input parameters of a reactor that have a significant impact on changes in the spatiotemporal field distribution. Identifying these parameters helps engineers focus on core design variables, thereby enabling efficient design optimization or safety margin analysis.

[0077] In this embodiment, the server determines the sensitivity parameters affecting the spatiotemporal field distribution based on reactor physical field samples and diffusion coordinates. Specifically, the server establishes a mapping relationship between the sample set of reactor input parameters and diffusion coordinates, and determines the sensitivity parameters by analyzing the contribution of the input parameters to the changes in diffusion coordinates.

[0078] In another embodiment, the server uses reactor input parameters (such as control rod insertion depth, coolant inlet temperature, etc.) as features and the diffusion coordinates corresponding to each sample as the target variable to construct a regression model (such as a random forest regressor). By analyzing the importance indices of each input feature in the regression model, such as importance based on permutation or importance based on Gini impurity reduction, these importance indices are ranked, and the input parameter with the highest ranking is determined as the key sensitivity parameter affecting the spatiotemporal field distribution.

[0079] In another embodiment, the server can directly calculate the mutual information or maximum information coefficient between each input parameter and each principal axis of the diffusion coordinates in a low-dimensional space. This information-theoretic approach can capture both linear and nonlinear dependencies. Input parameters with high mutual information values ​​with the diffusion coordinates are identified as sensitivity parameters.

[0080] In another embodiment, the server employs a sensitivity analysis method based on mutual information. The server calculates the mutual information value between each input parameter and the diffusion coordinates in each dimension, and identifies parameters whose mutual information values ​​exceed a set threshold as sensitive parameters, thereby identifying input parameters that have a critical impact on the spatiotemporal field distribution.

[0081] Among them, sensitivity parameters are used to guide the design optimization or safety margin analysis of nuclear reactors.

[0082] In the aforementioned methods for determining the sensitivity parameters of nuclear reactors, traditional sensitivity analysis methods typically focus only on isolated extreme points in the spatiotemporal field, such as peak temperature or maximum stress. While this method is computationally simple, it severely loses the overall structure and dynamic characteristics of the physical field during its spatiotemporal evolution. Because it ignores the influence of parameter changes on the overall field distribution and its evolution, traditional methods struggle to accurately identify sensitivity parameters that have a global impact on the system's overall behavior. This application's embodiment achieves a complete capture of the global morphological characteristics of the physical field by projecting the entire spatiotemporal field dataset onto a manifold structure. Based on this, by constructing a composite kernel matrix and extracting diffusion coordinates, the complex spatiotemporal evolution process is represented as a few essential characteristic coordinates. By analyzing the influence of input parameters on these essential characteristic coordinates, this application's embodiment can accurately identify sensitivity parameters that have a global impact on the entire spatiotemporal evolution process. Compared to traditional methods, this application significantly improves the accuracy of sensitivity parameter determination by preserving complete spatiotemporal field information, capturing global morphological characteristics, and analyzing the influence of parameters on essential characteristic coordinates, providing a more reliable basis for nuclear reactor design optimization and safety margin analysis.

[0083] In one exemplary embodiment, such as Figure 4 As shown, the above "determining the diffusion coordinates of the spatiotemporal field dataset on the manifold structure based on the composite kernel matrix" includes steps 401 to 402. Wherein:

[0084] Step 401: Perform transformation and normalization on the composite kernel matrix to obtain the transition probability matrix.

[0085] The transformation process refers to converting the composite kernel matrix, which describes the similarity between data, into a form more suitable for probabilistic interpretation or graph structure analysis. Its purpose is to lay the foundation for subsequent construction of stochastic processes (such as diffusion processes), typically involving constructing a matrix that reflects the weights of local connections.

[0086] Normalization refers to scaling a transformed matrix so that its row sum or column sum meets the requirements of a specific probability distribution. Specifically, in the embodiments of this application, the purpose of normalization is to ensure that the sum of the elements in each row of the final matrix is ​​1, so that it can be interpreted as a probability transition matrix, where each element represents the probability of transitioning from one state to another.

[0087] The transition probability matrix is ​​a square matrix with rows summing to 1. In this context, it defines the probability that, on a graph composed of data points, one will "difflight" or jump from one data point (node) to another data point through a single random walk. This matrix is ​​central to the theory of diffusion maps, capturing the dynamic nature of the local connectivity of data on a manifold structure.

[0088] In this embodiment, the server performs transformation and normalization on the composite kernel matrix to obtain the transition probability matrix. Specifically, the server first calculates the corresponding diagonal matrix based on the composite kernel matrix, where each diagonal element of the diagonal matrix is ​​the sum of all elements in the corresponding row of the composite kernel matrix; then, the server uses the diagonal matrix to normalize the composite kernel matrix, thereby obtaining the required transition probability matrix.

[0089] In another embodiment, the server employs the graph Laplace concept for transformation. The server first constructs a symmetric adjacency matrix using a composite kernel matrix, then calculates the degree matrix of this adjacency matrix (a diagonal matrix whose diagonal elements are the sum of corresponding rows). Next, the server obtains an asymmetric transition probability matrix by solving for the product of the inverse of the degree matrix and the adjacency matrix. This matrix directly defines the probability of random walks on the data graph.

[0090] Step 402: Perform eigenvalue decomposition on the transition probability matrix to obtain the diffusion coordinates of the spatiotemporal field dataset on the manifold structure.

[0091] The diffusion coordinates, obtained through eigenvalue decomposition, are a new coordinate system used to describe the position of data on the manifold. They consist of the principal eigenvectors of the transition probability matrix. In this coordinate system, the Euclidean distance between data points reflects their reachability to each other through the diffusion process on the original high-dimensional manifold, thus more effectively revealing the clustering structure and inherent patterns of the data.

[0092] In this embodiment, the server performs eigenvalue decomposition on the transition probability matrix to obtain the diffusion coordinates of the spatiotemporal field dataset on the manifold structure. Specifically, the server performs eigenvalue decomposition on the transition probability matrix, extracts the first g principal eigenvectors and their corresponding eigenvalues, and calculates the final diffusion coordinates based on these eigenvalues ​​and eigenvectors.

[0093] In another embodiment, the server performs generalized eigenvalue decomposition to enhance numerical stability. Instead of directly decomposing the transition probability matrix, the server combines it with the degree matrix derived from the composite kernel matrix to form a generalized eigenvalue problem. By solving this problem, the server obtains a set of eigenvalues ​​and eigenvectors. Subsequently, the server ignores the largest eigenvalue (which can be 1) and its corresponding eigenvector, and then selects the eigenvectors corresponding to the next g eigenvalues ​​in descending order. These eigenvectors are then combined row-wise to form the data's diffusion coordinates. This method better handles cases of uneven data distribution.

[0094] In one exemplary embodiment, such as Figure 5 As shown, the above-mentioned "transformation and normalization of the composite kernel matrix to obtain the transition probability matrix" includes steps 501 to 502. Wherein:

[0095] Step 501: Determine the diagonal matrix based on the composite kernel matrix.

[0096] In this case, each diagonal element of the diagonal matrix is ​​the sum of all elements in the corresponding row of the composite kernel matrix.

[0097] A diagonal matrix is ​​the degree matrix derived from a composite kernel matrix. All off-diagonal elements of this matrix are zero, while the diagonal elements have a clear physical meaning—the value of each diagonal element is equal to the sum of all elements in the corresponding row of the composite kernel matrix, representing the sum of the connection strengths of that data point with all other data points (including itself) on the manifold graph, and is called the degree of that node.

[0098] In this embodiment, the server determines the diagonal matrix based on the composite kernel matrix. Specifically, after reading the composite kernel matrix, the server constructs an empty diagonal matrix with the same dimensions, then iterates through each row of the composite kernel matrix, calculates the sum of all elements in that row, and uses the calculation result as the value of the diagonal element at the corresponding position in the diagonal matrix, thus finally generating the required diagonal matrix.

[0099] In another embodiment, the server optimizes the computation process using a matrix operations library. The server directly calls the row summation function from the linear algebra library to perform row-wise summation on the composite kernel matrix, generating a vector containing all row sums. This vector is then used as the diagonal elements to construct a diagonal matrix. This method is more computationally efficient and particularly suitable for handling large-scale kernel matrices.

[0100] Step 502: Normalize the diagonal matrix to obtain the transition probability matrix.

[0101] In this embodiment, the server normalizes the diagonal matrix to obtain the transition probability matrix. Specifically, the server first calculates the inverse of the diagonal matrix, then performs matrix multiplication on the inverse matrix and the composite kernel matrix. The resulting product matrix is ​​the transition probability matrix, where each element represents the corresponding transition probability.

[0102] In another embodiment, the server employs regularization techniques to enhance numerical stability. Before calculating the inverse matrix, the server performs a slight regularization on the diagonal matrix by adding a small positive number to each diagonal element to prevent numerical singularities. The server then uses the inverse of this regularized diagonal matrix to multiply with the composite kernel matrix, ensuring that the generated transition probability matrix is ​​more robust and reliable in numerical computation.

[0103] In one exemplary embodiment, such as Figure 6 As shown, the above-mentioned "performing eigenvalue decomposition on the transition probability matrix to obtain the diffusion coordinates of the spatiotemporal field dataset on the manifold structure" includes steps 601 to 602. Wherein:

[0104] Step 601: Perform eigenvalue decomposition on the transition probability matrix to extract the first g principal eigenvectors and the corresponding eigenvalues.

[0105] Here, the principal eigenvectors refer to the eigenvectors corresponding to the top g largest eigenvalues ​​after sorting the eigenvalues ​​by their magnitudes from largest to smallest. These eigenvectors capture the most persistent and important diffusion direction of data on the manifold and are the foundation for constructing low-dimensional representations.

[0106] Eigenvalues ​​are scalar values ​​that are paired with eigenvectors in eigenvalue decomposition. For a transition probability matrix, the magnitude of the eigenvalues ​​reflects the stability of the diffusion mode represented by the corresponding eigenvector; larger eigenvalues ​​correspond to slower decay and more important diffusion modes.

[0107] In this embodiment, the server performs eigenvalue decomposition on the transition probability matrix to extract the top g principal eigenvectors and their corresponding eigenvalues. Specifically, the server calls a numerical computation library to perform a complete eigenvalue decomposition on the transition probability matrix, then sorts the eigenvalues ​​from largest to smallest magnitude, and selects the top g largest eigenvalues ​​and their corresponding eigenvectors as the output.

[0108] In another embodiment, the server employs an efficient iterative algorithm to process large-scale matrices. Since the transition probability matrix is ​​typically large and sparse, the server uses an iterative algorithm to compute only the first g largest eigenvalues ​​and their corresponding eigenvectors.

[0109] Step 602: Determine the diffusion coordinates based on the eigenvalues ​​and the principal eigenvectors.

[0110] In this embodiment, the server determines the diffusion coordinates based on eigenvalues ​​and principal eigenvectors. Specifically, the server sorts the extracted first g principal eigenvectors according to the magnitude of their corresponding eigenvalues, and then combines these eigenvectors column-wise into a matrix. Each row of this matrix constitutes the diffusion coordinates of the corresponding spatiotemporal field data sample on the manifold structure.

[0111] In another embodiment, the server introduces a weighting mechanism for the eigenvalues. When constructing the diffusion coordinates, the server multiplies each eigenvector by an appropriate power of its corresponding eigenvalue (typically a function related to the time parameter t), thereby emphasizing the diffusion characteristics at different time scales. This weighting process allows the generated diffusion coordinates to better reflect the geometric structure of the data at multiple scales, providing richer feature information for subsequent sensitivity analysis.

[0112] In one exemplary embodiment, such as Figure 7 As shown, the above "determining the composite kernel matrix based on spatial and temporal representations" includes steps 701 to 703. Wherein:

[0113] Step 701: Determine the spatial kernel matrix based on the spatial representation.

[0114] In this system, each element in the spatial kernel matrix corresponds to a spatial similarity. Spatial similarity is used to quantify the similarity in spatial distribution patterns between any two spatiotemporal field data samples; the larger the value, the closer the spatial characteristics of the two samples are.

[0115] Spatial representation refers to the low-dimensional feature representation of spatiotemporal field data in a manifold structure that is related to the spatial dimension. It captures the main patterns and structural features of physical quantities in spatial distribution.

[0116] The spatial kernel matrix is ​​a symmetric matrix composed of the spatial similarity between all sample pairs as its elements. It fully describes the similarity relationship of each sample in the dataset in terms of spatial features.

[0117] Step 702: Determine the time kernel matrix based on the time representation.

[0118] Each element in the time kernel matrix corresponds to a time similarity.

[0119] Temporal representation refers to the low-dimensional feature representation of spatiotemporal field data in a manifold structure that is related to the time dimension. It describes the main laws and dynamic characteristics of the evolution of physical fields over time. Temporal similarity is used to quantify the degree of similarity between any two spatiotemporal field data samples in terms of their temporal evolution laws. The larger the value, the more similar the temporal dynamic characteristics of the two samples are.

[0120] The temporal kernel matrix is ​​a symmetric matrix composed of the temporal similarity between all sample pairs as its elements. It fully describes the similarity relationship of each sample in the dataset in terms of temporal dynamic characteristics.

[0121] Step 703: Determine the composite kernel matrix based on the spatial kernel matrix and the temporal kernel matrix.

[0122] In one embodiment of this application, the server employs a dynamic feature weighting strategy to construct a composite kernel matrix. The server first analyzes the eigenvalue distributions of the spatial and temporal kernel matrices separately, and automatically determines the fusion weights based on the decay rate of their eigenvalues. For kernel matrices with faster eigenvalue decay, indicating a more concentrated information content, the server assigns them higher weights; conversely, for kernel matrices with a more gradual eigenvalue distribution, relatively lower weights are assigned. Through this adaptive weighting method based on information concentration, the server synthesizes the two kernel matrices into a composite kernel matrix.

[0123] In another embodiment, the server introduces a hierarchical fusion strategy based on physical mechanisms. Considering that spatial distribution in reactor physics is typically more constrained, while temporal evolution exhibits stronger stochastic characteristics, the server employs a staged fusion approach: first, principal component extraction is performed on the spatial kernel matrix to retain its main feature patterns; then, these spatial features are collaboratively filtered with the temporal kernel matrix to select feature combinations that are significant in both the spatiotemporal dimensions; finally, a composite kernel matrix is ​​constructed based on these common features. This method effectively highlights physical processes that are significant in both the spatiotemporal dimensions, providing a more reliable foundation for subsequent sensitivity analysis.

[0124] In an exemplary embodiment, the aforementioned spatiotemporal field dataset includes multiple spatiotemporal field data samples, and the aforementioned "determining the time kernel matrix based on time representation" includes:

[0125] Based on spatial representation, the spatial similarity between every two spatiotemporal field data samples is calculated, and a spatial kernel matrix is ​​constructed based on the spatial similarity.

[0126] In this embodiment, the server calculates the spatial similarity between every two spatiotemporal field data samples based on the spatial representation, and constructs a spatial kernel matrix based on the spatial similarity. Specifically, the server iterates through all sample pairs, calculates the inner product of the spatial representation vectors of each sample pair as the spatial similarity, and fills the corresponding positions in the spatial kernel matrix.

[0127] In another embodiment, the server uses a distance-based kernel function to calculate similarity. The server uses a Gaussian radial basis function to calculate spatial similarity, that is, it obtains similarity values ​​based on the Euclidean distance between spatial representation vectors through an exponential function mapping.

[0128] In an exemplary embodiment, the above-mentioned "determining the time kernel matrix based on time representation" includes:

[0129] Based on the time representation, the temporal similarity between every two spatiotemporal field data samples is calculated, and a temporal kernel matrix is ​​constructed based on the temporal similarity.

[0130] In this embodiment of the application, the server calculates the temporal similarity between every two spatiotemporal field data samples based on the time representation, and constructs a temporal kernel matrix based on the temporal similarity.

[0131] In another embodiment, the server uses a linear kernel function to compute the inner product between time representation vectors as the temporal similarity. This approach can better handle nonlinear similarity relationships in spatial features while maintaining the efficiency of temporal similarity computation.

[0132] In an exemplary embodiment, the above-mentioned "determining the composite kernel matrix based on the spatial kernel matrix and the temporal kernel matrix" includes:

[0133] The composite kernel matrix is ​​obtained by multiplying the spatial kernel matrix and the temporal kernel matrix.

[0134] In this embodiment, the server performs a product operation or an addition operation on the spatial kernel matrix and the temporal kernel matrix to obtain a composite kernel matrix. Specifically, when the product operation is selected, the server multiplies the corresponding elements of the two kernel matrices to generate the composite kernel matrix.

[0135] In an exemplary embodiment, the above-mentioned "determining the composite kernel matrix based on the spatial kernel matrix and the temporal kernel matrix" includes:

[0136] The composite kernel matrix is ​​obtained by adding the spatial kernel matrix and the temporal kernel matrix.

[0137] In this embodiment, the server performs a product operation or an addition operation on the spatial kernel matrix and the temporal kernel matrix to obtain a composite kernel matrix. Specifically, when the addition operation is selected, the server adds corresponding elements of the two kernel matrices to generate a composite kernel matrix.

[0138] In another embodiment, the server uses a weighted combination approach for matrix fusion. The server assigns different weight coefficients to the spatial kernel matrix and the temporal kernel matrix based on specific application requirements, and then performs an addition operation on the two weighted matrices. For example, in applications emphasizing spatial distribution characteristics, a higher weight is assigned to the spatial kernel matrix; in applications focusing on dynamic evolution processes, a higher weight is assigned to the temporal kernel matrix.

[0139] In one exemplary embodiment, such as Figure 8 As shown, the above-mentioned "projecting the spatiotemporal field dataset onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure" includes steps 801 to 802. Wherein:

[0140] Step 801: For each spatiotemporal field data sample, perform singular value decomposition on the spatiotemporal field data sample to obtain the left singular matrix and the right singular matrix.

[0141] Singular value decomposition (SVD) is a mathematical method that decomposes any matrix into the product of three specific matrices. For spatiotemporal field data matrices, this method can separate their main variation patterns into different subspaces, making it an effective tool for extracting the essential features of the data.

[0142] The left singular matrix is ​​the left unitary matrix obtained in singular value decomposition, and its column vectors form an orthonormal basis of the original data matrix in the row space. For spatiotemporal field data, rows usually correspond to spatial locations, so the column vectors of this matrix represent the typical spatial distribution patterns present in the data.

[0143] The right singular matrix is ​​a right unitary matrix obtained from singular value decomposition. Its column vectors form an orthonormal basis of the original data matrix in the column space. For spatiotemporal field data, columns typically correspond to time steps; therefore, the column vectors of this matrix describe the evolution of various spatial patterns over time.

[0144] In this embodiment, the server performs singular value decomposition (SVD) on each spatiotemporal field data sample to obtain a left singular matrix and a right singular matrix. Specifically, the server treats each spatiotemporal field data sample as a two-dimensional matrix, where rows represent spatial locations and columns represent time steps. By calling a numerical computation library to execute a standard singular value decomposition algorithm, the server obtains the corresponding left singular matrix, singular value matrix, and right singular matrix.

[0145] In another embodiment, the server employs truncated singular value decomposition to improve computational efficiency. Based on a preset energy threshold or the number of components to retain, the server only computes the top k largest singular values ​​and their corresponding left and right singular vectors. This method significantly reduces computational complexity and storage requirements while preserving the main characteristics of the data, making it particularly suitable for processing high-dimensional spatiotemporal field data.

[0146] Step 802: Use the column space of the left singular matrix as the spatial representation and the column space of the right singular matrix as the temporal representation.

[0147] Here, the column space refers to the vector space spanned by all the column vectors of the matrix. The column space of the left singular matrix contains all possible spatial distribution patterns of the original spatiotemporal field data; the column space of the right singular matrix contains all possible temporal evolution patterns of these spatial patterns.

[0148] In this embodiment, the server uses the column space of the left singular matrix as the spatial representation and the column space of the right singular matrix as the temporal representation. Specifically, the server directly uses the first few column vectors of the left singular matrix as the basis vectors of the spatial representation and the first few column vectors of the right singular matrix as the basis vectors of the temporal representation, thereby obtaining a low-dimensional representation of each spatiotemporal field data sample on the manifold structure.

[0149] In another embodiment, the server constructs a weighted spatial-temporal representation by combining singular values. The server multiplies each column vector of the left singular matrix by its corresponding singular value to obtain a weighted spatial representation, thus assigning greater weight to more important spatial patterns; similarly, a similar weighting process is applied to the right singular matrix to obtain a weighted temporal representation. This weighting method more accurately reflects the relative importance of different spatial and temporal patterns in the original data.

[0150] In one exemplary embodiment, the method further includes:

[0151] Step 1: Project reactor physics field samples onto Grassmann manifold

[0152] In reactor design and analysis, the goal is to understand and represent samples of reactor physical fields. The spatiotemporal distribution of these data is shown. To efficiently process this data, it is projected onto a Grassmann manifold. The Grassmann manifold is an important mathematical structure, particularly suitable for representing subspaces and the relationships between them.

[0153] Assumption It has a low-rank structure (i.e., the number of linearly independent columns is less than the total number of columns). For Perform Singular Value Decomposition (SVD): in It is a diagonal matrix containing singular values. These singular values ​​reflect the magnitude of variance in different directions of the data. and These are the left singular matrix and the right singular matrix, respectively, representing the projections of the data onto the spatial and temporal dimensions.

[0154] Here, p represents the Grassmann dimension preserved in the singular value decomposition, which is an important parameter that determines... and The rank of p affects the accuracy of the data representation on the Grassmann manifold. Choosing an appropriate p value can help reduce computational complexity while preserving important information. This value can be specified by the user, for example, it can be any of the input matrices. The lowest rank in the system.

[0155] The Grassmann manifold is defined as: and These represent the set of p-dimensional subspaces (or planes) embedded in m-dimensional (or n-dimensional) Euclidean space.

[0156] Step 2: Define the kernel mapping function and construct the kernel matrix

[0157] In machine learning and data analytics, kernel methods are a powerful tool that can capture more complex patterns by mapping data to a higher-dimensional space.

[0158] Define a kernel mapping function, denoted as Two points on the Grassmann manifold (i.e. The two subspaces in the manifold are mapped to a real value. The Grassmann kernel captures the similarity or distance between different points on the manifold. Its form is: .here and These are two subspaces on the Grassmann manifold. The value of the kernel function reflects the similarity between these two subspaces. By choosing an appropriate kernel function, the geometric relationships between different points on the manifold can be effectively captured.

[0159] Based on this kernel mapping function, a kernel matrix can be constructed, represented as: and For example, optionally, the mapping kernel function used is defined as:

[0160]

[0161] in, This represents the Frobenius norm. The Frobenius norm is the Euclidean norm of a matrix, calculated as the square root of the sum of the squares of all its elements. A composite kernel matrix is ​​obtained by multiplying the corresponding kernels using the Hadamard product, expressed as: The Hadamard product refers to element-wise multiplication. A composite kernel matrix can also be created by directly adding two kernel matrices: .

[0162] Step 3: Construct a random walk model

[0163] Step 3.1: Construct a diagonal matrix

[0164] First, construct a diagonal matrix. Its diagonal elements Defined as state Total number of connections ,here, Representing state and state The connection weights between states. By calculating the number of connections for each state, we can reflect the degree of each state, that is, the activity level of the state.

[0165] After constructing the diagonal matrix, the stationary distribution of the random walk can be determined. :

[0166]

[0167] Here, This indicates that after a long period of operation, the random walk remains in the state. The probability of.

[0168] Step 3.2: Normalize the kernel matrix

[0169] Next, the connection matrix is ​​normalized, and the normalized kernel matrix is ​​defined. for: The purpose of this normalization is to adjust the kernel value in order to more accurately represent the relative transition probabilities between different states.

[0170] Subsequently, the normalized kernel matrix was used Construct the transition probability matrix , used to describe the probability of transitioning from one state to another on a Grassmann manifold:

[0171]

[0172] Represents from state Transition to state The probability is calculated using the probability matrix. This probability matrix is ​​the core of the random walk model and can effectively describe the dynamic relationships between states.

[0173] Step 4: Perform eigenvalue decomposition on the transition probability matrix

[0174] Performing eigenvalue decomposition on matrix P yields the following results: eigenvectors and corresponding eigenvalues , so that: ,in ,because in Indicates the capability threshold, usually The accuracy is 0.995. This means that by selecting the first g representative eigenvectors, an accuracy of 0.995 can be achieved. Since g is much smaller than N, a very small number of eigenvectors g can be used to characterize N spatial field variables. The value of g is generally chosen based on experience.

[0175] Feature vector It provides diffusion coordinates on the manifold, reflecting the main structural features of the data.

[0176] For a probability matrix P, the first eigenvalue of the eigenvalue decomposition is usually... The corresponding eigenvector is a constant vector. This eigenvalue represents a uniform distribution and usually does not provide additional information, so it can be omitted in practical applications. The main focus is on... Initial eigenvalues ​​and eigenvectors.

[0177] Eigenvalue decay refers to the rapid decrease in smaller eigenvalues ​​relative to larger eigenvalues. This property indicates that only a few eigenvalues ​​play a significant role in the geometric structure of the data. Typically, eigenvalue decay allows us to retain only the first g diffusion coordinates, which are sufficient to capture the basic geometry of the data. This choice not only simplifies data representation but also preserves key information, thereby improving computational efficiency and the feasibility of analysis.

[0178] For each sample The Grassmann diffusion coordinates are calculated as follows:

[0179] These coordinates are used to describe the location and structure of the data on the Grassmann manifold.

[0180] Step 5: Build a machine learning model and perform sensitivity analysis.

[0181] First, we use the parameter variable X as the feature and the manifold coordinates as the prediction target to construct a machine learning model. Various machine learning algorithms can be chosen for modeling, such as the RandomForest Regressor.

[0182] Stochastic gradient boosting regressors. These models perform well when dealing with nonlinear relationships and high-dimensional data, effectively capturing complex patterns in the data.

[0183] Sensitivity analysis is used to evaluate the impact of input variables on the model output. In this step, sensitivity analysis is performed using the SALIB library, specifically using the Sobol or Morris methods. These methods help to understand the contribution of each input feature to the model output in manifold coordinates Θ.

[0184] In this embodiment, g can be very small, for example, g=3. In this case, the three-dimensional spatiotemporal field distribution (m,n) is reduced to three parameters (population coordinates). By constructing a machine learning model, the importance of the input variable X relative to these three coordinates can be obtained.

[0185] Clearly, these three popular coordinates are spatially or temporally independent of the actual reactor geometry. Therefore, compared to traditional sensitivity analysis based on the maximum value of the three-dimensional (power) distribution (worst operating point), this method avoids the overlap and intersection of sensitivity weights for different parameters at different times. Taking two random variables as an example, the sensitivity plot at this time is as follows: Figure 9 As shown.

[0186] Figure 9 This is a schematic diagram showing the sensitivity weight distribution of different input variables across various dimensions of the manifold coordinates. From Figure 9 As can be seen, variables 1 and 2 exhibit significant differences in sensitivity across different manifold coordinate dimensions: for the first dimension of the manifold coordinate ( Regarding the third dimension of the manifold coordinates, the sensitivity weight of variable 1 is significantly higher than that of variable 2, indicating that this dimension mainly captures the system feature patterns dominated by variable 1; while in the third dimension of the manifold coordinates ( On the dimension, the weight values ​​of variable 1 and variable 2 are relatively close, indicating that this dimension reflects the coupling effect of the two variables working together.

[0187] This hierarchical sensitivity distribution reveals the essential structure of parameter influence: Variable 1 exists in multiple dimensions (especially the dominant dimension). ) all maintain a high weight, indicating that they play a decisive role in the overall shape of the three-dimensional spatiotemporal field distribution; while variable 2 only has a high weight in certain specific dimensions (such as The effect is significant, but its scope of influence is relatively limited. This provides clear guidance: in the reactor design phase, priority should be given to the precise control and optimization of variable 1, as it has a global impact on system behavior; at the same time, attention should be paid to the coupling effect between variable 1 and variable 2 in specific dimensions to avoid potential nonlinear risks. This sensitivity weighting analysis method breaks through the limitations of traditional single-index evaluation. Through multi-dimensional decomposition of manifold coordinates, it achieves a refined characterization of the parameter influence, providing a theoretical basis for the controllability design and safety margin improvement of complex engineering systems.

[0188] In one exemplary embodiment, the method further includes:

[0189] Step 1: Convert the reactor physics field samples into a spatiotemporal field dataset. For each spatiotemporal field data sample in the spatiotemporal field dataset, perform singular value decomposition to obtain the left singular matrix and the right singular matrix.

[0190] Step 2: Use the column space of the left singular matrix as the spatial representation and the column space of the right singular matrix as the temporal representation.

[0191] Step 3: Based on the spatial representation, calculate the spatial similarity between every two spatiotemporal field data samples, and construct a spatial kernel matrix based on the spatial similarity; where each element in the spatial kernel matrix corresponds to a spatial similarity; and based on the temporal representation, calculate the temporal similarity between every two spatiotemporal field data samples, and construct a temporal kernel matrix based on the temporal similarity; where each element in the temporal kernel matrix corresponds to a temporal similarity.

[0192] Step 4: Perform product or addition operations on the spatial kernel matrix and the temporal kernel matrix to obtain the composite kernel matrix.

[0193] Step 5: Determine the diagonal matrix based on the composite kernel matrix; where each diagonal element of the diagonal matrix is ​​the sum of all elements in the corresponding row of the composite kernel matrix.

[0194] Step 6: Normalize the diagonal matrix to obtain the transition probability matrix.

[0195] Step 7: Perform eigenvalue decomposition on the transition probability matrix to extract the first g principal eigenvectors and their corresponding eigenvalues.

[0196] Step 8: Determine the diffusion coordinates based on the eigenvalues ​​and the principal eigenvectors.

[0197] Step 9: Based on the reactor physical field samples and diffusion coordinates, determine the sensitivity parameters that affect the spatiotemporal field distribution; the sensitivity parameters are used to guide the design optimization or safety margin analysis of the nuclear reactor.

[0198] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0199] Based on the same inventive concept, this application also provides a nuclear reactor sensitivity parameter determination apparatus for implementing the above-described method for determining nuclear reactor sensitivity parameters. The solution provided by this apparatus is similar to the implementation described in the above-described method. Therefore, the specific limitations of one or more embodiments of the nuclear reactor sensitivity parameter determination apparatus provided below can be found in the limitations of the nuclear reactor sensitivity parameter determination method described above, and will not be repeated here.

[0200] In one exemplary embodiment, such as Figure 10 As shown, a device for determining the sensitivity parameters of a nuclear reactor is provided, comprising: a projection module 901, a matrix determination module 902, a coordinate determination module 903, and a parameter determination module 904, wherein:

[0201] Projection module 901 is used to convert reactor physics field samples into spatiotemporal field datasets and project the spatiotemporal field datasets onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field datasets on the manifold structure.

[0202] The matrix determination module 902 is used to determine the composite kernel matrix based on spatial and temporal representations;

[0203] The coordinate determination module 903 is used to determine the diffusion coordinates of the spatiotemporal field dataset on the manifold structure based on the composite kernel matrix;

[0204] The parameter determination module 904 is used to determine the sensitivity parameters that affect the spatiotemporal field distribution based on the reactor physical field samples and diffusion coordinates; the sensitivity parameters are used to guide the design optimization or safety margin analysis of the nuclear reactor.

[0205] In an exemplary embodiment, the coordinate determination module 903 is specifically used to perform transformation and normalization processing on the composite kernel matrix to obtain the transition probability matrix; and to perform eigenvalue decomposition processing on the transition probability matrix to obtain the diffusion coordinates of the spatiotemporal field dataset on the manifold structure.

[0206] In an exemplary embodiment, the coordinate determination module 903 is specifically used to determine a diagonal matrix based on a composite kernel matrix; wherein each diagonal element of the diagonal matrix is ​​the sum of all elements in the corresponding row of the composite kernel matrix; and the diagonal matrix is ​​normalized to obtain a transition probability matrix.

[0207] In an exemplary embodiment, the coordinate determination module 903 is specifically used to perform eigenvalue decomposition on the transition probability matrix, extract the first g principal eigenvectors and the eigenvalues ​​corresponding to the principal eigenvectors, and determine the diffusion coordinates based on the eigenvalues ​​and principal eigenvectors.

[0208] In an exemplary embodiment, the aforementioned spatiotemporal field dataset includes multiple spatiotemporal field data samples. The aforementioned matrix determination module 902 is specifically used to calculate the spatial similarity between every two spatiotemporal field data samples based on the spatial representation, and construct a spatial kernel matrix based on the spatial similarity; wherein each element in the spatial kernel matrix corresponds to a spatial similarity; calculate the temporal similarity between every two spatiotemporal field data samples based on the temporal representation, and construct a temporal kernel matrix based on the temporal similarity; wherein each element in the temporal kernel matrix corresponds to a temporal similarity; and perform a product operation or an addition operation on the spatial kernel matrix and the temporal kernel matrix to obtain a composite kernel matrix.

[0209] In an exemplary embodiment, the projection module 901 is specifically used to perform singular value decomposition on each spatiotemporal field data sample to obtain a left singular matrix and a right singular matrix; the column space of the left singular matrix is ​​used as a spatial representation, and the column space of the right singular matrix is ​​used as a temporal representation.

[0210] The modules in the aforementioned nuclear reactor sensitivity parameter determination device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0211] In one embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above method embodiments.

[0212] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps in the above method embodiments.

[0213] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0214] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0215] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0216] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for determining sensitivity parameters of a nuclear reactor, characterized in that, The method includes: The reactor physics field samples are converted into a spatiotemporal field dataset, and the spatiotemporal field dataset is projected onto a manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure. Based on the spatial and temporal representations, determine the composite kernel matrix; Based on the composite kernel matrix, the diffusion coordinates of the spatiotemporal field dataset on the manifold structure are determined; Based on the reactor physical field sample and the diffusion coordinates, the sensitivity parameters affecting the spatiotemporal field distribution are determined; the sensitivity parameters are used to guide the design optimization or safety margin analysis of the nuclear reactor.

2. The method according to claim 1, characterized in that, Determining the diffusion coordinates of the spatiotemporal field dataset on the manifold structure based on the composite kernel matrix includes: The composite kernel matrix is ​​transformed and normalized to obtain the transition probability matrix; The transition probability matrix is ​​subjected to eigenvalue decomposition to obtain the diffusion coordinates of the spatiotemporal field dataset on the manifold structure.

3. The method according to claim 2, characterized in that, The transformation and normalization of the composite kernel matrix to obtain the transition probability matrix includes: A diagonal matrix is ​​determined based on the composite kernel matrix; wherein each diagonal element of the diagonal matrix is ​​the sum of all elements in the corresponding row of the composite kernel matrix; The diagonal matrix is ​​normalized to obtain the transition probability matrix.

4. The method according to claim 2, characterized in that, The step of performing eigenvalue decomposition on the transition probability matrix to obtain the diffusion coordinates of the spatiotemporal field dataset on the manifold structure includes: The transition probability matrix is ​​subjected to eigenvalue decomposition to extract the first g principal feature vectors and the feature values ​​corresponding to the principal feature vectors; The diffusion coordinates are determined based on the eigenvalues ​​and the principal eigenvectors.

5. The method according to claim 1, characterized in that, The determination of the composite kernel matrix based on the spatial and temporal representations includes: Based on the spatial representation, a spatial kernel matrix is ​​determined; wherein each element in the spatial kernel matrix corresponds to a spatial similarity. Based on the time representation, a time kernel matrix is ​​determined; wherein each element in the time kernel matrix corresponds to a time similarity. The composite kernel matrix is ​​determined based on the spatial kernel matrix and the temporal kernel matrix.

6. The method according to claim 5, characterized in that, The spatiotemporal field dataset includes multiple spatiotemporal field data samples. The determination of the time kernel matrix based on the time representation includes: Based on the spatial representation, the spatial similarity between every two spatiotemporal field data samples is calculated, and the spatial kernel matrix is ​​constructed based on the spatial similarity.

7. The method according to claim 6, characterized in that, The determination of the time kernel matrix based on the time representation includes: Based on the time representation, the time similarity between every two spatiotemporal field data samples is calculated, and the time kernel matrix is ​​constructed based on the time similarity.

8. The method according to claim 5, characterized in that, Determining the composite kernel matrix based on the spatial kernel matrix and the temporal kernel matrix includes: The composite kernel matrix is ​​obtained by performing a product operation on the spatial kernel matrix and the temporal kernel matrix.

9. The method according to claim 5, characterized in that, Determining the composite kernel matrix based on the spatial kernel matrix and the temporal kernel matrix includes: The composite kernel matrix is ​​obtained by adding the spatial kernel matrix and the temporal kernel matrix.

10. The method according to claim 6, characterized in that, The step of projecting the spatiotemporal field dataset onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field dataset on the manifold structure includes: For each of the aforementioned spatiotemporal field data samples, singular value decomposition is performed on the spatiotemporal field data sample to obtain a left singular matrix and a right singular matrix. The column space of the left singular matrix is ​​used as the spatial representation, and the column space of the right singular matrix is ​​used as the temporal representation.

11. A device for determining the sensitivity parameters of a nuclear reactor, characterized in that, The device includes: The projection module is used to convert reactor physics field samples into spatiotemporal field datasets and project the spatiotemporal field datasets onto the manifold structure to obtain the spatial and temporal representations of the spatiotemporal field datasets on the manifold structure. The matrix determination module is used to determine the composite kernel matrix based on spatial and temporal representations. The coordinate determination module is used to determine the diffusion coordinates of the spatiotemporal field dataset on the manifold structure based on the composite kernel matrix; The parameter determination module is used to determine the sensitive parameters that affect the spatiotemporal field distribution based on reactor physics field samples and diffusion coordinates; the sensitive parameters are used to guide the design optimization or safety margin analysis of nuclear reactors.

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