A regression calculation method for the gamma-ray cumulative factor of shielding materials based on the limit tree

Abstract

The present invention provides a regression calculation method for the gamma-ray buildup factor of shielding materials based on extreme trees. By learning a large number of data samples of gamma-ray buildup factors of various common engineering materials, an extreme tree regression model with excellent performance is established with simple parameter tuning or even without any parameter tuning. The known data of gamma-ray buildup factors are unbiasedly predicted, and the unknown data are accurately predicted, so as to make the calculation of gamma-ray buildup factors of various common radiation shielding materials more efficient on the premise of ensuring accuracy.

Description

Technical Field

[0001] The present invention relates to a regression method for quickly and accurately calculating the gamma-ray buildup factor of various shielding materials. Background Art

[0002] Gamma rays have the characteristics of strong penetration ability and great damage to biological tissues, so they have become the main protection objects considered in nuclear radiation safety. The buildup factor represents the ratio of the total radiation intensity at a certain point to the radiation intensity not including scattered radiation at the same point in the radiation passing through the medium, and is mainly used to analyze the transmission and scattering of gamma rays. In the research of gamma radiation shielding design or irradiated dose assessment, secondary radiation may be caused by the collision of the incident light beam with the substance, which will bring additional difficulties to the work related to radiation analysis. Therefore, determining the buildup factor can correct the effective energy deposition in different shielding materials, thereby contributing to a more detailed study of the safe use of gamma radiation, radioactive substances, and nuclear energy in various fields.

[0003] At present, the commonly used calculation methods for the gamma-ray buildup factor of materials mainly include semi-empirical formulas, machine learning regression algorithms, etc. When using machine learning regression algorithms to calculate the buildup factor, models such as neural networks and support vector regression are mainly used. Support vector regression has the problem of insufficient accuracy, and at the same time, both algorithms need to go through a complex parameter tuning process to obtain better model parameters. Semi-empirical formulas such as GP fitting formula, Taylor fitting formula, and polynomial fitting, etc., require relatively professional fitting skills in the process of deriving the fitting parameters of the formula, and often have a large parameter library, resulting in inconvenient formula use and cumbersome calculation process.

[0004] In summary, developing a calculation method for the gamma-ray buildup factor of shielding materials that combines accuracy and efficiency and is easy to implement plays a very important role in improving the protection level of gamma rays and ensuring the health and safety of personnel and the environment in radioactive practice activities. Summary of the Invention

[0005] The object of the present invention is: for the calculation of the gamma-ray buildup factor of various shielding materials, in order to overcome the problems existing in the current methods, such as the calculation process being cumbersome due to many parameters involved in the calculation and the complex process of establishing the algorithm model, etc., a calculation method for the gamma-ray buildup factor of shielding materials based on extreme tree is proposed. Through learning a large number of data samples of the gamma-ray buildup factor of various commonly used engineering materials, without any parameter tuning or with simple parameter tuning, an extreme tree regression model with excellent performance is established to make an unbiased prediction of the known data of the gamma-ray buildup factor and a high-precision prediction of the unknown data, so as to make the calculation of the gamma-ray buildup factor of various commonly used radiation shielding materials more efficient on the premise of ensuring accuracy.

[0006] The object of the present invention is achieved as follows:

[0007] (1) Obtain the cumulative factor sample data of various shielding materials from the datasets of γ-ray cumulative factors of various common engineering materials;

[0008] (2) Select appropriate attributes according to the influencing factors of the cumulative factor and the characteristics of the sample data, and define the input space;

[0009] (3) Calculate the effective atomic number of the mixture / compound;

[0010] (4) Establish a training dataset for model learning;

[0011] (5) Learn from the training dataset to establish an extreme tree regression model;

[0012] (6) Use the extreme tree regression model to calculate the cumulative factor.

[0013] In step (2), the definition of the input space is as follows:

[0014] According to the main influencing factors of the cumulative factor: the atomic number Z of the material, the material thickness t, and the incident γ-ray energy E (MeV), the input space is defined as (Z, t, E), where t is expressed in terms of the number of mean free paths, and the conversion between t and the geometric thickness d is through the following formula:

[0015]

[0016] In the formula, ρ is the density of the medium material, g / cm 3 ; (μ / ρ) is the mass attenuation coefficient of the material, cm 2 / g.

[0017] The effective atomic number of the mixture / compound is calculated using the following formula:

[0018]

[0019] In the formula, Z eff is the effective atomic number of the mixture / compound; Z i is the atomic number of the i-th element constituting the mixture / compound; f i is the electron number fraction of the i-th element.

[0020] In step (5), the process of establishing the extreme tree regression model includes:

[0021] 1) Based on the original training set, randomly select n sub features from all n features and use them as the tree-building features of a decision regression tree;

[0022] 2) Among the extracted nsub Among these features, select an optimal feature n i as the partitioning feature of the node;

[0023] 3) Randomly select a feature value of feature n i to partition the node into two child nodes;

[0024] 4) Before further partitioning the child nodes obtained in step 3), first check whether the child nodes meet the node partitioning termination condition. If so, terminate the partitioning and complete the tree construction. Otherwise, repeat steps 2) and 3) to continue partitioning the child nodes to generate new child nodes;

[0025] 5) When the number of constructed decision trees reaches the set value T, complete the establishment of the extreme tree regression model. Otherwise, repeat all the above steps.

[0026] In step (6), the method for calculating the cumulative factor of a certain material using the established extreme tree regression model is as follows:

[0027] For a single-element material, according to its atomic number Z, the shielding thickness t of interest, and the incident ray energy E, construct the input space (Z, t, E) of this data, and input it into the extreme tree regression model to output the corresponding cumulative factor value. For a mixture / compound, after determining the equivalent atomic number of the mixture / compound according to the detailed description in item (3) of this technical solution, the corresponding cumulative factor value can be calculated and output through the extreme tree regression model.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows: The process of constructing the cumulative factor calculation model in the present invention is relatively simple. And because the extreme tree algorithm has good adaptability to the cumulative factor data, it enables the model to have excellent fitting ability for the cumulative factor data without complex parameter tuning or even without parameter tuning during the modeling process. Therefore, the present invention has the characteristics of accurate calculation and easy implementation. When the cumulative factor data needs to be updated and the fitting parameters need to be re-determined, the present invention can greatly reduce the workload of re-fitting the data. At the same time, in practical applications, the present invention requires fewer parameters to be calculated, simplifies the cumulative factor calculation process, and has a simple model structure and fast computer processing speed. The above advantages enable the present invention to accurately and more efficiently calculate the γ-ray cumulative factors of various shielding materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the overall calculation process;

[0030] Figure 2 Schematic diagram of the modeling process of the extreme tree regression model;

[0031] Figure 3Schematic diagram of the test results of the algorithm generalization performance;

[0032] Figure 4 Curve graph of the algorithm calculation time varying with the sample size;

[0033] Among them, Figure 3 |Dev| in it refers to the absolute value of the relative deviation between the sample predicted value and the target value, and |Dev_max| refers to the maximum value of the absolute value of the relative deviation; RAD refers to the relative average deviation, that is, the average value of |Dev|. Specific implementation manners

[0034] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0035] In conjunction with Figures 1 to 4 , the present invention relates to the efficient and accurate calculation of the gamma-ray buildup factor in the field of radiation protection. The present invention includes: obtaining a large amount of buildup factor sample data from the publicly available buildup factor dataset; selecting appropriate attributes according to the influencing factors of the buildup factor and the characteristics of the sample data, and defining the input space; calculating the effective atomic number of the mixture / compound; establishing a training dataset for model learning; learning the training dataset to establish an extreme tree regression model; and using the extreme tree regression model to calculate the buildup factor.

[0036] The present invention adopts the following technical solutions for specific implementation ( Figure 1 ):

[0037] The program code of the present invention takes PyCharm Community Edition 2021.1.1 x64 as the integrated development platform and is programmed and implemented in the python language. Its main function is to efficiently and accurately calculate the gamma-ray exposure buildup factor of a certain material at a specific thickness and specific incident gamma-ray energy.

[0038] 1. In the document "New Gamma-Ray Buildup Factor Data for Point Kernel Calculations: ANS-6.4.3 Standard Reference Data" published by the Radiation Shielding Information Center of the Oak Ridge National Laboratory in the United States, obtain the gamma-ray exposure buildup factor data, which covers 26 materials, the shielding thickness reaches 40 mfp (mean free path), and the ray energy range is 0.015 - 15 MeV.

[0039] 2. According to the characteristics of the data, analyze and consider three main influencing factors of the buildup factor: the atomic number Z of the material, the shielding thickness t, and the ray energy E. Thus, the input space is defined as (Z, t, E).

[0040] 3. For a compound / mixture, its effective atomic number is calculated using the following formula:

[0041]

[0042] where Z eff is the effective atomic number of the mixture / compound; Z i is the atomic number of the i-th element that makes up the mixture / compound; f i is the electron number fraction of the i-th element.

[0043] 4. According to the cumulative factor data obtained in step 1, each piece of data is organized into the form of (Z, t, E, B), where B is the exposure cumulative factor. Finally, these data are collected in an Excel table as the training data set for model learning.

[0044] 5. Learn from the training data set and establish an extreme tree regression model according to the Figure 2 process:

[0045] 1) Based on the original training set, randomly select n sub features from all n features and use them as the tree-building features of a decision regression tree;

[0046] 2) Among the n sub features extracted, select an optimal feature n i as the partitioning feature of the node;

[0047] 3) Randomly select a feature value of feature n i to partition the node and divide the node into two child nodes;

[0048] 4) Before further partitioning the child nodes obtained in step 3), first check whether the child nodes meet the node partitioning termination condition. If so, terminate the partitioning and complete the tree building. Otherwise, repeat steps 2) and 3) to continue partitioning the child nodes to generate new child nodes;

[0049] 5) When the number of built decision trees reaches the set value T, complete the establishment of the extreme tree regression model. Otherwise, repeat all the above steps.

[0050] These modeling steps have been deployed in the sciket-learn module toolkit of python. You can directly import the extreme tree for regression into the program. Through learning the data, the model training is completed.

[0051] 6. The cumulative factor of the shielding material is calculated using the extreme tree regression model. The test results show that the present invention has a very good fitting effect on the exposure cumulative factor in the ANS-6.4.3 cumulative factor standard database, and the algorithm has excellent generalization performance (as Figure 3 shown, the relative average deviation between the sample predicted value and the target value is 1.48%), and very high calculation efficiency (as Figure 4 shown, the time required to calculate 150,000 sample data is less than 0.5 s).

Claims

1. A regression calculation method for the gamma-ray cumulative factor of a shielding material based on an extreme tree, characterized in that, The steps are as follows: Step 1: In the engineering material γ-ray cumulative factor dataset, obtain the cumulative factor sample data of the shielding material; Step 2: Select appropriate attributes according to the influencing factors of the cumulative factor and the characteristics of the sample data, and define the input space; Step 3: Calculate the effective atomic number of the mixture / compound; Step 4: Establish a training dataset for model learning; Step 5: Learn from the training dataset and establish an extreme tree regression model; (1) Based on the original training set, randomly select n features from all n features and use them as the features for building a decision regression tree; sub features, and use them as the features for building a decision regression tree; (2) Among the n sub extracted features, select an optimal feature n i as the splitting feature of the node; (3) Randomly select a feature value division node of feature n i and divide the node into two child nodes; (4) Before further dividing the child node obtained in step (3), first detect whether the child node meets the node division termination condition. If so, terminate the division and complete the tree construction. Otherwise, repeat steps (2) and (3) to continue dividing the child node to generate new child nodes; (5) When the number of built decision trees reaches the set value T, complete the establishment of the extreme tree regression model. Otherwise, repeat all the above steps; Step 6: Use the extreme tree regression model to calculate the cumulative factor.

2. A regression calculation method for the gamma-ray buildup factor of a shielding material based on an extreme tree according to claim 1, characterized in that In step 2, the definition of the input space is: According to the influencing factors of the cumulative factor: material atomic number Z, material thickness t, and incident γ-ray energy E, the input space is defined as (Z, t, E), where t is expressed in terms of the mean free path number, and the conversion between t and the geometric thickness d is through the following formula: where ρ is the density of the medium material, g / cm 3 ; (μ / ρ) is the mass attenuation coefficient of the material, cm 2 / g; The effective atomic number of the mixture / compound is calculated using the following formula: where Z eff is the effective atomic number of the mixture / compound; Z i is the atomic number of the i-th element that makes up the mixture / compound; f i is the electron number fraction of the i-th element.

3. A method for calculating the regression of the gamma-ray cumulative factor of a shielding material based on an extreme tree according to claim 1, characterized in that In step 6, the method for calculating the cumulative factor of a certain material using the established extreme tree regression model is: for a single-element material, according to its atomic number Z, the shielding thickness t of interest, and the incident ray energy E, construct the input space (Z, t, E) of this piece of data, and input it into the extreme tree regression model to output the corresponding cumulative factor value.

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