Method and system for determining neutron flux distribution and effective multiplication coefficient of a core under test, computer storage medium

Abstract

Embodiments of the present application relate to the field of computer-aided design, in particular to a method and system for determining neutron flux distribution and effective multiplication coefficient of a to-be-tested core and a computer storage medium. The method comprises: determining a physically parameter field of a randomly generated diffusion coefficient, a macroscopic absorption cross section, a macroscopic fission cross section, a real flux distribution of the core, and a real effective multiplication coefficient of the core; obtaining a Fourier neural operator meeting predetermined requirements. The physically parameter field of the diffusion coefficient, the macroscopic absorption cross section, and the macroscopic fission cross section of the material of the to-be-tested core is determined. The neutron flux distribution and the effective multiplication coefficient of the to-be-tested core are determined according to the physically parameter field of the diffusion coefficient, the macroscopic absorption cross section, and the macroscopic fission cross section of the to-be-tested core and the determined Fourier neural operator. The method can quickly determine the neutron flux distribution and the effective multiplication coefficient of the to-be-tested core, reduce the time consumption of determining the neutron flux distribution and the effective multiplication coefficient, and improve the determination efficiency.

Description

Technical Field

[0001] The embodiments of this application relate to the field of computer-aided design, specifically to a method and system for determining the neutron flux distribution and effective multiplication factor of a reactor core under test, and a computer storage medium. Background Technology

[0002] The statements herein are provided merely as background information in connection with this application and do not necessarily constitute prior art.

[0003] During the operation of a nuclear reactor, the reactor core is where nuclear fission reactions occur, responsible for generating heat to provide energy for power generation or heating. Therefore, the reactor core is an important component that is related to the realization of the function of the nuclear reactor, so it is necessary to determine the design of the reactor core when building a nuclear reactor.

[0004] When determining the design of a reactor core, it is usually necessary to determine the neutron flux distribution and effective multiplication factor of the core. However, the current technology for determining the neutron flux distribution and effective multiplication factor of the core still has many limitations. Summary of the Invention

[0005] A brief overview of this application is provided below to offer a basic understanding of certain aspects thereof. It should be understood that this overview is not an exhaustive summary of the application. It is not intended to identify key or essential parts of the application, nor is it intended to limit its scope. Its purpose is merely to present certain concepts in a simplified form as a prelude to the more detailed description that follows.

[0006] To address the aforementioned issues, embodiments of this application provide a method and system for determining the neutron flux distribution and effective multiplication factor of a reactor core under test, as well as a computer storage medium.

[0007] In a first aspect, embodiments of this application provide a method for determining the neutron flux distribution and effective multiplication coefficient of a reactor core under test, the method comprising the following steps S10 to S60.

[0008] S10: Determine the diffusion coefficient of the randomly generated core material. Macroscopic absorption cross section of the core material And the macroscopic fission cross section of the core material. The physical parameter field.

[0009] S20: Based on macroscopic fission cross section The physical parameter field is used to determine the true flux distribution in the reactor core. Compared with the actual effective multiplication factor of the reactor core .

[0010] S30: Diffusion coefficient Macroscopic absorption cross section Macroscopic fission cross section Physical parameters of the field and the actual flux distribution and the true effective proliferation coefficient The dataset is divided into a training set and a test set.

[0011] S40: Use the training set and test set to train and test the Fourier neural operator to obtain a Fourier neural operator whose performance meets the predetermined requirements.

[0012] S50: Determine the diffusion coefficient of the core under test. Macroscopic absorption cross section of the material in the reactor core under test And the macroscopic fission cross section of the material in the reactor core under test. The physical parameter field.

[0013] S60: Based on the diffusion coefficient of the core under test Macroscopic absorption cross section of the material in the reactor core under test Macroscopic fission cross section of the material in the reactor core under test The physical parameter field and the Fourier neural operator determined by the S40 step are used to determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

[0014] The method provided in the embodiments of this application determines the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of a randomly generated core, and determines the true flux distribution and the true effective multiplication coefficient of the core. This enables the Fourier neural operator to be trained using the aforementioned determined data to obtain a Fourier neural operator that meets predetermined requirements. After obtaining a Fourier neural operator that meets predetermined requirements, the neutron flux distribution and effective multiplication coefficient of the core under test can be determined by determining the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of the core under test, thereby enabling the rapid determination of the neutron flux distribution and effective multiplication coefficient of the core under test, reducing the time required to determine the neutron flux distribution and effective multiplication coefficient, and improving the determination efficiency.

[0015] Secondly, embodiments of this application provide a system for determining the neutron flux distribution and effective multiplication coefficient of a reactor core under test. The system includes: a random parameter determination unit, a real parameter determination unit, a data partitioning unit, a Fourier neural operator, and a reactor core parameter determination unit.

[0016] The random parameter determination unit is used to determine the diffusion coefficient of the randomly generated core material. Macroscopic absorption cross section of the core material And the macroscopic fission cross section of the reactor core material. The physical parameter field.

[0017] The true parameter determination unit is used based on the macroscopic fission cross section. The physical parameter field is used to determine the true flux distribution in the reactor core. Compared with the actual effective multiplication factor of the reactor core .

[0018] Data partitioning units are used to divide the diffusion coefficient Macroscopic absorption cross section Macroscopic fission cross section Physical parameters of the field and the actual flux distribution and the true effective proliferation coefficient The dataset is divided into a training set and a test set; the training set and the test set can be used to train and test the Fourier neural operator to obtain a Fourier neural operator that meets the predetermined requirements.

[0019] The core parameter determination unit is used to determine the diffusion coefficient of the core under test. Macroscopic absorption cross section of the material in the reactor core under test And the macroscopic fission cross section of the material in the reactor core under test. The physical parameter field.

[0020] The determination element is used based on the diffusion coefficient of the core under test. Macroscopic absorption cross section of the material in the reactor core under test Macroscopic fission cross section of the material in the reactor core under test The physical parameter field and Fourier neural operator are used to determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

[0021] The system provided in the embodiments of this application determines the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of a randomly generated core through a random parameter determination unit, and determines the true flux distribution and the true effective multiplication coefficient of the core through a true parameter determination unit. This allows the Fourier neural operator to be trained using the aforementioned determined data to obtain a Fourier neural operator that meets predetermined requirements. After obtaining a Fourier neural operator that meets predetermined requirements, the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of the core under test are determined by the core parameter determination unit. Then, the neutron flux distribution and effective multiplication coefficient of the core under test can be determined by the determination unit using the trained Fourier neural operator. This enables rapid determination of the neutron flux distribution and effective multiplication coefficient of the core under test, reduces the time required to determine the neutron flux distribution and effective multiplication coefficient, and improves the determination efficiency.

[0022] Thirdly, embodiments of this application provide a computer storage medium storing a computer program, which, when executed by a processor, implements the method provided in the embodiments of the first aspect of this application. Attached Figure Description

[0023] Other objects and advantages of this application will become apparent from the following description of embodiments of this application with reference to the accompanying drawings, and will help to provide a comprehensive understanding of this application.

[0024] Figure 1a This is a schematic diagram of the diffusion coefficient of the randomly generated core material.

[0025] Figure 1b This is a schematic diagram of the macroscopic absorption cross section of the randomly generated core material.

[0026] Figure 1c This is a schematic diagram of the physical parameter field of the macroscopic fission cross section of the randomly generated core material.

[0027] Figure 2 This is a schematic diagram illustrating the acceleration effect and error when using the method provided in the embodiments of this application to determine the neutron flux distribution and effective multiplication coefficient.

[0028] Figure 3 This is a schematic diagram illustrating the acceleration effect and error when using the method provided in the embodiments of this application to determine the neutron flux distribution and effective multiplication factor at another resolution.

[0029] Figure 4 This is a schematic diagram illustrating the acceleration effect and error of determining high-precision neutron flux distribution and effective multiplication coefficient using the method provided in the embodiments of this application.

[0030] Figure 5 This is a schematic diagram illustrating the acceleration effect and error of determining high-precision neutron flux distribution and effective multiplication coefficient at another resolution using the method provided in the embodiments of this application.

[0031] Figure 6 This is a schematic diagram of the structure of the Fourier neural operator involved in the method provided in the embodiments of this application.

[0032] Explanation of reference numerals in the attached figures: 100. Fourier neural operator; 10. Multichannel input layer; 20. Lifting layer; 30. Fourier layer; 40. Projection layer; 50. Neutron flux distribution; 60. Effective multiplication coefficient; 200, Multilayer Perceptron; 300, Global Average Pooling Layer.

[0033] It should be noted that the accompanying drawings are not necessarily drawn to scale, but are shown only in a schematic manner without affecting the reader's understanding. Detailed Implementation

[0034] Exemplary embodiments of this application will be described below with reference to the accompanying drawings. For clarity and brevity, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the development of any such actual embodiment to achieve the developer's specific goals, such as complying with constraints related to the system and business, and these constraints may vary depending on the implementation. Furthermore, it should be understood that while development work can be very complex and time-consuming, such development work is merely a routine task for those skilled in the art who benefit from the content of this application.

[0035] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the equipment structure and / or processing steps closely related to the solution according to this application are shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0036] In related technologies, a combination of source iteration and Krylov subspace methods (such as the BiCGSTAB algorithm) is usually used to determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test. However, the determination process suffers from low determination rate and long time consumption.

[0037] To address the aforementioned issues, embodiments of this application provide a method and system, as well as a computer storage medium, for determining the neutron flux distribution and effective multiplication coefficient of a reactor core under test, in order to improve computational efficiency and reduce computation time.

[0038] Embodiments of this application provide a method for determining the neutron flux distribution and effective multiplication factor of a reactor core under test, which may include the following steps S10 to S60.

[0039] S10: Determine the diffusion coefficient of the randomly generated core material. Macroscopic absorption cross section of the core material And the macroscopic fission cross section of the reactor core material. The physical parameter field, wherein the diffusion coefficient of the randomly generated core material is determined. Macroscopic absorption cross section of the core material And the macroscopic fission cross section of the reactor core material. The physical parameters of the field can be as follows Figures 1a to 1c As shown, Figure 1a This is a schematic diagram of the diffusion coefficient of the randomly generated core material. Figure 1b This is a schematic diagram of the macroscopic absorption cross-section of the randomly generated core material. Figure 1c This is a schematic diagram of the physical parameter field of the macroscopic fission cross section of the randomly generated core material.

[0040] S20: Based on macroscopic fission cross section The physical parameter field is used to determine the true flux distribution in the reactor core. Compared with the actual effective multiplication factor of the reactor core .

[0041] S30: Diffusion coefficient Macroscopic absorption cross section Macroscopic fission cross section Physical parameters of the field and the actual flux distribution and the true effective proliferation coefficient The dataset is divided into a training set and a test set.

[0042] S40: Use the training set and test set to train and test the Fourier neural operator to obtain a Fourier neural operator whose performance meets the predetermined requirements.

[0043] S50: Determine the diffusion coefficient of the core under test. Macroscopic absorption cross section of the material in the reactor core under test And the macroscopic fission cross section of the material in the reactor core under test. The physical parameter field.

[0044] S60: Based on the diffusion coefficient of the core under test Macroscopic absorption cross section of the material in the reactor core under test Macroscopic fission cross section of the material in the reactor core under test The physical parameter field and the Fourier neural operator determined by the S40 step are used to determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

[0045] The method provided in the embodiments of this application determines the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of a randomly generated core, and determines the true flux distribution and the true effective multiplication coefficient of the core. This enables the Fourier neural operator to be trained using the aforementioned determined data to obtain a Fourier neural operator that meets predetermined requirements. After obtaining a Fourier neural operator that meets predetermined requirements, the neutron flux distribution and effective multiplication coefficient of the core under test can be determined by determining the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of the core under test, thereby enabling the rapid determination of the neutron flux distribution and effective multiplication coefficient of the core under test, reducing the time required to determine the neutron flux distribution and effective multiplication coefficient, and improving the determination efficiency.

[0046] See Figure 2 , Figure 2 This is a schematic diagram illustrating the acceleration effect and error when using the method provided in the embodiments of this application to determine the neutron flux distribution and effective multiplication coefficient. Figure 2The broken line 71 in the figure represents the ratio between the acceleration when determining the neutron flux distribution and effective multiplication factor of the reactor core under test using the method provided in the embodiments of this application, and the acceleration when determining the neutron flux distribution and effective multiplication factor of the reactor core under test using the method in the related art; Figure 2 The broken line 72 in the figure represents the error between the neutron flux distribution and effective multiplication factor of the test core determined by the method provided in the embodiments of this application and the neutron flux distribution and effective multiplication factor of the test core determined by the method in the related art.

[0047] Depend on Figure 2 As can be seen, compared with the methods in the related technologies, the method provided by the embodiments of this application achieves an average speedup of 352.9 times at an average error level of 126.5 pcm, thus indicating that the method provided by the embodiments of this application has higher determination efficiency and shorter determination time compared with the methods in the related technologies.

[0048] In some embodiments, the resolution of the true flux distribution and the true effective multiplication coefficient of the core determined in step S20 is the same as the resolution of the physical parameter fields of the randomly generated diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section determined in step S10. Similarly, the resolution of the physical parameter fields of the diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section of the core material determined in step S50, and the resolution of the neutron flux distribution and effective multiplication coefficient of the core determined in step S60, are also the same as the resolution of the physical parameter fields of the randomly generated diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section determined in step S10.

[0049] In some embodiments, in step S10, the resolution of the physical parameter field of the randomly generated diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section can be 128×128.

[0050] In other embodiments, in step S10, the resolution of the physical parameter field of the randomly generated diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section can be 256×256.

[0051] See Figure 3 , Figure 3 This is a schematic diagram illustrating the acceleration effect and error when using the method provided in the embodiments of this application to determine the neutron flux distribution and effective multiplication factor at another resolution, wherein... Figure 3 The corresponding resolution is 256×256. Figure 2 The corresponding resolution is 128×128. Figure 3The broken line 81 in the figure represents the ratio between the acceleration when determining the neutron flux distribution and effective multiplication factor of the reactor core under test using the method provided in the embodiments of this application, and the acceleration when determining the neutron flux distribution and effective multiplication factor of the reactor core under test using the method in the related art; Figure 3 The broken line 82 in the figure represents the error between the neutron flux distribution and effective multiplication factor of the test core determined by the method provided in the embodiments of this application and the neutron flux distribution and effective multiplication factor of the test core determined by the method in the related art.

[0052] Depend on Figure 2 and Figure 3 It can be seen that although the method provided by the embodiments of this application increases the average error level from 126.5 pcm to 653.8 pcm at a resolution of 256×256 compared to 128×128, compared with the methods in the related art, the method provided by the embodiments of this application still achieves an average speedup of 1074.6 times at a resolution of 256×256 with a limited error level. Therefore, it can still be shown that the method provided by the embodiments of this application has higher determination efficiency and shorter determination time than the methods in the related art.

[0053] In some embodiments, the method provided by the present application may further include the following steps: determining a high-precision neutron flux distribution and effective multiplication coefficient of the core under test based on the neutron flux distribution and effective multiplication coefficient of the core under test determined in step S60 and the source iteration method. In such embodiments, the above steps combine the Fourier neural operator with the source iteration method, thereby improving the efficiency in determining the neutron flux distribution and effective multiplication coefficient of the core under test while ensuring the accuracy of the determined neutron flux distribution and effective multiplication coefficient, thus providing data support for core optimization.

[0054] See Figure 4 and Figure 5 , Figure 4 This is a schematic diagram illustrating the acceleration effect and error of determining high-precision neutron flux distribution and effective multiplication coefficient using the method provided in the embodiments of this application. Figure 5 This is a schematic diagram illustrating the acceleration effect and error of determining high-precision neutron flux distribution and effective multiplication coefficient at another resolution using the method provided in the embodiments of this application. Figure 4 The corresponding resolution is 128×128. Figure 5 The corresponding resolution is 256×256.

[0055] Figure 4The broken line 701 in the figure represents the ratio between the acceleration when determining the neutron flux distribution and effective multiplication factor of the test core using the method provided in the embodiments of this application, and the acceleration when determining the neutron flux distribution and effective multiplication factor of the test core using the method in the related art. Figure 4 The broken line 702 in the figure represents the error between the high-precision neutron flux distribution and effective multiplication factor of the test core determined by the method provided in the embodiments of this application and the neutron flux distribution and effective multiplication factor of the test core determined by the method in the related art.

[0056] Figure 5 The broken line 801 in the figure represents the ratio between the acceleration when determining the neutron flux distribution and effective multiplication factor of the test core using the method provided in the embodiments of this application, and the acceleration when determining the neutron flux distribution and effective multiplication factor of the test core using the method in the related art. Figure 5 The broken line 802 in the figure represents the error between the high-precision neutron flux distribution and effective multiplication factor of the test core determined by the method provided in the embodiments of this application and the neutron flux distribution and effective multiplication factor of the test core determined by the method in the related art.

[0057] Depend on Figure 4 As can be seen, compared with the methods in related technologies, the method provided by the embodiments of this application achieves an average speedup of 3.17 times at an average error level of 1.21 pcm, which shows that the method provided by the embodiments of this application still has higher determination efficiency and shorter determination time when determining the neutron flux distribution and effective multiplication coefficient of the test core with high precision.

[0058] Depend on Figure 4 and Figure 5 It can be seen that although the method provided by the embodiments of this application increases the average error level from 1.21 pcm to 2.17 pcm at a resolution of 256×256 compared to 128×128, compared with the methods in related technologies, the method provided by the embodiments of this application still achieves an average speedup of 2.83 times at a limited error level at a resolution of 256×256. This still shows that the method provided by the embodiments of this application has higher determination efficiency and shorter determination time when determining the neutron flux distribution and effective multiplication coefficient of the reactor core under test with high precision.

[0059] In some embodiments, the neutron flux distribution of the test core determined in step S60 can be used as the initial value of the inner iteration in the source iteration, and the effective multiplication coefficient of the test core determined in step S60 can be used as the initial value of the outer iteration in the source iteration. Relay iteration is carried out under the strict constraint of the neutron diffusion physics equation to obtain a neutron flux distribution and effective multiplication coefficient that strictly satisfy the conservation of neutron number, i.e., a high-precision neutron flux distribution and effective multiplication coefficient of the test core.

[0060] In some embodiments, the resolution used can be determined based on the actual requirements for determining the neutron flux distribution and effective multiplication factor of the reactor core under test.

[0061] Specifically, see Table 1 below. Table 1 shows the average speedup ratio and average error of the neutron flux distribution and effective multiplication factor of the reactor core corresponding to different resolutions. In this table, No. 1 corresponds to the determination of the neutron flux distribution and effective multiplication factor of the reactor core using the method provided in the embodiments of this application, and No. 2 corresponds to the determination of the neutron flux distribution and effective multiplication factor of the reactor core with high precision using the method provided in the embodiments of this application.

[0062] Table 1. Neutron flux distribution and effective multiplication factor of the reactor core at different resolutions, along with average acceleration ratio and average error. As shown in Table 1, when determining the neutron flux distribution and effective multiplication factor of the reactor core, the average error is reduced at a resolution of 128×128 compared to a resolution of 256×256, but the average speedup ratio is also reduced. Therefore, if there is a requirement for the average error when determining the neutron flux distribution and effective multiplication factor of the reactor core, the determination can be performed at a resolution of 128×128; if there is a requirement for the average speedup ratio, the determination can be performed at a resolution of 256×256.

[0063] Similarly, as shown in Table 1, when determining high-precision neutron flux distribution and effective multiplication factor, the average error and average speedup are similar at a resolution of 128×128 compared to 256×256. However, at 128×128 resolution, the average speedup is greater than at 256×256 resolution, while the average error is smaller. Therefore, if there are no requirements for the average error or average speedup when determining high-precision neutron flux distribution and effective multiplication factor of the reactor core, the determination can be performed at either 128×128 or 256×256 resolution. Conversely, if there are requirements for the average error or average speedup, the determination can be performed at 128×128 resolution.

[0064] See Figure 6 , Figure 6 This is a schematic diagram of the structure of the Fourier neural operator 100 involved in the method provided in the embodiments of this application. In some embodiments, in step S40, the Fourier neural operator 100 may include a multi-channel input layer 10, a lifting layer 20, several Fourier layers 30, and a projection layer 40. The data input to the Fourier neural operator 100 passes through the multi-channel input layer 10, enters the lifting layer 20, and is converted into frequency domain information by the lifting layer 20; the frequency domain information enters the several Fourier layers 30, and from the several Fourier layers 30 enters the projection layer 40, and is output from the projection layer 40.

[0065] In related technologies, when determining the neutron flux distribution and effective multiplication coefficient of a complex reactor core with strong non-uniformity and large gradient physical interfaces (such as strong absorbing control rods and high enrichment fuels arranged alternately), the condition number of the stiffness matrix after spatial discretization increases rapidly, making it difficult to determine quickly and time-consuming. Therefore, in the embodiments of this application, by setting up a booster layer 20 to convert the data input to the Fourier neural operator 100 into frequency domain information, and by having the frequency domain information enter the projection layer 40 after entering several Fourier layers 30, the adaptability to complex reactor cores can be improved, thereby reducing the time consumed in determining the neutron flux distribution and effective multiplication coefficient of complex reactor cores, which is beneficial to improving the determination efficiency; and by setting up a multi-channel input layer 10, in the subsequent determination process, the physical parameter fields of the diffusion coefficient of the reactor core under test, the macroscopic absorption cross section of the material of the reactor core under test, and the macroscopic fission cross section of the material of the reactor core under test can be simultaneously input into the Fourier neural operator 100, so that the Fourier neural operator 100 can determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test based on the input data, thereby realizing the rapid determination of the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

[0066] See Figure 6 In some embodiments, the data output from the projection layer 40 can enter both the multilayer sensor 200 and the global average pooling layer 300. After processing by the multilayer sensor 200, the data outputs a neutron flux distribution 50, which is the determined neutron flux distribution of the core under test. The data entering the global average pooling layer 300 then enters another multilayer sensor 200, from which an effective multiplication factor 60 is output. This effective multiplication factor 60 is the determined effective multiplication factor of the core under test.

[0067] In some embodiments, the Fourier neural operator 100 may further include a loss function, which may be determined by the following steps: determining the relative norm error between the predicted and true values ​​of the neutron flux distribution; determining the mean square error between the predicted and true values ​​of the effective multiplication coefficient; and determining the loss function based on the relative norm error and the mean square error. Compared to related techniques that use mean square error or relative error to determine the loss function, the embodiments of this application, by determining the relative norm error between the predicted and true values ​​of the neutron flux distribution, and then determining the loss function based on the determined relative norm error, can eliminate the influence of different core structures on the determination of the neutron flux distribution and the effective multiplication coefficient. This allows the Fourier neural operator 100 to be used to quickly determine the neutron flux distribution and effective multiplication coefficient of test cores with different structures.

[0068] Specifically, see Tables 2 and 3 below. Table 2 shows the average error and acceleration effect corresponding to the neutron flux distribution and effective multiplication coefficient of reactor cores with different structures. Table 3 shows the average error and acceleration effect corresponding to the high-precision neutron flux distribution and effective multiplication coefficient of reactor cores with different structures.

[0069] Table 2. Average error and acceleration effect corresponding to neutron flux distribution and effective multiplication coefficient of reactor cores with different structures. Table 3. Average error and acceleration effect corresponding to high-precision neutron flux distribution and effective multiplication coefficient of reactor cores with different structures. As can be seen from Tables 2 and 3, for different core structures, the methods provided by the embodiments of this application can achieve an acceleration effect of more than 2 times with a limited error level. This shows that the methods provided by the embodiments of this application can quickly determine the neutron flux distribution and effective multiplication coefficient of cores with different core structures, and that the methods provided by the embodiments of this application can quickly determine the high-precision neutron flux distribution and effective multiplication coefficient of cores with different core structures.

[0070] In some embodiments, the loss function, relative norm error, and mean squared error can conform to the following relationship: , In the formula, This represents the loss function.

[0071] Indicates relative norm error, This represents the predicted value of the neutron flux distribution. This represents the true value of the neutron flux distribution.

[0072] This represents the mean square error. This represents the predicted value of the effective proliferation coefficient. This represents the true value of the effective multiplication coefficient.

[0073] This represents the weighting coefficient.

[0074] In such an embodiment, the above-mentioned relationship facilitates the rapid determination of the loss function of the Fourier neural operator 100, which in turn facilitates the rapid determination of the Fourier neural operator 100 that meets the predetermined requirements, and improves the efficiency of determining the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

[0075] In some embodiments, in step S20, the determined true effective multiplication factor of the reactor core is... The range can be 0.8 to 1.4.

[0076] Because the data range of the randomly generated diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section physical parameter fields is large, the physical parameter fields of the diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section may not all conform to the actual situation of the reactor core. If all randomly generated diffusion coefficient, macroscopic absorption cross section, and macroscopic fission cross section physical parameter fields are used, it will not only be meaningless for training the Fourier neural operator 100 to determine the actual neutron flux distribution and effective multiplication coefficient of the reactor core, but will also lead to an increase in training difficulty.

[0077] Therefore, in the embodiments of this application, the actual effective multiplication factor of the reactor core is used. The range can be 0.8 to 1.4, so that the data used to train the Fourier neural operator 100 conforms to the actual situation of the core, which is conducive to making the Fourier neural operator 100 have lower and more stable errors during training, and also helps to reduce the difficulty of training the Fourier neural operator 100.

[0078] In some embodiments, strong absorbers can be inserted at any location in the core to increase the true effective multiplication factor of the core. The value is within the range of 0.8 to 1.4. Since in actual reactors, the true effective multiplication factor of the core is limited by inserting strong absorbers into the core, the embodiments of this application, by inserting strong absorbers at any location in the core, simulate the actual operating conditions of the reactor. This makes the true effective multiplication factor of the core determined using the method provided in the embodiments of this application closer to the true effective multiplication factor of the core under actual reactor operating conditions. Consequently, the determined neutron flux distribution and effective multiplication factor of the core under test are closer to the true neutron flux distribution and effective multiplication factor of the core under test.

[0079] In some embodiments, the macroscopic absorption cross section of the core material can be adjusted. The value is used to determine the true effective multiplication factor of the reactor core. The value is within the range of 0.8 to 1.4. In actual reactors, adjusting the density of the effective components of the material is equivalent to adjusting the value of the macroscopic absorption cross section of the core material, thus limiting the true effective multiplication factor of the core. Therefore, the embodiments of this application, by adjusting the value of the macroscopic absorption cross section of the core material to simulate the actual operating conditions of the reactor, make the true effective multiplication factor of the core determined using the method provided in the embodiments of this application closer to the true effective multiplication factor of the core under actual reactor operating conditions. This results in the determined neutron flux distribution and effective multiplication factor of the tested core being closer to the true neutron flux distribution and effective multiplication factor of the tested core.

[0080] Embodiments of this application also provide a system for determining the neutron flux distribution and effective multiplication coefficient of a reactor core under test, which may include: a random parameter determination unit, a real parameter determination unit, a data partitioning unit, a Fourier neural operator, and a reactor core parameter determination unit.

[0081] The random parameter determination unit is used to determine the diffusion coefficient of the randomly generated core material. Macroscopic absorption cross section of the core material And the macroscopic fission cross section of the reactor core material. The physical parameter field.

[0082] The true parameter determination unit is used based on the macroscopic fission cross section. The physical parameter field is used to determine the true flux distribution in the reactor core. Compared with the actual effective multiplication factor of the reactor core .

[0083] Data partitioning units are used to divide the diffusion coefficient Macroscopic absorption cross section Macroscopic fission cross section Physical parameters of the field and the actual flux distribution and the true effective proliferation coefficient The dataset is divided into a training set and a test set; the training set and the test set can be used to train and test the Fourier neural operator to obtain a Fourier neural operator that meets the predetermined requirements.

[0084] The core parameter determination unit is used to determine the diffusion coefficient of the core under test. Macroscopic absorption cross section of the material in the reactor core under test And the macroscopic fission cross section of the material in the reactor core under test. The physical parameter field.

[0085] The determination element is used based on the diffusion coefficient of the core under test. Macroscopic absorption cross section of the material in the reactor core under test Macroscopic fission cross section of the material in the reactor core under test The physical parameter field and Fourier neural operator are used to determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

[0086] The system provided in the embodiments of this application determines the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of a randomly generated core through a random parameter determination unit, and determines the true flux distribution and the true effective multiplication coefficient of the core through a true parameter determination unit. This allows the Fourier neural operator to be trained using the aforementioned determined data to obtain a Fourier neural operator that meets predetermined requirements. After obtaining a Fourier neural operator that meets predetermined requirements, the diffusion coefficient, macroscopic absorption interface, and macroscopic fission cross section of the core under test are determined by the core parameter determination unit. Then, the neutron flux distribution and effective multiplication coefficient of the core under test can be determined by the determination unit using the trained Fourier neural operator. This enables rapid determination of the neutron flux distribution and effective multiplication coefficient of the core under test, reduces the time required to determine the neutron flux distribution and effective multiplication coefficient, and improves the determination efficiency.

[0087] Embodiments of this application also provide a computer storage medium storing a computer program that, when executed by a processor, implements the method provided in any embodiment of this application.

[0088] Regarding the embodiments of this application, it should also be noted that, without conflict, the embodiments of this application and the features in the embodiments can be combined with each other to obtain new embodiments.

[0089] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. The scope of protection of this application shall be determined by the scope of the claims.

Claims

1. A method for determining the neutron flux distribution and effective multiplication factor of a reactor core under test, characterized in that, The method includes the following steps: S10: Determine the diffusion coefficient of the randomly generated core material. Macroscopic absorption cross section of the core material and the macroscopic fission cross section of the material of the reactor core. The physical parameters of the field; S20: Based on the macroscopic fission cross section The physical parameter field is used to determine the true flux distribution of the reactor core. With respect to the actual effective multiplication factor of the reactor core ; S30: The diffusion coefficient The macroscopic absorption cross section The macroscopic fission cross section The physical parameter field, the actual flux distribution and the true effective multiplication coefficient The dataset is divided into a training set and a test set; S40: The Fourier neural operator is trained and tested using the training set and the test set to obtain the Fourier neural operator whose performance meets the predetermined requirements; S50: Determine the diffusion coefficient of the core under test. The macroscopic absorption cross section of the material of the core under test. and the macroscopic fission cross section of the material of the reactor core under test. The physical parameters of the field; S60: Based on the diffusion coefficient of the core under test The macroscopic absorption cross section of the material of the core under test. Macroscopic fission cross section of the material of the reactor core under test The physical parameter field and the Fourier neural operator determined in step S40 are used to determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

2. The method according to claim 1, characterized in that, The method further includes the following steps: Based on the neutron flux distribution and effective multiplication coefficient of the test core determined in step S60 and the source iteration method, a high-precision neutron flux distribution and effective multiplication coefficient of the test core are determined.

3. The method according to claim 1, characterized in that, In step S40, The Fourier neural operator includes a multi-channel input layer, a lifting layer, several Fourier layers, and a projection layer. The data input to the Fourier neural operator passes through the multi-channel input layer, enters the lifting layer, and is converted into frequency domain information by the lifting layer. The frequency domain information enters the plurality of Fourier layers, and from the plurality of Fourier layers enters the projection layer, and from the projection layer is output.

4. The method according to claim 3, characterized in that, The Fourier neural operator also includes a loss function. The loss function is determined using the following steps: Determine the relative norm error between the predicted and actual values ​​of the neutron flux distribution; Determine the mean square error between the predicted and actual values ​​of the effective multiplication coefficient; The loss function is determined based on the relative norm error and the mean square error.

5. The method according to claim 4, characterized in that, The loss function, the relative norm error, and the mean square error conform to the following relationship: ， In the formula, Denotes the loss function, This represents the relative norm error. This represents the predicted value of the neutron flux distribution. This represents the true value of the neutron flux distribution. This represents the mean square error. This represents the predicted value of the effective proliferation coefficient. This represents the true value of the effective proliferation coefficient. This represents the weighting coefficient.

6. The method according to claim 1, characterized in that, In step S20, the true effective multiplication factor of the reactor core is determined. The range is 0.8 to 1.

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7. The method according to claim 6, characterized in that, Strong absorbers are inserted at any location in the reactor core to increase the true effective multiplication factor of the reactor core. It falls within the range of 0.8 to 1.

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8. The method according to claim 6, characterized in that, Adjusting the macroscopic absorption cross section of the core material The value is used to determine the true effective multiplication factor of the core. It falls within the range of 0.8 to 1.

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9. A system for determining the neutron flux distribution and effective multiplication factor of a reactor core under test, characterized in that, The system includes: The random parameter determination unit is used to determine the diffusion coefficient of the randomly generated core material. Macroscopic absorption cross section of the core material and the macroscopic fission cross section of the material of the reactor core. The physical parameters of the field; The real parameter determination unit is used to determine the parameters based on the macroscopic fission cross section. The physical parameter field is used to determine the true flux distribution of the reactor core. With respect to the actual effective multiplication factor of the reactor core ; Data partitioning unit, the data partitioning unit is used to partition the diffusion coefficient The macroscopic absorption cross section The macroscopic fission cross section The physical parameter field, the actual flux distribution and the true effective multiplication coefficient The dataset is divided into a training set and a test set; the training set and the test set can be used to train and test the Fourier neural operator to obtain the Fourier neural operator with the desired effect. The core parameter determination unit is used to determine the diffusion coefficient of the core under test. The macroscopic absorption cross section of the material of the core under test. and the macroscopic fission cross section of the material of the reactor core under test. The physical parameters of the field; The determining unit is used to determine the diffusion coefficient of the core under test. The macroscopic absorption cross section of the material of the core under test. Macroscopic fission cross section of the material of the reactor core under test The physical parameter field and the Fourier neural operator are used to determine the neutron flux distribution and effective multiplication coefficient of the reactor core under test.

10. A computer storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the method described in any one of claims 1-8.

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