Monte Carlo shielding simulation method and device based on full-automatic importance sampling

Abstract

The invention relates to the technical field of radiation shielding design, in particular to a Monte Carlo shielding simulation method, device and equipment based on full-automatic importance sampling. According to the Monte Carlo shielding simulation method based on full-automatic importance sampling, a plurality of irregular virtual surfaces are generated according to the direct penetration probability of each grid position relative to a source item and the penetration probability threshold of a corresponding subspace; the automatic generation of the irregular AIS virtual surface for the global problem is realized, and the Monte Carlo calculation whole process is set, so that the usability of the AIS method is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of radiation shielding design, and in particular to a Monte Carlo shielding simulation method, device, and equipment based on fully automatic importance sampling. Background Art

[0002] The development of nuclear energy science and nuclear technology has enabled the wide application of ionizing radiation in many fields such as nuclear weapon technology, nuclear energy technology, and civilian non-power nuclear technology. However, while bringing various benefits to people, ionizing radiation may inevitably cause certain radioactive hazards to humans. Therefore, certain radiation protection measures need to be adopted to reduce the possibility of ionizing radiation causing harm to the human body to an acceptable level. In addition to increasing the distance between the radiation source and the human body and shortening the irradiation time, another main method of radiation protection is radiation shielding. Radiation shielding protection refers to setting an object with a certain thickness that can attenuate rays between the radiation source and the human body, so that the effective dose received by personnel within a certain time is lower than the safety limit. Therefore, the design of the shielding body will greatly affect the effect of radiation protection.

[0003] When conducting radiation shielding design, it is necessary to consider the material selection and geometric design of the shielding body, and comprehensively consider various factors such as the structural performance of the shielding material, the shielding performance of the shielding body, economic cost, durability, and stability to obtain an optimal design scheme. For large nuclear facilities and radiation devices such as nuclear power plants and accelerators, shielding design is a time-consuming and complex process. Traditional radiation shielding calculation methods mainly include empirical / semi-empirical formulas, theoretical analytical methods, and deterministic methods. Although empirical / semi-empirical formulas are relatively simple and fast to calculate, their accuracy is insufficient, and the solution results may have a large difference from the experimental results, and there are also inapplicable situations, which cannot meet the requirements of refined radiation shielding calculation. Theoretical analytical methods such as the point kernel integral method have a fast calculation speed and can handle relatively complex geometries, but their ability to handle particle scattering is limited. The deterministic method is to iteratively solve the Boltzmann transport equation by numerical methods, and the solution speed is relatively fast, which is a commonly used method in radiation protection design and reactor physics. However, it has defects in dealing with complex geometries and accurate source descriptions, so its solution accuracy is not high in many shielding problems, which limits the development and application of the deterministic method in refined radiation shielding calculation. With the development of nuclear technology, various new nuclear facilities have more complex geometric structures and reaction mechanisms, and stronger anisotropy. When dealing with such problems, the above methods can no longer guarantee the accuracy of the calculation results.

[0004] To solve such complex particle transport problems and improve the accuracy and reliability of shielding calculation results, the most accurate method is the simulation method based on random sampling and probability statistics to describe the physical process of particle transport - the Monte Carlo method (abbreviated as the "Monte Carlo method"). The Monte Carlo method can accurately describe the transport behavior of each particle, with a small approximation degree, can construct complex geometric structures, and use probability statistics methods to calculate the solution of the problem. Therefore, the Monte Carlo method has unique advantages in the accurate solution of physical problems. For simple problems, the calculation results of the Monte Carlo method can converge to the exact solution within a reasonable time (generally considered when the Monte Carlo relative error is less than 5% at a 68.3% confidence level). However, the direct Monte Carlo simulation method without any techniques often cannot accurately solve deep penetration and complex shielding structure problems within an acceptable time.

[0005] The deep penetration problem is one of the most representative difficult problems in the field of Monte Carlo shielding calculation and often appears in some typical projects such as reactor shielding design and accelerator shielding design. The characteristic of the deep penetration problem is that when the shielding body between the source region and the statistical region is thick enough and the shielding effect is good enough, the probability of particles penetrating the shielding body to reach the statistical region is extremely low, becoming a small probability event. In the case of insufficient simulated particle numbers, the calculation results obtained in the statistical region are lower than the true values and converge extremely slowly. Therefore, it is necessary to simulate a large number of particle numbers and consume an extremely long simulation time to solve the accurate results.

[0006] The Monte Carlo shielding calculation method based on the automatic importance sampling (AIS) method was proposed in 2008. Compared with the currently commonly used regional importance and weight window variance reduction methods, it simplifies the parameter input, does not require setting complex variance reduction parameters, and does not occupy too much memory, improving the usability for users. The AIS method uses a series of virtual surfaces in the calculation space to divide the entire calculation region into a series of subspaces. During the transport process of particles in the previous calculation region, virtual particles are generated on the next virtual surface. After the transport in this layer of subspace is completed, the next layer of subspace uses the virtual particles generated by the previous layer of subspace as the source term to continue transporting forward, and automatically adjusts the particle weights and controls the number on the virtual surface to ensure that the number of virtual particles on the virtual surface is consistent.

[0007] Under the same geometric conditions, if the virtual surface division method is different, the distribution of virtual particles generated on the virtual surface will also change, thus affecting the calculation results. However, in existing methods, the setting process of the AIS virtual surface often depends on user experience, and the usability and accuracy need to be further improved. Summary of the Invention

[0008] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the generation of virtual surfaces in the automatic importance sampling method in the prior art depends on manual work.

[0009] To solve the above technical problems, the present invention provides a Monte Carlo shielding simulation method based on fully automatic importance sampling, including:

[0010] Automatically generating a plurality of irregular virtual surfaces by using radiation field parameters;

[0011] Performing Monte Carlo transport based on automatic importance sampling based on the generated plurality of irregular virtual surfaces, and outputting statistical results.

[0012] Preferably, the automatically generating a plurality of irregular virtual surfaces by using radiation field parameters includes:

[0013] Automatically generating a plurality of irregular virtual surfaces by using the penetration probabilities of each position in space relative to the source term in the radiation field parameters, including:

[0014] Step 1: Determine the Monte Carlo statistical region of the target and perform grid division on it;

[0015] Step 2: Obtain the direct penetration probabilities of each grid position in the Monte Carlo statistical region relative to the source term;

[0016] Step 3: Divide sub-spaces according to the penetration probabilities of each grid in space relative to the grid of the source term position, the penetration probabilities of the boundary positions relative to the grid of the source term position, and the number of virtual surfaces, determine the penetration probability thresholds in each sub-space, and ensure that the direct penetration probabilities in each sub-space are the same;

[0017] Step 4: Generate a plurality of irregular virtual surfaces according to the direct penetration probabilities of each grid position relative to the source term and the penetration probability thresholds of their corresponding sub-spaces.

[0018] Preferably, the generating a plurality of irregular virtual surfaces according to the direct penetration probabilities of each grid position relative to the source term and the penetration probability thresholds of their corresponding sub-spaces includes:

[0019] Starting from the grid of the source term position, search layer by layer from the inside outwards;

[0020] Judge whether the direct penetration probability of each grid is greater than the penetration probability threshold of its corresponding sub-space, and record the grids that meet the conditions;

[0021] After the search of each layer is completed, select the outer surfaces of all the recorded grids as the irregular virtual surfaces of this layer, and remove the parts overlapping with the grid of the source term position and the boundary of the Monte Carlo statistical space region.

[0022] Preferably, before determining the Monte Carlo statistical region of the target and performing grid division on it, it further includes:

[0023] Performing Monte Carlo ensemble modeling on the target and initializing the Monte Carlo calculation program;

[0024] Parse the configuration file to read the geometric structure, source term distribution, statistical region, material properties, and variance reduction parameters.

[0025] Preferably, after parsing the configuration file to read the geometric structure, source term distribution, statistical region, material properties, and variance reduction parameters, it further includes:

[0026] Accept user instructions;

[0027] If the user instruction is not to enable the automatic importance sampling method, directly perform Monte Carlo transport and output the statistical results;

[0028] If the user instruction is to enable the automatic importance sampling method and not to enable the automatic generation of irregular virtual surfaces, after initializing the automatic importance sampling method in the Monte Carlo program, perform Monte Carlo transport and output the statistical results;

[0029] If the user instruction is to enable the automatic importance sampling method and to enable the automatic generation of irregular virtual surfaces, perform Monte Carlo transport and output the statistical results.

[0030] Preferably, if the automatic importance sampling method is enabled, after the Monte Carlo transport process in each subspace ends, adjust the weights and quantities of the generated virtual particles to ensure that the number of virtual particles is the same as the number of source particles.

[0031] Preferably, the automatic generation of multiple irregular virtual surfaces using the radiation field parameters includes:

[0032] Use the radiation field parameters to construct a neural network model to automatically generate multiple irregular virtual surfaces, including:

[0033] Step 1: Construct a neural network model based on the radiation field parameters;

[0034] Step 2: Input the geometric information and source term intensity information in the three-dimensional space into the neural network model to obtain the preliminary predicted distribution of the full-space radiation field;

[0035] Step 3: Based on the preliminary predicted distribution of the full-space radiation field, extract the high-intensity regions and flux attenuation directions of the radiation field, and generate irregular virtual surfaces adapted to the global radiation flux predicted distribution.

[0036] Preferably, the automatic generation of multiple irregular virtual surfaces using the radiation field parameters includes:

[0037] Use the weight window parameters in the radiation field parameters to automatically generate multiple irregular virtual surfaces, including:

[0038] Step 1: Initialize the weight window parameters;

[0039] Step 2: Extract high-weight regions based on the weight window parameters after initialization processing;

[0040] Step 3: Generate irregular virtual surfaces matching the region boundaries based on the high-weight regions and perform dynamic optimization.

[0041] The present invention also provides a Monte Carlo shielding simulation device based on fully automatic importance sampling, including:

[0042] A virtual surface generation module that automatically generates a plurality of irregular virtual surfaces using radiation field parameters;

[0043] A Monte Carlo simulation module for performing Monte Carlo transport based on automatic importance sampling based on the generated plurality of irregular virtual surfaces and outputting statistical results.

[0044] The present invention also provides a Monte Carlo shielding simulation device based on fully automatic importance sampling, including:

[0045] A memory for storing computer programs;

[0046] A processor for implementing the steps of the above-mentioned Monte Carlo shielding simulation method based on fully automatic importance sampling when executing the computer program.

[0047] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned Monte Carlo shielding simulation method based on fully automatic importance sampling are implemented.

[0048] The above technical solutions of the present invention have the following advantages compared with the prior art:

[0049] The Monte Carlo shielding simulation method based on fully automatic importance sampling according to the present invention generates a plurality of irregular virtual surfaces according to the direct penetration probability of each grid position relative to the source term and the penetration probability threshold of its corresponding subspace, realizes the automatic generation of irregular AIS virtual surfaces for global problems, and sets the full process of Monte Carlo calculation, improving the usability of the AIS method. Description of the Drawings

[0050] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the drawings, where:

[0051] Figure 1 is a flowchart of the implementation of a Monte Carlo shielding simulation method based on fully automatic importance sampling provided by the present invention;

[0052] Figure 2Implementation flowchart of the automatic generation method of irregular AIS virtual surfaces based on the penetration probability of each position in space relative to the source term provided by the present invention;

[0053] Figure 3 Schematic diagram of the algorithm flow for generating irregular AIS virtual surfaces;

[0054] Figure 4 Schematic diagram of an example of merging irregular AIS virtual surfaces;

[0055] Figure 5 Implementation flowchart of the Monte Carlo shielding simulation method based on fully automatic importance sampling provided by an embodiment of the present invention;

[0056] Figure 6 Schematic diagram of a simplified reactor example;

[0057] Figure 7 Frequency histogram of the statistical error of neutron flux in the MESH grid of the simplified reactor model;

[0058] Figure 8 Schematic diagram of the cumulative probability distribution of the statistical error of neutron flux in the MESH grid of the simplified reactor model. Specific implementation manners

[0059] The core of the present invention is to provide a Monte Carlo shielding simulation method, device, and equipment based on fully automatic importance sampling, which effectively realizes the automatic generation of irregular AIS virtual surfaces and improves the usability of the AIS method.

[0060] In order to enable those skilled in the art to better understand the solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0061] Please refer to Figure 1 , Figure 1 Implementation flowchart of a Monte Carlo shielding simulation method based on fully automatic importance sampling provided by the present invention; the specific operation steps are as follows:

[0062] S101: Automatically generate a plurality of irregular virtual surfaces by using radiation field parameters.

[0063] Automatically generate a plurality of irregular virtual surfaces by using the penetration probability of each position in space relative to the source term in the radiation field parameters;

[0064] Construct a neural network model by using the radiation field parameters and automatically generate a plurality of irregular virtual surfaces;

[0065] Automatically generate a plurality of irregular virtual surfaces by using the weight window parameter in the radiation field parameters.

[0066] S102: Perform Monte Carlo transport based on automatic importance sampling based on the generated plurality of irregular virtual surfaces, and output statistical results.

[0067] In the Monte Carlo calculation program, the Monte Carlo calculation of the deep penetration radiation field of the reactor is divided into three steps: (1) Source particle sampling: Sample according to the source term distribution function to obtain the initial state of the source particle (2) Simulation of the particle transport process: Determine a series of states of the source particle and its secondary particles in space by sampling. From the previous state of the particle obtain the next state of the particle by random sampling Loop through this sampling process until the particle dies or reaches a convenient position; (3) Statistics and output: During the above particle transport simulation process, record the physical quantities required to be statistically analyzed by the user, and output after the particle transport process simulation is completed. In the Monte Carlo calculation program used in the present invention, the entire particle transport process is described by five core classes, namely Simulation, Cycle, History, Route, and Step. The five classes are called layer by layer from top to bottom to control each link of the particle transport.

[0068] In the AIS method, whenever a particle collides, virtual particles are generated on the nearest virtual surface. Therefore, it is necessary to determine the position where the particle reaches the virtual surface along the current forward direction. In order to process irregular virtual surfaces, the Monte Carlo calculation program has been improved. In the Monte Carlo calculation program, there are two geometric description methods: parallel geometry and true geometry. Parallel geometry only contains the geometric structure defined by the user, while true geometry contains both geometric structure and material information. Although both parallel geometry and true geometry coexist in the calculation space, and particles will stay at the boundaries of both geometries during the transport process, physical reactions only occur in true geometry.

[0069] In this Monte Carlo program, for each irregular virtual surface, a corresponding parallel geometry is established respectively, and all sub-virtual surfaces of the irregular virtual surface are established therein. In the parallel geometry, a thin body geometry with a thickness of 0.001 mm is used to simulate the virtual surface function in the AIS method. This implementation method divides the space into multiple sub-spaces. For each particle, only one surface of the thin body geometry is visible. Therefore, the effect of this thin body is equivalent to that of the virtual surface. In the AIS method, the boundary surface of the above-mentioned geometry approximates the virtual surface. During the transport process of particles, virtual particles are generated and reside on these boundary surfaces. In addition, in the Monte Carlo program, there is already a mature algorithm for judging the distance of the geometry, which can be directly used without additional programming. When the user specifies to use the fully automatic calculation scheme based on AIS, the program will automatically calculate the direct penetration probability of each position in the space relative to the source term, and generate the virtual surface required by the AIS method based on this, and then perform the Monte Carlo transport calculation.

[0070] Please refer to Figure 2 , Figure 2 which is the implementation flowchart of the automatic generation method of the irregular AIS virtual surface based on the penetration probability of each position in the space relative to the source term provided by the present invention; the specific operation steps are as follows:

[0071] S201: Determine the Monte Carlo statistical region of the target and perform grid division on it;

[0072] In some embodiments, the target can be, for example, a reactor. A reactor is a device that uses a controllable nuclear fission chain reaction to release nuclear energy, and is mainly used in fields such as power generation, scientific research, nuclear fuel production, isotope production, and ship power. The core part of the reactor is the core, which contains fuel elements, moderators, coolants, etc., and is used to maintain and control the nuclear fission reaction.

[0073] In reactor physics analysis, the application of the Monte Carlo statistical region mainly includes the following aspects:

[0074] Calculation of neutron flux distribution in the core: By dividing the statistical region, the neutron flux distribution at different positions in the core can be accurately calculated.

[0075] Reaction rate statistics: Used to calculate reaction rates such as absorption, scattering, and fission, and then evaluate the physical performance of the core.

[0076] Burnup calculation: In the burnup calculation, the statistical region is used to track the burnup depth of the fuel and the change of nuclide density.

[0077] Optimizing calculation efficiency: By reasonable region division and parallel calculation, the efficiency of Monte Carlo simulation can be significantly improved, which is suitable for large-scale full-core calculations.

[0078] S202: Obtain the direct penetration probability of each grid position in the Monte Carlo statistical region relative to the source term;

[0079] S203: Divide the sub - space according to the penetration probability of each grid in the space relative to the grid of the source term position, the penetration probability of the boundary position relative to the grid of the source term position, and the number of virtual surfaces, determine the penetration probability threshold in each sub - space, and ensure that the direct penetration probability in each sub - space is consistent;

[0080] S204: Generate a plurality of irregular virtual surfaces according to the direct penetration probability of each grid position relative to the source term and the penetration probability threshold of its corresponding sub - space;

[0081] Based on the above embodiments, this embodiment will elaborate on step S201:

[0082] In some embodiments, before determining the Monte Carlo statistical region of the target and performing grid division, it further includes:

[0083] Perform Monte Carlo ensemble modeling on the target and initialize the Monte Carlo calculation program;

[0084] Parse the configuration files (config, GDML), and read information such as geometric structure, source term distribution, statistical region, material properties, and variance reduction parameters.

[0085] In some embodiments, after parsing the configuration files and reading the geometric structure, source term distribution, statistical region, material properties, and variance reduction parameters, it further includes:

[0086] Accept user instructions;

[0087] If the user instruction is not to enable the automatic importance sampling method, directly perform Monte Carlo transport and output the statistical results;

[0088] If the user instruction is to enable the automatic importance sampling method and not to enable the automatic generation of irregular virtual surfaces, after initializing the automatic importance sampling method in the Monte Carlo program, perform Monte Carlo transport and output the statistical results;

[0089] If the user instruction is to enable the automatic importance sampling method and to enable the automatic generation of irregular virtual surfaces, perform Monte Carlo transport and output the statistical results.

[0090] In a specific embodiment, after completing the Monte Carlo geometric modeling, determine the statistical region R 3 , and divide the entire statistical region into a number of N x , N y , N z of grids along the X, Y, and Z axes respectively

[0091] Based on the above embodiments, this embodiment elaborates on step S202 in detail:

[0092] In a specific embodiment, the entire statistical space R is calculated 3 where the grid N i,j,k (0 ≤ i < N x , 0 ≤ j < N y , 0 ≤ k < N z ) at the position with respect to the direct penetration probability P relative to the source term position i,j,k ;

[0093]

[0094] wherein, is the direction vector of each position in the space with respect to the source term position ; Σ t is the macroscopic cross-section, and E i is the particle energy.

[0095] Based on the above embodiments, this embodiment elaborates on step S203 in detail:

[0096] In Monte Carlo simulation, a subspace refers to multiple local regions formed by dividing through virtual surfaces. Each subspace has its own boundary (virtual surface), and when particles are transported between these subspaces, weight adjustment and quantity control will be performed. This division method can effectively improve the calculation efficiency, especially when dealing with small probability events (such as deep penetration problems).

[0097] In a specific embodiment, according to the penetration probability P of the grid N s at the source term position s , calculate the penetration probability P at the boundary position end and the number of virtual surfaces N, and determine the penetration probability θ n (0 ≤ n < N) in each subspace to ensure that the direct penetration probability in each subspace is consistent:

[0098] Starting from the grid at the source term position, determine the penetration probability threshold θ n of the nth subspace as:

[0099] θ n = P s - (P s - P end ) / N * n

[0100] where P s is the penetration probability of the grid at the source term position, P endTo calculate the penetration probability of the boundary position, N is the number of virtual planes, and n is the subspace index.

[0101] Based on the above embodiments, this embodiment will elaborate on step S204:

[0102] In a reactor, due to strong geometric anisotropy, it is often difficult to obtain good variance reduction calculation results using a single conventional virtual plane. The irregular AIS virtual plane can be described as a set composed of a finite number of planes and cylindrical surfaces, and each plane and cylindrical surface has its own parametric equation. Their parametric equations can be represented as a set and spliced in space. Suppose there are N planes and M cylindrical surfaces, and their parametric equations are respectively:

[0103] F i (u i ,v i )=(x i (u i ,v i ),y i (u i ,v i ),z i (u i ,v i )) (2)

[0104] G j (u j ,v j )=(x j (u j ,v j ),y j (u j ,v j ),z j (u j ,v j )) (3)

[0105] Represent these parametric equations as a set

[0106] S={F i (u i ,v i )G j (u j ,v j )|1≤i≤N,1≤j≤M} (4)

[0107] Based on a series of conventional virtual planes (planes, cylindrical surfaces), users can combine them to form virtual planes suitable for different geometric shapes. Among them, each virtual plane is composed of several sub-virtual planes, and the sub-virtual planes are spliced to form a complete plane for particle transport calculation. Then, the irregular AIS virtual plane can be expressed as:

[0108] S = {F i ∪ F i+1 ∪ … ∪ G j ∪ G j+1 , |1 ≤ i ≤ N, 1 ≤ j ≤ M} (5)

[0109] Based on a series of conventional virtual surfaces (plane, cylindrical surface), users can combine them to form virtual surfaces suitable for different geometric shapes. Among them, each virtual surface is composed of several sub - virtual surfaces, and the sub - virtual surfaces are spliced to form a complete surface for particle transport calculation. Then, the irregular AIS virtual surface can be expressed as:

[0110] S = {F i ∪ F i+1 ∪ … ∪ G j ∪ G j+1 , |1 ≤ i ≤ N, 1 ≤ j ≤ M} (6)

[0111] Assume that in the entire calculation space R 3 in, the position coordinates at each location in the space are X i , the direct penetration probability is p i , and the class value is y i . Among them, X i is a column vector containing 3 elements, that is, X i ∈ R 3 , representing the coordinates in three - dimensional space respectively. Assume that the direct penetration probability in each subspace is θ. Then, the class value y 3 at each location in the calculation space R i and the direct penetration probability p i have the following relationship:

[0112] p i ≥ θ, y i = +1 (7)

[0113] p i < θ, y i = -1

[0114] The following form of data set can be obtained:

[0115] (X1, y1), (X2, y2), …, (X n , y n ) (8)

[0116] Among them, X i ∈ R 3 , representing the three - dimensional coordinates of each location in three - dimensional space respectively; y i is a scalar, y ∈ {+1, -1}, when y i = +1, it means X iBelonging to the positive category, y i When = -1, it represents X i Belongs to the negative category.

[0117] Under the simple geometric conditions of isotropy, the problem of generating the AIS virtual surface is essentially a binary linear classification problem in three-dimensional space, and it can usually be processed by using the plane Support Vector Machine (SVM) algorithm. Find the support vectors in the dataset to separate the samples of different categories, maximize the interval between the two categories, so as to obtain the optimal separation hyperplane with different penetration probabilities, that is, the required virtual surface parameters. In the complex geometry in the reactor, the complexity of the geometry in space makes it impossible to achieve ideal calculation results by using a single conventional virtual surface.

[0118] In some embodiments, according to the direct penetration probability of each grid position relative to the source term and the penetration probability threshold of its corresponding subspace, generating a plurality of irregular virtual surfaces includes:

[0119] Starting from the grid at the source term position, search layer by layer from the inside out;

[0120] Judge whether the direct penetration probability of each grid is greater than the penetration probability threshold of its corresponding subspace, and record the grids that meet the conditions;

[0121] After the search of each layer is completed, select the outer surfaces of all the recorded grids as the irregular virtual surface of this layer, and remove the parts that overlap with the grid at the source term position and the boundary of the Monte Carlo statistical space region.

[0122] In one embodiment, the present invention also provides an automatic generation method for an irregular AIS virtual surface based on a neural network, specifically as follows:

[0123] (1) Selection and construction of the neural network model:

[0124] Use the neural network to solve the transport equation, such as the neutron transport equation under steady state:

[0125]

[0126] Among them, ψ(r,Ω,E) is the neutron angular flux density, which represents the neutron flux per unit volume at position r, direction Ω and energy E. Σ t (r,E) is the total cross section, which represents the total probability of neutrons interacting with matter at position r and energy E. Σs(r,E′→E,Ω′→Ω) is the scattering cross section, which represents the probability that neutrons are scattered from energy E′ and direction Ω′ to energy E and direction Ω. S(r,Ω,E) is the source term, including external sources and fission sources, etc.

[0127] The selected neural network has the ability to solve partial differential equations, including but not limited to Fourier Neural Operator (FNO), Deep Operator Network (DeepONet), Physics-Informed Neural Network (PINN), etc. By training on the radiation field data of existing benchmark problems, the network model has strong radiation field distribution prediction ability.

[0128] (2) Definition of input and output data:

[0129] The input of the neural network is the geometric information and source term intensity information in three-dimensional space, and the output is the preliminary predicted distribution of the radiation field in the whole space.

[0130] Input features: Include key information such as voxel geometric features, material properties, source term distribution, etc.

[0131] Output features: Spatial distribution of radiation field flux

[0132] (3) Prediction of radiation field distribution:

[0133] Input the data of the target geometric region and the source term intensity into the neural network to obtain the preliminary predicted distribution of the radiation field in the whole space. Since there may be certain deviations in the calculation results of the neural network, this radiation field distribution is not completely accurate, but it can reflect the overall trend of the radiation field.

[0134] (4) Setting of virtual surface parameters:

[0135] According to the radiation field distribution output by the neural network, extract the high-intensity regions and flux attenuation directions of the radiation field, and set the AIS virtual surface based on this. The position, shape, and number of the virtual surface are dynamically adjusted according to the irregularity of the radiation field distribution, so as to optimize the coverage of the virtual surface for key regions.

[0136] (5) Automatic generation of AIS virtual surface:

[0137] Based on the set virtual surface parameters, automatically generate irregular AIS virtual surfaces adapted to the geometric structure. The virtual surface serves as the basis for important sampling, further improving the accuracy and efficiency of radiation field calculation.

[0138] (6) Verification and optimization:

[0139] Verify the generated AIS virtual surface, and evaluate the applicability of the virtual surface through the actual transport calculation results. Iteratively optimize the neural network model and the virtual surface generation strategy according to the evaluation results to ensure the stability and robustness of the method.

[0140] This method fully combines the efficient prediction ability of neural networks with the flexibility of the AIS virtual surface, enabling the rapid construction of highly adaptable irregular virtual surfaces in complex geometric structures, significantly improving the solution efficiency of the transport equation, and providing a new idea for radiation field calculation and related engineering applications.

[0141] In one embodiment, the present invention also provides a method for automatically generating an irregular AIS virtual surface based on weight window parameters, which is as follows:

[0142] This method uses the weight window parameter (Weight Window Parameter, WWP) in the radiation field distribution to dynamically generate an irregular AIS virtual surface, realizing efficient sampling and calculation of the radiation field. The following is a specific description:

[0143] (1) Definition and initialization of weight window parameters:

[0144] The weight window parameter (WWP) is used to describe the importance weights of different regions in space and is often calculated from the radiation field intensity and gradient changes. It can be set through physical prior knowledge or by solving the adjoint transport equation, etc.

[0145] (2) Automatic generation of the irregular AIS virtual surface:

[0146] a. Extract high-weight regions from the weight window parameter distribution.

[0147] b. Use an algorithm to generate an irregular virtual surface that matches the region boundary.

[0148] c. Dynamically optimize the position and shape of the virtual surface to ensure that the sampling covers important regions.

[0149] The present invention realizes the automatic generation function of the virtual surface of the automatic importance sampling method, solves the problem that the setting process of the AIS virtual surface overly relies on user experience, and further improves the calculation efficiency of the Monte Carlo program compared with the manually set AIS virtual surface.

[0150] As Figure 3 shown, in a specific embodiment:

[0151] Starting from the grid N s at the source term, search layer by layer from the inside out, and judge whether the direct penetration probability P i,j,k of each grid N i,j,k is greater than the penetration probability θ n in each subspace, and at the same time record the index of the grid N i,j,k ;

[0152] After the search of each layer of virtual surface grid is completed, select the outer surface of all the recorded grids as the virtual surface of this layer, excluding the source term grid N s and the transport space R3 The overlapping parts of the boundaries are used to ensure that the virtual surfaces are spliced completely without omission, and the virtual surface information of this layer is output according to the requirements;

[0153] Finally, N irregular virtual surfaces are generated.

[0154] As described above, the grid-based irregular AIS virtual surface is formed by splicing each grid surface in each space as each sub-virtual surface of the irregular virtual surface to obtain a complete irregular AIS virtual surface. However, usually, in order to obtain refined calculation results, the grids in the calculation space are often divided densely, resulting in a very large number of sub-virtual surfaces and excessive discretization of the virtual surface. For example: in a cubic calculation space, if the calculation space is divided into 100 grids along the X, Y, and Z directions respectively, then a plane virtual surface perpendicular to the coordinate axis with the smallest number of grids also needs to be spliced by at least 10,000 planes. Too many sub-virtual surfaces may increase the complexity of the irregular virtual surface combination, and the complexity of virtual particle positioning calculation also increases accordingly. Therefore, an algorithm needs to be designed to merge adjacent virtual surfaces to reduce the complexity of the irregular virtual surface combination. In order to merge the virtual surfaces relatively evenly and without obvious directionality, while taking into account intuitiveness and operational simplicity.

[0155] In one embodiment, an iterative method is used to merge the irregular AIS virtual surfaces:

[0156] After the irregular virtual surfaces of each layer are generated, all sub-virtual surfaces of the irregular virtual surfaces of this layer are divided according to the virtual surface normal vector, and in the same normal vector, all sub-virtual surfaces are classified according to the coordinate axes;

[0157] In each class of sub-virtual surfaces with the same coordinates, they are sorted according to any of the remaining two coordinates;

[0158] After the sorting is completed, two adjacent sub-virtual surfaces that can be merged are merged, and after the merging is completed, another coordinate is replaced to re-sort the sub-virtual surfaces, and this step is repeated until there are no adjacent sub-virtual surfaces that can be merged.

[0159] As Figure 4 shown, in a specific embodiment:

[0160] (1) Read in any layer of irregular AIS virtual surface S i ={F i,j ∪F i,j+1 ,|1≤i≤K}, which is constructed by several regular sub-virtual surfaces F i (u i ,v i );

[0161] (2) All sub-virtual surfaces Fj (u j , v j ) is divided according to the virtual plane normal vector , and in the same normal vector , the sub-virtual plane F j (u j , v j ) is classified according to the coordinate axes;

[0162] (3) In each category of sub-virtual plane F j (u j , v j ) with the same coordinates, according to any one of the remaining two coordinates, the sub-virtual plane F j (u j , v j ) is sorted;

[0163] (4) After sorting, check whether two adjacent sub-virtual planes F j (u j , v j ) can be merged. If merged, process the indices i, j of the sub-virtual plane F j (u j , v j );

[0164] (5) After the current sub-virtual plane F j (u j , v j ) is merged, reverse the previous sorting coordinates and re-sort the sub-virtual plane F j (u j , v j );

[0165] (6) Iterate steps (4) and (5) until there are no adjacent sub-virtual planes F j (u j , v j ) that can be merged, then the optimization process of the irregular AIS virtual plane S i = {F i,j ∪ F i,j+1 , |1 ≤ i ≤ K} terminates.

[0166] This embodiment realizes the automatic generation function of the virtual plane of the automatic importance sampling method, and solves the problem that the setting process of the AIS virtual plane relies too much on user experience.

[0167] In one embodiment, for the case of an irregular virtual surface, the present invention calculates the division of MESH grids in space, calculates the direct penetration probability of the center position of each MESH grid relative to the source term position, and uses the direct penetration probability at different positions as the division basis, with the surface of the MESH grid as the irregular virtual surface, as Figure 5 shown:

[0168] (1) Complete Monte Carlo geometry modeling, initialize the Monte Carlo calculation program, parse the config and GDML files, and read information such as geometry, source term, statistics, materials, and variance reduction. If the user selects to use the AIS method, then execute step

[0169] (2), otherwise execute step (7);

[0170] (2) If the user selects automatic generation of the AIS virtual surface, then execute step (3), otherwise complete the initialization of the AIS method in the Monte Carlo calculation program and execute step (7);

[0171] (3) Determine the statistical region R 3 , and divide the entire statistical region along the X, Y, and Z axes into numbers N x , N y , N z of grids, and calculate the direct penetration probability P 3 in the entire transport space R i,j,k (0 ≤ i < N x , 0 ≤ j < N y , 0 ≤ k < N z ) of the position relative to the source term position ; i,j,k ;

[0172] (4) According to the penetration probability P of the grid N s at the source term position s , calculate the penetration probability P at the boundary position end and the number N of virtual surfaces, and determine the penetration probability threshold θ n (0 ≤ n < N) in each subspace to ensure that the direct penetration probability in each subspace is consistent;

[0173] (5) Based on the penetration probability threshold θ i (0 ≤ i < N) in each subspace, and in the entire transport space R 3 , for each grid N i,j,k (0 ≤ i < N x , 0 ≤ j < N y , 0 ≤ k < N z ) of the position relative to the source term position Direct penetration probability P i,j,k , generate N AIS virtual surfaces;

[0174] (6) Update the generated AIS virtual surfaces in the Monte Carlo calculation program and complete the initialization of the AIS method;

[0175] (7) Start the particle transport calculation, transport all particle processes respectively, and record the statistical results during the transport process. If the user chooses to use the AIS method, virtual particles are normally generated during the transport process, and the weights and quantities of virtual particles are adjusted after the transport of this subspace is completed to ensure that the number of virtual particles is the same as the number of source particles;

[0176] (8) The particle transport process ends, output the statistical results, and end the Monte Carlo transport process.

[0177] The present invention divides grids in the calculation space, does not involve coupling with other commercial software, and does not require grid meshing. The setting method of the grid is also the same as that of the MESH grid in the Monte Carlo program, which will not bring additional usage difficulties to users.

[0178] As Figure 6 shown, in one embodiment, a simplified reactor example is used to verify the proposed scheme of the present invention, and the calculation efficiencies of the AIS method and the CADIS method are compared. Table 1 shows the proportion of grids with different statistical errors in the calculation results under different calculation methods. Table 2 shows the comparison of the calculation efficiency statistical results under different calculation methods. Figure 7 is the frequency histogram of the MESH grid statistical error under different calculation methods. Figure 8 is the cumulative probability distribution of the MESH grid statistical error under different calculation methods.

[0179] Table 1 Statistical errors of neutron flux with different virtual surfaces and different numbers of particles in the simplified reactor model

[0180]

[0181] Table 2 Calculation efficiencies with different virtual surfaces and different numbers of particles in the simplified reactor model

[0182]

[0183] The results show that the irregular virtual surface has a certain improvement in the grid average statistical error compared with the CADIS method. There are almost no MESH grids with a statistical error greater than 50.00% in the statistical results of the two methods, which is significantly improved compared with the conventional virtual surface method. In terms of calculation efficiency, the calculation efficiency of the irregular virtual surface method is about 2 times higher than that of the CADIS method and about 2 - 7 times higher than that of the conventional virtual surface method.

[0184] The solution proposed by the present invention divides grids in the calculation space, calculates the direct penetration probability of the center position of each grid relative to the source term position, and generates irregular virtual surfaces based on this for Monte Carlo calculation. During the whole process, there is no need to use a deterministic program and a Monte Carlo program for coupled calculation, and only one set of programs is required for one simulation calculation. The present invention realizes the automatic generation, simplification and automatic calculation process of irregular AIS virtual surfaces, and improves the calculation effect of the original AIS method in the calculation of the deep penetration radiation field of a reactor. The fully automatic calculation solution for the deep penetration radiation field has certain advantages over the CADIS method in terms of usability and calculation efficiency.

[0185] The embodiment of the present invention also provides a Monte Carlo shielding simulation device based on fully automatic importance sampling; the specific device may include:

[0186] A virtual surface generation module that automatically generates a plurality of irregular virtual surfaces using radiation field parameters;

[0187] A Monte Carlo simulation module for performing Monte Carlo transport based on the generated plurality of irregular virtual surfaces and outputting statistical results.

[0188] The Monte Carlo shielding simulation device based on fully automatic importance sampling in this embodiment is used to implement the aforementioned Monte Carlo shielding simulation method based on fully automatic importance sampling. Therefore, the specific implementation manners in the Monte Carlo shielding simulation device based on fully automatic importance sampling can be seen in the embodiment part of the aforementioned Monte Carlo shielding simulation method based on fully automatic importance sampling. For example, the virtual surface generation module and the Monte Carlo simulation module are respectively used to implement steps S101 and S102 in the aforementioned Monte Carlo shielding simulation method based on fully automatic importance sampling. Therefore, its specific implementation manners can refer to the descriptions of the corresponding individual embodiment parts and will not be elaborated here.

[0189] The specific embodiment of the present invention also provides a Monte Carlo shielding simulation device based on fully automatic importance sampling, including: a memory for storing a computer program; a processor for implementing the steps of the aforementioned Monte Carlo shielding simulation method based on fully automatic importance sampling when executing the computer program.

[0190] The specific embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored, and the computer program realizes the steps of the aforementioned Monte Carlo shielding simulation method based on fully automatic importance sampling when executed by a processor.

[0191] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0192] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0193] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0194] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0195] Obviously, the above embodiments are merely examples given for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to exhaustively list all the implementation manners here. And the obvious changes or variations derived therefrom still fall within the protection scope of the present invention.

Claims

1. A Monte Carlo simulation method based on fully automatic importance sampling, characterized in that: include: Automatically generate multiple irregular virtual surfaces using radiation field parameters; Based on the generated multiple irregular virtual surfaces, Monte Carlo transport based on automatic importance sampling is performed to output statistical results.

2. The Monte Carlo simulation method based on fully automatic importance sampling according to claim 1 is characterized in that: The method of automatically generating a plurality of irregular virtual surfaces by using radiation field parameters comprises: A plurality of irregular virtual surfaces are automatically generated using the penetration probability of each spatial position relative to the source term in the radiation field parameters, including: Step 1: Determine the Monte Carlo statistical area of ​​the target and divide it into grids; Step 2: Obtain the direct penetration probability of each grid position in the Monte Carlo statistical area relative to the source item; Step 3: Divide the subspace according to the penetration probability of each grid in the space relative to the source position grid, the penetration probability of the boundary position relative to the source position grid, and the number of virtual faces, determine the penetration probability threshold in each subspace, and ensure that the direct penetration probability in each subspace is consistent; Step 4: Generate multiple irregular virtual surfaces based on the direct penetration probability of each grid position relative to the source item and the penetration probability threshold of its corresponding subspace.

3. The Monte Carlo simulation method based on fully automatic importance sampling according to claim 2 is characterized in that: The step of generating a plurality of irregular virtual surfaces according to the direct penetration probability of each grid position relative to the source item and the penetration probability threshold of the corresponding subspace includes: Starting with the source item position grid, search from the inside out hierarchically; Determine whether the direct penetration probability of each grid is greater than the penetration probability threshold of the corresponding subspace, and record the grids that meet the conditions; After each layer of search is completed, the outer surfaces of all recorded grids are selected as the irregular virtual surfaces of this layer, and the parts overlapping with the source item position grid and the Monte Carlo statistical space region boundary are removed.

4. The Monte Carlo simulation method based on fully automatic importance sampling according to claim 2 is characterized in that: The method of determining the Monte Carlo statistical area of ​​the target and dividing it into grids also includes: Perform Monte Carlo ensemble modeling on the target and initialize the Monte Carlo calculation program; Parse the configuration file to read the geometry, source term distribution, statistical regions, material properties, and variance reduction parameters.

5. The Monte Carlo simulation method based on fully automatic importance sampling according to claim 4 is characterized in that: The analytical configuration file, after reading the geometric structure, source term distribution, statistical area, material properties and variance reduction parameters, also includes: Accept user instructions; If the user instruction is not to start the automatic importance sampling method, the Monte Carlo transport is directly performed to output the statistical results; If the user instruction is to start the automatic importance sampling method and not to start the automatic generation of irregular virtual surfaces, then after the initialization of the automatic importance sampling method is completed in the Monte Carlo program, the Monte Carlo transport is performed and the statistical results are output; If the user instruction is to start the automatic importance sampling method and start the automatic generation of irregular virtual surfaces, Monte Carlo transport is performed and the statistical results are output.

6. The Monte Carlo simulation method based on fully automatic importance sampling according to claim 3 is characterized in that: If the automatic importance sampling method is turned on, after the Monte Carlo transport process of each subspace is completed, the weights and number of generated virtual particles are adjusted to ensure that the number of virtual particles is consistent with the number of source particles.

7. The Monte Carlo simulation method based on fully automatic importance sampling according to claim 1, characterized in that: The method of automatically generating a plurality of irregular virtual surfaces by using radiation field parameters comprises: The radiation field parameters are used to construct a neural network model to automatically generate multiple irregular virtual surfaces, including: Step 1: constructing a neural network model based on the radiation field parameters; Step 2: Input the geometric information and source term intensity information in the three-dimensional space into the neural network model to obtain the preliminary predicted distribution of the radiation field in the whole space; Step 3: Based on the preliminary predicted distribution of the full-space radiation field, extract the high-intensity area and flux attenuation direction of the radiation field, and generate an irregular virtual surface that is compatible with the predicted distribution of the global radiation flux.

8. The Monte Carlo simulation method based on fully automatic importance sampling according to claim 1, characterized in that: The method of automatically generating a plurality of irregular virtual surfaces by using radiation field parameters comprises: A plurality of irregular virtual surfaces are automatically generated using the weight window parameters in the radiation field parameters, including: Step 1: Initialize the weight window parameters; Step 2: Extract high-weight areas based on the weight window parameters after initialization; Step 3: Based on the high-weight region, an irregular virtual surface matching the region boundary is generated and dynamically optimized.

9. A Monte Carlo simulation device based on fully automatic importance sampling, characterized in that: include: Virtual surface generation module, which uses radiation field parameters to automatically generate multiple irregular virtual surfaces; The Monte Carlo simulation module is used to perform Monte Carlo transport based on automatic importance sampling based on multiple generated irregular virtual surfaces and output statistical results.

10. A Monte Carlo masking simulation device based on fully automatic importance sampling, characterized in that: include: Memory for storing computer programs; A processor is used to implement the steps of a Monte Carlo masking simulation method based on fully automatic importance sampling as described in any one of claims 1 to 8 when executing the computer program.

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