JP2022019280A - Reactor core analysis method, program, and reactor core analysis device - Google Patents

Abstract

To calculate a heat flux hot channel factor of a nuclear reactor in consideration of inaccuracy due to bending of fuel assemblies.SOLUTION: A reactor core analysis method includes the steps of: creating a plurality of bending patterns by perturbing core patterns, which is data on a plurality of fuel assemblies contained in a reactor core, on the basis of probability distribution which is data on the bending amount of the fuel assemblies; creating gap patterns for the bending patterns by converting the bending amount into gaps between adjacent fuel assemblies; setting the gap patterns as input parameters so as to calculate heat flux hot channel factors using a calculation code; performing statistical processing on the calculated plurality of heat flux hot channel factors; and calculating, as an analysis result of reactor core characteristics, the heat flux hot channel factors including inaccuracy due to the bending amount on the basis of the values obtained by the statistical processing.SELECTED DRAWING: Figure 7

Description

The present disclosure relates to a core analysis method, a program and a core analysis device.

Conventionally, a technique for evaluating the characteristics of a nuclear reactor is known. For example, in Patent Document 1,
In the core analysis, macrocovariance data on the uncertainty of the macrocross section is generated based on the data on the uncertainty of the microcross section of the nucleus, and further, the core calculation is performed based on the macrocovariance data to perform the core characteristics. A method of generating the uncertainty of is generated as an output value is disclosed.

Further, Patent Document 2 discloses, for example, a method for evaluating the subcriticality of a fuel assembly contained in a spent fuel pit. In this uncertainty evaluation method, the nuclear data of the fuel assembly and the production tolerance parameters are perturbed and combined to derive multiple sets of input parameters, and multiple effective multiplication factors are derived based on the combined multiple sets of input parameters. , A method of deriving an effective multiplication factor including uncertainty by statistically processing a plurality of derived effective multiplication factors is disclosed.

JP-A-2019-152448 Japanese Patent Application No. 2019-179019

By the way, one of the items to be evaluated in the core analysis is the heat flux hydrothermal channel coefficient. The heat flux hydrothermal channel coefficient is a parameter indicating the maximum value of the local output in the core. Here, the plurality of fuel assemblies arranged in the reactor may be bent in the direction orthogonal to the axial direction. Therefore, the distance between adjacent fuel assemblies changes, and as a result, the local output also changes. Therefore, a method for calculating the heat flux hydrothermal channel coefficient in consideration of the influence of uncertainty due to the bending of the fuel assembly is required.

The present invention has been made in view of the above, and an object of the present invention is to calculate a heat flux hydrothermal channel coefficient of a nuclear reactor in consideration of uncertainty due to bending of a fuel assembly.

In order to solve the above-mentioned problems and achieve the object, the core analysis method according to the present disclosure uses the core pattern, which is data on a plurality of fuel aggregates contained in the core, as the data on the bending amount of the fuel aggregates. A step of creating a plurality of bent patterns perturbated based on a certain probability distribution, a step of converting the amount of bending into a gap between adjacent fuel aggregates for the bending pattern, and a step of creating the gap pattern. As an input parameter, a step of calculating the heat flux hydrothermal channel coefficient using a calculation code, a step of statistically processing a plurality of the calculated heat flux hydrothermal channel coefficients, and a value obtained by the statistical processing. Based on this, it includes a step of calculating the heat flux hydrothermal channel coefficient including the uncertainty due to the bending amount as the analysis result of the core characteristics.

In order to solve the above-mentioned problems and achieve the object, the program according to the present disclosure is a probability that the core pattern, which is data on a plurality of fuel aggregates contained in the core, is data on the bending amount of the fuel aggregates. A step of creating a plurality of bent patterns perturbed based on the distribution, a step of creating a gap pattern in which the bending amount is converted into a gap between adjacent fuel aggregates for the bent pattern, and a step of inputting the gap pattern. Based on a step of calculating the heat flux hydrothermal channel coefficient using a calculation code as a parameter, a step of statistically processing a plurality of the calculated heat flux hydrothermal channel coefficients, and a value obtained by the statistical processing. , The computer is made to perform the step of calculating the heat flux hydrothermal channel coefficient including the uncertainty due to the bending amount as the analysis result of the core characteristics.

In order to solve the above-mentioned problems and achieve the object, the core analysis device according to the present disclosure includes a control unit for analyzing the core characteristics of the nuclear reactor, and the control unit is a plurality of fuel assemblies contained in the core. A step of creating a plurality of bending patterns in which the core pattern, which is the data related to the above-mentioned, is perturbed based on the probability distribution, which is the data regarding the bending amount of the fuel assembly, and the fuel assembly in which the bending amounts are adjacent to each other for the bending pattern. A step of creating a gap pattern converted into a gap between bodies, a step of calculating a heat flux hydrothermal channel coefficient using a calculation code with the gap pattern as an input parameter, and a plurality of the calculated heat flux hot water. A step of statistically processing the path coefficient and a step of calculating the heat flux hydrothermal channel coefficient including the uncertainty due to the bending amount as the analysis result of the core characteristics based on the value obtained by the statistical processing are executed. ..

The core analysis method, program, and core analysis device according to the present invention have an effect that the heat flux hydrothermal channel coefficient of the reactor can be calculated in consideration of the uncertainty due to the bending of the fuel assembly.

FIG. 1 is a schematic configuration diagram schematically showing a core analysis device according to an embodiment. FIG. 2 is an explanatory diagram schematically showing the core to be analyzed. FIG. 3 is a cross-sectional view when the fuel assembly to be analyzed is cut along a plane orthogonal to the axial direction. FIG. 4 is an explanatory diagram schematically showing a part of a plurality of fuel assemblies. FIG. 5 is an explanatory diagram showing an example of the probability distribution (presence ratio) of the bending amount. FIG. 6 is a flowchart showing an example of a process of calculating a heat flux hydrothermal channel coefficient including uncertainty. FIG. 7 is a flowchart showing an example of a process of calculating a coefficient including geometric shape uncertainty. FIG. 8 is a schematic diagram schematically showing an example of a process of calculating a coefficient including geometric shape uncertainty. FIG. 9 is an explanatory diagram showing an example of the probability distribution (presence ratio) of uncertainty due to the amount of bending.

Hereinafter, the core analysis method, the program, and the embodiment of the core analysis apparatus according to the present invention will be described in detail with reference to the drawings. The present invention is not limited to this embodiment.

FIG. 1 is a schematic configuration diagram schematically showing a core analysis device according to an embodiment. The core analysis device 10 is a device for analyzing the core characteristics of a nuclear reactor. In the present embodiment, the core analysis device 10 calculates the heat flux hydrothermal channel coefficient _FQ as one of the parameters indicating the core characteristics. The heat flux hydrothermal channel coefficient _FQ is a parameter indicating the maximum value of the local output in the core. In the following description, the heat flux hydrothermal channel coefficient is simply referred to as a "coefficient" as appropriate.

(Core)
FIG. 2 is an explanatory diagram schematically showing the core to be analyzed. FIG. 3 is a cross-sectional view when the fuel assembly to be analyzed is cut along a plane orthogonal to the axial direction. As shown in FIG. 2, the reactor core 5 is stored in the reactor, which is the target of the core design. The core 5 includes a plurality of fuel assemblies 6. The fuel is exchanged in units of 6 fuel assemblies.

(Fuel assembly and fuel rods)
Each fuel assembly 6 includes a plurality of fuel rods 29 having a fuel pellet 30 and a cladding tube 31 covering the fuel pellets 30, and a grid (not shown) for bundling the cladding tubes 31 of the plurality of fuel rods 29. The inside of the fuel assembly 6 is filled with the moderator (coolant) 33, and a plurality of control rods 34 and the inner core instrumentation 35 can be inserted. In the fuel rod 29, a plurality of fuel pellets 30 having a cylindrical shape are arranged side by side in the axial direction, and the outside thereof is covered with a cladding tube 31.

The fuel assembly 6 is formed in a rectangular cross section, and is composed of, for example, 17 × 17 cells 40. The control rods 34 are inserted into the 24 cells 40 of the 17 × 17 cells 40, and the inner core instrumentation 35 is inserted into the cell 40 at the center of the aggregate. At this time, the cell 40 into which the control rod 34 is inserted is referred to as a control rod guide pipe, and the cell 40 into which the inner core instrumentation 35 is inserted is referred to as an instrumentation guide pipe. Further, fuel rods 29 are inserted into the other cells 40, respectively. When the fuel assembly 6 is used in a boiling water reactor (BWR), the outside of the fuel assembly 6 is covered with a channel box. On the other hand, when the fuel assembly 6 is used in a pressurized water reactor (PWR), the outside of the fuel assembly 6 is open. Then, in the case of BWR, there is an inter-aggregate gap 32 outside the channel box, and in the case of PWR, outside the fuel assembly 6.

(About the bending that occurs in the fuel assembly)
FIG. 4 is an explanatory diagram schematically showing a part of a plurality of fuel assemblies. In the following description, the axial direction of the fuel assembly 6 is referred to as "Z direction", one direction orthogonal to the axial direction is referred to as "X direction", and the X direction and the direction orthogonal to the Z direction are referred to as "Y direction". As shown in FIG. 4, the plurality of fuel assemblies 6 are arranged side by side along the X direction and the Y direction.

The fuel assembly 6 may be bent. At this time, as illustrated in FIG. 4, the fuel assembly 6 is curved so as to draw an unevenness in the X direction or the Y direction. As a result, the gap G between the adjacent fuel assemblies 6 may change. In the present embodiment, the bending amount of the fuel assembly 6 is the amount of deviation from the axis in the X direction or the Y direction at the position of the lower end 6a of the fuel assembly 6. Such a change in the gap between the fuel assemblies 6 may locally promote fission and increase the local output. Therefore, the coefficient F _Q may be affected by the bending (change in gap G) that occurs in the fuel assembly 6. Hereinafter, as the core analysis device and the core analysis method according to the present embodiment, the configuration and method for calculating the coefficient _FQ in consideration of the bending generated in the fuel assembly 6 will be described.

(Structure of core analyzer)
Returning to the description of FIG. The core analysis device 10 includes an input unit 12, a display unit 14, a control unit 16, and a storage unit 18. The core analysis device 10 may be configured as a single device, integrally with other devices, or as a system in which various devices such as an arithmetic unit and a data server are combined. Well, it is not particularly limited.

The input unit 12 is an input device such as a keyboard, and information is input by the user of the core analysis device 10. The display unit 14 is a display device such as a monitor, and displays the analysis result by the core analysis device 10 to the user. The control unit 16 executes various programs to execute various processes.

The storage unit 18 stores various programs and data. The storage unit 18 stores, for example, an analysis program _P including a calculation code for calculating the coefficient FQ as one of the programs for core analysis. Further, the storage unit 18 stores data D1 regarding the core 5 to be analyzed. The data D1 is input by the user. Further, in the storage unit 18, the core pattern data D2, which is data on a plurality of fuel assemblies 6 arranged in an arbitrary core, and the probability distribution (presence ratio) of the bending amount of the plurality of fuel assemblies 6 are stored. D3 and data D4 of the probability distribution (presence ratio) of the manufacturing tolerances of the plurality of fuel rods 29 are stored.

In the present embodiment, the core pattern data D2 includes data on a plurality of fuel assemblies 6 arranged in a plurality of arbitrary cores. The data D2 may be data manually created by the user, or may be automatically created by an arithmetic unit having a learning function. The data D3 of the probability distribution of the bending amount of the plurality of fuel assemblies 6 is created by the user based on the bending amount of the fuel assembly 6 generated in the reactor of the actual machine by the user in advance. It is the data to be done. FIG. 5 is an explanatory diagram showing an example of the probability distribution (presence ratio) of the bending amount. Further, in the data D4 of the probability distribution of the manufacturing tolerances of the plurality of fuel rods 29, the user obtains in advance the manufacturing tolerances of the fuel rods 29 used in the reactor of the actual machine (for example, the manufacturing tolerances related to the diameter and density of the fuel rods 29). However, it is the data created by the user based on the acquired manufacturing tolerance of the actual machine.

(Core analysis method)
Next, as a core analysis method according to the embodiment, a process of calculating a coefficient _FQ including uncertainty will be described. FIG. 6 is a flowchart showing an example of a process of calculating a heat flux hydrothermal channel coefficient including uncertainty. The process shown in FIG. 6 is executed by the control unit 16 based on the user's instruction. Hereinafter, the design value of the coefficient F _Q calculated as the final analysis result by the processing of FIG. 6 is referred to as “coefficient F _QD ”.

As shown in FIG. 6, the control unit 16 acquires the data D1 of the core 5 to be analyzed, and calculates the value of the coefficient _FQC using the calculation code based on the data D1 (step S10). The coefficient F _QC here is a value that does not include various uncertainties considered in the present embodiment. Next, the control unit 16 acquires the coefficient ΔF _QUA including the uncertainty of the calculation code (step S20). The coefficient ΔF _QUA is a value calculated in advance using a predetermined analysis program, and is stored in the storage unit 18 in the present embodiment. In step S20, the coefficient ΔF _QUA may be calculated using a predetermined analysis program.

Next, the control unit 16 acquires the coefficient ΔF _QEB including the bending amount of the plurality of fuel assemblies 6 and the uncertainty due to the manufacturing tolerance of the plurality of fuel rods 29 and the bias f (B) due to the bending amount (step S30). .. In the following description, the coefficient ΔF QEB including the uncertainty due to the bending amount of the plurality of fuel assemblies 6 and the manufacturing tolerances of the plurality of fuel rods 29 is _{appropriately} referred to as “the coefficient ΔF _QEB including the geometrical shape uncertainty”. The method for calculating the coefficient ΔF _QEB will be described later. Further, the bias f (B) is a bias given in consideration of the fact that the coefficient F _Q becomes larger by considering the bending amount of the fuel assembly 6 as compared with the case where the bending amount is not considered.

The control unit 16 calculates the coefficient F _QD as an analysis result according to the following equation (1) based on the coefficients F _QC , ΔF _QUA , ΔF _QEB , and bias f (B) acquired in steps S10 to S30 (step S10). Step S40). "ΔF _QUA / F _QC " included in the right side of the equation (1) indicates the uncertainty of the calculation code, and "ΔF _QEB / F _QC " indicates the geometric shape uncertainty.

(Calculation of coefficient ΔF _{QEB including} geometrical shape uncertainty)
Next, the process of calculating the coefficient ΔF _QEB including the geometrical shape uncertainty will be described. FIG. 7 is a flowchart showing an example of a process of calculating a coefficient including geometric shape uncertainty. FIG. 8 is a schematic diagram schematically showing an example of a process of calculating a coefficient including geometric shape uncertainty.

As shown in FIG. 7, the control unit 16 first acquires the core pattern data D2 stored in the storage unit 18 (step S51). As shown in FIG. 8, the data D2 includes a plurality of (N in this embodiment) arbitrary core patterns PA _i (i is an integer from 1 to N), and each core pattern PA _i is a plurality. Contains data on the fuel assembly 6 of. The number N of the core pattern PA _i is set to an arbitrary number in advance by the user. Next, the control unit 16 acquires the data D3 of the probability distribution of the bending amount stored in the storage unit 18 and the data D4 of the probability distribution of the manufacturing tolerance (step S52).

When the control unit 16 acquires the input parameters in steps S51 and S52, the control unit 16 perturbs each core pattern PA _i included in the data D2 by random sampling based on the acquired data D3 of the probability distribution of the bending amount, and the core pattern For each PA _i , a plurality of (M in this embodiment) bending patterns PB _j (j is an integer from 1 to M) are created (step S53). The number M of the bending pattern PB _j is set to an arbitrary number in advance by the user. Further, when creating the bending pattern PB _j , the upper limit value of the bending amount of the fuel assembly 6 can be set to an arbitrary value. Each bending pattern PB _j is data obtained by randomly assigning a bending amount to a plurality of fuel assemblies 6 included in the core pattern PA _i . Further, the control unit 16 creates a gap pattern PC _j in which the bending amount of each bending pattern PB _j is converted into a gap G by using a predetermined processing program (step S54). As with the bending pattern PB _j , M gap patterns PC _j will be created for each of the core patterns PA _i . Therefore, as a whole, N × M gap patterns PC _j are created.

Next, the control unit 16 perturbs each core pattern PA _i included in the data D2 by random sampling based on the data D4 of the probability distribution of the manufacturing tolerance acquired in step S52, and is one of the core patterns PA _i . For each, a plurality of (M in this embodiment) tolerance pattern PD _j (j is an integer from 1 to M) is created (step S55). Tolerance pattern PD _j is created in the same number as the gap pattern PC _j . Each tolerance pattern PD _j is data in which manufacturing tolerances are randomly assigned to a plurality of fuel rods 29 of a plurality of fuel assemblies 6 included in the core pattern PA _i .

Then, the control unit 16 appropriately combines the gap pattern PC _j and the tolerance pattern PD _j for each of the core patterns PA _i to make a plurality of sets of input parameters. Any combination method may be used. For example, M gap patterns PC _j and M tolerance patterns PD _j are randomly (randomly) combined to generate M input parameters. Alternatively, M gap patterns PC _j and M tolerance patterns PD _j may be associated with each other on a one-to-one basis to generate M input parameters.

The control unit 16 executes a calculation code for calculating the coefficient F _Q for each core pattern PA _i using M input parameters in which the gap pattern PC _j and the tolerance pattern PD _j are combined. , M coefficients ΔF _QEBj (j is an integer from 1 to M) are calculated (step S56). Therefore, as a whole, N × M coefficients ΔF _QEBj are calculated.

The control unit 16 calculates the coefficient ΔF _{QEB including the geometrical shape uncertainty by statistically processing the calculated N × M coefficients ΔF QEBj (} step S57). Specifically, the control unit 16 calculates the average value by arithmetically averaging the calculated N × M coefficients ΔF _QEBj . Subsequently, the control unit 16 calculates the standard deviation based on the calculated N × M coefficients ΔF _QEBj . Then, the control unit 16 multiplies the standard deviation by the confidence coefficient and calculates the coefficient ΔF _QEB based on the standard deviation multiplied by the confidence coefficient. For the calculation of the confidence coefficient, a bootstrap method that does not require specification of the probability distribution followed by ΔF _QEBj can also be applied. The bootstrap method is a method of estimating the properties of a population from a sample, and can be applied not only to a normal distribution but also to an arbitrary probability distribution.

As a result, the coefficient ΔF _{QEB including} the geometrical shape uncertainty acquired in step S30 of FIG. 6 is calculated. The coefficient ΔF _QEB including the geometrical shape uncertainty calculated by the above processing is calculated based on the plurality of core patterns PA _i , the probability distribution of the bending amount, and the probability distribution of the manufacturing tolerance.

(Evaluation of uncertainty based on the amount of bending)
Next, the evaluation of uncertainty based on the amount of bending will be described. FIG. 9 is an explanatory diagram showing an example of the probability distribution (presence ratio) of uncertainty due to the amount of bending. The horizontal axis of FIG. 9 is the amount of change in the local output due to the amount of bending. When calculating the probability distribution shown in FIG. 9, the number of samples can be arbitrarily set by the user. Further, when calculating the probability distribution shown in FIG. 9, the upper limit of the bending amount can be arbitrarily set by the user.

In the example shown in FIG. 9, it can be seen that the probability distribution of uncertainty due to the amount of bending does not have a normal distribution. Therefore, the bootstrap method can also be used when statistically processing the probability distribution of uncertainty due to the amount of bending illustrated in FIG. Here, the confidence coefficient is determined using the bootstrap method, and the determined confidence coefficient is multiplied by the standard deviation σ to calculate the uncertainty.

As described above, in the core analysis method according to the embodiment, the core pattern PA _i , which is data related to a plurality of fuel aggregates 6 included in the core 5, is converted into a probability distribution, which is data related to the bending amount of the fuel aggregate 6. Step S53 to create a plurality of bending patterns PB _j perturbed based on the basis, and step S54 to create a gap pattern PC _j in which the bending amount is converted into a gap G between adjacent fuel aggregates 6 for the bending pattern PB _j . , Step S56 for calculating the heat flux hydrothermal channel coefficient ΔF _QEBj using the calculation code with the gap pattern PC _j as an input parameter, and step S57 for statistically processing the calculated plurality of heat flux hydrothermal channel coefficients ΔF _QEBj . In step S40, the heat flux hydrothermal channel coefficient F _QD including the uncertainty due to the bending amount is calculated as the analysis result of the core characteristics based on the value obtained by the statistical processing (heat flux hydrothermal channel coefficient ΔF _QEB ). include.

With this configuration, based on the data of the bending amount generated in the fuel assembly 6, the fuel assembly 6 contained in the core 5 is randomly bent, and the heat flux hydrothermal channel coefficient F _QD including the uncertainty due to the bending amount is included. Can be obtained.

Further, the step S55 for creating a plurality of tolerance patterns PD _j in which the core pattern PA _i is perturbed based on the probability distribution which is the data regarding the manufacturing tolerances of the plurality of fuel rods 29 is further included, and the heat flux hydrothermal channel coefficient ΔF is further included. In step S56 for calculating _QEBj , the heat flux hydrothermal channel coefficient ΔF _QEBj is calculated using the calculation code with the gap pattern PC _j and the tolerance pattern PD _j as input parameters. With this configuration, it is possible to calculate the heat flux hydrothermal channel coefficient _FQD in consideration of the uncertainty due to the manufacturing tolerance of the fuel rods 29 in addition to the influence of the bending generated in the fuel assembly 6.

Further, the core analysis method according to the embodiment further includes step S20 for acquiring the uncertainty of the calculation code, and step _S40 for calculating the analysis result further includes the uncertainty due to the calculation code. Is calculated as the analysis result. With this configuration, it is possible to calculate the heat flux hydrothermal channel coefficient _FQD in consideration of the uncertainty due to the calculation code in addition to the influence of the bending generated in the fuel assembly 6.

5 Core 6 Fuel assembly 6a Lower end of fuel assembly 10 Core analyzer 12 Input unit 14 Display unit 16 Control unit 18 Storage unit 29 Fuel rod G gap PA _i Core pattern PB _j Bending pattern PC _j Gap pattern PD _j Tolerance pattern

Claims (5)

A step of creating a plurality of bending patterns in which a core pattern, which is data on a plurality of fuel assemblies contained in the core, is perturbed based on a probability distribution, which is data on a bending amount of the fuel assembly.
With respect to the bending pattern, a step of creating a gap pattern in which the bending amount is converted into a gap between adjacent fuel assemblies, and a step of creating a gap pattern.
A step of calculating the heat flux hydrothermal channel coefficient using the calculation code with the gap pattern as an input parameter, and
A step of statistically processing a plurality of the calculated heat flux hydrothermal channel coefficients, and
A core analysis method including a step of calculating the heat flux hydrothermal channel coefficient including uncertainty due to the bending amount as an analysis result of core characteristics based on the value obtained by the statistical processing. Further including the step of creating a plurality of tolerance patterns in which the core pattern is perturbed based on a probability distribution which is data on the manufacturing tolerances of a plurality of fuel rods.
The core analysis method according to claim 1, wherein the step of calculating the heat flux hot water channel coefficient uses the gap pattern and the tolerance pattern as input parameters and uses the calculation code to calculate the heat flux hot water channel coefficient. .. Further including the step of acquiring the uncertainty of the calculation code,
The core analysis method according to claim 1 or 2, wherein the step of calculating the analysis result is to calculate the heat flux hydrothermal channel coefficient including the uncertainty due to the calculation code as the analysis result. A step of creating a plurality of bending patterns in which a core pattern, which is data on a plurality of fuel assemblies contained in the core, is perturbed based on a probability distribution, which is data on a bending amount of the fuel assembly.
With respect to the bending pattern, a step of creating a gap pattern in which the bending amount is converted into a gap between adjacent fuel assemblies, and a step of creating a gap pattern.
A step of calculating the heat flux hydrothermal channel coefficient using the calculation code with the gap pattern as an input parameter, and
A step of statistically processing a plurality of the calculated heat flux hydrothermal channel coefficients, and
A program that causes a computer to perform a step of calculating the heat flux hydrothermal channel coefficient including uncertainty due to the bending amount as an analysis result of core characteristics based on the value obtained by the statistical processing. Equipped with a control unit that analyzes the core characteristics of a nuclear reactor
The control unit
A step of creating a plurality of bending patterns in which a core pattern, which is data on a plurality of fuel assemblies contained in the core, is perturbed based on a probability distribution, which is data on a bending amount of the fuel assembly.
With respect to the bending pattern, a step of creating a gap pattern in which the bending amount is converted into a gap between adjacent fuel assemblies, and a step of creating a gap pattern.
A step of calculating the heat flux hydrothermal channel coefficient using the calculation code with the gap pattern as an input parameter, and
A step of statistically processing a plurality of the calculated heat flux hydrothermal channel coefficients, and
A core analysis device that executes a step of calculating the heat flux hydrothermal channel coefficient including uncertainty due to the bending amount as an analysis result of core characteristics based on the value obtained by the statistical processing.

Images