Method and system for processing a neutron transport equation in a nuclear reactor

Abstract

The embodiment of the application discloses a kind of methods and systems of processing nuclear reaction neutron transport equation, it is related to nuclear power technology field, method includes: obtaining the neutron flux matrix associated with multiple first neutron flux, multiple first neutron flux in it is obtained by source iteration processing to neutron transport equation, neutron transport equation is obtained based on the transport process of neutron in nuclear reaction;In the case where neutron flux matrix is processed in dimension reduction, according to the neutron flux matrix after dimension reduction processing, determine the theory matrix, and according to theory matrix and multiple first neutron flux, determine theoretical convergence neutron flux;Based on theoretical convergence neutron flux, source iteration processing is carried out to neutron transport equation, the convergence speed of using source iteration processing neutron transport equation can be improved, and the calculation efficiency of neutron transport is improved.

Description

Technical Field

[0001] This application relates to the field of nuclear power technology, and in particular to a method and system for processing neutron transport equations in nuclear reactions. Background Technology

[0002] The neutron transport equations are fundamental equations describing the transport of neutrons in matter. They comprehensively consider various physical processes such as neutron production, absorption, and scattering, providing a solid theoretical foundation for research in many fields, including nuclear reactor physics, radiation protection, and neutron detection. Calculating the neutron transport equations not only helps engineers optimize reactor design and ensure the reactor reaches criticality during operation, but also enables the assessment of reactor thermal performance and safety, as well as the prediction of the impact of fuel consumption and fission product accumulation on reactor performance. This is crucial for the design, safety analysis, and operational control of nuclear reactors.

[0003] In related technologies, numerical methods such as source iteration are often used to simulate and analyze neutron transport and calculate neutron transport equations. However, source iteration may have a slow convergence rate, affecting the computational efficiency of neutron transport.

[0004] It is evident that the current calculation of the neutron transport equation suffers from low computational efficiency.

[0005] Application content

[0006] In view of this, one of the objectives of this application is to provide a method and system for processing neutron transport equations in nuclear reactions, which can improve the convergence speed of processing neutron transport equations using source iteration and improve the computational efficiency of neutron transport.

[0007] To achieve the above objectives, the technical solution of this application is implemented as follows:

[0008] In a first aspect, embodiments of this application provide a method for processing neutron transport equations in nuclear reactions, including:

[0009] The neutron flux matrix associated with multiple first neutron fluxes is obtained. These multiple first neutron fluxes are obtained by source iteration processing of the neutron transport equation, which is constructed based on the neutron transport process in nuclear reactions.

[0010] With the neutron flux matrix reduced in dimension, the theoretical matrix is ​​determined based on the dimensionality-reduced neutron flux matrix.

[0011] Based on the theoretical matrix and multiple first neutron fluxes, the theoretical convergent neutron flux is determined;

[0012] The neutron transport equation is processed by source iteration based on theoretically convergent neutron flux.

[0013] In one possible implementation, when the neutron flux matrix is ​​reduced in dimension, the theoretical matrix is ​​determined based on the reduced neutron flux matrix, including:

[0014] Based on multiple first neutron fluxes, determine the first matrix and the second matrix, which are adjacent term difference matrices.

[0015] The second matrix is ​​reduced in dimensionality, and the neutron flux matrix includes the first and second matrices.

[0016] Based on the dimension-reduced neutron flux matrix, the theoretical matrix is ​​determined, including:

[0017] The theoretical matrix is ​​determined based on the first matrix and the second matrix after dimensionality reduction.

[0018] In one possible implementation, the theoretical matrix is ​​determined based on the first matrix and the dimension-reduced second matrix, including:

[0019] Perform singular value decomposition on the second matrix to obtain the left singular matrix, the singular value matrix, and the right singular matrix;

[0020] According to the preset truncation rank, the left singular matrix, the singular value matrix and the right singular matrix are truncated in sequence to obtain the truncated left singular matrix, the truncated singular value matrix and the truncated right singular matrix.

[0021] The theoretical matrix is ​​determined based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

[0022] The second matrix after dimensionality reduction includes the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

[0023] In one possible implementation, the theoretical matrix is ​​determined based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix, including:

[0024] Obtain the transpose of the truncated left singular matrix and the inverse of the truncated singular value matrix;

[0025] The theoretical matrix is ​​determined based on the transpose of the left singular matrix, the first matrix, the truncated right singular matrix, and the inverse of the singular value matrix.

[0026] In one possible implementation, the theoretical convergent neutron flux is determined based on the theoretical matrix and multiple first neutron fluxes, including:

[0027] Obtain at least one eigenvalue of the theoretical matrix;

[0028] When all eigenvalues ​​of the theoretical matrix are less than a preset threshold, the theoretical convergent neutron flux is determined based on the theoretical matrix, multiple first neutron fluxes, and the identity matrix.

[0029] In one possible implementation, after obtaining at least one eigenvalue of the theoretical matrix, the method further includes:

[0030] If the largest eigenvalue in at least one eigenvalue of the theoretical matrix is ​​greater than or equal to a preset threshold, the number of iterations of the source iteration process for the neutron transport equation is increased to obtain at least one second neutron flux and a new theoretical matrix, until all eigenvalues ​​of the new theoretical matrix are less than the preset threshold, at which point the source iteration process is stopped.

[0031] The theoretical convergent neutron flux is determined based on the new theoretical matrix, multiple first neutron fluxes, at least one second neutron flux, and the identity matrix.

[0032] Secondly, embodiments of this application provide a system for processing neutron transport equations in nuclear reactions, the system comprising:

[0033] The acquisition module is used to acquire the neutron flux matrix associated with multiple first neutron fluxes. The multiple first neutron fluxes are obtained by source iteration processing of the neutron transport equation, which is constructed based on the neutron transport process in nuclear reactions.

[0034] The first determining module is used to determine the theoretical matrix based on the dimension-reduced neutron flux matrix after dimensionality reduction.

[0035] The second determining module is used to determine the theoretical convergent neutron flux based on the theoretical matrix and multiple first neutron fluxes.

[0036] The iterative processing module is used to perform source iterative processing on the neutron transport equation based on the theoretically convergent neutron flux.

[0037] Thirdly, embodiments of this application provide an electronic device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, it implements the method for processing neutron transport equations in nuclear reactions provided in the first aspect.

[0038] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by one or more processors, implements a method for processing neutron transport equations in nuclear reactions provided in the first aspect.

[0039] Fifthly, embodiments of this application provide a computer program product, which includes a computer program that, when executed by one or more processors, implements a method for processing neutron transport equations in nuclear reactions provided in the first aspect.

[0040] This application provides a method for processing neutron transport equations in nuclear reactions. It obtains a neutron flux matrix associated with multiple first neutron fluxes, which are obtained through source iteration processing of the neutron transport equations, which are constructed based on the neutron transport process in nuclear reactions. Next, after dimensionality reduction of the neutron flux matrix, a theoretical matrix is ​​determined based on the dimensionality-reduced neutron flux matrix. Then, based on the theoretical matrix and the multiple first neutron fluxes, a theoretically convergent neutron flux is determined. Finally, source iteration processing of the neutron transport equations can be performed based on the theoretically convergent neutron flux, thereby improving the convergence speed and computational efficiency of neutron transport. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. It should be understood that the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A flowchart illustrating a method for processing neutron transport equations in nuclear reactions, provided as an embodiment of this application;

[0043] Figure 2 A comparative experimental diagram illustrating a method for processing neutron transport equations in nuclear reactions provided in this application embodiment;

[0044] Figure 3 A schematic diagram of the functional modules of a system for processing neutron transport equations in nuclear reactions, provided in an embodiment of this application;

[0045] Figure 4 This is a diagram illustrating the internal structure of an electronic device as provided in an embodiment of this application.

[0046] Explanation of reference numerals in the attached figures:

[0047] The system 300 for processing neutron transport equations in nuclear reactions includes an acquisition module 310, a first determination module 320, a second determination module 330, and an iterative processing module 340. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0049] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0050] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0051] In various embodiments of this application, the expression "or" or "at least one of A and / or B" includes any combination or all combinations of the words listed simultaneously. For example, the expression "A or B" or "at least one of A and / or B" may include A, may include B, or may include both A and B.

[0052] In the description of this application, it should be noted that if terms such as "upper," "lower," "inner," or "outer" are used to indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of the invention is usually placed during use, they are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0053] Furthermore, the terms "first" and "second" are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0054] It should be noted that, where there is no conflict, the features in the embodiments of this application can be combined with each other.

[0055] Furthermore, in the embodiments of this application, the term "connection" can refer to "electrical connection" or "direct connection." "Electrical connection" can refer to two components being directly electrically connected, or it can refer to two components being electrically connected via one or more normally open tubes or other components.

[0056] To facilitate a better understanding of the solutions in the embodiments of this application, the relevant technologies will be introduced first below.

[0057] The neutron transport equation describes the transport process of a neutron population within a medium. The fundamental physical quantity in the neutron transport equation is the neutron angular flux, also known as neutron density. The neutron angular flux is a function of space, time, energy, and direction of motion. Therefore, under steady-state conditions, the neutron transport equation can be written as a differential-integral equation dependent on space, time, energy, and direction.

[0058] Neutron flux refers to the number of neutrons passing through a unit area per unit time. In nuclear reactions, neutron flux is a measure of the probability of a neutron interacting with matter. For example, in a nuclear reactor, a higher neutron flux means more neutrons are available to initiate nuclear fission. The power of a nuclear reactor is closely related to its neutron flux. The reactor power can be adjusted by controlling the neutron flux. When power needs to be increased, measures can be taken to increase the neutron flux, such as removing control rods (control rods absorb neutrons, and removing them increases the neutron flux). Conversely, when power needs to be reduced, control rods are inserted to decrease the neutron flux.

[0059] The neutron transport equation, under steady-state conditions, can be written in the form of a differential-integral equation. This equation has strong nonlinearity and can generally be solved numerically.

[0060] Source iteration is a numerical solution method used to solve the neutron transport equations. Specifically, it can directly iterate based on the neutron production and transport processes. The discretized neutron transport equations form a large system of nonlinear (linear) equations, whose numerical solution is very complex, computationally intensive, and time-consuming. For the discretized neutron transport equations, multiple levels of iterative methods are required for solving them; in such cases, source iteration can be used.

[0061] To address the technical problems in the background art, embodiments of this application provide a method and system for processing neutron transport equations in nuclear reactions. The method for processing neutron transport equations in nuclear reactions provided by embodiments of this application will be described first below.

[0062] The following embodiments of this application can improve the convergence speed of neutron transport equations using source iteration and improve the computational efficiency of neutron transport. The process of processing neutron transport equations using source iteration will be illustrated below.

[0063] In a reactor, assuming isotropic heat dissipation and a given neutron interface, the expression for the neutron transport equation corresponding to the nuclear reaction can be set as formula (1):

[0064] a+b=c+d, (1)

[0065] in,

[0066]

[0067] The total power P of the reactor can be expressed by formula (2):

[0068]

[0069] In formula (1-1):

[0070] r represents the spatial position of the reactor in a three-dimensional Cartesian coordinate system. E represents the direction of motion of the neutron, and E represents the energy distribution of the neutron. Let r be the spatial location to be solved. The angular flux of a continuous neutron at energy E along a spatial angle (direction of motion). 'a' represents the neutron at a certain spatial position 'r' along a certain direction of motion. And the loss or gain rate when energy E moves. Specifically, Let ψ represent the gradient of the neutron angular flux with respect to the spatial position r, that is, the rate of change of the neutron angular flux at a spatial position. Indicates the direction of neutron motion The rate of change of angular flux.

[0071] In formula (1-2):

[0072] Σ t (r,E) represents the total neutron reaction cross section of the material at spatial location r and energy E in the reactor, which can describe the macroscopic cross section of any reaction (absorption or scattering) between neutrons and the material. In terms of spatial position r and direction of motion At energy E, the probability of a neutron reacting with the material across the entire cross-section per unit time. In the neutron transport equation, equation (1-2), as a loss term, can represent the neutron's position r and direction of motion in space. The rate of reaction decreases at energy E.

[0073] In formula (1-3):

[0074] Σ s (r,E′→E) represents the scattering cross section at spatial position r where the neutron's energy transfers from E' to E, describing the probability of a neutron scattering from energy E' to energy E. φ(r,E′) is the neutron flux (distinguished from angular flux) at spatial position r and energy E', representing the number of neutrons per unit time, per unit area, and per unit energy range.

[0075] In formula (1-4):

[0076] λ represents the scalar eigenvalue, or, in other literature, the neutron effective multiplication factor k. eff It means, and χ(r,E) is the fission neutron spectrum at energy E at spatial location r (the energy distribution of neutrons produced by the fission reaction). Σ f (r, E′) represents the cross section (probability) of the fission reaction, and υ is the number of neutrons produced in each fission. d can be expressed as: at position r, neutrons produced by the fission reaction are released at various energies E′ and concentrated at energy E.

[0077] In formula (2), κ represents the energy released in each fission.

[0078] Define an angle integral operation as follows:

[0079]

[0080] Define the scalar neutron φ:

[0081]

[0082] Define neutron flow J:

[0083]

[0084] Regarding the above formula, Indicates a transport leakage item. The collision term can be simplified to an operator acting on... Regarding angular flux:

[0085]

[0086] in, For the scattering source term, it can be simplified to c represents the scattering efficiency at different energies. For strong scattering systems, c usually approaches 1.0.

[0087] Represented as fission source terms (after eigenvalue normalization), they are simplified as follows:

[0088] The source iteration process for formula (1) above may include the following steps:

[0089] Step (1), initialization.

[0090] Before the iteration, the neutron standard flux φ (0) and eigenvalues ​​λ (0) Make an initial estimate. The initial estimate can be obtained through various techniques (such as an initial guess given by the program or solving a similar diffusion problem).

[0091] Step (2), transport calculation given a fixed source.

[0092] First, utilize the latest neutron standard flux φ (n) and eigenvalues ​​λ (n) Estimate the scattering source and the fission source, i.e., solve for c and d in formula (1). Then, based on the given scattering source and fission source, perform neutron transport calculations, i.e., solve for a and b in formula (1).

[0093]

[0094] Based on the definition of standard flux, equation (6) can be transformed into equation (7):

[0095] φ (n+1) =<ψ (n+1) >=L -1 M, (7)

[0096] in,

[0097]

[0098] That is, formula (7) can be written as:

[0099]

[0100] Formula (7) can be further transformed into formula (9):

[0101] φ (n+1) =Aφ (n) (9)

[0102] Step (3) Update the eigenvalues ​​and neutron standard flux according to formulas (10) and (11), and check the convergence criteria according to formulas (12) and (13).

[0103]

[0104] If the updated eigenvalues ​​and calibrated fluxes simultaneously satisfy the eigenvalue convergence criterion (13) and the neutron calibrated flux convergence criterion (12), then the iterative calculation is performed; otherwise, the process jumps to step (2).

[0105] Please see below. Figure 1 , Figure 1 The flowchart illustrates a method for processing neutron transport equations in nuclear reactions, provided as an embodiment of this application. This method can be applied to electronic devices, including personal computers, servers, mobile devices, cloud computing platforms, and supercomputers. The method specifically includes the following steps:

[0106] Step 110: Obtain the neutron flux matrix associated with multiple first neutron fluxes. The multiple first neutron fluxes are obtained by source iteration processing of the neutron transport equation, which is constructed based on the neutron transport process in nuclear reactions.

[0107] Step 120: After reducing the dimensionality of the neutron flux matrix, determine the theoretical matrix based on the reduced dimensionality neutron flux matrix.

[0108] Step 130: Determine the theoretical convergent neutron flux based on the theoretical matrix and multiple first neutron fluxes.

[0109] Step 140: Perform source iteration processing on the neutron transport equation based on the theoretically convergent neutron flux.

[0110] This application provides a method for processing neutron transport equations in nuclear reactions. It obtains a neutron flux matrix associated with multiple first neutron fluxes, which are obtained through source iteration processing of the neutron transport equations, which are constructed based on the neutron transport process in nuclear reactions. Next, after dimensionality reduction of the neutron flux matrix, a theoretical matrix is ​​determined based on the dimensionality-reduced neutron flux matrix. Then, based on the theoretical matrix and the multiple first neutron fluxes, a theoretically convergent neutron flux is determined. Finally, source iteration processing of the neutron transport equations can be performed based on the theoretically convergent neutron flux, thereby improving the convergence speed and computational efficiency of neutron transport.

[0111] The following will discuss how Figure 1 The steps of the Chinese method are explained in detail.

[0112] In step 110, the electronic device may acquire a neutron flux matrix associated with a plurality of first neutron fluxes.

[0113] The first neutron flux can be found in the aforementioned introduction to neutron flux, which is the number of neutrons passing through a unit area per unit time. The first neutron flux includes multiple neutron numbers, and its unit is n / cm². 2 ·s (neutrons per square centimeter per second).

[0114] Multiple first neutron fluxes can be obtained by the electronic device performing multiple iterations of the neutron transport equation using the source iteration processing method. For example, the neutron transport equation can be iterated K times (K>1) using the source iteration processing method. The specific value of K can be set according to actual needs, and this embodiment does not make specific limitations here.

[0115] The neutron flux matrix can be determined by electronic devices based on multiple first neutron fluxes, and based on the neutron flux matrix, the electronic devices can further analyze the multiple first neutron fluxes.

[0116] In some embodiments, before the electronic device acquires the neutron flux matrix associated with the plurality of first neutron fluxes, the electronic device may perform the acquisition action in step S110 upon receiving a processing instruction. The processing instruction may be used to instruct the electronic device to process the neutron transport equations, that is, to acquire the neutron flux matrix associated with the plurality of first neutron fluxes.

[0117] Given that electronic devices may be in a complex computing environment, the neutron transport equations may be stored in specific files, databases, or memory. Electronic devices may not be able to quickly determine the exact location of the neutron transport equations when processing them.

[0118] In some embodiments, the processing instructions may also include storage location information for the neutron transport equations.

[0119] For example, if the neutron transport equation is stored in a specific file, the processing instruction may include the file path information of that specific file, such as "E:\desktop". After receiving the processing instruction, the electronic device can quickly locate the neutron transport equation from "E:\desktop" based on the file path information in the processing instruction, which can also indirectly improve the efficiency of processing neutron transport equations for nuclear reactions.

[0120] In step 120, the electronic device can perform dimensionality reduction processing on the neutron flux matrix obtained in the aforementioned steps. This can reduce the dimensionality of the neutron flux matrix, which not only reduces the large amount of data storage space occupied by high-dimensional matrices, but also reduces the time complexity of computational operations in subsequent computational processes and improves the computational output speed.

[0121] The theoretical matrix can be understood as a matrix that theoretically exists in the process of processing the neutron transport equation based on the conventional source iteration. According to formula (9) in the aforementioned source iteration content, the existence of this theoretical matrix can be inferred, namely matrix A in formula (9).

[0122] In some embodiments, the electronic device may perform dimensionality reduction on the neutron flux matrix based on principal component analysis.

[0123] In some embodiments, the electronic device can also reduce the dimensionality of the neutron flux matrix using singular value decomposition.

[0124] This embodiment does not limit the specific dimensionality reduction method of the neutron flux matrix.

[0125] In steps 130 and 140, the theoretical convergent neutron flux determined by the electronic device based on the theoretical matrix and multiple first neutron fluxes in the aforementioned steps can be regarded as a neutron flux convergence value.

[0126] Substituting the theoretically convergent neutron flux into the source iteration process described above can reduce the number of source iterations, thereby improving the computational efficiency of neutron transport.

[0127] In one possible implementation, when the neutron flux matrix is ​​reduced in dimension, the theoretical matrix is ​​determined based on the reduced neutron flux matrix, including:

[0128] Based on multiple first neutron fluxes, determine the first matrix and the second matrix, which are adjacent term difference matrices.

[0129] The second matrix is ​​reduced in dimensionality, and the neutron flux matrix includes the first and second matrices.

[0130] Based on the dimension-reduced neutron flux matrix, the theoretical matrix is ​​determined, including:

[0131] The theoretical matrix is ​​determined based on the first matrix and the second matrix after dimensionality reduction.

[0132] Specifically, the multiple first neutron fluxes can be expressed as (φ (1) ,…,φ (K) ), where φ (K) ∈R N This represents the field distribution of the physical quantity of interest, where N is the degree of freedom of the field, which is usually high-dimensional, for example, N≥10000.

[0133] The neutron flux matrix determined by the electronic device based on multiple first neutron fluxes may include formulas (14) and (15) as follows:

[0134] Y + =[φ (3) -φ (2) ,…,φ (K) -φ (K-1) ], (14)

[0135] Y _ =[φ (2) -φ (1) ,…,φ (K-1) -φ (K-2) ], (15)

[0136] Where Y+ represents the first matrix and Y- represents the second matrix, the first matrix and the second matrix are adjacent term difference matrices.

[0137] The electronic device can use principal component analysis or singular value decomposition to reduce the dimensionality of the second matrix, and then determine the theoretical matrix based on the first matrix and the dimensionality-reduced second matrix.

[0138] It should be noted that, based on formula (9) in the aforementioned content, it can be found that there is a matrix A in the source iteration process. If matrix A is unchanged, then the following relationship exists between multiple first neutron fluxes:

[0139] φ (3) -φ (2) =A*(φ (2) -φ (1) (16)

[0140] φ (K) -φ (K-1) =A*(φ (K-1) -φ (K-2) (17)

[0141] It can be observed that the first matrix and the second matrix have the following relationship:

[0142] Y + =A*Y - (18)

[0143] Assume there exists a neutron flux convergence value, which is the theoretical convergent neutron flux that needs to be calculated in the aforementioned embodiment, i.e., φ. (∞) Then the following relationship exists:

[0144] (φ-I)(φ (∞) -φ (K-1) )=φ (K) -φ (K-1) (19)

[0145] Where I represents the identity matrix.

[0146] In the actual iterative process, matrix A changes with each iteration. This embodiment reduces the dimensionality of the second matrix, Y-, in the neutron flux matrix, extracting the low-order invariant simulation components of the neutron flux during iterative calculations while removing higher-order changing components. Then, based on the first matrix and the dimensionality-reduced second matrix, the theoretical matrix can be determined. In subsequent operations, the theoretically convergent neutron flux is calculated based on the theoretical matrix, reducing the number of iterations at the source iteration point and achieving rapid convergence.

[0147] In one possible implementation, the theoretical matrix is ​​determined based on the first matrix and the dimension-reduced second matrix, including:

[0148] Perform singular value decomposition on the second matrix to obtain the left singular matrix, the singular value matrix, and the right singular matrix;

[0149] According to the preset truncation rank, the left singular matrix, the singular value matrix and the right singular matrix are truncated in sequence to obtain the truncated left singular matrix, the truncated singular value matrix and the truncated right singular matrix.

[0150] The theoretical matrix is ​​determined based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

[0151] The second matrix after dimensionality reduction includes the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

[0152] Specifically, in this embodiment, the Singular Value Decomposition (SVD) method is used to decompose the second matrix, and the following decomposition results are obtained:

[0153] Y - =UΣV T (20)

[0154] Where U represents the N*K left singular matrix, Σ represents the K*K singular value matrix, and V represents the K*K right singular matrix, meaning that both the singular value matrix and the right singular matrix are orthogonal matrices, and K < <N。

[0155] Considering that singular value decomposition requires a high computational complexity of O(NK) 2 In some embodiments, given the (K-1)th source iteration calculation, the electronic device can employ the iterative singular value decomposition (ISVD) method, based on the left singular matrix, singular value matrix, and right singular matrix, combined with the φ obtained from the latest iteration. (K) -φ (K-1) This allows for the updating of the left singular matrix, singular value matrix, and right singular matrix, thereby simplifying computational complexity.

[0156] Considering that N≥10000, the dimensionality is very large. To further simplify the calculation, the electronic device can truncate the above SVD according to a preset truncation rank r, retaining only the r largest singular values ​​in Σ. For example, deleting values ​​less than 10 in Σ. -6 The singular values. After truncation, we get:

[0157]

[0158] in, This represents the truncated left singular matrix (N*r). This represents the truncated singular value matrix (an r*r non-zero diagonal matrix). This represents the right singular matrix (an orthogonal matrix of K*r) after truncation.

[0159] The electronic device can determine the theoretical matrix based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

[0160] In one possible implementation, the theoretical matrix is ​​determined based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix, including:

[0161] Obtain the transpose of the truncated left singular matrix and the inverse of the truncated singular value matrix;

[0162] The theoretical matrix is ​​determined based on the transpose of the left singular matrix, the first matrix, the truncated right singular matrix, and the inverse of the singular value matrix.

[0163] Specifically, the electronic device determines the theoretical matrix based on the following formula.

[0164]

[0165] in, This represents the transpose of the truncated left singular matrix. This represents the inverse of the singular value matrix after truncation.

[0166] In one possible implementation, the theoretical convergent neutron flux is determined based on the theoretical matrix and multiple first neutron fluxes, including:

[0167] Obtain at least one eigenvalue of the theoretical matrix;

[0168] When all eigenvalues ​​of the theoretical matrix are less than a preset threshold, the theoretical convergent neutron flux is determined based on the theoretical matrix, multiple first neutron fluxes, and the identity matrix.

[0169] At least one eigenvalue of the theoretical matrix can be obtained using λ1, ..., λ k This indicates that if all eigenvalues ​​of the theoretical matrix are less than a preset threshold, it means that the electronic device has made a relatively accurate estimate of the theoretical matrix during processing. The electronic device can determine the theoretical convergent neutron flux based on the theoretical matrix, multiple first neutron fluxes, and the unit matrix.

[0170] In some embodiments, an electronic device can be used to find the largest eigenvalue among at least one eigenvalue, and then determine whether the largest eigenvalue is less than a preset threshold. This allows determination of whether all eigenvalues ​​of the theoretical matrix are less than the preset threshold. The preset threshold can be set according to actual needs.

[0171] In some embodiments, the preset threshold is 1.

[0172] In one possible implementation, after obtaining at least one eigenvalue of the theoretical matrix, the method further includes:

[0173] If the largest eigenvalue in at least one eigenvalue of the theoretical matrix is ​​greater than or equal to a preset threshold, the number of iterations of the source iteration process for the neutron transport equation is increased to obtain at least one second neutron flux and a new theoretical matrix, until all eigenvalues ​​of the new theoretical matrix are less than the preset threshold, at which point the source iteration process is stopped.

[0174] The theoretical convergent neutron flux is determined based on the new theoretical matrix, multiple first neutron fluxes, at least one second neutron flux, and the identity matrix.

[0175] Specifically, if the largest eigenvalue among at least one eigenvalue is greater than or equal to a preset threshold, it indicates that the theoretical matrix obtained by the electronic device during processing is inaccurate and that a sufficient number of source iterations are still needed to accumulate a sufficient amount of neutron flux (i.e., the K value mentioned above is large enough) before the theoretical matrix is ​​re-determined.

[0176] The neutron flux obtained by increasing the number of iterations is at least one second neutron flux in this embodiment. In the process of recalculating the theoretical matrix, it needs to be combined with the first neutron flux obtained earlier to participate in the calculation.

[0177] In some embodiments, when increasing the number of iterations for source iteration processing of the neutron transport equation, the theoretical matrix can be recalculated for each additional iteration. Alternatively, the theoretical matrix can be recalculated for each additional iteration, such as 100 iterations; no specific limitation is made here.

[0178] Based on the new theoretical matrix, multiple first neutron fluxes, at least one second neutron flux, and the identity matrix, the theoretical convergent neutron flux φ is determined. (∞) This can be achieved using the following formula:

[0179]

[0180] The theoretically convergent neutron flux φ (∞) Substituting into formulas (10) and (11) in the aforementioned content source iteration, that is, φ in formulas (10) and (11) (n+1) Replace with φ (∞) By continuing the source iteration process, the convergence speed of the neutron transport equation can be improved, thus increasing the computational efficiency of neutron transport.

[0181] Please see Figure 2 , Figure 2This is an experimental comparison graph illustrating a method for processing neutron transport equations in nuclear reactions provided in this application. The horizontal axis represents the number of iterations, the vertical axis represents the L2 residual, and curve S1 represents the change in neutron flux distribution (i.e., φ) corresponding to the convergence of the neutron flux distribution using the method described in the above embodiments of this application. (K) -φ (K-1) Curve S2 is the neutron flux distribution change curve corresponding to the convergence of the neutron flux distribution using source iteration processing, and curve S3 is the neutron flux distribution change curve corresponding to the convergence of the neutron flux distribution using ordinary linear extrapolation processing.

[0182] It can be observed that the method for processing the neutron transport equation of nuclear reaction in the above embodiments of this application requires the fewest iterations to reach the convergence of the neutron flux distribution. In other words, the method for processing the neutron transport equation of nuclear reaction provided by the embodiments of this application can improve the convergence speed of processing the neutron transport equation using source iteration and improve the computational efficiency of neutron transport.

[0183] Corresponding to the above method embodiments, this application also provides a system for processing neutron transport equations in nuclear reactions. Please refer to [link to relevant documentation]. Figure 3 , Figure 3 A functional module diagram of a system for processing neutron transport equations in nuclear reactions is provided in an embodiment of this application. The system 300 for processing neutron transport equations in nuclear reactions includes:

[0184] The acquisition module 310 is used to acquire the neutron flux matrix associated with multiple first neutron fluxes. The multiple first neutron fluxes are obtained by source iteration processing of the neutron transport equation, which is constructed based on the neutron transport process in nuclear reactions.

[0185] The first determining module 320 is used to determine the theoretical matrix based on the dimension-reduced neutron flux matrix after the neutron flux matrix has been dimension-reduced.

[0186] The second determining module 330 is used to determine the theoretical convergent neutron flux based on the theoretical matrix and multiple first neutron fluxes.

[0187] The iterative processing module 340 is used to perform source iterative processing on the neutron transport equation based on the theoretically convergent neutron flux.

[0188] The system for processing neutron transport equations in nuclear reactions provided in this application embodiment can achieve, for example... Figure 1 The various processes implemented in the Chinese method embodiments can achieve similar or the same technical effects, and will not be described again here to avoid repetition.

[0189] In one possible implementation, the first determining module 320 is further configured to:

[0190] Based on multiple first neutron fluxes, determine the first matrix and the second matrix, which are adjacent term difference matrices.

[0191] The second matrix is ​​reduced in dimensionality, and the neutron flux matrix includes the first and second matrices.

[0192] Based on the dimension-reduced neutron flux matrix, the theoretical matrix is ​​determined, including:

[0193] The theoretical matrix is ​​determined based on the first matrix and the second matrix after dimensionality reduction.

[0194] In one possible implementation, the first determining module 320 includes a first determining submodule, which is used for:

[0195] Perform singular value decomposition on the second matrix to obtain the left singular matrix, the singular value matrix, and the right singular matrix;

[0196] According to the preset truncation rank, the left singular matrix, the singular value matrix and the right singular matrix are truncated in sequence to obtain the truncated left singular matrix, the truncated singular value matrix and the truncated right singular matrix.

[0197] The theoretical matrix is ​​determined based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

[0198] The second matrix after dimensionality reduction includes the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

[0199] In one possible implementation, the first determining submodule includes a first determining unit, which is configured to:

[0200] Obtain the transpose of the truncated left singular matrix and the inverse of the truncated singular value matrix;

[0201] The theoretical matrix is ​​determined based on the transpose of the left singular matrix, the first matrix, the truncated right singular matrix, and the inverse of the singular value matrix.

[0202] In one possible implementation, the second determining module 330 is further configured to:

[0203] Obtain at least one eigenvalue of the theoretical matrix;

[0204] When all eigenvalues ​​of the theoretical matrix are less than a preset threshold, the theoretical convergent neutron flux is determined based on the theoretical matrix, multiple first neutron fluxes, and the identity matrix.

[0205] In one possible implementation, the system 300 for processing neutron transport equations in nuclear reactions further includes a judgment module, which is used to:

[0206] If the largest eigenvalue in at least one eigenvalue of the theoretical matrix is ​​greater than or equal to a preset threshold, the number of iterations of the source iteration process for the neutron transport equation is increased to obtain at least one second neutron flux and a new theoretical matrix, until all eigenvalues ​​of the new theoretical matrix are less than the preset threshold, at which point the source iteration process is stopped.

[0207] The theoretical convergent neutron flux is determined based on the new theoretical matrix, multiple first neutron fluxes, at least one second neutron flux, and the identity matrix.

[0208] This application also provides an electronic device. Please refer to [link to previous application]. Figure 4 , Figure 4 This is a structural diagram of an electronic device provided in an embodiment of this application. The electronic device includes a processor, a memory, and a network interface connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program. When executed by the processor, this computer program enables the processor to implement the method for processing neutron transport equations in nuclear reactions applied to the electronic device in the above embodiment. The internal memory may also store a computer program, which, when executed by the processor, enables the processor to perform the method for processing neutron transport equations in nuclear reactions. Those skilled in the art will understand that... Figure 4 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 electronic device to which the present application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0209] This application also discloses a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the method for processing neutron transport equations in nuclear reactions as described in the method embodiments.

[0210] This application provides a computer program product stored in a storage medium. The program product is executed by at least one processor to implement the various processes of the embodiments of the method for processing neutron transport equations in nuclear reactions as described above, and can achieve similar or the same technical effects. To avoid repetition, it will not be described again here.

[0211] 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. This 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, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0212] 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 specification.

Claims

1. A method for processing neutron transport equations in nuclear reactions, characterized in that, The method includes: Obtain a neutron flux matrix associated with multiple first neutron fluxes, which are obtained by source iteration processing of the neutron transport equation, which is constructed based on the neutron transport process in nuclear reactions; Based on the plurality of first neutron fluxes, a first matrix and a second matrix are determined, wherein the first matrix and the second matrix are adjacent term difference matrices. The second matrix is ​​subjected to dimensionality reduction processing, and the neutron flux matrix includes the first matrix and the second matrix; The theoretical matrix is ​​determined based on the first matrix and the second matrix after dimensionality reduction. Obtain at least one eigenvalue of the theoretical matrix; When all eigenvalues ​​of the theoretical matrix are less than a preset threshold, the theoretical convergent neutron flux is determined based on the theoretical matrix, the plurality of first neutron fluxes, and the identity matrix. The neutron transport equation is subjected to source iteration based on the theoretically convergent neutron flux.

2. The method according to claim 1, characterized in that, The step of determining the theoretical matrix based on the first matrix and the dimension-reduced second matrix includes: Perform singular value decomposition on the second matrix to obtain the left singular matrix, the singular value matrix, and the right singular matrix; The left singular matrix, the singular value matrix, and the right singular matrix are truncated sequentially according to a preset truncation rank to obtain the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix. The theoretical matrix is ​​determined based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix. The second matrix after dimensionality reduction includes the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix.

3. The method according to claim 2, characterized in that, Determining the theoretical matrix based on the first matrix, the truncated left singular matrix, the truncated singular value matrix, and the truncated right singular matrix includes: Obtain the transpose of the truncated left singular matrix and the inverse of the truncated singular value matrix; The theoretical matrix is ​​determined based on the transpose of the truncated left singular matrix, the first matrix, the truncated right singular matrix, and the inverse of the truncated singular value matrix.

4. The method according to claim 1, characterized in that, After obtaining at least one eigenvalue of the theoretical matrix, the method further includes: If the largest eigenvalue among at least one eigenvalue of the theoretical matrix is ​​greater than or equal to the preset threshold, the number of iterations of the source iteration process for the neutron transport equation is increased to obtain at least one second neutron flux and a new theoretical matrix, until all eigenvalues ​​of the new theoretical matrix are less than the preset threshold, at which point the source iteration process is stopped. The theoretical convergent neutron flux is determined based on the new theoretical matrix, multiple first neutron fluxes, at least one second neutron flux, and the identity matrix.

5. A system for processing neutron transport equations in nuclear reactions, characterized in that, The system includes: The acquisition module is used to acquire a neutron flux matrix associated with multiple first neutron fluxes, wherein the multiple first neutron fluxes are obtained by source iteration processing of the neutron transport equation, and the neutron transport equation is constructed based on the neutron transport process in nuclear reactions; A first determining module is configured to determine a first matrix and a second matrix based on the plurality of first neutron fluxes, wherein the first matrix and the second matrix are adjacent term difference matrices; perform dimensionality reduction processing on the second matrix, wherein the neutron flux matrix includes the first matrix and the second matrix; and determine a theoretical matrix based on the first matrix and the dimensionality-reduced second matrix. The second determining module is used to obtain at least one eigenvalue of the theoretical matrix; and, when all eigenvalues ​​of the theoretical matrix are less than a preset threshold, to determine the theoretical convergent neutron flux based on the theoretical matrix, the plurality of first neutron fluxes, and the identity matrix. The iterative processing module is used to perform source iterative processing on the neutron transport equation based on the theoretically converged neutron flux.

6. The system according to claim 5, characterized in that, The system also includes: The judgment module is configured to, when the largest eigenvalue among at least one eigenvalue of the theoretical matrix is ​​greater than or equal to the preset threshold, increase the number of iterations of the source iteration process for the neutron transport equation to obtain at least one second neutron flux and a new theoretical matrix, until all eigenvalues ​​of the new theoretical matrix are less than the preset threshold, and then stop the source iteration process; and determine the theoretical convergent neutron flux based on the new theoretical matrix, multiple first neutron fluxes, at least one second neutron flux, and the identity matrix.

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