CN110633454B - CHF relational DNBR limit value statistical determination method based on correction method - Google Patents

CHF relational DNBR limit value statistical determination method based on correction method Download PDF

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CN110633454B
CN110633454B CN201910887234.5A CN201910887234A CN110633454B CN 110633454 B CN110633454 B CN 110633454B CN 201910887234 A CN201910887234 A CN 201910887234A CN 110633454 B CN110633454 B CN 110633454B
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刘伟
杜思佳
张渝
张虹
黄慧剑
徐良剑
刘余
陆祺
冷贵君
李庆
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Abstract

The invention relates to the technical field of nuclear reactor thermal hydraulic design and safety analysis, and particularly discloses a CHF relational DNBR limit value statistical determination method based on a correction method. The method specifically comprises the following steps: 1. collecting and acquiring CHF experimental data of the fuel assembly; 2. obtaining M/P data of the position of an experimental burning point; 3. carrying out Bartlett test on the M/P data of the position of the experimental burning point; 4. carrying out homogeneity test on the data mean value; 5. carrying out normal distribution test; 6. determining DNBR limits using the Owen criterion; 7. when the M/P data can not pass any one of the tests in the steps 3 to 5, utilizing Satterhwaite to correct the degree of freedom; 8. and (4) substituting the correction freedom degree obtained in the step (7) into an Owen coefficient expression to solve and obtain an Owen coefficient, thereby determining the DNBR limiting value. The method can obtain strict, accurate and relatively conservative CHF relational DNBR limit values, can calculate key parameters for CHF relational development and CHF experimental data evaluation, and provides design limit values of most concern for nuclear safety departments.

Description

CHF relational DNBR limit value statistical determination method based on correction method
Technical Field
The invention belongs to the technical field of nuclear reactor thermal hydraulic design and safety analysis, and particularly relates to a CHF relational DNBR limit value statistical determination method based on a correction method.
Background
The Critical Heat Flux (CHF) relationship is used to predict the Critical Heat Flux value of the core, and the safety and economy of the core are closely related to the CHF relationship. DNBR (departure from nucleate boiling ratio) is defined as the ratio of the heat flow density value calculated by the CHF relationship to the local actual heat flow density value. The accurate prediction of the DNBR value of the reactor core is the core content of reactor thermal hydraulic design and safety analysis, is an important criterion for whether the reactor core is safe in steady-state thermal hydraulic and I, II and part III accident analysis of the reactor core, and is also a design limit value which is most concerned by a nuclear safety evaluation department.
The DNBR thermal margin is the ratio of the difference between the minimum DNBR value and the DNBR limit to the DNBR limit. The thermal margin of the reactor is increased mainly to prevent the reactor from deviating from the design safety limit during normal operation, thereby increasing the capability of the reactor to cope with accidents. In the design of a third generation pressurized water reactor nuclear power plant, user documents such as URD and EUR require that the reactor has 15% of thermal margin.
The DNBR limits are matched to a particular CHF relationship and are determined using the Owen criterion after a series of statistical analyses and tests based on M/P data for locations of burnout points (or minimum DNBR points) of the CHF experiment. When the DNBR limit is determined in a traditional manner, only normal distribution test is generally carried out, and in some cases, variance (ANOVA) test is added. When the ANOVA test cannot be passed, the average value and the standard deviation of the sample need to be corrected with punitive property. Obviously, this processing method is not perfect, especially when multiple sets of data come from different sample spaces or the user has special requirements, the conventional method is not sufficient.
Disclosure of Invention
The invention aims to provide a correction method-based statistical determination method for DNBR limits of a CHF relational expression, which solves the problem that DNBR limits in the CHF relational expression are strict, accurate and relatively conservatively obtained.
The technical scheme of the invention is as follows: a CHF relational DNBR limit value statistical determination method based on a correction method specifically comprises the following steps:
step 1, collecting and acquiring CHF experimental data of a fuel assembly;
step 2, obtaining M/P data of the position of an experimental burning point on the basis of the determined CHF relational expression of the fuel assembly;
step 3, carrying out Bartlett test on the M/P data of the experimental burning point position;
step 4, homogeneity test of the data mean value is carried out;
performing a mean homogeneity test on experimental data passing the Bartlett test, wherein ANOVA test is adopted for multiple groups of data, and t test is adopted for two groups of data;
step 5, carrying out a normal distribution test after the whole data passes a Bartlett test and a homogeneity test of a data mean value;
step 6, determining a DNBR limit value by using an Owen criterion;
step 7, utilizing Satterhwaite to correct the degree of freedom when the M/P data can not pass any one of Bartlett test, homogeneity test of data mean value and normal distribution test in the steps 3-5;
and 8, substituting the correction freedom degree obtained in the step 7 into an Owen coefficient expression to solve and obtain an Owen coefficient, and determining the DNBR limit value.
The specific steps of carrying out Bartlett test on the M/P data of the position of the experimental burning point in the step 3 are as follows:
utilizing a Bartlett test to test the homogeneity of the variance of the M/P data of the burning point position of the collected fuel assembly;
Figure BDA0002207682790000031
Figure BDA0002207682790000032
Figure BDA0002207682790000033
wherein, v t Is the sample degree of freedom, t is the data sample,
Figure BDA0002207682790000034
for corresponding degree of freedom v t The variance of the sample t of (d); the number of K samples, alpha, beta and N are statistics calculated by the formula, and no special physical meaning exists;
statistical quantity alpha/beta approximately obeys chi with degree of freedom of K-1 2 Distribution (chi-square distribution), whereby at a given level of significance (α = 0.05), χ is looked at 2 Available distribution table
Figure BDA0002207682790000035
A value; if it is not
Figure BDA0002207682790000036
The Bartlett test is passed, otherwise it does not.
The specific steps of performing the homogeneity test of the mean value by adopting ANOVA test in the step 4 for multiple groups of data are as follows:
step 4.1, carrying out homogeneity test on the mean value of a plurality of groups of data by using ANOVA test;
setting statistics as follows: f = S 1 /S 2
Mean variance between groups:
Figure BDA0002207682790000037
mean variance within group:
Figure BDA0002207682790000038
wherein, X ri Ith data which is an r-th group;
Figure BDA0002207682790000039
is the average value of the r group data;
Figure BDA00022076827900000310
mean values of the overall data;
statistic F obeying degree of freedom v 1 K-1 and v 2 F distribution of = n-K; a critical value F for the statistic F with a given significance level α =0.05 1-α (ν 1 ,ν 2 ) By comparison, if F < F 1-α (ν 1 ,ν 2 ) Then the ANOVA test is passed, otherwise it does not.
The step 4 of performing the homogeneity test of the mean value by adopting t test for two groups of data comprises the following specific steps:
step 4.2, performing homogeneity test on the mean values of the two groups of data by using t test;
the homogeneity of the mean value of the two data sets is tested by using t test, namely, mu is judged 1 ＝μ 2 Is established, wherein mu 1 Is the mean, μ, of the first set of data 2 Is the mean of the second set of data;
Figure BDA0002207682790000041
Figure BDA0002207682790000042
when the significance level is alpha =0.05, looking up the t distribution table can obtain t a/2,n1+n2-2 (ii) a If, t > t a/2,n1+n2-2 Then reject μ 1 ＝μ 2 Otherwise, it is not rejected.
The specific steps of performing normal distribution test in the step 5 are as follows:
performing normal distribution test on the data passing the Bartlett test and the homogeneity test of the data mean value by using a D' test method;
recording n independent observed values as x in ascending order 1 ，x 2 ，…x n ，
Statistics: d' = T/S
Figure BDA0002207682790000043
Figure BDA0002207682790000044
The Z can be obtained by looking up a table according to the quantile alpha =0.05 and the sample size n a/2 And Z 1-a/2 If Z is a/2 ≤D′≤Z 1-a/2 The assumption of normal distribution is accepted, otherwise, it is rejected.
The specific step of determining the DNBR limit value by using the Owen criterion in the step 6 is as follows:
after the M/P data all passed the checks of steps 3-5, DNBR limits were determined using the Owen criterion:
Figure BDA0002207682790000051
wherein k (β, γ, ν) is an Owen coefficient corresponding to a likelihood β, a confidence γ, and a sample degree of freedom ν;
Figure BDA0002207682790000052
the average value of the M/P data is obtained; s is the standard deviation of the M/P data; c is a DNBR limit;
when both likelihood and confidence are 95%:
Figure BDA0002207682790000053
v takes the best estimate freeDegree, v = N T -1- η, substituting the expression k (v) to solve the Owen coefficient.
The specific steps of correcting the degree of freedom by using the Satterhwaite in the step 7 are as follows:
correction of degree of freedom v = v using Satterhwaite Total -1-η
In the formula:
Figure BDA0002207682790000054
Figure BDA0002207682790000055
ν W v as a degree of freedom of the total data W ＝N T -n
ν C V as a degree of freedom of the number of data sets C ＝n-1
η is the number of CHF relational coefficients;
Figure BDA0002207682790000056
Figure BDA0002207682790000057
Figure BDA0002207682790000061
Figure BDA0002207682790000062
N T total number of data points; n is a radical of i The number of data points of the ith group;
Figure BDA0002207682790000063
is the average value of the ith group of data; n is the total data set number; sigma i Is the standard deviation of the i-th group.
The step 8 is specifically as follows: and (5) substituting the correction freedom degree obtained in the step (7) into a k (v) expression to solve and obtain an Owen coefficient, thereby determining the DNBR limiting value.
The invention has the remarkable effects that: the correction method-based CHF relational DNBR limit statistical determination method can obtain strict, accurate and relatively conservative CHF relational DNBR limits based on the established M/P database and the statistical analysis and inspection method, can calculate key parameters for CHF relational development and CHF experimental data evaluation, and can also provide design limits of most concern for nuclear safety departments.
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FIG. 1 is a flow chart of a correction method-based statistical determination method for limits of a CHF relational DNBR according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
As shown in fig. 1, a method for statistically determining a limit value of a CHF relational DNBR based on a correction method specifically includes the steps of:
step 1, collecting and acquiring CHF experimental data of a fuel assembly;
step 2, obtaining M/P data of the position of an experimental burning point on the basis of the determined CHF relational expression of the fuel assembly;
step 3, carrying out Bartlett test on the M/P data of the experimental burning point position;
testing the variance homogeneity of the collected M/P data (M/P: CHF value predicted by an experimentally measured CHF value/CHF relational expression) of the burning point position of the fuel assembly by using a Bartlett test;
Figure BDA0002207682790000071
Figure BDA0002207682790000072
Figure BDA0002207682790000073
wherein, v t Is the sample degree of freedom, t is the data sample,
Figure BDA0002207682790000074
for corresponding degree of freedom v t The variance of the sample t of (d); the number of K samples, alpha, beta and N are statistics calculated by the formula, and no special physical meaning exists;
statistical quantity alpha/beta approximately obeys chi with degree of freedom of K-1 2 Distribution (chi-square distribution), whereby at a given level of significance (α = 0.05), χ is looked at 2 Available distribution table
Figure BDA0002207682790000075
A value; if it is not
Figure BDA0002207682790000076
The test is passed by Bartlett, otherwise the test is not passed;
step 4, homogeneity test of the data mean value is carried out;
performing a mean homogeneity test on experimental data passing the Bartlett test, wherein ANOVA test is adopted for multiple groups of data, and t test is adopted for two groups of data;
step 4.1, carrying out homogeneity test on the mean value of a plurality of groups of data by ANOVA test;
setting statistics as follows: f = S 1 /S 2
Mean variance between groups:
Figure BDA0002207682790000077
mean variance within group:
Figure BDA0002207682790000078
wherein, X ri Ith data which is an r-th group;
Figure BDA0002207682790000079
is the average value of the r group data;
Figure BDA00022076827900000710
mean values of the overall data;
statistic F obeying degree of freedom v 1 K-1 and v 2 F distribution of = n-K; a critical value F for the statistic F with a given significance level α =0.05 1-α (ν 1 ,ν 2 ) By comparison, if F < F 1-α (ν 1 ,ν 2 ) Checking by ANOVA, otherwise, not passing;
4.2, carrying out homogeneity test on the mean value of the two groups of data by using t test;
the homogeneity of the mean value of the two data sets is tested by using t test, namely, mu is judged 1 ＝μ 2 Is established, wherein mu 1 Is the mean, μ, of the first set of data 2 Is the mean of the second set of data;
Figure BDA0002207682790000081
Figure BDA0002207682790000082
when the significance level is alpha =0.05, looking up the t distribution table can obtain t a/2,n1+n2-2 (ii) a If, t > t a/2,n1+n2-2 Then reject μ 1 ＝μ 2 Else not reject;
step 5, carrying out a normal distribution test after the whole data passes a Bartlett test and a homogeneity test of a data mean value;
performing normal distribution test on the data passing the Bartlett test and the homogeneity test of the data mean by using a D' test method;
recording n independent observed values as x in ascending order 1 ，x 2 ，…x n ，
Statistics: d' = T/S
Figure BDA0002207682790000083
Figure BDA0002207682790000084
The Z can be obtained by looking up a table according to the quantile alpha =0.05 and the sample size n a/2 And Z 1-a/2 If Z is a/2 ≤D′≤Z 1-a/2 If yes, the assumption of normal distribution is accepted, otherwise, the assumption is rejected;
step 6, determining a DNBR limit value by using an Owen criterion;
after the M/P data all passed the checks of steps 3-5, DNBR limits were determined using the Owen criterion:
Figure BDA0002207682790000091
wherein k (β, γ, ν) is an Owen coefficient corresponding to a likelihood β, a confidence γ, and a sample degree of freedom ν;
Figure BDA0002207682790000096
the average value of the M/P data is obtained; s is the standard deviation of the M/P data; c is a DNBR limit;
when both likelihood and confidence are 95%:
Figure BDA0002207682790000092
v is the best estimation freedom, v = N T -1- η, substituting k (v) expression to solve Owen coefficient;
step 7, utilizing Satterhwaite to correct the degree of freedom when the M/P data can not pass any one of Bartlett test, homogeneity test of data mean value and normal distribution test in the steps 3-5;
correction of degree of freedom v = v using Satterhwaite Total -1-η
In the formula:
Figure BDA0002207682790000093
Figure BDA0002207682790000094
ν W v, being the degree of freedom of the total data W ＝N T -n
ν C V as a degree of freedom of the number of data sets C ＝n-1
η is the number of CHF relational coefficients;
Figure BDA0002207682790000095
Figure BDA0002207682790000101
Figure BDA0002207682790000102
Figure BDA0002207682790000103
N T is the total number of data points; n is a radical of i The number of data points of the ith group;
Figure BDA0002207682790000104
is the average value of the ith group of data; n is the total data set number; sigma i Standard deviation for group i;
and 8, substituting the correction freedom degree obtained in the step 7 into a k (v) expression to solve and obtain an Owen coefficient, thereby determining the DNBR limit value.

Claims (7)

1. A CHF relational DNBR limit value statistical determination method based on a correction method is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1, collecting and acquiring CHF experimental data of a fuel assembly;
step 2, obtaining M/P data of the position of an experimental burning point on the basis of the determined CHF relational expression of the fuel assembly;
step 3, carrying out Bartlett test on the M/P data of the position of the experimental burning point;
step 4, homogeneity test of the data mean value is carried out;
performing a mean homogeneity test on experimental data passing the Bartlett test, wherein ANOVA test is adopted for multiple groups of data, and t test is adopted for two groups of data;
step 5, carrying out a normal distribution test after the whole data passes a Bartlett test and a homogeneity test of a data mean value;
step 6, determining a DNBR limit value by using an Owen criterion;
step 7, utilizing Satterhwaite to correct the degree of freedom when the M/P data can not pass any one of Bartlett test, homogeneity test of data mean value and normal distribution test in the steps 3-5;
the specific steps of correcting the degree of freedom by using the Satterhwaite in the step 7 are as follows:
correction of degree of freedom v = v using Satterhwaite Total -1-η
In the formula:
Figure FDA0003668230930000011
Figure FDA0003668230930000012
ν W v, being the degree of freedom of the total data W ＝N T -n
ν C Degree of freedom, v, being the number of data sets C ＝n-1
Eta is the number of CHF relational coefficients;
Figure FDA0003668230930000021
Figure FDA0003668230930000022
Figure FDA0003668230930000023
Figure FDA0003668230930000024
N T total number of data points; n is a radical of i The number of data points of the ith group;
Figure FDA0003668230930000025
is the average value of the ith group of data; n is the total data set number; sigma i Standard deviation for group i;
and 8, substituting the correction freedom degrees obtained in the step 7 into an Owen coefficient expression to solve and obtain an Owen coefficient, so as to determine a DNBR limiting value.
2. A correction-based CHF relational DNBR limit statistical determination method according to claim 1, wherein: the specific steps of carrying out Bartlett test on the M/P data of the position of the experimental burning point in the step 3 are as follows:
utilizing a Bartlett test to test the homogeneity of the variance of the M/P data of the burning point position of the collected fuel assembly;
Figure FDA0003668230930000026
Figure FDA0003668230930000027
Figure FDA0003668230930000028
wherein, v t Is the sample degree of freedom, t is the data sample,
Figure FDA0003668230930000031
for a corresponding degree of freedom v t The variance of the sample t of (d); the number of K samples, alpha, beta and N are statistics calculated by the formula, and no special physical meaning exists;
statistical quantity alpha/beta approximately obeys chi with degree of freedom of K-1 2 Distribution whereby at a given significance level α =0.05, χ is looked at 2 Distribution table availability
Figure FDA0003668230930000032
A value; if it is not
Figure FDA0003668230930000033
The Bartlett test is passed, otherwise it does not.
3. A method of statistical determination of CHF relational DNBR limits based on a correction method according to claim 1, characterized in that: the specific steps of performing the homogeneity test of the mean value by adopting ANOVA test in the step 4 for multiple groups of data are as follows:
step 4.1, carrying out homogeneity test on the mean value of a plurality of groups of data by using ANOVA test;
setting statistics as follows: f = S 1 /S 2
Mean variance between groups:
Figure FDA0003668230930000034
mean variance within group:
Figure FDA0003668230930000035
wherein, X ri Ith data of the r-th group;
Figure FDA0003668230930000036
is the average value of the r group data;
Figure FDA0003668230930000037
mean values of the overall data;
statistic F obeying degree of freedom v 1 K-1 and v 2 F distribution of = n-K; a critical value F for the statistic F with a given significance level α =0.05 1-α (ν 1 ,ν 2 ) By comparison, if F < F 1-α (ν 1 ,ν 2 ) Then the ANOVA test is passed, otherwise it does not.
4. A correction-based CHF relational DNBR limit statistical determination method according to claim 1, wherein: the step 4 of performing the homogeneity test of the mean value by adopting t test for two groups of data comprises the following specific steps:
4.2, carrying out homogeneity test on the mean value of the two groups of data by using t test;
using t test to test the homogeneity of the mean value of two groups of data, namely judging mu 1 ＝μ 2 Is established, wherein mu 1 Is the mean, μ, of the first set of data 2 Is the mean of the second set of data;
Figure FDA0003668230930000041
Figure FDA0003668230930000042
when water is significantWhen the average is alpha =0.05, look up the t distribution table to obtain t a/2,n1+n2-2 (ii) a If, t > t a/2,n1+n2-2 Then reject μ 1 ＝μ 2 Otherwise, it is not rejected.
5. A correction-based CHF relational DNBR limit statistical determination method according to claim 1, wherein: the specific steps of performing normal distribution test in the step 5 are as follows:
performing normal distribution test on the data passing the Bartlett test and the homogeneity test of the data mean value by using a D' test method;
recording n independent observed values as x in ascending order 1 ，x 2 ，…x n ，
Statistics: d' = T/S
Figure FDA0003668230930000043
Figure FDA0003668230930000044
The Z can be obtained by looking up a table according to the quantile alpha =0.05 and the sample size n a/2 And Z 1-a/2 If Z is a/2 ≤D′≤Z 1-a/2 The assumption of normal distribution is accepted, otherwise, it is rejected.
6. A correction-based CHF relational DNBR limit statistical determination method according to claim 1, wherein: the specific step of determining the DNBR limit value by using the Owen criterion in step 6 is as follows:
after the M/P data all passed the checks of steps 3-5, DNBR limits were determined using the Owen criterion:
Figure FDA0003668230930000045
wherein k (beta, gamma, v)) Is an Owen coefficient corresponding to a likelihood β, a confidence γ, and a sample degree of freedom ν;
Figure FDA0003668230930000051
the average value of the M/P data is obtained; s is the standard deviation of the M/P data; c is a DNBR limit;
when both likelihood and confidence are 95%:
Figure FDA0003668230930000052
v is the best estimated degree of freedom, v = N T -1- η, substituting the expression k (v) to solve the Owen coefficient.
7. A method of statistical determination of DNBR limits for CHF based on a correction method according to claim 6, characterized in that: the step 8 is specifically as follows: and (5) substituting the correction freedom degree obtained in the step (7) into a k (v) expression to solve and obtain an Owen coefficient, thereby determining the DNBR limit value.
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