Method and system for eliminating Monte Carlo variance underestimation phenomenon, and acquisition method

Abstract

The present invention provides a method and system for eliminating the low- variance underestimation phenomenon in Monte Carlo calculations, and a method for obtaining Monte Carlo calculation results. The elimination method includes: obtaining the generation interval n0 with approximate neglect of the inter-generation correlation of the fission source distribution; determining the group length l of the group statistical method as l = n0; and using the group statistical method to obtain the Monte Carlo calculation results that completely eliminate the low- variance underestimation phenomenon in Monte Carlo calculations. The elimination method, system, and method for obtaining Monte Carlo calculation results achieve effective prediction and elimination of the low- variance underestimation phenomenon in Monte Carlo calculations, can meet engineering practicality, and improve the accuracy of the calculation results obtained based on the Monte Carlo algorithm.

Description

Technical Field

[0001] The present invention specifically relates to a method and system for eliminating the low - estimation phenomenon of Monte Carlo variance, and a method for obtaining Monte Carlo calculation results. Background Art

[0002] The Monte Carlo transport code is one of the commonly used tools in the field of Monte Carlo nuclear physics calculations. Using the Monte Carlo transport code, physical modeling and particle transport calculations of nuclear - related facilities such as reactor cores and critical safety devices can be carried out. The Monte Carlo algorithm usually adopts a source iteration process. A user - defined source is used as the initial source, and transport simulations are performed and its descendants are stored in the particle library; during the next - generation sampling, a new source distribution is obtained by randomly sampling from the neutron library of the previous generation, and transport simulations are performed again to obtain a new particle library. This process is repeated until a converged source distribution is obtained and then the statistics of each physical quantity are started. During the source iteration process, since there is an obvious physical and mathematical relationship between the particle library of each generation and the sampling source distribution of this generation, there is a certain correlation between the source distributions of each converged generation. And the calculation variance of Monte Carlo will be lower than the true variance value due to the influence of the source distribution correlation. This phenomenon is called the low - estimation phenomenon of Monte Carlo variance.

[0003] To reduce the low - estimation phenomenon of variance, researchers have proposed various methods. Brissenden and Garlick proposed the super - history method to reduce the inter - generation correlation (see: R.J. Brissenden, A.R. Garlick. Biases in the estimation of Keff and its error by Monte Carlo methods[J]. Annals of Nuclear Energy, Volume 13, 1986). Gelbard and Prael proposed using the method of group statistics, grouping multiple active generations into one group, thereby reducing the inter - group correlation and obtaining a statistical variance closer to the true variance (see: Gelbard E M, Prael R. Computation of standard deviations in Eigenvalue calculations. Progress in Nuclear Energy, 1990). However, how to determine the number of active generations that each group should contain is a difficult point. In 2013, She Ding proposed in his doctoral thesis that the number of non - active generations can be used as the length of group statistics, but there is a lack of a rigorous theoretical basis (see: She Ding, Research on Burnup and Source Convergence Problems Based on the Self - developed Monte Carlo Code RMC for Reactor Applications[D], Beijing: Department of Engineering Physics, Tsinghua University, 2013).

[0004] Another theoretical approach lies in estimating the variance underestimation coefficient, that is, obtaining the ratio of the statistical variance to the true variance through some statistics. MacMillan proposed using a variance correction formula based on the dominance ratio (see: MacMillan DB. Monte Carlo confidence limits for iterated-source calculations[J]. Nuclear Science and Engineering, 1973), Ueki used the autocorrelation sequence analysis method to study the underestimation phenomenon (see: Ueki T, Nease B R. Time series analysis of monte carlo fission sources-II: confidence interval estimation[J]. Nuclear science and engineering, 2006), and Kiedrowski attempted to apply the Wielandt method to variance underestimation correction (see: Kiedrowski B C, Brown FB. Using Wielandt's method to eliminate confidence interval underprediction bias in MCNP5 criticality calculations[J]. Transactions of the American Nuclear Society, 2008). Among them, the theory based on the covariance matrix of the fission source distribution has been relatively well-developed through the work of many researchers. This theory was initially applied by Ueki, Mori, and Nakagawa to the correction of the variance underestimation of Keff. In 2009, Shim generalized this theory to a correction theory that can calculate the variance underestimation of local counters, related the variance underestimation coefficient of local counters to the covariance matrix of the fission source distribution (FSD) through a mathematical relationship, and proposed a calculation method for estimating the FSD covariance matrix (see: Shim H J, Kim C H. Real variance estimation using an intercycle fission source correlation for Monte Carlo eigenvalue calculations[J]. Nuclear science and engineering, 2009). However, the implementation of this theory depends on grid division and the calculation process is relatively cumbersome, so its practicality is not high.During 2014-2018, based on the work of Ueki et al., Miao et al. conducted a large number of theoretical studies on the calculation of the autocorrelation coefficient (ACC), but still failed to realize the practical application of the calculation of the low variance estimation coefficient (see: Jilang Miao, Benoit Forget, Kord Smith. Analysis of correlations and their impact on convergence rates in Monte Carlo eigenvalue simulations[J]. Annals of Nuclear Energy, Volume 92, 2016).

[0005] In summary, the current theoretical research on the low variance estimation phenomenon is relatively in-depth, but the existing methods for eliminating the low variance estimation phenomenon still have the following problems: the calculation method of the low estimation coefficient does not have engineering operability; the group statistical method lacks a theoretical basis for judging the number of active generations that each group should contain, so the accuracy of the calculation results cannot be guaranteed. From the perspective of engineering calculations, since a large number of reactors and critical safety facilities need to use the Monte Carlo algorithm for modeling and simulation calculations, and the nuclear field has high requirements for the accuracy of the calculation results, there is an urgent need for a method for eliminating the low variance estimation phenomenon to solve the problems that the existing methods do not have engineering practicability and the accuracy of the calculation results is low. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method and system for eliminating the low variance estimation phenomenon of Monte Carlo, and a method for obtaining Monte Carlo calculation results, which can meet engineering practicability and make the calculation results obtained based on the Monte Carlo algorithm highly accurate, aiming at the above-mentioned deficiencies existing in the prior art.

[0007] In the first aspect, the present invention provides a method for eliminating the low variance estimation phenomenon of Monte Carlo, including: obtaining the number of generations n between which the inter-generation correlation of the fission source distribution is approximately ignored 0 ; determining the group length l=n of the group statistical method 0 ; using the group statistical method to obtain Monte Carlo calculation results that completely eliminate the low variance estimation phenomenon of Monte Carlo.

[0008] Preferably, the obtaining the number of generations n between which the inter-generation correlation of the fission source distribution is approximately ignored 0 , specifically includes: using the Sliced Wasserstein distance to characterize the correlation of the fission source distribution; obtaining the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations based on the relationship between the Sliced Wasserstein distance and the number of generations, so as to obtain the number of generations n between which the inter-generation correlation is approximately ignored 0 .

[0009] Preferably, obtain the semi - quantitative relationship of the inter - generation correlation of the fission source distribution with the number of generations apart according to the relationship between the Sliced Wasserstein distance and the number of generations apart, so as to obtain the number of generations apart n when the inter - generation correlation can be approximately ignored 0 , specifically including: calculating the semi - quantitative relationship of the inter - generation correlation of the fission source distribution with the number of generations apart along any one of the x / y / z directions according to the following formula, so as to obtain the Sliced Wasserstein distance of the one - dimensional slice of the fission source distribution in the x / y / z direction separated by j generations:

[0010]

[0011] where S i and S i-j are the fission source distributions of the i - th generation and the (i - j) - th generation, SW x is the Sliced Wasserstein distance along the x - direction, x i , x i-j are the slice sequences of the fission source distributions of the i - th generation and the (i - j) - th generation along the x - direction respectively, d(x,y) is the distance function between x i , x i-j , N is the length of the slice sequence of the fission source distribution along the x - direction, e (i) -e (i-j) is the inter - generation correlation separated by j generations calculated according to the error between the fission source distributions of the i - th generation and the (i - j) - th generation, and satisfies the following formula:

[0012]

[0013] where e (i) is the vector definition formula of the error term of the fission source distribution of the i - th generation, A is the error transfer matrix in the Monte Carlo source iteration process, ε (i) is the random error introduced in the i - th generation. As j increases, the error of the fission source distribution separated by j generations gradually increases and gradually approaches the norm value of the random error term itself of the current generation:

[0014] ||e (i) ||>||e (i) -e (i-j) ||>…||e (i) -e (i-1) ||

[0015] When E(||e (i) ||)≈E(||e (i) -e (i-n) ||), based on statistical significance, the average correlation of the fission source distributions separated by n generations can be approximately ignored, where E is the mathematical expectation, ||e (i) || is e(i) The norm; combine the Sliced Wasserstein distances of three one-dimensional slices of the fission source distributions separated by j generations along the x, y, and z directions to obtain the average Sliced Wasserstein distance; determine the number of generations n between generations when the average Sliced Wasserstein distance first reaches the maximum value as the number of generations between generations with approximately negligible inter-generation correlation. 0 。

[0016] Preferably, before calculating the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations between generations along any one of the x / y / z directions, the method for eliminating the Monte Carlo variance underestimation phenomenon further includes: according to the similarity between the Sliced Wasserstein distance and the Wasserstein distance, use the Sliced Wasserstein distance to calculate the distance between two probability distributions, and the specific calculation formula is as follows:

[0017]

[0018] where S n and S r are two probability distributions,

[0019] is and the distance function of the

[0020]

[0021] values, and the Wasserstein distance satisfies the following formula:

[0022] where γ(x,y) is the probability density function and d(x,y) is the distance function of x and y values;

[0023] Based on the application of the Monte Carlo algorithm, the calculation formula for characterizing the fission source distribution error term using the Sliced Wasserstein distance is as follows: (i) -e (i-j) || = SW(S i ,S i-j )

[0024] where the distance function of the Sliced Wasserstein distance selects the 1-norm, and S i and S i-j are the fission source distributions of the i-th generation and the i-j-th generation; according to the Sliced Wasserstein distance and its calculation formula for characterizing the fission source distribution error term, deduce the calculation formula for the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations between generations along any one of the x / y / z directions.

[0025] Preferably, combining the Sliced Wasserstein distances of three one-dimensional slices of the fission source distributions separated by j generations along the x, y, and z directions specifically includes: combining the Sliced Wasserstein distances of three one-dimensional slices of the fission source distributions separated by j generations along the x, y, and z directions according to the method of quadrature or summation.

[0026] Preferably, the group length l of the group statistical method is n 0 , specifically including: when the Sliced Wasserstein distances separated by n 0 generations satisfy the following relationship::

[0027]

[0028] Then it is determined that there is no mathematical correlation in the statistical sense between the fission source distributions separated by n 0 generations; according to the law of large numbers, it is obtained that: (j > n, l is large enough),

[0029]

[0030] wherein, the group length l of the group statistical method is taken as n 0 , and the expression of the group statistical method is obtained:

[0031]

[0032] In a second aspect, the present invention also provides a method for obtaining Monte Carlo calculation results, including: preparing an input first card and an input second card of a Monte Carlo program; using an in-coupling or out-coupling Monte Carlo program and the method for eliminating the low Monte Carlo variance estimation phenomenon described in the first aspect to calculate the input first card, obtaining the average Sliced Wasserstein distance and the number of generations n 0 separated; using the group statistical method of Monte Carlo and the method for eliminating the low Monte Carlo variance estimation phenomenon described in the first aspect with the number of generations n 0 separated as the group length to calculate the input second card, obtaining the Monte Carlo calculation result.

[0033] In a third aspect, the present invention also provides a system for eliminating the low Monte Carlo variance estimation phenomenon, including an acquisition module, a determination module, and a calculation module.

[0034] The acquisition module is used to acquire the number of generations n separated when the inter-generation correlation of the fission source distribution can be approximately ignored 0 . The determination module is connected to the acquisition module and is used to determine that the group length l of the group statistical method is n 0. A calculation module, connected to the determination module, is used to calculate the Monte Carlo calculation result that completely eliminates the low estimation phenomenon of Monte Carlo variance by using the group statistical method.

[0035] Preferably, the acquisition module includes a first acquisition unit and a second acquisition unit.

[0036] The first acquisition unit is used to characterize the correlation of the fission source distribution by using the Sliced Wasserstein distance. The second acquisition unit, connected to the first acquisition unit, is used to obtain the semi-quantitative relationship of the inter-generation correlation of the fission source distribution with the number of generations apart according to the relationship between the Sliced Wasserstein distance and the number of generations apart, so as to obtain the number of generations apart n when the inter-generation correlation is approximately negligible. 0 .

[0037] Preferably, the second acquisition unit includes a calculation component, a combination component and a determination component.

[0038] The calculation component is used to calculate the semi-quantitative relationship of the inter-generation correlation of the fission source distribution with the number of generations apart along any one of the x / y / z directions according to the following formula, so as to obtain the Sliced Wasserstein distance of the one-dimensional slice of the fission source distribution along any one of the x / y / z directions separated by j generations:

[0039]

[0040] where S i and S i-j are the fission source distributions of the i-th generation and the i-j-th generation, SW x is the Sliced Wasserstein distance along the x direction, x i , x i-j are the slice sequences of the fission source distributions of the i-th generation and the i-j-th generation along the x direction respectively, d(x,y) is the distance function of x i , x i-j , N is the length of the slice sequence of the fission source distribution along the x direction, e (i) -e (i-j) is the inter-generation correlation separated by j generations calculated according to the error of the fission source distributions of the i-th generation and the i-j-th generation, and satisfies the following formula:

[0041]

[0042] where e (i) is the vector definition formula of the error term of the fission source distribution of the i-th generation, A is the error transfer matrix in the Monte Carlo source iteration process, ε (i) is the random error introduced in the i-th generation. As j increases, the error of the fission source distribution separated by j generations gradually increases and gradually approaches the norm value of the random error term of the current generation itself:

[0043] ||e (i) || > ||e (i) -e (i-j) || > … > ||e (i) -e (i-1) ||

[0044] When E(||e (i) ||) ≈ E(||e (i) -e (i-n) ||), based on statistical significance, the average correlation of the fission source distributions separated by n generations is approximately negligible, where E is the mathematical expectation, ||e (i) || is the norm of e (i) The combination component, connected to the calculation component, is used to combine the Sliced Wasserstein distances of three one-dimensional slices of the fission source distributions separated by j generations along the x, y, and z directions to obtain the average Sliced Wasserstein distance. The determination component, connected to the combination component, is used to determine the number of generations n at which the average Sliced Wasserstein distance first reaches the maximum value as the number of generations separated by which the inter-generation correlation is approximately negligible 0 .

[0045] Preferably, the second acquisition unit further includes a deduction component

[0046] The deduction component, connected to the calculation component, is used to calculate the distance between two probability distributions using the Sliced Wasserstein distance according to the similarity between the Sliced Wasserstein distance and the Wasserstein distance. The specific calculation formula is as follows

[0047]

[0048] where S n and S r are two probability distributions

[0049] is and the distance function of the values. The Wasserstein distance satisfies the following formula

[0050]

[0051] where γ(x,y) is the probability density function and d(x,y) is the distance function of x and y values

[0052] And based on the application of the Monte Carlo algorithm, the calculation formula for characterizing the fission source distribution error term using the Sliced Wasserstein distance is as follows

[0053] ||e (i) -e (i-j) || = SW(S i , S i-j )

[0054] Among them, the distance function of the Sliced Wasserstein distance selects the 1-norm, S i and S i-j are the fission source distributions of the i-th generation and the (i - j)-th generation,

[0055] And, a calculation formula for the semi-quantitative relationship of the inter-generation correlation of the fission source distribution along any of the x / y / z directions with the number of generations apart is deduced according to the calculation formula of the Sliced Wasserstein distance and its error term representing the fission source distribution.

[0056] Preferably, the determination module includes a determination unit and a selection unit.

[0057] The determination unit, when the Sliced Wasserstein distance between n 0 generations satisfies the following relationship:

[0058]

[0059] Then

[0060] is used to determine that there is no mathematical correlation in the statistical sense between the fission source distributions of n 0 generations,

[0061] And, according to the law of large numbers, it is obtained that: (j > n, l is large enough),

[0062]

[0063] The selection unit, connected to the determination unit, is used to take the group length l = n of the group statistical method 0 , and obtain the expression of the group statistical method:

[0064]

[0065] The method and system for eliminating the Monte Carlo variance low estimation phenomenon and the method for obtaining the Monte Carlo calculation result of the present invention reasonably predict the inter-generation correlation existing in the fission source distribution during the source iteration process of the Monte Carlo algorithm for the Monte Carlo low estimation phenomenon. By obtaining the number of generations n 0 when the inter-generation correlation of the fission source distribution can be approximately ignored, and using the number of generations n 0The group length as a group statistical method is used to obtain Monte Carlo calculation results with accurate confidence intervals that can completely eliminate the phenomenon of low estimation of Monte Carlo variance. Thus, the problem of the systematic low estimation of the calculation results of the Monte Carlo algorithm in the field of Monte Carlo nuclear physics calculation is effectively solved, enabling the calculation results obtained based on the Monte Carlo algorithm to have accurate confidence intervals, and thus obtaining highly accurate Monte Carlo calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 FIG. 6 is a schematic flowchart of the method for eliminating the phenomenon of low Monte Carlo variance provided in Embodiment 1 of the present invention;

[0067] Figure 2 FIG. 10 is an architecture diagram of the external coupling algorithm;

[0068] Figure 3 FIG. 14 is a schematic diagram showing the relationship between the FSD average Sliced Wasserstein distance and the number of generations apart;

[0069] Figure 4 FIG. 18 is a model diagram of the spherical array benchmark problem in Embodiment 1;

[0070] Figure 5 FIG. 22 is a schematic diagram showing the relationship between the FSD average Sliced Wasserstein distance and the number of generations apart of the spherical array model in Embodiment 1;

[0071] Figure 6 FIG. 26 is a full-core model diagram of the BEAVRS benchmark problem in Embodiment 1;

[0072] Figure 7 FIG. 30 is a schematic diagram showing the relationship between the FSD average Sliced Wasserstein distance and the number of generations apart of the BEAVRS full-core model in Embodiment 1;

[0073] Figure 8 FIG. 34 is a schematic structural diagram of the system for eliminating the phenomenon of low Monte Carlo variance provided in Embodiment 3 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0074] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0075] Embodiment 1:

[0076] Monte Carlo transport programs can perform physical modeling and particle transport calculations for nuclear-related facilities such as reactor cores and critical safety devices. The Monte Carlo algorithm usually adopts a source iteration process, and the Monte Carlo low-estimation phenomenon stems from the inter-generation correlation in the fission source distribution during the source iteration process of the Monte Carlo algorithm. For example, when obtaining the Monte Carlo calculation results of various physical quantities (physical quantities include the effective multiplication factor Keff of critical safety facilities, the flux, power, etc. of reactor core facilities) using the Monte Carlo algorithm, the calculation variance of Monte Carlo will be lower than the true variance value, resulting in low accuracy of the obtained calculation results. Therefore, this embodiment provides a method for eliminating the Monte Carlo variance low-estimation phenomenon.

[0077] As Figure 1 shown, the method for eliminating the Monte Carlo variance low-estimation phenomenon includes:

[0078] Step 101, obtain the number of generations n when the inter-generation correlation of the fission source distribution is approximately ignored 0 .

[0079] In this embodiment, the Wasserstein distance algorithm, Sliced Wasserstein distance algorithm or other algorithms can be used to obtain the number of generations n when the inter-generation correlation of the fission source distribution is approximately ignored 0 .

[0080] Optionally, to obtain the number of generations n when the inter-generation correlation of the fission source distribution is approximately ignored 0 , specifically including: using the Sliced Wasserstein distance to characterize the correlation of the fission source distribution; obtaining the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations according to the relationship between the Sliced Wasserstein distance and the number of generations, so as to obtain the number of generations n when the inter-generation correlation is approximately ignored 0 .

[0081] In this embodiment, the relationship between the Sliced Wasserstein distance and the number of generations can be calculated by means of an external script (i.e., external coupling) or internal coupling. The coupling method of the external script is as Figure 2As shown. In Monte Carlo calculations, the fission source distribution of each generation is output to a file. In an external script, the Sliced Wasserstein distance of the FSD separated by m (m = 0, 1, 2, …) generations is calculated, and the average Sliced Wasserstein distance of the FSD separated by m generations is obtained. The internal coupling calculation method requires implementing functions such as saving the fission source generation by generation, calculating the Sliced Wasserstein distance, and maintaining the data memory space inside the Monte Carlo program. Specifically, according to the relationship between the Sliced Wasserstein distance and the number of generations apart, a semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations apart is obtained to get the number of generations n when the inter-generation correlation can be approximately ignored 0 , specifically including:

[0082] Step 1011, calculate the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations apart along any one of the x / y / z directions according to the following formula to obtain the Sliced Wasserstein distance of the one-dimensional slice of the fission source distribution along any one of the x / y / z directions separated by j generations:

[0083]

[0084] Among them, S i and S i-j are the fission source distributions of the i-th generation and the i-j-th generation, SW x is the Sliced Wasserstein distance along the x direction, x i and x i-j are the slice sequences of the fission source distributions of the i-th generation and the i-j-th generation along the x direction respectively, d(x, y) is the distance function of x i , x i-j , N is the length of the slice sequence of the fission source distribution along the x direction, e (i) -e (i-j) is the inter-generation correlation separated by j generations calculated according to the error between the fission source distributions of the i-th generation and the i-j-th generation, and satisfies the following formula:

[0085]

[0086] Among them, e (i) is the vector definition formula of the error term of the fission source distribution of the i-th generation, A is the error transfer matrix in the Monte Carlo source iteration process, ε (i) is the random error introduced in the i-th generation. As j increases, the error of the fission source distribution separated by j generations gradually increases and gradually approaches the norm value of the random error term itself of the current generation:

[0087] ||e (i) || > ||e (i) -e(i-j) ||>…||e (i) -e (i-1) ||

[0088] When E(||e (i) ||)≈E(||e (i) -e (i-n) ||), the average correlation of the fission source distributions separated by n generations is approximately negligible based on statistical significance, where E is the mathematical expectation, and ||e (i) || is the norm of e (i) .

[0089] Step 1012: Combine the Sliced Wasserstein distances of three one-dimensional slices of the fission source distribution separated by j generations along the x, y, and z directions to obtain the average Sliced Wasserstein distance.

[0090] In this embodiment, change x in the calculation formula of the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations separated to y or z to obtain the Sliced Wasserstein distance of a one-dimensional slice of the fission source distribution separated by j generations along any one of the y or z directions, and the average Sliced Wasserstein distance is the combination of the Sliced Wasserstein distances of the three one-dimensional slices. Optionally, in step 1012: Combine the Sliced Wasserstein distances of three one-dimensional slices of the fission source distribution separated by j generations along the x, y, and z directions, specifically including: Combine the Sliced Wasserstein distances of three one-dimensional slices of the fission source distribution separated by j generations along the x, y, and z directions according to the method of integration or summation to obtain the distance between the fission source distributions of adjacent j generations, and further use it as a measure of the difference between the fission source distribution error terms.

[0091] In this embodiment, the combination method is not limited to summing or integrating the Sliced Wasserstein (abbreviated as SW) distances of the three one-dimensional slices in the example, and other combination methods can also be used. This embodiment is explained by the method of integration. When SW(x slice)=2, SW(y slice)=4, SW(z slice)=5, then the average SW (two distributions)=SW(x slice)*SW(y slice)*SW(z slice)=2*4*5 = 40.

[0092] Step 1013: Determine the number of generations separated n when the average Sliced Wasserstein distance first reaches the maximum value as the number of generations separated when the inter-generation correlation is approximately negligible 0. In this embodiment, since the average Sliced Wasserstein distance can characterize the distance between fission source distributions, when the average Sliced Wasserstein distance reaches its maximum value for the first time and starts to fluctuate, it can be considered that there is no longer a correlation between the fission source distributions. In addition, the three one-dimensional slices of the fission source distributions in the x, y, and z directions for adjacent j generations can be processed and output through a multi-threaded parallel summarization and segmented sorting data processing process.

[0093] Optionally, before calculating the semi-quantitative relationship between the inter-generation correlations of fission source distributions along any one of the x / y / z directions with the number of generations apart, the elimination method further includes:

[0094] According to the similarity between the Sliced Wasserstein distance and the Wasserstein distance, the Sliced Wasserstein distance is used to calculate the distance between two probability distributions. The specific calculation formula is as follows:

[0095]

[0096] where S n and S r are two probability distributions,

[0097] is and the distance function of the values. The Wasserstein distance satisfies the following formula:

[0098]

[0099] where γ(x,y) is the probability density function and d(x,y) is the distance function of x and y values;

[0100] Based on the application of the Monte Carlo algorithm, the calculation formula for using the Sliced Wasserstein distance to characterize the fission source distribution error term is as follows:

[0101] ||e (i) -e (i-j) || = SW(S i , S i-j )

[0102] where the distance function of the Sliced Wasserstein distance selects the 1-norm, and S i and S i-j are the fission source distributions of the i-th generation and the i-j-th generation;

[0103] According to the formula of the Sliced Wasserstein distance and its formula for characterizing the fission source distribution error term, the formula for the semi-quantitative relationship of the inter-generation correlation of the fission source distribution along any of the x / y / z directions with the number of generations apart is deduced.

[0104] In this embodiment, the Wasserstein distance originates from the shortest transport problem. The original definition is the shortest distance between two discrete probability distributions, and later it can be developed to characterize the shortest distance between any two probability distributions. Due to its excellent characterization performance, it is often used in the fields of information theory and artificial intelligence as an algorithm for measuring the value function of the probability distribution distance. Later, researchers proved that the Sliced Wasserstein distance has similar properties to the Wasserstein distance and can also better characterize the distance between two distributions. Therefore, based on this, this embodiment uses the Sliced Wasserstein distance to characterize the correlation of the fission source distribution in order to obtain the number of generations n apart when the inter-generation correlation of the fission source distribution is approximately negligible. 0 。

[0105] Step 102, determine that the group length l of the group statistical method is l = n 0 。

[0106] Specifically, determining that the group length l of the group statistical method is l = n 0 includes:

[0107] When the Sliced Wasserstein distance at n 0 generations apart satisfies the following relationship:

[0108]

[0109] then

[0110] it is determined that there is no mathematical correlation in the statistical sense between the fission source distributions at n 0 generations apart;

[0111] According to the law of large numbers, it is obtained that: (j > n, l is large enough),

[0112]

[0113] where

[0114] take the group length l of the group statistical method as l = n 0 , and obtain the expression of the group statistical method:

[0115]

[0116] Step 103: Obtain the Monte Carlo calculation result that completely eliminates the low - estimation phenomenon of Monte Carlo variance by using the group - statistical method.

[0117] The steps in using the Monte Carlo program for calculation specifically include: preparing Monte Carlo input cards 1 and 2, calculating the relationship between the FSD average Sliced Wasserstein distance and the number of generations apart in the first step, and estimating the number of generations apart n at which the correlation is completely eliminated. 0 , such as Figure 3 shown, the FSD average Sliced Wasserstein distance gradually increases with the increase in the number of generations apart and tends to be stable. When the FSD average Sliced Wasserstein distance becomes gradually stable, the number of generations apart n corresponding to when the average Sliced Wasserstein distance reaches the maximum value and starts to fluctuate can be obtained. 0 . In the second step, use l = n 0 as the group length to perform Monte Carlo simulation calculations, and processes such as organizing the calculation results. To facilitate the understanding of the Monte Carlo variance low - estimation phenomenon elimination algorithm and verify the functionality of this algorithm, the following two examples are used for detailed explanation.

[0118] (1) The sphere - array model is a simple 3D model from the OECD / NEA (Organization for Economic Co - operation and Development / Nuclear Energy Agency) source - convergence benchmark problem, consisting of metal spheres arranged in a 5x5x1 array in air, as Figure 4 shown (see: R. Blomquist A. Nouri M. Armishaw O. Jacquet Y. Naito Y. Miyoshi T. Yamamoto. OECD / NEA source - convergence benchmark program Overview and summary of results. 2003.). The metal spheres contain highly enriched uranium. In this example, the use effect of the semi - quantitative prediction elimination algorithm for the low - estimation phenomenon of variance is studied at 50,000 particles per generation. The number of non - active generations is set to 5,000 generations, and the number of active generations is 20,000 generations so that the statistical results are obtained after the source is fully converged.

[0119] Flux counters are set at the position of each sphere, and 30 independent calculations are performed by setting different random - number seeds to obtain the reference solution and the corresponding standard deviation values. At 50,000 particles per generation, the values of the reference solution and the relative standard deviation are shown in Table 1. The position number of the upper - left - corner sphere is (1,1).

[0120] Table 1 Statistical reference solutions and relative standard deviations of the fluxes of small balls at different positions in the spherical array model

[0121]

[0122] After obtaining the reference solution, the effectiveness and accuracy of the method for eliminating the low Monte Carlo variance estimation phenomenon in this embodiment are verified below. First, perform the first calculation to obtain the relationship graph of the average Sliced Wasserstein distance of FSD with the number of generations apart at different numbers of particles per generation, as Figure 5 shown. It can be seen that the average Sliced Wasserstein distance of FSD reaches the maximum value and begins to fluctuate around 50 generations apart. Therefore, it is estimated that the number of generations apart n 0 should be 50 generations.

[0123] Use l = n 0 as the group length to perform the second calculation, and use the average underestimation coefficient of the standard deviation of 25 ball fluxes as the analysis object.

[0124]

[0125] In the formula, Underestimate Ratio refers to the average underestimation coefficient of the standard deviation;

[0126] σ i refers to the calculated standard deviation of the flux of the i-th counter;

[0127] refers to the true standard deviation of the flux of the i-th counter;

[0128] N tally refers to the total number of counters.

[0129] It can be obtained that when the group statistical method (group length is 1 generation) is not used, the average underestimation coefficient of the standard deviation of the small ball flux value is about 37%; when the group length is 50 generations, it is reduced to within ±5%. Therefore, using 50 generations obtained from the first calculation as the estimated value of the group length can effectively eliminate the low variance estimation phenomenon.

[0130] (2) The BEAVRS full-core model is taken from the BEAVRS benchmark problem (see: Horelik, N., Herman, B., Forget, B., Smith, K. Benchmark for evaluation and validation of reactor simulations (beavrs), v1.0.1, Proc. Int. Conf. Mathematics and Computational Methods Applied to Nuc. Sci. & Eng[J], 2013). The core consists of 193 fuel assemblies arranged in a 15×15 pattern. Flux counters are set in each assembly of the 1 / 4 core, as shown in Figure 6 . In this example, the effect of using the semi-quantitative prediction elimination algorithm for low variance estimation phenomenon was studied at 50,000 particles per generation. The number of non-active generations was set to 5,000, and the number of active generations was 20,000 to ensure that the statistical results were obtained after the source had fully converged.

[0131] Flux counters are set in each assembly of the 1 / 4 core. Thirty independent calculations were performed by setting different random number seeds to obtain the reference solution and the corresponding relative standard deviation values, as shown in Table 2. The position number of the central assembly in the core is (1, 1).

[0132] Table 2 Reference solutions and relative standard deviations of component flux statistics for the BEAVRS model

[0133]

[0134]

[0135] After obtaining the reference solution, the effectiveness and accuracy of the method for eliminating the Monte Carlo low variance estimation phenomenon in this embodiment were verified. First, the first calculation was performed to obtain the relationship graph of the average Sliced Wasserstein distance of FSD with the number of generations apart at different numbers of particles per generation, as shown in Figure 7 . It can be seen that at 50,000 particles per generation, the average Sliced Wasserstein distance of FSD reaches the maximum value and begins to fluctuate at around 500 generations apart, and it conforms to the monotonically increasing prediction before reaching the maximum value. Therefore, the predicted number of generations apart n 0 should be 500 generations.

[0136] Use l = n 0Perform a second calculation for the group length and use the average low - estimation coefficient of the standard deviation of each component flux as the analysis object. It can be obtained that when not using the group statistical method (group length of 1 generation), the average low - estimation coefficient of the standard deviation of the component flux values is about 87%; it decreases to within ±1% when the group length is 500 generations. Therefore, using 500 generations obtained from the first calculation as the estimated amount of the group length can effectively eliminate the phenomenon of low - variance estimation.

[0137] The method for eliminating the Monte Carlo variance low - estimation phenomenon in this embodiment outputs the fission source distribution of each generation of particles through a three - dimensional Monte Carlo program, uses statistical tools to test the average distance between the fission source distributions separated by n generations, and obtains a semi - quantitative relationship between the inter - generation correlation of the fission source distribution and the number of separated generations based on the relationship between the average distance and the number of separated generations, thereby obtaining the number of separated generations n with approximately negligible inter - generation correlation. 0 , and then use l = n 0 as the group length of the group statistical method to obtain Monte Carlo calculation results with accurate confidence intervals that can completely eliminate the Monte Carlo variance low - estimation phenomenon. This method realizes the effective prediction and elimination of the Monte Carlo variance low - estimation phenomenon, is an advanced and engineering - feasible method for correcting Monte Carlo nuclear physics calculation results, and can improve the accuracy of Monte Carlo calculation results.

[0138] The method for eliminating the Monte Carlo variance low - estimation phenomenon in this embodiment effectively solves the problem of the systematic variance low - estimation phenomenon in the calculation results of the Monte Carlo algorithm in the field of Monte Carlo nuclear physics. For the inter - generation correlation existing in the source iteration process of the Monte Carlo algorithm, reasonable prediction and judgment are made using statistical tools, and the number of separated generations n with negligible inter - generation correlation in statistics is proposed. 0 as the group length of the group statistical method to obtain Monte Carlo calculation results with accurate confidence intervals that can completely eliminate the Monte Carlo variance low - estimation phenomenon. In addition, the verification calculation results of the two calculation examples provided in this embodiment are basically consistent with the Monte Carlo repeated calculation results, can be applied to the calculation of accurate confidence intervals of various Monte Carlo statistics, and prove that the elimination method in this embodiment can effectively solve the key algorithm problem of eliminating the Monte Carlo method variance low - estimation phenomenon.

[0139] Embodiment 2:

[0140] This embodiment provides a method for obtaining Monte Carlo calculation results, including:

[0141] Step 201, prepare the first input card and the second input card of the Monte Carlo program.

[0142] Step 202, use the Monte Carlo program and the method for eliminating the Monte Carlo variance low - estimation phenomenon described in Embodiment 1 to calculate the first input card, and obtain the average Sliced Wasserstein distance and the number of separated generations n 0 .

[0143] Step 203: Calculate the input second card using the Monte Carlo set statistical method and the method for eliminating the low Monte Carlo variance estimation phenomenon described in Embodiment 1 to obtain the Monte Carlo calculation result.

[0144] The method for obtaining the Monte Carlo calculation result in this embodiment includes two calculation processes. Among them, the first calculation process aims to obtain the average Sliced Wasserstein distance between the fission source distributions of adjacent j generations after convergence, which can be calculated based on external coupling or internal coupling. In the domestic independent Monte Carlo program RMC (Reactor Monte Carlo), the calculation method of external coupling is implemented. The external module for implementing external coupling can run independently and can be conveniently coupled with any Monte Carlo program that can output the fission source distribution. See the calculation process of the external module in Figure 2 . In Monte Carlo calculation, the fission source distribution of each generation is output to a file. Calculate the Sliced Wasserstein distance of the FSD separated by m (m = 0, 1, 2...) generations in an external script, and obtain the average Sliced Wasserstein distance of the FSD separated by m generations.

[0145] Through the calculation of the first step, a relationship graph of the average Sliced Wasserstein distance of the FSD with the number of separated generations can be obtained, as shown in Figure 3 . It can be seen from the figure that the average Sliced Wasserstein distance of the FSD gradually increases with the increase of the number of separated generations and tends to be stable. When the average Sliced Wasserstein distance of the FSD gradually stabilizes, the number of separated generations n when the average Sliced Wasserstein distance reaches the maximum value for the first time and begins to fluctuate 0 can be determined as the group length of the group statistical method. Perform the second calculation process. The second calculation uses the group statistical method, and uses l = n 0 as the group length, then a calculation result with a reliable confidence interval that eliminates the low variance estimation phenomenon (that is, the influence of low variance estimation can be ignored) can be obtained. For example, in Figure 3 , the group length should be set to 50 generations.

[0146] The method for obtaining the Monte Carlo calculation result in this embodiment effectively eliminates the low variance estimation phenomenon of the Monte Carlo method, making the obtained Monte Carlo calculation result highly accurate and having engineering practicability.

[0147] Embodiment 3:

[0148] As shown in Figure 8As shown in the figure, this embodiment provides a system for eliminating the low Monte Carlo variance estimation phenomenon, including an acquisition module 31, a determination module 32, and a calculation module 33.

[0149] The acquisition module 31 is used to acquire the number of generations n with approximately negligible inter-generation correlation of the fission source distribution. 0 The determination module 32 is connected to the acquisition module 31 and is used to determine that the group length l of the group statistical method is l = n. 0 The calculation module 33 is connected to the determination module 32 and is used to calculate the Monte Carlo calculation result that completely eliminates the low Monte Carlo variance estimation phenomenon by using the group statistical method.

[0150] Optionally, the acquisition module includes a first acquisition unit and a second acquisition unit.

[0151] The first acquisition unit is used to characterize the correlation of the fission source distribution by using the Sliced Wasserstein distance. The second acquisition unit is connected to the first acquisition unit and is used to obtain the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations based on the relationship between the Sliced Wasserstein distance and the number of generations, so as to obtain the number of generations n with approximately negligible inter-generation correlation. 0 .

[0152] Optionally, the second acquisition unit includes a calculation component, a combination component, and a determination component.

[0153] The calculation component is used to calculate the semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations along any one of the x / y / z directions according to the following formula, so as to obtain the Sliced Wasserstein distance of the one-dimensional slice of the fission source distribution along any one of the x / y / z directions at the j-th generation interval:

[0154]

[0155] Among them, S i and S i-j are the fission source distributions of the i-th generation and the i-j-th generation, SW x is the Sliced Wasserstein distance along the x direction, x i , x i-j are the slice sequences of the fission source distributions of the i-th generation and the i-j-th generation along the x direction respectively, d(x,y) is the distance function between x i , x i-j , N is the length of the slice sequence of the fission source distribution along the x direction, e (i) -e (i-j) is the cost correlation at the j-th generation interval calculated according to the error between the fission source distributions of the i-th generation and the i-j-th generation, and satisfies the following formula:

[0156]

[0157] Among them, e (i) is the vector definition formula of the error term of the fission source distribution in the i-th generation, A is the error transfer matrix in the Monte Carlo source iteration process, and ε (i) is the random error introduced in the i-th generation. As j increases, the error of the fission source distribution separated by j generations gradually increases and gradually approaches the norm value of the random error term itself in the current generation:

[0158] ||e (i) || > ||e (i) - e (i-j) || > … ||e (i) - e (i-1) ||

[0159] When E(||e (i) ||) ≈ E(||e (i) - e (i-n) ||), based on statistical significance, the average correlation of the fission source distributions separated by n generations is approximately ignored, where E(x) is the mathematical expectation of the random variable x, and ||e (i) || is the norm of e (i) .

[0160] Combination component, connected to the calculation component, used to combine the Sliced Wasserstein distances of three one-dimensional slices of the fission source distributions separated by j generations along the x, y, and z directions to obtain the average Sliced Wasserstein distance.

[0161] Determination component, connected to the combination component, used to determine the number of generations n between generations when the average Sliced Wasserstein distance reaches the maximum value for the first time as the number of generations between generations when the inter-generation correlation is approximately ignored 0 .

[0162] Optionally, the second acquisition unit further includes a deduction component.

[0163] Deduction component, connected to the calculation component, the deduction component is used to calculate the distance between two probability distributions using the Sliced Wasserstein distance according to the similarity between the Sliced Wasserstein distance and the Wasserstein distance. The specific calculation formula is as follows:

[0164]

[0165] Among them, S n and S r are two probability distributions,

[0166] is and For the distance function of values, the Wasserstein distance satisfies the following formula:

[0167]

[0168] where γ(x,y) is the probability density function and d(x,y) is the distance function of the values of x and y,

[0169] And based on the application of the Monte Carlo algorithm, the calculation formula for characterizing the fission source distribution error term using the Sliced Wasserstein distance is as follows:

[0170] ||e (i) -e (i-j) || = SW(S i , S i-j )

[0171] where the distance function of the Sliced Wasserstein distance selects the 1-norm, and S i and S i-j are the fission source distributions of the i-th generation and the (i - j)-th generation,

[0172] And, the calculation formula for the semi-quantitative relationship of the inter-generation correlation of the fission source distribution along any one of the x / y / z directions with the number of generations apart is deduced according to the calculation formula of the Sliced Wasserstein distance and its characterization of the fission source distribution error term.

[0173] Optionally, the combination component is specifically used to combine the Sliced Wasserstein distances of the three one-dimensional slices of the fission source distribution in the x, y, and z directions separated by j generations in a way of quadrature or summation.

[0174] Optionally, the determination module includes a determination unit and a selection unit.

[0175] The determination unit, when the Sliced Wasserstein distance separated by n 0 generations satisfies the following relationship:

[0176]

[0177] then

[0178] is used to determine that there is no mathematical correlation in the statistical sense between the fission source distributions separated by n 0 generations,

[0179] And, according to the law of large numbers, it is obtained that: (j > n, l is large enough),

[0180]

[0181] A selection unit, connected to the determination unit, for obtaining the group length l = n of the group statistical method 0 , and obtaining the expression of the group statistical method:

[0182]

[0183] It can be understood that the above embodiments are merely exemplary embodiments adopted to illustrate the principle of the present invention. However, the present invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also regarded as the protection scope of the present invention.

Claims

1. A method for eliminating the low Monte Carlo variance estimation phenomenon, characterized in that, comprising: Obtain the number of generations n between which the inter-generation correlation of the fission source distribution is approximately ignored 0 ; Determine that the group length l of the group statistical method is l = n 0 ; Using the group statistical method to obtain the Monte Carlo calculation result that completely eliminates the low Monte Carlo variance estimation phenomenon, wherein, the number of generations n with the inter-generation correlation of the obtained fission source distribution approximately ignored 0 , specifically including: Using the Sliced Wasserstein distance to characterize the correlation of the fission source distribution; Obtain the semi - quantitative relationship between the inter - generation correlation of the fission source distribution and the number of generations apart according to the relationship between the Sliced Wasserstein distance and the number of generations apart, so as to obtain the number of generations apart \(n\) when the inter - generation correlation can be approximately ignored 0 , Among them, the semi - quantitative relationship between the inter - generation correlation of the fission source distribution and the number of generations apart is obtained according to the relationship between the Sliced Wasserstein distance and the number of generations apart, so as to obtain the number of generations apart \(n\) when the inter - generation correlation can be approximately ignored 0 , specifically including: Calculating the semi-quantitative relationship of the inter-generation correlation of the fission source distribution along any one of the x / y / z directions with the number of generations apart according to the following formula to obtain the Sliced Wasserstein distance of the one-dimensional slice of the fission source distribution along any one of the x / y / z directions separated by j generations: Among them, S i and S i-j are the fission source distributions of the i-th generation and the (i - j)-th generation, SW x is the Sliced Wasserstein distance along the x-direction, x i , x i-j are the sliced sequences of the fission source distributions of the i-th generation and the (i - j)-th generation along the x-direction respectively, d(x, y) is the distance function between x i , x i-j , N is the length of the sliced sequence of the fission source distribution along the x-direction, e (i) -e (i-j) is the inter-generation correlation separated by j generations calculated according to the error between the fission source distributions of the i-th generation and the (i - j)-th generation, and satisfies the following formula: where, e (i) is the vector definition formula of the error term of the fission source distribution of the i-th generation, A is the error transfer matrix in the Monte Carlo source iteration process, and ε (i) is the random error introduced in the i-th generation. As j increases, the error of the fission source distribution separated by j generations gradually increases and gradually approaches the norm value of the random error term itself in the current generation: ||e (i) ||>||e (i) -e (i-j) ||>…>||e (i) -e (i-1) || When E(||e (i) ||) ≈ E(||e (i) -e (i-n) ||), the average correlation of the fission source distributions separated by n generations is approximately negligible based on statistical significance, where E is the mathematical expectation and ||e (i) || is the norm of e (i) ; Combining the Sliced Wasserstein distances of the three one-dimensional slices of the fission source distribution along the x, y, and z directions separated by j generations to obtain the average Sliced Wasserstein distance; Determine the number of generations apart \(n\) when the average Sliced Wasserstein distance reaches its maximum value for the first time as the number of generations apart at which the inter-generation correlation can be approximately ignored. 0 , Among them, the group length l of the group statistical method is l = n 0 , specifically including: When the Sliced Wasserstein distance separated by n 0 generations satisfies the following relationship: Then Determine the separation by n 0 There is no statistically significant mathematical correlation between the fission source distributions separated by According to the law of large numbers, we have: (j > n, l is large enough), Among them, the group length l of the group statistical method is l = n 0 , and the expression of the group statistical method is obtained:

2. The method for eliminating the low Monte Carlo variance estimation phenomenon according to claim 1, characterized in that, Before calculating the semi-quantitative relationship of the inter-generation correlation of the fission source distribution along any one of the x / y / z directions with the number of generations apart, it further comprises: According to the similarity between the Sliced Wasserstein distance and the Wasserstein distance, using the Sliced Wasserstein distance to calculate the distance between two probability distributions, and the specific calculation formula is as follows: where S n and S r are two probability distributions For and the distance function of the value, the Wasserstein distance satisfies the following formula: where γ(x,y) is the probability density function, and d(x,y) is the distance function of the x and y values; Based on the application of the Monte Carlo algorithm, the calculation formula for characterizing the error term of the fission source distribution using the Sliced Wasserstein distance is as follows: ||e (i) -e (u-j) || = SW(S i , S i-j ) Among them, the distance function of the Sliced Wasserstein distance selects the 1-norm, S i and S i-j are the fission source distributions of the i-th generation and the (i - j)-th generation; According to the Sliced Wasserstein distance and its calculation formula for characterizing the error term of the fission source distribution, deduce the calculation formula for the semi-quantitative relationship of the inter-generation correlation of the fission source distribution along any one of the x / y / z directions with the number of generations apart.

3. The method for eliminating the low Monte Carlo variance estimation phenomenon according to claim 1, characterized in that, The combination of the Sliced Wasserstein distances of the three one-dimensional slices of the fission source distribution along the x, y, and z directions separated by j generations specifically includes: Combining the Sliced Wasserstein distances of the three one-dimensional slices of the fission source distribution along the x, y, and z directions separated by j generations according to the method of quadrature or summation.

4. A method for obtaining the Monte Carlo calculation result, characterized in that, comprising: Preparing the first input card and the second input card of the Monte Carlo program; Calculate the input first card using an in-coupled or out-coupled Monte Carlo program and the method for eliminating the Monte Carlo variance low estimation phenomenon according to any one of claims 1-3, and obtain the average Sliced Wasserstein distance and the number of generations n apart 0 ; With an interval of n generations 0 Using the Monte Carlo set statistical method and the elimination method for the low Monte Carlo variance estimation phenomenon described in any one of claims 1-3 as the group length, calculate the input second card to obtain the Monte Carlo calculation result.

5. A system for eliminating the low Monte Carlo variance estimation phenomenon, characterized in that, comprising an acquisition module, a determination module and a calculation module, An acquisition module for acquiring the number of generations n between which the inter-generation correlation of the fission source distribution is approximately ignored 0 , Determination module, connected to the acquisition module, for determining that the group length l of the group statistical method is l = n 0 , The calculation module is connected to the determination module and is used to calculate the Monte Carlo calculation result that completely eliminates the low Monte Carlo variance estimation phenomenon by using the group statistical method, The acquisition module includes a first acquisition unit and a second acquisition unit, The first acquisition unit is used to characterize the correlation of the fission source distribution using the Sliced Wasserstein distance, A second acquisition unit, connected to the first acquisition unit, is configured to obtain a semi-quantitative relationship between the inter-generation correlation of the fission source distribution and the number of generations apart according to the relationship between the Sliced Wasserstein distance and the number of generations apart, so as to obtain the number of generations apart n when the inter-generation correlation can be approximately ignored 0 , The second acquisition unit includes a calculation component, a combination component and a determination component, A calculation component is used to calculate the semi - quantitative relationship of the inter - generation correlation of the fission source distribution along any one of the x / y / z directions with the number of generations apart according to the following formula, so as to obtain the Sliced Wasserstein distance of the one - dimensional slice of the fission source distribution along any one of the x / y / z directions with j generations apart. where S i and S i-j are the fission source distributions of the i-th generation and the (i - j)-th generation, SW x is the Sliced Wasserstein distance in the x direction, x i , x i-j are the slice sequences of the fission source distributions of the i-th generation and the (i - j)-th generation in the x direction respectively, d(x, y) is the distance function between x i , x i-j , N is the length of the slice sequence of the fission source distribution in the x direction, e (i) -e (i-j) is the inter-generation correlation separated by j generations calculated according to the error between the fission source distributions of the i-th generation and the (i - j)-th generation, and satisfies the following formula: where e (i) is the vector definition formula of the error term of the fission source distribution in the i-th generation, A is the error transfer matrix in the Monte Carlo source iteration process, and ε (i) is the random error introduced in the i-th generation. As j increases, the error of the fission source distribution separated by j generations gradually increases and gradually approaches the norm value of the random error term itself in the current generation: ||e (i) ||>||e (i) -e (i-j) ‖>…>‖e (i) -e (i-1) || When E(||e (i) ||) ≈ E(||e (i) -e (i-n) ||), the average correlation of the fission source distributions separated by n generations is approximately negligible based on statistical significance, where E is the mathematical expectation, ||e (i) || is the norm of e (i) . A combination component is connected to the calculation component and is used to combine the Sliced Wasserstein distances of the three one - dimensional slices of the fission source distribution along the x, y, and z directions with j generations apart to obtain the average Sliced Wasserstein distance. Determine the component, which is connected to the combined component and is used to determine the number of generations apart \(n\) corresponding to the generation interval correlation approximately ignored when the average Sliced Wasserstein distance reaches the maximum value for the first time 0 , Among them, the determination module includes a judgment unit and a selection unit. Determination unit, when the Sliced Wasserstein distance separated by n 0 generations satisfies the following relationship: Then For determining that there is no statistically significant mathematical correlation between the fission source distributions separated by n 0 generations, Also, according to the law of large numbers, we have: (j > n, l is large enough), Selection unit, connected to the determination unit, for obtaining the group length l = n of the group statistical method 0 , to obtain the expression of the group statistical method:

6. The Monte Carlo variance low - estimation phenomenon elimination system according to claim 5. It is characterized in that The second acquisition unit further includes a deduction component. The deduction component is connected to the calculation component. The deduction component is used to calculate the distance between two probability distributions using the Sliced Wasserstein distance according to the similarity between the Sliced Wasserstein distance and the Wasserstein distance. The specific calculation formula is as follows: where S n and S r are two probability distributions For and the distance function of values, the Wasserstein distance satisfies the following formula: Among them, γ(x,y) is the probability density function, and d(x,y) is the distance function of the x and y values. And based on the application of the Monte Carlo algorithm, the calculation formula for characterizing the fission source distribution error term using the Sliced Wasserstein distance is as follows: ||e (i) -e (i-j) || = SW(S i ,S i-j ) Among them, the distance function of the Sliced Wasserstein distance selects the 1-norm, and S i and S i-j are the fission source distributions of the i-th generation and the (i - j)-th generation, And, it is used to deduce the calculation formula for the semi - quantitative relationship of the inter - generation correlation of the fission source distribution along any one of the x / y / z directions with the number of generations apart according to the Sliced Wasserstein distance and its calculation formula for characterizing the fission source distribution error term.

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