Uncertainty evaluation method and uncertainty evaluation device

Abstract

To reduce uncertainty of nuclear characteristics in a system with unknown measurement values without limiting the nuclear characteristics subject to the uncertainty evaluation.SOLUTION: An uncertainty evaluation method of nuclear characteristics, where the uncertainty of the nuclear characteristics are caused by uncertainty of nuclear data of the nuclear characteristics and uncertainty of a calculation method for calculating the nuclear characteristics, executes the steps of: acquiring the nuclear data in a first system in which measurement values of the nuclear characteristics are unknown, and covariance of the nuclear data; adjusting the covariance of the data based on correlation between the first system and a second system in which the measurement values of the nuclear characteristics are known; and acquiring the nuclear data by a random sampling method based on the covariance of the nuclear data after the adjustment, executing nuclear characteristic calculation based on the acquired nuclear data, calculating the nuclear characteristics in the first system, statistically processing the calculated nuclear characteristics and calculating uncertainty of the nuclear characteristics in the first system.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present disclosure relates to an uncertainty evaluation method and an uncertainty evaluation device. [Background technology]

[0002] Conventionally, a calculation error estimation method is known in which calculations are performed using experimental measurement values ​​involving uncertainty to calculate physical quantities of a target system, and errors contained in the calculation results are estimated using the results of a simulation experiment that simulates the target system (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2016-71421 A Summary of the Invention [Problem to be solved by the invention]

[0004] In the calculation error estimation method of Patent Document 1, the uncertainty of the input parameters for calculating physical quantities is expressed by an input parameter covariance error matrix, and this is an uncertainty evaluation method based on the so-called generalized perturbation theory.

[0005] Incidentally, when evaluating uncertainties, there are cases where systems where the measured values ​​are unknown (hereinafter simply referred to as unknown systems) are handled, rather than systems where the measured values ​​are known (hereinafter simply referred to as known systems). When evaluating and reducing the uncertainties of physical quantities such as nuclear characteristics in unknown systems, it is possible to use the extended cross-section adjustment method, which can take into account the differences between systems. In the extended cross-section adjustment method, cross-section adjustment is performed using sensitivity coefficients based on generalized perturbation theory. However, since the extended cross-section adjustment method uses sensitivity coefficients, it has the drawback that only uncertainties of nuclear characteristics for which sensitivity coefficients can be calculated can be considered, and the nuclear characteristics for which uncertainties can be considered are limited.

[0006] Therefore, an objective of the present disclosure is to provide an uncertainty evaluation method and an uncertainty evaluation device that can reduce the uncertainty of nuclear characteristics in a system whose measured values ​​are unknown, without limiting the nuclear characteristics that are the subject of uncertainty evaluation. [Means for solving the problem]

[0007] The uncertainty evaluation method disclosed herein is an uncertainty evaluation method for evaluating uncertainty of a nuclear characteristic in a first system in which the measurement value of the nuclear characteristic is unknown, the uncertainty of the nuclear characteristic being due to uncertainty of nuclear data for the nuclear characteristic and uncertainty of a calculation method for calculating the nuclear characteristic, and includes the steps of: acquiring the nuclear data that serve as input parameters for calculating the nuclear characteristic in the first system and a covariance of the nuclear data; adjusting the covariance of the nuclear data based on a correlation between the first system and a second system in which the measurement value of the nuclear characteristic is known; acquiring the nuclear data by a random sampling method based on the adjusted covariance of the nuclear data, performing a nuclear characteristic calculation based on the acquired nuclear data to calculate the nuclear characteristic in the first system, and statistically processing the calculated nuclear characteristics to calculate the uncertainty of the nuclear characteristic in the first system.

[0008] The uncertainty evaluation device disclosed herein is an uncertainty evaluation device that evaluates the uncertainty of a nuclear characteristic in a first system in which the measurement value of the nuclear characteristic is unknown, and the uncertainty of the nuclear characteristic is due to the uncertainty of nuclear data for the nuclear characteristic and the uncertainty of a calculation method for calculating the nuclear characteristic. The uncertainty evaluation device includes a control unit that calculates the uncertainty of the nuclear characteristic, and the control unit executes the following steps: acquiring the nuclear data that serve as input parameters for calculating the nuclear characteristic in the first system and a covariance of the nuclear data; adjusting the covariance of the nuclear data based on a correlation between the first system and a second system in which the measurement value of the nuclear characteristic is known; acquiring the nuclear data by a random sampling method based on the adjusted covariance of the nuclear data, performing a nuclear characteristic calculation based on the acquired nuclear data to calculate the nuclear characteristic in the first system, and statistically processing the calculated nuclear characteristics to calculate the uncertainty of the nuclear characteristic in the first system. Effect of the Invention

[0009] According to the present disclosure, it is possible to reduce the uncertainty of nuclear properties in a system whose measured values ​​are unknown, without limiting the nuclear properties that are the subject of uncertainty assessment. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a block diagram that illustrates an uncertainty evaluation device according to this embodiment. [Diagram 2] FIG. 2 is a flowchart showing the uncertainty evaluation method according to this embodiment. [Diagram 3] FIG. 3 is an explanatory diagram relating to the uncertainty evaluation method according to the present embodiment. [Figure 4] FIG. 4 is a graph showing the correlation between the first system and the second system. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, the embodiments of the present disclosure will be described in detail with reference to the drawings. Note that the present invention is not limited to these embodiments. In addition, the components in the following embodiments include those that are easily replaceable by those skilled in the art, or those that are substantially the same. Furthermore, the components described below can be appropriately combined, and when there are multiple embodiments, the respective embodiments can be combined.

[0012] [Embodiment] The uncertainty evaluation method and the uncertainty evaluation device 10 according to the present embodiment are a method and device for evaluating the uncertainty of nuclear characteristics in a system (first system: also called an unknown system) in which the measured values ​​of the nuclear characteristics are unknown. Specifically, the unknown system is a core system in the design stage, and while the design related to the geometric shape and composition conditions of the nuclear fuel are known, the measured values ​​of the nuclear characteristics in actual operation are unknown. Here, the uncertainty of the nuclear characteristics in the unknown system is caused by the uncertainty of the nuclear data for the nuclear characteristics and the uncertainty of the calculation method for calculating the nuclear characteristics. For this reason, the uncertainty evaluation method and the uncertainty evaluation device 10 evaluate the uncertainty of the nuclear characteristics caused by the uncertainty of the nuclear data and the calculation method.

[0013] (Uncertainty evaluation device) An uncertainty evaluation device 10 will be described with reference to Fig. 1. Fig. 1 is a block diagram showing a schematic diagram of an uncertainty evaluation device according to this embodiment. The uncertainty evaluation device 10 has a control unit 11, a storage unit 12, an output unit 13, and an input unit 14.

[0014] The control unit 11 includes an integrated circuit such as a CPU (Central Processing Unit). The control unit 11 executes various calculation processes for evaluating the uncertainty of nuclear properties in an unknown system. The storage unit 12 is an arbitrary storage device such as a semiconductor storage device and a magnetic storage device. The storage unit 12 stores various programs for executing various calculation processes and various data used in the calculation processes. The various programs are nuclear property calculation codes for calculating nuclear properties, and the various data are nuclear data and nuclear data covariances as input information input to the nuclear property calculation codes. The output unit 13 is a display device such as a liquid crystal display. The input unit 14 is an input device such as a keyboard and a mouse.

[0015] (Uncertainty evaluation method) Next, an uncertainty evaluation method executed by the uncertainty evaluation device 10 will be described with reference to Fig. 2 to Fig. 4. Fig. 2 is a flowchart relating to the uncertainty evaluation method according to this embodiment. Fig. 3 is an explanatory diagram relating to the uncertainty evaluation method according to this embodiment. Fig. 4 is a graph showing the correlation between the first system and the second system.

[0016] 2 and 3, in the uncertainty evaluation method, first, the control unit 11 acquires nuclear data and nuclear data covariance from a nuclear data library (cross section library) (step S1). The nuclear data are microscopic cross sections at continuous energies, and the nuclear data covariance is microscopic covariance data that is data related to the uncertainty of the microscopic cross sections.

[0017] In the uncertainty evaluation method, after executing step S1, the control unit 11 executes step S2 of acquiring multi-group nuclear data and nuclear data covariance based on the acquired nuclear data and nuclear data covariance. In step S2, cross section processing is performed using a nuclear data processing code based on the acquired nuclear data and nuclear data covariance to generate and acquire nuclear data and nuclear data covariance W in a multi-group energy group. The nuclear data is a microscopic cross section in a multi-group energy group, and the nuclear data covariance W is microscopic covariance data that is data related to the uncertainty of the microscopic cross section.

[0018] In the uncertainty evaluation method, after executing step S2, the control unit 11 executes step S3 of adjusting the nuclear data covariance W based on the correlation between the unknown system and a system in which the measurement values ​​of the nuclear characteristics are known (second system: also called known system). In step S3, the nuclear data covariance is adjusted based on a random sampling method using the adjustment formula (1) shown below.

[0019]

number

[0020] Here, each parameter included in equation (1) is obtained by performing nuclear property calculations in advance for known systems. Therefore, parameters such as ΔR1 are known. In equation (1), the terms enclosed by dotted lines indicate the correlation between the unknown system and the known system, and V m 12 This is a term that includes.

[0021] V m 12 represents the correlation between the unknown system and the known system. This correlation is the uncertainty of the calculation method that takes into account the correlation between the unknown system and the known system, and the uncertainty of the calculation method is calculated using formula (2).

[0022]

number

[0023] Each parameter included in the formula (2) is also obtained by performing a nuclear property calculation in a known geometry and a nuclear property calculation in an unknown geometry in advance. The design code is a nuclear property calculation code, and the reference solution code is, for example, a continuous energy Monte Carlo code.

[0024] Figure 4 compares the frequency distribution of the difference in the calculated values ​​of the nuclear properties of known systems with the frequency distribution of the difference in the calculated values ​​of the nuclear properties of unknown systems. In Figure 4, the vertical axis represents the proportion of the nuclear properties, and the horizontal axis represents the difference in the calculated values ​​of the nuclear properties, ΔR 1,m , ΔR 2,m As shown in Figure 4, the difference in the calculated nuclear properties for a known system, ΔR 1,m and the difference ΔR between the calculated nuclear properties in an unknown system 2,m The correlation between the systems shown in Figure 4 is expressed by equation (2). m 12 is not particularly limited to the correlation using formula (2), and may be expressed using a different calculation formula. The control unit 11 executes step S3 using formulas (1) and (2) to obtain the adjusted nuclear data covariance W'.

[0025] 2 and 3, in the uncertainty evaluation method, after step S3, the control unit 11 executes step S4 of calculating nuclear characteristics in an unknown system by using a random sampling method to execute nuclear characteristic calculations based on the covariance of the adjusted nuclear data. In step S4, the control unit 11 calculates N nuclear data perturbation amounts by the random sampling method using the adjusted nuclear data covariance W'. Then, the control unit 11 executes core calculations based on each nuclear data representing perturbation amounts 1 to N, thereby calculating N nuclear characteristics corresponding to perturbation amounts 1 to N.

[0026] In the uncertainty evaluation method, after executing step S4, the control unit 11 performs statistical processing on the calculated N nuclear properties (step S5) to calculate the uncertainty of the nuclear properties in the unknown system and executes step S6 to obtain the uncertainty as an evaluation result. In step S5, the difference of each nuclear property from the average value of the N nuclear properties is obtained as a relative difference, and in step S6, the standard deviation σ in the distribution of the relative differences of the nuclear properties is obtained as the uncertainty of the nuclear property.

[0027] Here, the nuclear characteristics include at least one of the effective multiplication factor, void reactivity, control rod worth, and power distribution, and there is no need to evaluate the sensitivity coefficients corresponding to these nuclear characteristics.

[0028] As described above, the uncertainty evaluation method and the uncertainty evaluation apparatus 10 described in this embodiment can be understood, for example, as follows.

[0029] The uncertainty evaluation method according to the first aspect is an uncertainty evaluation method for evaluating uncertainty of a nuclear characteristic in a first system in which a measurement value of the nuclear characteristic is unknown, the uncertainty of the nuclear characteristic being due to uncertainty of nuclear data for the nuclear characteristic and uncertainty of a calculation method for calculating the nuclear characteristic, and the method includes the steps of: acquiring the nuclear data and a covariance of the nuclear data, which are input parameters for calculating the nuclear characteristic in the first system; adjusting the covariance of the nuclear data based on a correlation between the first system and a second system in which the measurement value of the nuclear characteristic is known; acquiring the nuclear data by a random sampling method based on the adjusted covariance of the nuclear data, performing a nuclear characteristic calculation based on the acquired nuclear data, calculating the nuclear characteristic in the first system, and statistically processing the calculated nuclear characteristics to calculate the uncertainty of the nuclear characteristic in the first system.

[0030] According to this configuration, the covariance of the nuclear data can be adjusted based on the correlation between the first and second systems, so that it is possible to reduce the uncertainty of the nuclear characteristics in the first system. In other words, by appropriately adjusting the covariance in the first system based on the correlation, it is possible to reduce the variance of the nuclear data obtained by the random sampling method based on the covariance. This also reduces the variance of the calculated values ​​of the nuclear characteristics calculation based on the nuclear data, so that it is possible to reduce the uncertainty of the nuclear characteristics. In addition, by using the random sampling method, it is possible to adjust the covariance without using the sensitivity coefficient, so that it is possible to evaluate and reduce the uncertainty of all nuclear characteristics in unknown systems without limiting the nuclear characteristics for which the uncertainty can be considered.

[0031] As a second aspect, in step S3 of adjusting the covariance of the nuclear data, the covariance of the nuclear data is adjusted based on a random sampling method using an adjustment formula given by formula (1).

[0032] According to this configuration, by adding a term (term surrounded by a dotted line) relating to the correlation between the first system and the second system, the covariance of the nuclear data can be suitably adjusted.

[0033] As a third aspect, the correlation between the first system and the second system is the uncertainty of the calculation method taking into account the correlation between the first system and the second system, and the uncertainty of the calculation method is calculated using a calculation formula (2).

[0034] According to this configuration, it is possible to appropriately evaluate the uncertainty of the calculation method that takes into account the correlation between the first system and the second system.

[0035] As a fourth aspect, the nuclear characteristics calculated in the step of evaluating the uncertainty of the nuclear characteristics include at least one of an effective multiplication factor, a void reactivity, a control rod worth, and a power distribution.

[0036] According to this configuration, it is possible to evaluate the uncertainty of various nuclear characteristics, regardless of whether or not the sensitivity coefficients can be evaluated.

[0037] The uncertainty evaluation device according to the fifth aspect is an uncertainty evaluation device 10 that evaluates the uncertainty of a nuclear characteristic in a first system in which the measurement value of the nuclear characteristic is unknown, and the uncertainty of the nuclear characteristic is due to the uncertainty of the nuclear data for the nuclear characteristic and the uncertainty of a calculation method for calculating the nuclear characteristic. The uncertainty evaluation device includes a control unit 11 that calculates the uncertainty of the nuclear characteristic. The control unit 11 executes the following steps: Step S1: acquiring the nuclear data and the covariance of the nuclear data, which are input parameters for calculating the nuclear characteristic in the first system; Step S3: adjusting the covariance of the nuclear data based on the correlation between the first system and a second system in which the measurement value of the nuclear characteristic is known; and Steps S4 to S6: acquiring the nuclear data by a random sampling method based on the adjusted covariance of the nuclear data, performing nuclear characteristic calculations based on the acquired nuclear data, calculating the nuclear characteristic in the first system, and statistically processing the calculated nuclear characteristics to calculate the uncertainty of the nuclear characteristic in the first system.

[0038] According to this configuration, the covariance of the nuclear data can be adjusted based on the correlation between the first and second systems, so that it is possible to reduce the uncertainty of the nuclear characteristics in the first system. In other words, by appropriately adjusting the covariance in the first system based on the correlation, it is possible to reduce the variance of the nuclear data obtained by the random sampling method based on the covariance. This also reduces the variance of the calculated values ​​of the nuclear characteristics calculation based on the nuclear data, so that it is possible to reduce the uncertainty of the nuclear characteristics. In addition, by using the random sampling method, it is possible to adjust the covariance without using the sensitivity coefficient, so that it is possible to evaluate and reduce the uncertainty of all nuclear characteristics in unknown systems without limiting the nuclear characteristics for which the uncertainty can be considered. [Explanation of symbols]

[0039] 10 Uncertainty evaluation device 11 Control section 12 Storage section 13 Output section 14 Input section

Claims

1. An uncertainty evaluation method for evaluating uncertainty of a nuclear characteristic in a first system in which a measurement value of the nuclear characteristic is unknown, comprising the steps of: the uncertainty of the nuclear characteristics in the first system is due to the uncertainty of nuclear data for the nuclear characteristics and the uncertainty of a calculation method for calculating the nuclear characteristics; acquiring nuclear data serving as input parameters for calculating nuclear characteristics in the first geometry and a covariance of the nuclear data; adjusting the covariance of the nuclear data serving as the input parameters by a random sampling method based on a correlation between the first system and a second system in which the measured values ​​of the nuclear characteristics are known; acquiring nuclear data by the random sampling method using the covariance of the nuclear data adjusted in the adjusting step, performing a nuclear property calculation on the acquired nuclear data to calculate nuclear properties in the first system, and statistically processing the calculated nuclear properties to calculate the uncertainty of the nuclear properties in the first system.

2. 2. The uncertainty evaluation method according to claim 1, wherein in the adjusting step, a covariance of the nuclear data serving as the input parameters is adjusted using an adjustment formula represented by formula (1). [0010]

3. An uncertainty evaluation method as described in claim 1 or 2, in which, in the adjusting step, the correlation is the uncertainty of the calculation method taking into account the correlation between the first system and the second system, and the uncertainty of the calculation method is calculated using a calculation formula (2). [0025]

4. 4. The uncertainty assessment method according to claim 1, wherein the nuclear characteristics calculated in the calculating step include at least one of an effective multiplication factor, a void reactivity, a control rod worth, and a power distribution.

5. An uncertainty evaluation apparatus for evaluating uncertainty of a nuclear characteristic in a first system in which a measurement value of the nuclear characteristic is unknown, comprising: the uncertainty of the nuclear characteristics in the first system is due to the uncertainty of nuclear data for the nuclear characteristics and the uncertainty of a calculation method for calculating the nuclear characteristics; a control unit that calculates the uncertainty of a nuclear characteristic in the first system; The control unit is acquiring nuclear data serving as input parameters for calculating nuclear characteristics in the first geometry and a covariance of the nuclear data; adjusting the covariance of the nuclear data serving as the input parameters by a random sampling method based on a correlation between the first system and a second system in which the measured values ​​of the nuclear characteristics are known; acquiring nuclear data by the random sampling method using the covariance of the nuclear data adjusted in the adjusting step, performing nuclear property calculations on the acquired nuclear data to calculate nuclear properties in the first system, and statistically processing the calculated nuclear properties to calculate the uncertainty of the nuclear properties in the first system.

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