CN115099049A - Fission yield data optimization method based on irradiated sample nuclide stock measured value - Google Patents
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Abstract
The fission yield data optimization method based on the measured value of the nuclide stock of the irradiation sample comprises the steps of firstly adopting a Latin hypercube sampling method to sample model parameters built in a fission yield data calculation program for N times, replacing original parameters in the program with each set of parameter samples and calculating to obtain N sets of corresponding fission yield samples; secondly, selecting an irradiation sample of a fuel consumption benchmark experiment as a target sample, replacing fission yield data built in a pressurized water reactor nuclear design program with each set of fission yield sample, simulating the operation history of the target sample by the pressurized water reactor nuclear design program, and calculating N sets of target sample nuclide stock data samples; then comparing the calculated value sample data of each set of nuclide stock of the target sample with the measured value data of the nuclide stock of the target sample obtained from a spent fuel experiment database SFCOMPO-2.0, calculating the weight of each set of sample, and adjusting the built-in model parameters of the fission yield data calculation program based on the weight; and finally, calculating to obtain optimized fission yield data based on the adjusted model parameters.
Description
Technical Field
The invention relates to the technical field of physical calculation of nuclear reactors and calculation and evaluation of nuclear data, in particular to a fission yield data optimization method based on an actual measured value of a nuclide stock of an irradiation sample.
Background
The physical design of the core of the nuclear reactor depends on numerical simulation and calculation, wherein the burnup calculation is an important component in the physical design and calculation of the nuclear reactor, the change of nuclide components in fuel in the operation process of the reactor is simulated, and the method plays an important role in the subsequent safe operation of an actual reactor. The fission yield is important nuclear data in the fuel consumption calculation, represents the probability of fission product nuclide generated by the fission reaction of fuel, is important for simulating the stock change of the fission product nuclide in the fuel in the numerical calculation, and plays an important role in determining the effective multiplication coefficient, the power distribution, the fuel consumption depth, the decay heat after the reactor is stopped, the photon source item and other parameters in the operation process of the reactor. Thus, the accuracy of the fission yield data directly affects the accuracy of the core physical design and calculation.
At present, fission yield data used in nuclear reactor physical calculation are usually calculated based on some theoretical models, the mean value and uncertainty range of parameters of the theoretical models are determined based on experiments in a small part, and most of the fission yield data are directly determined by nuclear data evaluators based on experience. Therefore, different values of the model parameters have great influence on the calculation result of the fission yield, and the fission yield data calculated based on the model parameters are introduced into great uncertainty, so that great uncertainty is introduced into the above-mentioned macroscopic parameters in subsequent physical design and calculation of the reactor core, and great influence is caused on the physical design of the reactor core, the transportation of nuclear waste and the disposal precision of the reactor core.
In conclusion, in the current fission yield data determination process, the theoretical model parameters introduce larger uncertainty, and further the physical calculation of the reactor core contains larger uncertainty. Therefore, it is necessary to adjust the parameters of the above theoretical model in order to optimize the accuracy of the calculated fission yield data and to improve the accuracy of the reactor physics calculations.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a fission yield data optimization method based on an irradiation sample nuclide stock measured value, which starts with a fission yield calculation program with a built-in main model, firstly randomly samples original model parameters, calculates fission yield samples based on model parameter samples, and then simulates the operation history of a burnup benchmark experiment irradiation sample by adopting a pressurized water reactor nuclear design program based on the fission yield samples to obtain a calculation value sample of the nuclide stock of the irradiation sample; secondly, calculating the weight of each irradiated sample nuclide stock calculation value sample by introducing an irradiated sample nuclide stock measured value corresponding to a fuel consumption reference experiment in a spent fuel experiment database SFCOMPO-2.0, and obtaining a new model parameter mean value based on a weighted average mode; and finally, calculating by adopting a calculation program of the fission yield data based on the new model parameters to obtain the fission yield data with higher precision.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the fission yield data optimization method based on the measured value of the nuclide stock of the irradiated sample comprises the following steps:
step 1: randomly sampling model parameters built in a crack yield data calculation program for N times by adopting a latin hypercube sampling method to obtain N sets of model parameter samples;
step 2: replacing the original model parameters in the fission yield data calculation program by each set of model parameter samples obtained in the step 1, and performing calculation once after each replacement to obtain N sets of fission yield data samples;
and step 3: selecting a fuel irradiation sample of a burn-up benchmark experiment as a target sample, wherein the measured value data of the nuclide stock of the target sample can be obtained from a spent fuel experiment database SFCOMPO-2.0. Replacing the fission yield built in the PWR nuclear design program with each set of fission yield data sample obtained in the step 2, and simulating the operation history of the target sample by using the PWR nuclear design program after each replacement so as to obtain N sets of target sample nuclide stock calculation value samples corresponding to the actual measured value of the nuclide stock of the target sample;
and 4, step 4: screening out M fuel consumption reference experiment fuel irradiation samples similar to the target sample experiment conditions in the step 3, and obtaining nuclide stock measured values of the M irradiation samples from a spent fuel experiment database SFCOMPO-2.0; based on the measured nuclide stock values of the M irradiation samples, the sample covariance and the variance of any two measured nuclide stock values are counted, and then the correlation coefficient of any two measured nuclide stock values in the target sample is calculated through the formula (1):
in the formula:
cov(X,Y) multi -nuclide X and Y stock inventory found value sample covariance calculated based on the nuclide stock found values of M reference experimental fuel irradiated samples of similar condition to the target sample;
-calculating a stock measured value sample variance of nuclide X based on stock measured values of nuclides of M reference experimental fuel irradiated samples of similar condition to the target sample;
-stock real-time value sample variance of nuclide Y calculated based on stock-time values of nuclides of M reference experimental fuel irradiation samples of similar condition to the target sample;
based on the correlation coefficient of the stock measured values of nuclides X and Y in the target sample, the covariance of any two stock measured values of nuclides in the target sample can be calculated by equation (2):
in the formula:
cov(X,Y) T -covariance of measured values of stock of nuclides X and Y in the target sample;
-variance of measured nuclear species X stock data in the target sample provided by sfcomp-2.0 database;
-the variance of the measured values of nuclide Y inventory data in the target sample provided by the sfcomp-2.0 database;
and 5: based on the N sets of calculated values of the nuclide stock of the target sample obtained in the step 3 and the covariance of the measured values of the nuclide stock of the target sample obtained in the step 4, the square distance between the calculated value and the measured value of each set of sample is calculated through a formula (3):
in the formula:
the square distance between the calculated data of each set of samples of the target sample nuclide stock and the corresponding measured value data;
e, vectors formed by measured values of the stock of different nuclides in the target sample;
C i -a vector of data from the ith set of calculated nuclear species inventory samples of the target sample;
V E -inventory of different nuclides in the target sample calculated based on step 4A matrix of covariances between measured values;
and (3) obtaining the weight of each set of the calculated nuclide stock value sample of the target sample through a formula (4) based on the square distance:
in the formula:
ω i -weight of the calculated sample of nuclide inventory for the ith set of target samples;
calculating the weighted average of the model parameter samples extracted in the step 1 through a formula (5) based on the weight of each set of target sample nuclide stock calculation value samples, thereby obtaining the adjusted model parameters:
in the formula:
x' -a vector of adjusted model parameters;
x i the vector formed by the sample data of the model parameters before the ith set of adjustment;
step 6: and (5) replacing the original model parameters in the fission yield data calculation program with the adjusted model parameters in the step 5, and calculating to obtain optimized fission yield data.
Compared with the prior art, the method has the following advantages:
1. the method can calculate and obtain the fission yield data with higher precision based on the adjusted theoretical model parameters. In the process of adjusting the theoretical model parameters, linear approximation and solution of relative sensitivity coefficients introduced in the prior art are avoided through a random sampling method, and approximation introduced in the process of adjusting the model parameters is reduced.
2. The method introduces the actual measurement value of the nuclide of the fuel consumption reference experiment irradiation sample provided by a spent fuel experiment database SFCOMPO-2.0, and the actual measurement values provided by the database are all from fuel samples which are actually applied to different nuclear power stations, so that fission yield data obtained by optimizing calculation based on the actual measurement values are more suitable for actual engineering calculation.
3. According to the method, correlation coefficients of measured values of different nuclide stock data in the target sample are calculated through a burnup benchmark experiment with similar screening conditions, and further covariance of the measured data is obtained. Compared with the prior art that only the uncertainty of the measured value of the stock data of a single nuclide is considered, the method further considers the correlation among different nuclides, is closer to the actual situation, and effectively reduces the uncertainty introduced by the measured data.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention relates to a fission yield data optimization method based on an irradiation sample nuclide stock measured value, which adjusts the theoretical model parameters for calculating fission yield data based on the irradiation sample nuclide stock measured value of a fuel consumption benchmark experiment, and recalculates the fission yield data based on the adjusted model parameters, thereby reducing the uncertainty of the fission yield data and achieving the purpose of optimization. The method comprises the following specific steps:
step 1: and randomly sampling the model parameters built in the crack yield data calculation program for N times by adopting a latin hypercube sampling method to obtain N sets of model parameter samples.
Step 2: and (3) replacing the original model parameters in the fission yield data calculation program by each set of model parameter sample obtained in the step (1), and performing calculation once after each replacement to obtain N sets of fission yield data samples.
And step 3: selecting a fuel irradiation sample of a burn-up benchmark experiment as a target sample, wherein the measured value data of the nuclide stock of the target sample can be obtained from a spent fuel experiment database SFCOMPO-2.0. And (3) replacing the fission yield built in the PWR nuclear design program by each set of fission yield data sample obtained in the step (2), and simulating the operation history of the target sample by using the PWR nuclear design program after each replacement so as to obtain N sets of target sample nuclide stock calculation value samples corresponding to the actual measured value of the nuclide stock of the target sample.
And 4, step 4: and (4) screening out M fuel consumption reference experiment fuel irradiation samples similar to the target sample experiment conditions in the step (3), and obtaining nuclide stock measured values of the M irradiation samples from a spent fuel experiment database SFCOMPO-2.0. Based on the measured nuclide stock values of the M irradiation samples, the sample covariance and the variance of any two measured nuclide stock values are counted, and then the correlation coefficient of any two measured nuclide stock values in the target sample is calculated through the formula (1):
in the formula:
cov(X,Y) multi -nuclide X and Y stock inventory found value sample covariance calculated based on the nuclide stock found values of M reference experimental fuel irradiated samples of similar condition to the target sample;
-calculating a stock measured value sample variance of nuclide X based on stock measured values of nuclides of M reference experimental fuel irradiated samples of similar condition to the target sample;
based on M reference experiments similar to the conditions of the target sampleAnd calculating the stock measured value sample variance of the nuclide Y by using the stock measured value of the nuclide of the fuel irradiation sample.
Based on the correlation coefficient of the stock measured values of nuclides X and Y in the target sample, the covariance of any two stock measured values of nuclides in the target sample can be calculated by equation (2):
in the formula:
cov(X,Y) T -covariance of measured values of stock of nuclides X and Y in the target sample;
-the variance of the measured nuclear species X inventory data in the target sample provided by the sfcomp-2.0 database;
-the variance of the measured values of nuclide Y stock data in the target sample provided by the sfcomp-2.0 database.
And 5: based on the N sets of calculated value samples of the nuclide stock of the target sample obtained in the step 3 and the covariance of the actually measured value of the nuclide stock of the target sample obtained in the step 4, the square distance between the calculated value and the actually measured value of each set of sample is calculated through a formula (3):
in the formula:
the square distance between the calculated data of each set of samples of the target sample nuclide stock and the corresponding measured value data;
e, vectors formed by measured values of the stock of different nuclides in the target sample;
C i -vector of data from the computed sample of the nuclide inventory of the ith set of target samples;
V E -a matrix based on the covariances between the measured values of the stock of different nuclides in the target sample calculated in step 4.
And (3) obtaining the weight of each set of the calculated nuclide stock value sample of the target sample through a formula (4) based on the square distance:
in the formula:
ω i -weight of the calculated sample of nuclide inventory for the ith set of target samples;
Calculating the weighted average of the model parameter samples extracted in the step 1 through a formula (5) based on the weight of each set of target sample nuclide stock calculation value samples, thereby obtaining the adjusted model parameters:
in the formula:
x' -a vector formed by the adjusted model parameters;
x i and the ith set of vectors formed by the sample data of the model parameters before adjustment.
Step 6: and (5) replacing the original model parameters in the fission yield data calculation program with the adjusted model parameters in the step 5, and calculating to obtain optimized fission yield data.
The fission yield data calculation program used in the steps 1, 2 and 6 is not limited, and programs with fission yield calculation functions can be used, such as GEF programs developed by Bordeaux research center, France, and TALYS programs developed by Netherlands nuclear research and consultants.
The SFCOMPO-2.0 Spent Fuel experimental database used in steps 3, 4, 5 was developed by the OncD (OECD NEA) and is collectively referred to as the Spent Fuel Composition-2.0.
The pressurized water reactor nuclear design program used in the step 3 is not limited by the invention, and generally, programs with pressurized water reactor nuclear design and simulation functions can be used, such as a NECP-Bamboo program and a NECP-X program developed by the university of transport in Western Ann.
The invention does not limit the fuel consumption benchmark experiment selected in the step 3, and the fuel consumption benchmark experiment which generally contains the measured value of the nuclide stock of the irradiated sample in the SFCOMPO-2.0 spent fuel experiment database can be selected, such as the Three Mile Island-1 experiment in the United states, the Takahama-3 experiment in Japan, and the like.
The fission yield data obtained based on the method is applied to actual engineering calculation, and the adaptability of the fission yield data to engineering application can be obviously improved, so that the accuracy of the physical design of the reactor core is improved, and an effective basis is provided for the safety and the economy of the reactor operation.
Claims (2)
1. The fission yield data optimization method based on the measured value of the nuclide stock of the irradiated sample is characterized by comprising the following steps: the method comprises the following steps:
step 1: randomly sampling model parameters built in a crack yield data calculation program for N times by adopting a latin hypercube sampling method to obtain N sets of model parameter samples;
step 2: replacing the original model parameters in the fission yield data calculation program by each set of model parameter samples obtained in the step 1, and performing calculation once after each replacement to obtain N sets of fission yield data samples;
and step 3: selecting a fuel irradiation sample of a fuel consumption benchmark experiment as a target sample, and obtaining nuclide stock measured value data of the target sample from a spent fuel experiment database SFCOMPO-2.0; replacing the fission yield built in the pressurized water reactor nuclear design program with each set of fission yield data sample obtained in the step (2), and simulating the operation history of the target sample by using the pressurized water reactor nuclear design program after each replacement so as to obtain N sets of target sample nuclide stock calculation value samples corresponding to the actual nuclide stock value of the target sample;
and 4, step 4: screening out M fuel consumption reference experiment fuel irradiation samples similar to the target sample experiment conditions in the step 3, and obtaining nuclide stock measured values of the M irradiation samples from a spent fuel experiment database SFCOMPO-2.0; based on the M irradiated sample nuclide stock measured values, the sample covariance and the variance of any two nuclide stock measured values are counted, and then the correlation coefficient of any two nuclide stock measured values in the target sample is calculated through a formula (1):
in the formula:
cov(X,Y) multi -nuclide X and Y stock inventory found value sample covariance calculated based on the nuclide stock found values of M reference experimental fuel irradiated samples of similar condition to the target sample;
-calculating the stock of nuclides X based on the stock of nuclides measured for M reference test fuel irradiation samples of similar condition as the target sampleMeasuring the value of the sample variance;
-stock real-time value sample variance of nuclide Y calculated based on stock-time values of nuclides of M reference experimental fuel irradiation samples of similar condition to the target sample;
based on the correlation coefficient of the stock measured values of nuclides X and Y in the target sample, calculating the covariance of any two stock measured values of nuclides in the target sample by the formula (2):
in the formula:
cov(X,Y) T -covariance of measured values of stock of nuclides X and Y in the target sample;
-the variance of the measured nuclear species X inventory data in the target sample provided by the sfcomp-2.0 database;
-the variance of the measured values of nuclide Y stock data in the target sample provided by the sfcomp-2.0 database.
And 5: based on the N sets of calculated values of the nuclide stock of the target sample obtained in the step 3 and the covariance of the measured values of the nuclide stock of the target sample obtained in the step 4, the square distance between the calculated value and the measured value of each set of sample is calculated through a formula (3):
in the formula:
the square distance between the calculated data of each set of samples of the target sample nuclide stock and the corresponding measured value data;
e, vectors formed by measured values of the stock of different nuclides in the target sample;
C i -a vector of data from the ith set of calculated nuclear species inventory samples of the target sample;
V E -a matrix based on the covariances between the measured values of the stock of different nuclides in the target sample calculated in step 4.
And (3) obtaining the weight of the calculated value sample of the nuclide stock of each set of target samples through a formula (4) based on the square distance:
in the formula:
ω i -weight of the calculated sample of nuclide inventory for the ith set of target samples;
calculating the weighted average of the model parameter samples extracted in the step 1 through a formula (5) based on the weight of each set of target sample nuclide stock calculation value samples, thereby obtaining the adjusted model parameters:
in the formula:
x' -a vector of adjusted model parameters;
x i the vector formed by the sample data of the model parameters before the ith set of adjustment;
step 6: and (5) replacing the original model parameters in the fission yield data calculation program with the adjusted model parameters in the step 5, and calculating to obtain optimized fission yield data.
2. The method of optimizing fission yield data based on an actual measurement of irradiated sample nuclear inventory of claim 1, wherein: step 4, the fuel consumption benchmark experiment fuel irradiation sample similar to the experiment condition of the target sample needs to be screened. The invention defines the similar standards of experimental conditions as follows: the nuclear reactors of the burnup benchmark experiment have the same reactor type, the irradiation samples have the same material type, and the irradiation samples contain 235 The enrichment degree deviation of the U nuclide is not more than +/-0.2%, and the burn-up depth deviation of an irradiation sample is not more than +/-2 GWD/tHM.
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