A method for evaluating the similarity of nuclear systems based on sensitivity coating

Abstract

The present invention relates to a method for evaluating the similarity of nuclear systems based on sensitivity wrapping, belonging to the technical field of nuclear safety assessment, and includes the following steps: S1. Select the common nuclides to be evaluated from the first nuclear system and the second nuclear system respectively; S2. Select the nuclear cross-sections to be evaluated for each common nuclide; S3. Calculate the sensitivity of each nuclear cross-section selected in step S2 respectively; S4. Calculate the similarity index Sim of the two nuclear systems; S5. Calculate the component dSim of the similarity index of the two nuclear systems r ; S6. Calculate the reference similarity index Sim' of the two nuclear systems; S7. Based on the results of steps S4 - S6, determine whether the two nuclear systems meet the similarity requirements. The method provided by the present invention gives an index that can quantitatively judge similarity. Through this index, users can well judge the neutronics similarity of nuclear systems, and at the same time, users can also have a better understanding of the similarity of different nuclear cross-sections, guiding their evaluation, analysis and design work.

Description

Technical Field

[0001] The invention belongs to the technical field of nuclear safety assessment, and in particular is a method for assessing nuclear system similarity based on sensitivity coating. Background Art

[0002] According to GB 15146 and other regulatory standards, when using calculation programs for critical safety evaluation and analysis, relevant experimental critical data must be used for verification support. At the same time, these relevant data need to be used to verify the bias and uncertainty of the program.

[0003] There are many methods for evaluating and selecting relevant criticality data benchmarks, such as the traditional feature judgment method, which divides the nuclear system into several different macroscopic features and compares the similarity of these features. However, different nuclear systems often do not have high similarity in each feature, which makes it difficult to make a choice in the selection. The subjective factors are large, and it is also difficult to find a truly relevant criticality benchmark experiment. When conducting criticality safety analysis, the neutronics characteristics of the nuclear system are often more critical, and one of the important manifestations of the neutronics characteristics is the sensitivity of the proliferation factor (usually expressed as keff) of the nuclear system's finite reactor system. Summary of the invention

[0004] In order to solve the defects of the prior art, the purpose of the present invention is to provide a method for assessing the similarity of nuclear systems based on sensitivity coating, which can quantify the similarity of nuclear systems so as to screen critical experimental data and further assess the nuclear safety characteristics of nuclear systems.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A method for evaluating nuclear system similarity based on sensitivity coating includes the following steps:

[0007] S1. Select the common nuclides to be assessed from the first nuclear system and the second nuclear system respectively;

[0008] S2. Select the nuclear cross section that needs to be evaluated for each common nuclide;

[0009] S3, respectively calculating the sensitivity of each nuclear cross section selected in step S2;

[0010] S4, calculating the similarity index Sim of the two core systems;

[0011] S5. Calculate the similarity index component dSim of the two kernel systems r ;

[0012] S6, calculating the reference similarity index Sim' of the two kernel systems;

[0013] S7. Based on the results of steps S4 - S6, determine whether the two nuclear systems meet the similarity requirements.

[0014] Furthermore, in the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, the common nuclides mentioned in step S1 include nuclear materials, structural materials, or moderating materials shared by the two nuclear systems.

[0015] Furthermore, in the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, the types of nuclear cross - sections selected in step S2 include one or two or more of the total scattering cross - section, total absorption cross - section, and total fission cross - section.

[0016] Furthermore, in the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, each type of nuclear cross - section of the common nuclides selected in step S2 is unique, that is, the total cross - section and the component cross - section of the same type cannot be selected simultaneously.

[0017] Furthermore, in the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, the calculation formula for sensitivity in step S3 is:

[0018]

[0019] where α represents the input parameter, k represents the output parameter, and S k,α represents sensitivity.

[0020] Furthermore, in the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, in step S4, the first nuclear system is denoted as the nuclear system to be evaluated a, and the second nuclear system is denoted as the experimental nuclear system e. The calculation formula for the similarity index Sim of the two nuclear systems is:

[0021]

[0022] where:

[0023]

[0024] where n represents the type of nuclides, r represents the cross - section, g represents the energy group, Sim is a value between 0 and 1, where 1 represents that the two nuclear systems are completely correlated, and 0 represents that the two nuclear systems are not correlated.

[0025] Furthermore, in the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, the component dSim of the nuclear system similarity index in step S5 r is calculated as:

[0026]

[0027] where:

[0028]

[0029] Among them, dSim r is a value between 0 and 1. 1 represents that the two nuclear systems are completely correlated with respect to this cross-section, and 0 represents that the two nuclear systems are not correlated with respect to this cross-section.

[0030] Furthermore, for the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, the calculation formula for the reference similarity index Sim' in step S6 is:

[0031]

[0032] Among them, n represents the type of nuclide, x represents the total number of cross-sections, and D r represents the weight of each similarity index component.

[0033] Furthermore, for the method for evaluating the similarity of nuclear systems based on sensitivity wrapping as described above, according to the calculation results of the similarity index Sim, the similarity index component dSim r and the reference similarity index Sim' of the two nuclear systems, the similarity of the two nuclear systems is determined.

[0034] Adopting the method for evaluating the similarity of nuclear systems based on sensitivity wrapping described in the present invention has the following remarkable technical effects:

[0035] Based on the sensitivity of the nuclear system keff, the present invention gives an index that can quantitatively judge similarity. Through this index, users can well judge the neutronics similarity of nuclear systems, and at the same time, users can also have a better understanding of the similarity of different nuclear cross-sections, guiding their evaluation, analysis and design work. Description of the Drawings

[0036] Figure 1 is a flowchart of the method for evaluating the similarity of nuclear systems based on sensitivity wrapping provided in the specific embodiment of the present invention;

[0037] Figure 2 is another flowchart of the method for evaluating the similarity of nuclear systems based on sensitivity wrapping provided by the present invention. Specific Embodiments

[0038] The present invention will be further described below in conjunction with specific embodiments and the accompanying drawings of the specification.

[0039] Figure 1 shows a flowchart of the method for evaluating the similarity of nuclear systems based on sensitivity wrapping provided in the specific embodiment of the present invention. The method includes the following steps:

[0040] S1. Select the common nuclides to be evaluated from the first nuclear system and the second nuclear system respectively

[0041] Generally, it should include nuclear materials (such as U, Pu, etc.), main structural materials (such as Fe, Cr, Ni, etc.), main moderating materials (such as H, C, etc.), and other main materials, and select the common materials of the two nuclear systems from these materials.

[0042] S2. Select the nuclear cross-sections that need to be evaluated for each nuclide

[0043] Such nuclear cross-sections should be unique. For example, if the total inelastic scattering cross-section is selected, each component cross-section of the inelastic scattering cross-section should not be selected anymore. The selected cross-sections generally should include the total scattering cross-section, the total absorption cross-section, and the total fission cross-section. Of course, for different nuclides, not all of these cross-sections exist, and they should also be excluded in the calculation (for example, H does not have a fission cross-section).

[0044] S3. Calculate the sensitivity of each nuclear cross-section selected in step S2

[0045] Sensitivity is defined as the effect of the percentage change of certain responses caused by a certain percentage change of input parameters. The calculation method is shown in formula (1).

[0046]

[0047] Among them, α represents the input parameter, k represents the output parameter, and S k,α represents sensitivity.

[0048] Generally, there are direct perturbation method, differential operator method, adjoint calculation method for calculating sensitivity. These methods have their own advantages and disadvantages, and different methods should be selected according to different calculation objects and calculation environments in use. Since the calculation of sensitivity is not the focus of this invention, it will not be elaborated here. The energy group structure of the calculated sensitivity data should correspond to the energy group structure of the covariance data.

[0049] S4. Calculate the similarity index Sim of the two nuclear systems

[0050] Designate one of the nuclear systems as the object to be evaluated, denoted as a, and the other nuclear system as the experimental nuclear system, denoted as e. Judge the similarity between the experimental nuclear system and the object to be evaluated. The calculation method of the similarity index Sim is shown in formula (2).

[0051]

[0052] Among them:

[0053]

[0054] Among them, n represents the nuclide type, r represents the cross section, g represents the energy group, Sim is a value between 0 and 1, where 1 represents that the two nuclear systems are completely correlated, and 0 represents that the two nuclear systems are not correlated. According to the actual application scenario, generally, Sim values of 0.9, 0.8, and 0.7 can be selected as the similarity discrimination criteria, and if it is greater than this value, the two nuclear systems can be considered similar.

[0055] S5. Calculate the similarity index component dSim of the two nuclear systems r

[0056] The similarity index component of the nuclear system is the similarity caused by each cross section, denoted as dSim r , and the calculation method is shown in formula (3).

[0057]

[0058] Among them:

[0059]

[0060] dSim r is a value between 0 and 1, where 1 represents that the two nuclear systems are completely correlated with respect to this cross section, and 0 represents that the two nuclear systems are not correlated with respect to this cross section.

[0061] S6. Calculate the reference similarity index Sim' of the two nuclear systems

[0062] The overall reference similarity index is the weighted sum of each similarity index component. Here, the weight of each similarity index component is denoted as D r , calculate the reference similarity index for reference. The calculation method of the reference similarity index Sim' is shown in formula (4).

[0063]

[0064] Among them, n represents the nuclide type, and x represents the total number of cross sections.

[0065] S7. Integrate the results of steps S4 - S6 to determine whether the two nuclear systems meet the similarity requirements.

[0066] According to the similarity index Sim, similarity index component dSim of the two nuclear systems r and the calculation results of the reference similarity index Sim', determine the similarity of the two nuclear systems.

[0067] To describe the technical solution of the present invention more clearly, here, a three - group structure is taken as an example for description.

[0068] Step 1: Select two nuclides from nuclear system 1 and nuclear system 2, denoted as N 1 , N 2, where both nuclear systems contain these two nuclides.

[0069] Step 2: Select N 1 For the three cross-sections (total scattering cross-section, total absorption cross-section, total fission cross-section) of the nuclide, and N 2 For the two cross-sections (total scattering cross-section, total absorption cross-section) of the nuclide, a total of five cross-sections, denoted as R 11 , R 12 , R 13 , R 21 , R 22 .

[0070] Step 3: Use a computer program to calculate the sensitivities of the five cross-sections in Step 2 with respect to keff respectively. The sensitivities of the five cross-sections in the three-group structure with respect to keff are as follows:

[0071]

[0072]

[0073]

[0074]

[0075] Step 4: Calculate the similarity index Sim of the two nuclear systems.

[0076] Denote nuclear system 1 as the nuclear system a to be evaluated, and nuclear system 2 as the experimental nuclear system e, then S' e The calculation results are:

[0077]

[0078]

[0079] Then the similarity index Sim is:

[0080] Sim = 0.52

[0081] Step 5: Calculate the similarity index component dSim of the two nuclear systems r . The calculation results of the similarity index component are:

[0082]

[0083]

[0084] Step 6: Calculate the reference similarity index Sim' of the two nuclear systems.

[0085] Set all weight parameters to 1. According to the calculation results in Step 5, the reference similarity index is:

[0086] Sim' = 0.51

[0087] Step 7: Give the similarity conclusion.

[0088] Based on the calculation results in Steps 4, 5, and 6, if 0.7 is taken as the similarity discrimination criterion, only the R cross-section in the similarity components of the two systems has relatively high similarity, indicating that the experimental nuclear system only interprets the R cross-section of the nuclear system to be evaluated relatively well, while both the similarity index and the similarity reference index are less than 0.7. Therefore, it is judged that the similarity of the two systems is poor. 11 cross-section relatively well, while both the similarity index and the similarity reference index are less than 0.7. Therefore, it is judged that the similarity of the two systems is poor. 11 The method for evaluating the similarity of nuclear systems based on sensitivity coating provided by the present invention can calculate the similarity index of two nuclear systems through the concept of sensitivity coating, and can provide a quantitative determination criterion for the similarity of nuclear systems; it provides a strong basis for screening critical benchmark experiments, helps to improve the accuracy of nuclear safety assessment work, and provides help for nuclear critical safety assessment staff.

[0089] The above embodiments are only illustrative examples of the present invention. The present invention can also be implemented in other specific ways or other specific forms without departing from the gist or essential characteristics of the present invention. Therefore, the described embodiments should be regarded as illustrative rather than restrictive in any aspect. The scope of the present invention should be defined by the appended claims, and any changes equivalent to the intention and scope of the claims should also be included within the scope of the present invention.

[0090] The above embodiments are only illustrative examples of the present invention. The present invention can also be implemented in other specific ways or other specific forms without departing from the gist or essential characteristics of the present invention. Therefore, the described embodiments should be regarded as illustrative rather than restrictive in any aspect. The scope of the present invention should be defined by the appended claims, and any changes equivalent to the intention and scope of the claims should also be included within the scope of the present invention.

Claims

1. A method for evaluating the similarity of nuclear systems based on sensitivity covering, comprising the following steps: S1. Select the common nuclides to be evaluated from the first nuclear system and the second nuclear system respectively; S2. Select the nuclear cross-sections to be evaluated for each common nuclide; S3. Calculate the sensitivity of each nuclear cross-section selected in step S2 respectively; S4. Calculate the similarity index Sim of the two nuclear systems; S5. Calculate the similarity index component dSim of the two nuclear systems r ; S6. Calculate the reference similarity index Sim' of the two nuclear systems; S7. Based on the results of steps S4 - S6, determine whether the two nuclear systems meet the similarity requirements; In step S4, the first nuclear system is denoted as the nuclear system a to be evaluated, and the second nuclear system is denoted as the experimental nuclear system e. The calculation formula for the similarity index Sim of the two nuclear systems is: Where: where n represents the type of nuclide, r represents the cross-section, g represents the energy group, and Sim is a value between 0 and 1, where 1 represents that the two nuclear systems are completely correlated and 0 represents that the two nuclear systems are not correlated; The component dSim of the nuclear system similarity index in step S5 r has the following calculation formula: Where: where dSim r is a value between 0 and 1, with 1 indicating that the two nuclear systems are completely correlated with respect to this cross-section and 0 indicating that the two nuclear systems are uncorrelated with respect to this cross-section; The calculation formula for the reference similarity index Sim' in step S6 is: Among them, n represents the nuclide type, x represents the total number of cross-sections, and D r represents the weight of each similarity index component.

2. The method for evaluating the similarity of nuclear systems based on sensitivity covering according to claim 1, characterized in that the common nuclides in step S1 include the nuclear materials, structural materials or moderating materials common to the two nuclear systems.

3. The method for evaluating the similarity of nuclear systems based on sensitivity covering according to claim 2, characterized in that the nuclear cross-sections selected in step S2 include the total scattering cross-section, the total absorption cross-section or the total fission cross-section.

4. The method for evaluating the similarity of nuclear systems based on sensitivity covering according to claim 3, characterized in that the types of nuclear cross-sections of each common nuclide selected in step S2 are unique, that is, the total cross-section and the component cross-section of the same type cannot be selected simultaneously.

5. The method for evaluating the similarity of nuclear systems based on sensitivity covering according to any one of claims 1 - 4, characterized in that the calculation formula for the sensitivity in step S3 is: Among them, α represents the input parameter, k represents the output parameter, and S k,α represents the sensitivity.

6. The method for evaluating the similarity of nuclear systems based on sensitivity covering according to claim 5, characterized in that Based on the similarity index Sim of two nuclear systems and the component dSim of the similarity index r and the calculation result of the reference similarity index Sim', determine the similarity of the two nuclear systems.

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