Method and calculation device for obtaining radiation shielding material ratio based on genetic algorithm

Abstract

A method for obtaining a radiation shielding material ratio based on a genetic algorithm includes the following steps: first, randomly generating an initial population based on the composition range of the radiation shielding material; calculating the performance parameters of the initial population and establishing the objective function of the genetic algorithm; then, performing a non-dominated sort and using the genetic algorithm to perform crossover and mutation on the radiation shielding materials; and iterating according to constraints until a given number of iterations, N, is reached to obtain the optimized radiation shielding material ratio. This method can reduce the computational effort required to optimize multiple performance parameters of radiation shielding materials, thereby improving design efficiency. The present invention also provides a calculation device.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear power, and in particular relates to a method and a calculation device for obtaining a radiation shielding material ratio based on a genetic algorithm. Background Art

[0002] Radiation shielding materials are an important foundation for ensuring the safety of nuclear power facilities and isolating harmful radiation. The optional composition ratios of radiation shielding materials involve many elements. Traditional methods require technicians to provide an initial material combination based on their experience, perform shielding calculations and analysis on the shielding materials to verify their shielding performance, and then manually adjust the formulation parameters based on the calculation results and design goals. This process is highly dependent on the technicians' experience and is inefficient. Currently, some technical solutions use a combination of Monte Carlo methods and neural networks to use machine learning to predict the performance of shielding materials with different ratios. However, this method relies on large sample training data. If the number of samples is insufficient, it will lead to large deviations in the prediction results. Generating a sufficient number of training samples itself means consuming a large amount of computing resources, and efficiency and cost also need to be optimized. Therefore, providing a method for determining the ratio of radiation shielding materials with lower computational complexity is of positive significance for improving the design efficiency of radiation shielding materials. Summary of the Invention

[0003] The present invention aims to provide a method for obtaining the ratio of radiation shielding materials based on a genetic algorithm, thereby improving the design efficiency of radiation shielding materials. The present invention also provides a calculation device.

[0004] According to an embodiment of one aspect of the present invention, a method for obtaining a radiation shielding material ratio based on a genetic algorithm is provided, the method comprising the following steps:

[0005] a) providing the element composition and ratio range of the radiation shielding material, randomly generating an initial component ratio, and calculating the performance parameter f of the radiation shielding material under the initial component ratio i , wherein i is an integer from 1 to m, m is the total number of the performance parameters, the performance parameters include shielding performance parameters and physical parameters, the shielding performance parameters include neutron and / or photon fluence rate and / or dose rate, and the physical parameters include at least two of the mass, density and volume of the radiation shielding material;

[0006] b) Establish the objective function of the genetic algorithm minF(x) = [f1(x), ..., f m (x)] T ,in,

[0007] x=(x1,…x n ), and meet the following requirements:

[0008]

[0009] Where n is the number of elements contained in the composition ratio, x i is the proportion of the i-th element;

[0010] c) performing non-dominated sorting on the radiation shielding materials according to the objective function, and performing crossover and mutation on the radiation shielding materials using a genetic algorithm to generate a new generation of composition ratios and the corresponding shielding performance parameters f i ;

[0011] d) Repeating the steps b) and c) for N iterations to obtain an optimized radiation shielding material ratio; wherein N is a given number of iterations, and the constraint condition of the objective function is: if f i <f l , then f i =f hi +p i ×(f li -f i ) / (f hi -f li ); if f i >f hi , then f i =f hi +p i ×(f i -f hi ) / (f hi -f li ), where N is the given iterative number, f li f i The lower bound of the constraint, f hi f i The upper bound of the constraint, p i is a given sufficiently large penalty function.

[0012] The above method does not rely on the experience of researchers, consumes little computing resources, has high computational efficiency, and can quickly iterate to obtain the radiation shielding material ratio that meets the design requirements.

[0013] Furthermore, in some embodiments, the constituent elements of the radiation shielding material include one or more of yttrium, boron, gadolinium or dysprosium and hydrogen.

[0014] Furthermore, in some embodiments, the a) uses the U / Pu mixed neutron fission spectrum and photon fission spectrum as calculation conditions for the performance parameters.

[0015] Furthermore, in some embodiments, the neutrons include fast neutrons and thermal neutrons.

[0016] Furthermore, in some embodiments, the radiation shielding material has a fluence rate Φi,m The calculation method is:

[0017]

[0018]

[0019] Among them, r is the calculation grid radius, A is the calculation grid area, V is the calculation grid volume, S is the grid source strength, Σ i is the total reaction cross section, w is the weight of the quadrature group after the directional variables are discretized by the discrete total table method,

[0020]

[0021] Where ω is the angle between the particle motion direction and the radial direction, and ζ is the angle between the particle motion direction and the axial direction.

[0022] Furthermore, in some embodiments, the dose rate D of the radiation shielding material is calculated as follows:

[0023]

[0024] Among them, D n is the neutron dose rate, D γ is the photon dose rate, G n is the number of neutron energy groups, G γ is the number of photon energy groups, Φ n,g is the neutron flux rate, Φ γ,g is the photon fluence rate, C n,g is the neutron fluence rate-dose rate conversion factor, C γ,g is the photon fluence rate-dose rate conversion factor.

[0025] Furthermore, in some embodiments, the density ρ of the radiation shielding material satisfies

[0026]

[0027] The volume of the radiation shielding material V=πR 2 H, wherein R is the thickness of the radiation shielding material and H is the height of the radiation shielding material;

[0028] The mass of the radiation shielding material is W=ρV.

[0029] Furthermore, in some embodiments, the genetic algorithm in step b) and step c) adopts NSGA-III algorithm.

[0030] Furthermore, in some embodiments, the number of iterations N in step d) satisfies that the hypervolume HV of F(x) reaches a maximum value at the Nth iteration, Where δ is the Lebesgue measure, |S| is the number of non-dominated solution sets, v i is the hypervolume formed by the reference point and the i-th solution in the solution set.

[0031] According to an embodiment of another aspect of the present invention, a computing device is provided, which includes a memory and a processor, wherein the memory stores a computing program, and when the computing program is executed by the processor, it can implement the method for obtaining the radiation shielding material ratio based on the genetic algorithm provided in any of the aforementioned embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A schematic diagram of shielding performance calculation and analysis in one embodiment;

[0033] Figure 2 Flowchart of a method for obtaining a radiation shielding material ratio based on a genetic algorithm in one embodiment;

[0034] Figure 3 1 is a flowchart illustrating the NSGA-III evolutionary iterative process in one embodiment;

[0035] Figure 4 A schematic diagram of the trend of hypervolume changing with algebra in one embodiment;

[0036] Figure 5 2. The core neutron spectrum in one embodiment;

[0037] Figure 6 This is the core photon energy spectrum in one embodiment.

[0038] The purpose of the above drawings is to provide a detailed description of the present invention so that those skilled in the art can understand the technical concept of the present invention, and is not intended to limit the present invention. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below with reference to specific drawings and embodiments.

[0040] Mention of "embodiment" herein means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment herein. The phrase appearing in various places in the specification does not necessarily refer to the same embodiment, nor is it limited to mutually exclusive independent or alternative embodiments. It should be understood by those skilled in the art that the embodiments herein can be combined with other embodiments under the premise that no structural conflict occurs. In the description herein, terms such as "first" and "second" are only used to distinguish different objects, and cannot be understood as indicating relative importance or limiting the number, specific order or primary and secondary relationship of the technical features described. In the description herein, the meaning of "multiple" is at least two.

[0041] Traditional radiation shielding material optimization methods typically involve designers formulating an initial material composition based on experience. Shielding calculations and analyses are then performed on this material to verify its shielding performance. If the design objectives are not met, the composition must be adjusted and the shielding calculations and analyses repeated. This iterative process of repeated manual adjustments and verifications is inefficient for multi-objective optimization (including dose rate, shielding material volume, density, and so on), especially when the material composition is complex. Furthermore, it relies heavily on the technical expertise of the technicians, making it difficult to meet the design requirements of radiation shielding materials for new nuclear power plants. With the development of computational materials science, some approaches have adopted weighted methods to reduce the dimensionality of multiple objectives to a single objective, thereby simplifying the composition optimization calculation process. However, because the setting of sub-objective weighting factors also relies on subjective experience, the solution process may introduce significant approximations or uncertainties. The optimization result of this simplified approach is theoretically only one of a set of optimal solutions, requiring recalculation after any weighting factors are changed. Other approaches utilize Monte Carlo methods to generate a large number of radiation shielding material composition samples, use these samples to train a neural network, and then use the neural network to predict the shielding performance of a specific material composition. However, the training results of neural networks depend on the number of samples and the degree of match between the training samples and the actual application scenarios. In order to generate a sufficient number of training samples, the Monte Carlo program needs to consume a large amount of computing resources for sample generation; and if the training samples are insufficient, the relative deviation between the prediction results and the program calculation values ​​will increase, and even mislead the algorithm into falling into a local optimum.

[0042] In order to solve the above problems, an embodiment of the present invention provides a method for obtaining the ratio of radiation shielding materials based on a genetic algorithm, thereby achieving multi-objective optimization of radiation shielding materials.

[0043] like Figure 2 As shown, the method includes the following steps:

[0044] First, the parameters of the radiation shielding material are initialized. An initial composition ratio is randomly generated based on the given elemental composition and ratio range. In different embodiments, the elemental composition can include two or more components, such as a hydride material composed of one or more of yttrium, boron, gadolinium, or dysprosium and hydrogen. An initial population is generated, and an input file for the genetic algorithm is generated based on the initial population. In a preferred embodiment, the genetic algorithm uses the NSGA-III algorithm. The m performance parameters f of the radiation shielding material under the initial composition ratio are calculated. i , where i is an integer between 1 and m, and m is the total number of performance parameters, including shielding performance parameters (including neutron and / or photon fluence rate and / or dose rate after shielding by radiation shielding material) and physical parameters (at least two of the mass, density and volume of radiation shielding material). Specifically, in a preferred embodiment, the calculation conditions of the shielding performance parameters are as follows: Figure 1Neutron fission spectrum and photon fission spectrum of U / Pu mixture are shown.

[0045] Specifically, where the fluence rate Φ of the radiation shielding material i,m The calculation method is:

[0046]

[0047]

[0048] Among them, r is the calculation grid radius, A is the calculation grid area, V is the calculation grid volume, S is the grid source strength, Σ i is the total reaction cross section, w is the weight of the quadrature group after the directional variables are discretized by the discrete total table method,

[0049]

[0050] Where ω is the angle between the particle motion direction and the radial direction, is the angle between the particle motion direction and the axial direction.

[0051] The calculation method for the dose rate D of radiation shielding materials is:

[0052]

[0053] Among them, D n is the neutron dose rate, D γ is the photon dose rate, G n is the number of neutron energy groups, G γ is the number of photon energy groups, Φ n,g is the neutron flux rate, Φ γ,g is the photon fluence rate, C n,g is the neutron fluence rate-dose rate conversion factor, C γ,g is the photon fluence rate-dose rate conversion factor.

[0054] The density ρ of the radiation shielding material satisfies Volume V = πR 2 H, where R is the thickness of the radiation shielding material, H is the height of the radiation shielding material; the mass of the radiation shielding material W = ρV.

[0055] Next, establish the objective function of the genetic algorithm min F(x)=[f1(x),……,f m (x)] T , where x=(x1,…x n ),in Where n is the number of elements contained in the composition ratio, x i is the proportion of the i-th element.

[0056] Next, the radiation shielding materials are non-dominated sorted according to the objective function, and the genetic algorithm is used to generate a new generation of composition ratios after crossover and mutation of the radiation shielding materials. The population is updated using the new generation of composition ratios, and the corresponding input file is generated. The iterative calculation is repeated until the specified number of generations N is reached. N should be sufficient to make the population have sufficient diversity. Figure 3 As shown, during the iteration, the parent generation P that meets the conditions in the previous iteration obtained by the t-th generation screening is t Plus the generated new population Q t Combined to form R t , for R t Perform non-dominated sorting and reference point sorting, and eliminate unqualified populations to obtain the parent generation P for the next iteration t+1 , repeat this process until N iterations are completed. In a preferred embodiment, N satisfies that the hypervolume HV of F(x) reaches its maximum value at the Nth iteration, Where δ is the Lebesgue measure, |S| is the number of non-dominated solution sets, v i is the hypervolume formed by the reference point and the i-th solution in the solution set. The reference point takes the maximum value of the objective function in each generation of shielding material. During the iteration process, the constraint condition of the objective function is that if f in F(x) i <f l , then f i =f hi +p i ×(f li -f i ) / (f hi -f li ); if f i >f hi , then f i =f hi +p i ×(f i -f hi ) / (f hi -f li ), where f li f i The lower bound of the constraint, f hi f i The upper bound of the constraint, p i is a given sufficiently large penalty function, specifically, sufficiently large means p i The introduced offset can make f i Exceeding the screening conditions will cause the population that exceeds the constraint limit to be eliminated in the iteration. After N iterations, the obtained radiation shielding material composition ratio is the optimized composition ratio, and the shielding performance and physical properties of the radiation shielding material are optimized.

[0057] In a preferred embodiment, yttrium-based hydrides are optimized for radiation shielding materials, with a composition ratio ranging from 0.95-1% yttrium to 0-0.05% hydrogen. In various embodiments, the composition ratio range can be determined based on engineering experience or thermodynamic calculations to determine the composition range within which the component elements can form stable phases.

[0058] Step 1: Initialization of the material ratio. Randomly generate the proportions of yttrium (Y) and hydrogen (H) in the initial composition ratio within the composition ratio range as shown in Table 1.

[0059] Table 1 Initial ingredient ratio and performance parameters

[0060]

[0061] The simulation conditions for optimizing the radiation shielding material are 55 cm of air between the core irradiation source, a 2 cm thick hanging basket, a 21 cm reflector layer, 22 cm of water, and a 13 cm pressure vessel wall. Figure 5 As shown, the core photon spectrum is as follows Figure 6 shown.

[0062] Step 2: Based on the element ratios shown in Table 1, calculate the material density and mass. Use a discrete vertical scale program to calculate the dose rate after the shielding material is applied. The dose rate includes the sum of the neutron and photon dose rates. The calculated mass and dose rate are shown in Table 1. These mass and dose rate are used as the material performance parameters to be optimized.

[0063] Step 3: According to the objective function obtained in step 2 (including mass and dose rate after shielding by radiation shielding materials), the shielding materials are non-dominated sorted, and a new material composition ratio is generated after crossover and mutation using the NSGA-III genetic algorithm, and then step 2 is repeated for iteration. Calculate the hypervolume of the objective function, where f i 1 represents the quality of the i-th generation, f r 1 represents the reference solution of mass; f i 2 represents the dose rate of the i-th generation, f r 2 represents the reference solution of the dose rate; after 10 generations with 20 population iterations in each generation, the hypervolume reaches its maximum value, and the final optimized material is obtained as shown in Table 2. The required radiation shielding material is selected from the optimized material ratio according to the specific design requirements.

[0064] Table 2 Final optimized material ratio and performance parameters

[0065]

[0066] Using a genetic algorithm, the above embodiment performs 200 discrete ordinate calculations, which takes approximately 300 seconds on a general-purpose computer. However, if a Monte Carlo method combined with a neural network were used, the computing resources required would be an order of magnitude higher, based on an estimate of a single Monte Carlo run time of 1 minute. Therefore, the genetic algorithm-based method for determining radiation shielding material ratios provided in the above embodiment offers significant efficiency advantages.

[0067] In another preferred embodiment, for radiation shielding materials containing more neutral elements, the method used in the above embodiment is used to perform iteration based on the genetic algorithm, and the change trend of its hypervolume HV is as follows: Figure 4 As shown, the hypervolume reaches its maximum value after 40 iterations, indicating that the optimization result has basically converged. In other embodiments, the radiation shielding material can be a hydride composite material of yttrium, boron, gadolinium, and dysprosium.

[0068] Another embodiment of the present invention provides a computing device comprising a memory and a processor. The memory stores a computing program. When the computing program is executed by the processor, the computing device is capable of implementing the method for obtaining a radiation shielding material ratio based on a genetic algorithm as provided in any of the aforementioned embodiments. In various embodiments, the computing device can be configured as a general-purpose computer, a dedicated computing device, a virtual machine, or a cloud computing device. The computing program can be written in general-purpose software capable of executing a genetic algorithm, or directly in a general-purpose computer language.

[0069] The purpose of the above embodiments is to provide a further detailed description of the present invention in conjunction with the accompanying drawings so that those skilled in the art can understand the technical concept of the present invention. Within the scope of the present invention, optimization or equivalent replacement of the method steps involved, as well as combination of implementation methods in different embodiments without causing structural or principle conflicts, all fall within the scope of protection of the present invention.

Claims

1. A method for obtaining the ratio of radiation shielding materials based on genetic algorithm, characterized in that: The following steps are involved: a) providing the element composition and ratio range of the radiation shielding material, randomly generating an initial component ratio, and calculating the performance parameter f of the radiation shielding material under the initial component ratio i , wherein i is an integer from 1 to m, m is the total number of the performance parameters, the performance parameters include shielding performance parameters and physical parameters, the shielding performance parameters include neutron and / or photon fluence rate and / or dose rate, the physical parameters include at least two of the mass, density and volume of the radiation shielding material, and the U / Pu mixed neutron fission spectrum and photon fission spectrum are used as calculation conditions for the performance parameters; wherein the fluence rate Φ of the radiation shielding material i,m The calculation method is: ； ； Among them, r is the calculation grid radius, A is the calculation grid area, V is the calculation grid volume, S is the grid source strength, Σ t,i is the total reaction cross section of grid i, w is the quadrature group weight after the directional variables are discretized using the discrete ordinate method, ； Where ω is the angle between the particle motion direction and the radial direction, is the angle between the particle motion direction and the axial direction; b) Establish the objective function of the genetic algorithm minF(x)=[f1(x),……,f m (x)] T , where x=(x1,…x n ), and meet the following requirements: ， Where n is the number of elements contained in the composition ratio, x i is the proportion of the i-th element; c) performing non-dominated sorting on the radiation shielding materials according to the objective function, and performing crossover and mutation on the radiation shielding materials using a genetic algorithm to generate a new generation of composition ratios and the corresponding shielding performance parameters f i ; d) Repeat the steps b) and c) for N iterations to obtain an optimized radiation shielding material ratio; wherein N is a given number of iterations, and the constraint condition of the objective function is: if f i <f l , then f i =f hi +p i ×(f li -f i ) / (f hi -f li ); if f i >f hi , then f i =f hi +p i ×(f i -f hi ) / (f hi -f li ), where N is the given iterative number, f li f i The lower bound of the constraint, f hi f i The upper bound of the constraint, p i is a given sufficiently large penalty function.

2. The method for obtaining the ratio of radiation shielding materials based on genetic algorithm according to claim 1, characterized in that: The constituent elements of the radiation shielding material include one or more of yttrium, boron, gadolinium or dysprosium and hydrogen.

3. The method for obtaining the ratio of radiation shielding materials based on genetic algorithm according to claim 1, characterized in that: The neutrons include fast neutrons and thermal neutrons.

4. The method for obtaining the ratio of radiation shielding materials based on genetic algorithm according to claim 1, characterized in that: The calculation method of the dose rate D of the radiation shielding material is: ； Among them, D n is the neutron dose rate, D γ is the photon dose rate, G n is the number of neutron energy groups, G γ is the number of photon energy groups, Φ n,g is the neutron flux rate, Φ γ,g is the photon fluence rate, C n,g is the neutron fluence rate-dose rate conversion factor, C γ,g is the photon fluence rate-dose rate conversion factor.

5. The method for obtaining the ratio of radiation shielding materials based on a genetic algorithm according to any one of claims 1 to 3, characterized in that: The density ρ of the radiation shielding material satisfies , The volume of the radiation shielding material V=πR 2 H, wherein R is the thickness of the radiation shielding material and H is the height of the radiation shielding material; The mass of the radiation shielding material is W=ρV.

6. The method for obtaining the ratio of radiation shielding materials based on a genetic algorithm according to any one of claims 1 to 3, characterized in that: The genetic algorithm in the steps b) and c) adopts the NSGA-III algorithm.

7. The method for obtaining the ratio of radiation shielding materials based on a genetic algorithm according to any one of claims 1 to 3, characterized in that: The number of iterations N in step d) satisfies that the hypervolume HV of F(x) reaches its maximum value at the Nth iteration. , where δ is the Lebesgue measure, |S| is the number of non-dominated solution sets, and v i is the hypervolume formed by the reference point and the i-th solution in the solution set.

8. A computing device comprising a memory and a processor, characterized in that: The memory stores a calculation program, and when the calculation program is executed by the processor, the method for obtaining a radiation shielding material ratio based on a genetic algorithm according to any one of claims 1 to 7 can be implemented.

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