Method and system for uncertainty and sensitivity analysis of reactor severe accident

Abstract

The application discloses a method and system for reactor severe accident uncertainty and sensitivity analysis, determines target output parameters and selects uncertainty input parameters; based on the reference value of the input parameters, the best estimation program is used to model and debug the overall system and accident conditions of the nuclear power plant; the uncertainty analysis is carried out based on the input uncertainty quantification, the input parameter matrix is randomly extracted and the input file is batch generated, the calculation results are tested after batch calculation, if the normal distribution is met, the one-sided tolerance upper limit value of the target output parameter is calculated when the confidence level and the probability level are both 95%; finally, the sensitivity analysis is carried out, the sensitivity index analysis result is obtained, and the parameter importance information is acquired. The application solves the technical problems of excessive conservatism of the traditional deterministic analysis method and large uncertainty of the severe accident analysis, and the problem that the existing uncertainty analysis method cannot fully play a role in the field of severe accident analysis.

Description

Technical Field

[0001] This invention belongs to the field of reactor severe accident analysis technology, specifically relating to a method and system for uncertainty and sensitivity analysis of reactor severe accidents. Background Technology

[0002] A severe nuclear power plant accident refers to a series of processes resulting from the failure of a large area of ​​the reactor core's fuel cladding, threatening or damaging the integrity of the pressure vessel or containment structure, and triggering a leak of radioactive materials. The phenomenology involved in severe reactor accidents is highly complex, and current integrated analysis programs used for severe accident analysis heavily rely on user-defined empirical parameters, exhibiting considerable uncertainty. In fact, there is still relatively little work on the uncertainties in severe accident analysis. Due to the extremely high complexity and uncertainty inherent in severe accidents, conducting related work is of great significance for the safety design of nuclear power plants and the development of physical models for severe accidents.

[0003] Nuclear safety assessment methods mainly include deterministic and probabilistic methods. In the application of deterministic methods, due to cognitive limitations and insufficient experience, excessive conservatism may be introduced, leading to results that do not match reality and alterations in the accident process. Probabilistic methods, based on reliability theory and probability theory, analyze and evaluate accidents, yielding more realistic results. In 1988, the U.S. Nuclear Regulatory Commission (NRC) developed an optimal estimation plus uncertainty analysis method for reactor loss-of-coolant accident analysis, initiating a global trend of developing and applying such methods. Compared to conservative accident analysis methods, the optimal estimation plus uncertainty analysis method avoids significant discrepancies between results and reality due to excessive subjective assumptions, improving the economics of nuclear power plants while ensuring safety. Although some optimal estimation plus uncertainty analysis methods have been developed for nuclear power plant accident analysis, and some related uncertainty analysis work has been carried out both domestically and internationally, these methods are mostly applicable to design baseline accidents, with less attention and application in severe accident analysis and related simulation procedures. How to combine the optimal estimation plus uncertainty analysis method with severe accident analysis remains an important research topic. Summary of the Invention

[0004] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a method and system for uncertainty and sensitivity analysis of severe reactor accidents. This method combines optimal estimation with uncertainty analysis with the field of severe accident analysis to solve the problems of overly conservative traditional deterministic analysis methods and the inability of existing uncertainty analysis methods to fully play their role in the field of severe accident analysis.

[0005] The present invention adopts the following technical solution:

[0006] The method for uncertainty and sensitivity analysis of severe reactor accidents includes the following steps:

[0007] S1. Determine the accident conditions and reactor type to be studied, and identify the applicable integrated severe accident analysis procedure;

[0008] S2. Based on the integrated severe accident analysis program obtained in step S1, determine the target output parameters, and select the uncertainty input parameters based on the target output parameters and the physical model characteristics of the integrated severe accident analysis program ISAA, and specify the baseline value, distribution type and range.

[0009] S3. Based on the baseline values ​​of the uncertainty input parameters obtained in step S2, the overall system of the nuclear power plant and the accident conditions are modeled and debugged using the severe accident analysis program, and the baseline conditions are analyzed to obtain the conservative calculation results of the program, which are used for the analysis and comparison of uncertainty and sensitivity analysis in steps S4 to S7.

[0010] S4. Based on the uncertainty input parameters selected in step S2 and the modeling and debugging of the baseline working condition in step S3, uncertainty analysis is carried out. The input parameter matrix is ​​randomly sampled using the Latin hypercube sampling method and modified into the modeling card for batch calculation.

[0011] S5. Extract the calculation results obtained in step S4, and test the calculation results according to the normality test method;

[0012] S6. When the calculation result obtained in step S5 conforms to the normal distribution, the one-sided tolerance upper limit of the target output parameter is obtained by using the Irwin factor method, parametric statistical method and nonparametric statistical method to calculate the target output parameter when the confidence level and probability level are both 95%. The calculation results of different methods and the calculation results of the baseline working condition in step S3 are compared and analyzed to obtain a target output result that is closer to the actual situation.

[0013] S7. Based on the uncertainty analysis results obtained in steps S4 to S6, perform sensitivity analysis on the uncertainty input parameters and target output in step S2 to obtain the sensitivity index analysis results and acquire the importance information of the uncertainty input parameters.

[0014] Specifically, in step S2, the uncertain input parameters include radiation, heat conduction, heat convection, metal oxidation, decay heat model, fuel rod collapse, molten material repositioning, molten pool heat transfer, and the release and migration of fission products in the core heat transfer and oxidation model.

[0015] Specifically, in step S4, the Latin hypercube sampling method is used to randomly stratify and sample input parameters with different distributions, including normal distribution, log-normal distribution, uniform distribution, and triangular distribution. The sampled input parameters are randomly combined to generate input files corresponding to those in step S3 in batches. The system script is then used to call the integrated severe accident analysis program to perform batch calculations. The sample size is determined by the Wilks formula.

[0016] Specifically, in step S5, the Epps-Pulley test is used to test the normality of the population. The calculated result is substituted into the test formula and compared with the p-quantile of the test value. If the test value is less than the p-quantile corresponding to a specific sample size and significance level, then the population sample conforms to a normal distribution.

[0017] Specifically, in step S6, the Irwin factor method is as follows:

[0018] Find the Irwin factors at a certain probability level and a certain confidence level from the Irwin factor table, and determine the upper limit of the one-sided tolerance value x of the target output. U The calculation is as follows:

[0019]

[0020] in, denoted as the sample mean, k as the corresponding Irwin factor, and s as the sample standard deviation.

[0021] Specifically, in step S6, the parameter statistical method is as follows:

[0022] Calculate the population mean and population variance, find the corresponding values ​​in the p-quantile table of the standard normal distribution, and calculate the upper limit of one-sided tolerance (x) at a certain probability level and a certain confidence level. U as follows:

[0023] x U =+u p ×σ

[0024] Where μ represents the population mean, σ represents the population standard deviation, and u p The p-quantile of the standard normal distribution;

[0025] The population mean and population standard deviation are calculated as follows:

[0026]

[0027]

[0028] Where υ is the degree of freedom, t 1-a (υ) represents the quantile of the t-distribution at confidence level 1-a when the degrees of freedom are υ. For χ with degrees of freedom υ 2 The quantile of the significance level α of the distribution.

[0029] Specifically, in step S6, when the calculation result of the normality test method does not conform to the normality distribution, a nonparametric statistical method is used to calculate and sort all the output parameters. Based on the confidence level β, probability level γ, and number of samplings N, the order of the Wilks formula is determined, and the corresponding one-sided tolerance upper limit is obtained directly from the order.

[0030] Specifically, in step S7, Spearman correlation coefficient, Pearson correlation coefficient, partial correlation coefficient (PCC), and standardized regression coefficient (SRC) are used to quantify the impact of different input parameters on key events in the accident process, and the judgment coefficient R is adjusted accordingly. 2 Determine the accuracy of the fitting results.

[0031] Furthermore, the judgment coefficient R is corrected. 2 for:

[0032]

[0033] Among them, y j The output parameters are calculated for uncertainty. To adjust the output parameter y j The fitted model is estimated, where N is the sample size.

[0034] Secondly, embodiments of the present invention provide a system for analyzing uncertainties and sensitivity to severe reactor accidents, including:

[0035] The type module identifies the accident conditions and reactor type under study, and determines the applicable integrated severe accident analysis procedure;

[0036] The input module, based on the integrated severe accident analysis program obtained from the type module, determines the target output parameters, and selects uncertainty input parameters based on the target output parameters and the physical model characteristics of the integrated severe accident analysis program ISAA, and specifies the baseline value, distribution type and range;

[0037] The debugging module, based on the baseline values ​​of the uncertain input parameters obtained from the input module, uses a severe accident analysis program to model and debug the overall system and accident conditions of the nuclear power plant, and analyzes the baseline conditions to obtain the conservative calculation results of the program; based on the uncertain input parameters selected by the input module and the modeling and debugging of the baseline conditions, uncertainty analysis is carried out, and the input parameter matrix is ​​randomly sampled using the Latin hypercube sampling method and modified into the modeling card for batch calculation;

[0038] The calculation module extracts the calculation results and verifies them using the normality test method. When the calculation results conform to the normal distribution, the Ewen factor method, parametric statistics, and nonparametric statistics are used to calculate the one-sided tolerance upper limit of the target output parameters when the confidence level and probability level are both 95%. The calculation results of different methods and the calculation results of the debugging model benchmark working condition are compared and analyzed to obtain a target output result that is closer to the actual situation.

[0039] The analysis module performs sensitivity analysis on the uncertain input parameters and target output of the input module based on the uncertainty analysis results obtained from the calculation module, obtains the sensitivity index analysis results, and acquires the importance information of the uncertain input parameters.

[0040] Compared with the prior art, the present invention has at least the following beneficial effects:

[0041] This paper proposes a method for uncertainty and sensitivity analysis of severe reactor accidents, combining optimal estimation with uncertainty analysis in the field of severe accident analysis. First, the accident condition and reactor type under study are determined, and based on this, an applicable optimal estimation procedure is selected. Then, the target output parameters are determined, and initial uncertainty input parameters are selected based on the target output and the physical model characteristics of the optimal estimation procedure, specifying their baseline values, distribution types, and ranges. Next, based on the baseline values ​​of the input parameters, the optimal estimation procedure is used to model and debug the overall nuclear power plant system and the accident condition, and the baseline condition is analyzed. Finally, uncertainty analysis is conducted based on the quantification of input uncertainties. The input parameter matrix is ​​randomly sampled using the Latin hypercube sampling method, and input files are generated in batches, which are then used to perform batch calculations using the analysis procedure. Then, the calculation results are tested using distribution tests to determine whether they conform to a normal distribution. If they do, the one-sided upper tolerance limit of the target output parameter at a 95% confidence and probability level is calculated using the Irwin factor method, parametric statistics, and nonparametric statistics. Conversely, if the probability is not 95%, nonparametric statistics are used to calculate the one-sided upper tolerance limit of the target output parameter at a 95% confidence and probability level. Finally, sensitivity analysis is performed through correlation and regression analysis to obtain the sensitivity index analysis results and acquire parameter importance information.

[0042] Furthermore, the selected uncertainty parameters cover heat transfer models such as radiation, convection, and conduction during steady-state reactor operation, extending to oxidation and decay heat models for transient accident conditions, and encompassing the entire operation and accident process from fuel rod failure and collapse, molten material repositioning, and the formation of a molten pool and release of fission products during severe accidents. This allows for comprehensive consideration of the physical model parameters and plant state parameters throughout the entire accident process, enabling accurate analysis and simulation.

[0043] Furthermore, the Latin hypercube sampling method based on stratified sampling addresses the problem of excessively large sample sizes and low efficiency associated with the simple Monte Carlo method. The LHS method can accurately reconstruct the input distribution with fewer iterations, exhibiting higher sampling efficiency and shorter running time. It avoids duplicate and missing data and can fully cover the entire sampling area, improving both sampling efficiency and accuracy. Meanwhile, the Wilks method is the most widely used nonparametric statistical method in best-efficiency estimation and uncertainty analysis to date, and its sample size is independent of the number of input parameters. By reducing the computational sample size in a simple and effective way, computational efficiency is significantly improved.

[0044] Furthermore, the Epps-Pulley test from the national standard "Statistical Processing and Interpretation of Data - Normality Test" was used to test the normality of the sample population. This test method uses the idea of ​​statistical assumptions to examine the extent to which the sample data fits the distribution of a population with a specific distribution. The T parameter... EP By comparing the P-quantile with the corresponding sample size and significance level, it can be quickly determined whether it conforms to the normal distribution assumption.

[0045] Furthermore, when the output parameters meet the normality test, the one-sided tolerance limit of the target output can be calculated using various analytical methods such as parametric statistical methods and Irwin factor method. Different analytical methods can be compared to avoid introducing excessive conservatism and to carry out other actions of the nuclear power plant under the premise of ensuring safety.

[0046] Furthermore, when the output parameters do not conform to the normality test, various simple and efficient nonparametric statistical methods can be used to directly obtain the one-sided tolerance upper limit by simply sorting or interpolating the output parameters, without the need for extensive calculations.

[0047] Furthermore, sensitivity analysis is conducted using various correlation and regression analysis methods to screen key uncertain input parameters, identify those that significantly impact the target output parameters, and calculate their confidence levels. This allows for a simple and direct identification of the most influential input parameters while maintaining the confidence level. This approach is applicable to the field of severe nuclear power plant accidents, quantifying the uncertainties inherent in optimal estimation procedures and plant state parameters. It effectively reduces the impact of complex phenomenological factors in the simulation research of severe nuclear power plant accidents.

[0048] Furthermore, the modified judgment coefficient R is used. 2 To determine the accuracy of the fitting results, the R-squared value is calculated by comparing the fitting models from correlation and regression analyses with the actual calculated data scatter points. 2 This can further assist in verifying the importance of input parameters.

[0049] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0050] In summary, this invention, through modeling and debugging the research object, utilizes different analytical methods to quantify the uncertainty of the target output parameters based on input uncertainty quantification. Furthermore, by incorporating various sensitivity analyses, it identifies the uncertain input parameters that significantly impact the target output. This addresses the technical problem of overly conservative traditional deterministic analysis methods, as well as the limitation of existing uncertainty analysis methods in the field of severe accident analysis.

[0051] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0052] Figure 1 This is a flowchart of the present invention;

[0053] Figure 2 This is a calculation block diagram of the present invention;

[0054] Figure 3 This is a modeling diagram of a nuclear power plant for an example.

[0055] Figure 4 The graph shows the results of hydrogen uncertainty calculations for an example.

[0056] Figure 5 This is a box diagram illustrating the single-sided allowable upper limit of hydrogen production for an example.

[0057] Figure 6 This is a graph showing the results of the sensitivity analysis.

[0058] Figure 7 Fitting model R to scatter plot of important parameters 2 . Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0061] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0062] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0063] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0064] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0065] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0066] This invention provides a method for uncertainty and sensitivity analysis of severe reactor accidents. The method involves determining the accident condition and reactor type under study, and based on this, identifying the applicable optimal estimation procedure. It also involves determining the target output parameters, selecting uncertainty input parameters based on the target output and the physical model characteristics of the optimal estimation procedure, and specifying their baseline values, distribution types, and ranges. Based on the baseline values ​​of the input parameters, the optimal estimation procedure is used to model and debug the overall nuclear power plant system and the accident condition, and the baseline condition is analyzed. Finally, uncertainty analysis is conducted based on the quantification of input uncertainty. The Latin hypercube sampling method is used to randomly sample the input parameter matrix, and the input parameters are generated in batches. The process involves importing a file, calling an analysis program for batch calculations, and then testing the calculation results using distribution tests to determine if they conform to a normal distribution. If they do, the Owen factor method, parametric statistics, and nonparametric statistics are used to calculate the one-sided tolerance upper limit of the target output parameter at a 95% confidence and probability level. If they do not conform, nonparametric statistics are used to calculate the one-sided tolerance upper limit of the target output parameter at a 95% confidence and probability level. Finally, sensitivity analysis is performed using different methods such as correlation analysis and regression analysis to obtain sensitivity index analysis results and parameter importance information. Compared with existing technologies, this invention combines optimal estimation with uncertainty analysis methods in the field of severe accident analysis, and comprehensively considers various uncertainty analysis methods as well as various sensitivity analysis methods of correlation and regression analysis. This addresses the technical problems of overly conservative traditional deterministic analysis methods and large uncertainties in severe accident analysis, as well as the inability of existing uncertainty analysis methods to fully play their role in the field of severe accident analysis.

[0067] Please see Figure 2 The present invention provides a method for uncertainty and sensitivity analysis of severe reactor accidents, comprising the following steps:

[0068] S1. Determine the accident conditions and reactor type under study, and based on this, determine the applicable integrated severe accident analysis procedure;

[0069] The accident scenario studied is a severe accident in which the reactor core is severely damaged and melted, and the reactor type studied is a pressurized water reactor.

[0070] S2. Determine the target output parameters, and select the uncertainty input parameters based on the target output and the physical model characteristics of the best estimation procedure, and specify their baseline values, distribution types and ranges;

[0071] Based on the model inputs and their physical meanings in the optimal estimation procedure, the model input parameters corresponding to the key physical phenomena under the accident conditions are selected, including radiation, heat conduction, heat convection, metal oxidation, decay heat model, fuel rod collapse, molten material repositioning, molten pool heat transfer, and the release and migration of fission products in the core heat transfer and oxidation model.

[0072] S3. Based on the baseline values ​​of the input parameters, the best estimation program is used to model and debug the overall system and accident conditions of the nuclear power plant, and the baseline conditions are analyzed.

[0073] Numerical modeling of the primary and secondary loop systems of the reactor type under study was performed using an optimal estimation procedure, including the reactor coolant system and the passive emergency core cooling system. The simulated values ​​were compared with the actual steady-state operating parameters of the power plant; if they did not match, the established numerical model was adjusted.

[0074] S4. Based on the input uncertainty quantification, conduct uncertainty analysis, randomly extract the input parameter matrix using the Latin hypercube sampling method, modify it into the modeling card, and input it into the program for batch calculation;

[0075] The Latin hypercube sampling method is used to randomly stratify and sample input parameters from different distributions, including normal, log-normal, uniform, and triangular distributions. The sampled input parameters are randomly combined to generate batch input files corresponding to step S3, and the integrated severe accident analysis program is called to perform batch calculations. The sample size is determined by the Wilks formula.

[0076] The permissible limits for one-sided and two-sided cases are respectively calculated using the following formulas:

[0077]

[0078]

[0079] Where β is the confidence level, γ is the probability level, N is the number of calculations, and p is the target number of outputs or the order.

[0080] S5. Extract the calculation results and test them according to the normality test method to determine whether they conform to a normal distribution. If they do, proceed to step S6; otherwise, proceed to step S7.

[0081] The Epps-Pulley test is used to test for normality, and the test value T is... EP As shown below:

[0082]

[0083]

[0084] Where n is the sample size. Let m be the sample mean, and m2 be the sample second central moment.

[0085] Substitute the calculated result into the test formula and compare it with the p-quantile of the test value. If the test value is less than the p-quantile corresponding to a specific sample size and significance level, then the population sample is considered to conform to a normal distribution.

[0086] Table 1 Epps-Pulley Test T EP p quantile

[0087]

[0088] S6. Uncertainty Analysis Methods

[0089] The one-sided tolerance upper limit of the target output parameter is obtained by using the Irwin factor method, parametric statistics, and nonparametric statistics to calculate the parameter at a confidence level and a probability level of 95%.

[0090] The Irwin factor method and parametric statistical methods require the population sample to be normally distributed. Nonparametric statistical methods, on the other hand, effectively solve the problem of calculating the one-sided statistical tolerance limit when the distribution type is unknown. They are relatively simple and efficient to use. Therefore, nonparametric statistical methods can be used to calculate the limit when the population sample is not normally distributed.

[0091] S601, Irwin Factor Method: Find the Irwin factors at a certain probability level and a certain confidence level from the Irwin factor table, and substitute them into the formula to calculate the one-sided tolerance upper limit of the target output:

[0092]

[0093] in, denoted as the sample mean, k(N,p,1-a) is the Irwin factor corresponding to a sample size of N, a probability level of p, and a confidence level of 1-α, and s is the sample standard deviation.

[0094] Table 2. Irwin factors for different probability levels and sample sizes at a 95% confidence level.

[0095]

[0096] S602, Parameter Statistical Method:

[0097] Calculate the population mean and population variance, find the corresponding values ​​in the p-quantile table of the standard normal distribution, and use the formula to calculate the upper limit of one-sided tolerance at a certain probability level and a certain confidence level as follows:

[0098] x U =μ+up ×σ (6)

[0099] Where μ represents the population mean, σ represents the population standard deviation, and u p It represents the p-quantile of the standard normal distribution.

[0100] Table 3. p-quantiles of the standard normal distribution

[0101]

[0102] The population mean and population standard deviation can be calculated from the sample mean and sample standard deviation, using the following formulas:

[0103]

[0104] Where υ is the degree of freedom, t 1-a (υ) represents the quantile of the t-distribution at confidence level 1-a when the degrees of freedom are υ. For χ with degrees of freedom υ 2 The quantile of the significance level α of the distribution.

[0105] Table 4. Quantiles of the t-distribution

[0106]

[0107] Table 5χ 2 Distribution quantiles

[0108]

[0109]

[0110] S603, Using nonparametric statistical methods

[0111] Using Wilks' theory in step S4, the one-sided tolerance upper limit of the target output parameter is obtained when both the confidence level and probability level are 95%.

[0112] Sort all output parameters and determine the order of the Wilks formula based on the confidence level β, probability level γ, and number of samples N. The corresponding one-sided tolerance upper limit is directly obtained from the order; the order determines the largest value chosen as the one-sided tolerance upper limit.

[0113] S7. Use different methods such as correlation analysis and regression analysis to conduct sensitivity analysis, obtain sensitivity index analysis results, and obtain parameter importance information.

[0114] The impact of different input parameters on key events in the accident process was quantified using Pearson correlation coefficient, Spearman correlation coefficient, partial correlation coefficient (PCC), and standardized regression coefficient (SRC).

[0115] S701, Pearson correlation coefficient

[0116] The Pearson correlation coefficient is calculated directly using data values, and the formula is:

[0117]

[0118] Where N is the sample size; μ X μ Y and σ X σ Y Let x represent the mean and standard deviation of variables X and Y, respectively; x i and y i This represents the corresponding value of the input parameter and the output parameter of the i-th parameter during the k-th sampling. and This represents the sample mean.

[0119] S702, Spearman rank correlation coefficient

[0120] The Spearman correlation coefficient measures the correlation between the output and the input using the order of data values. The formula is as follows:

[0121]

[0122] Wherein, R(X) i ) represents X i The ordering of values ​​in all variables X; R(Y) i ) represents Y i The order of values ​​in all variables Y; N is the total sample size.

[0123] S703, Partial Correlation Coefficient (PCC)

[0124] The partial correlation coefficient (PCC) measures the linear correlation between a pair of input parameters in a set of n input parameters, after eliminating the influence of residual variables. The formula is:

[0125]

[0126] in, For X i With Y in eliminating other X -i The correlation coefficient, r, after the influence of variables a·b Let be the Pearson correlation coefficient between a and b.

[0127] S704, Standardized Regression Coefficient (SRC)

[0128] Standardized regression coefficients (SRCs) measure the sensitivity of multiple linear regression analysis.

[0129] First, the data needs to be standardized. This involves subtracting the mean of the relevant variable from the original data and then dividing by the standard deviation of that variable. The resulting regression equation is the standardized regression equation, and the corresponding coefficients are the standard regression coefficients. The calculation formula is as follows:

[0130]

[0131] Among them, b j X represents j Standardized regression coefficients of Y; Var(X) j ) and Var(Y) represent X and Var(Y), respectively. j The variance of Y.

[0132]

[0133] Where b0 is the intercept of the regression model; b j X represents j The standardized regression coefficients of Y.

[0134]

[0135] Corrected judgment coefficient R 2 Used to judge the accuracy of the fitting results; the larger the value, the higher the fitting accuracy.

[0136] S705, P-value, statistical significance of absolute values ​​in correlation analysis and regression analysis

[0137] To assess the reliability of the sensitivity analysis results, the p-values ​​of each coefficient in steps S701 to S704 are calculated:

[0138] When p < 0.05, the correlation calculation is considered statistically significant. Generally, high p and low p indicate correlation. The absolute value of the correlation coefficient reflects the sensitivity of the uncertainty of the input parameter to the output parameter. A positive sign indicates a positive correlation between the input and output, meaning that the target output parameter increases as the input parameter increases, and vice versa; similarly, a negative sign indicates a negative correlation between the input and output; zero indicates that the input and output are not correlated.

[0139] The closer the correlation coefficient is to 1.0, the stronger the correlation between the corresponding uncertain input parameter and the target output parameter; the closer the correlation coefficient is to 0.0, the weaker the correlation.

[0140] When the absolute value of the correlation coefficient is between 0.1 and 0.2, a weak correlation is considered to exist between the variables.

[0141] When the absolute value of the correlation coefficient is between 0.2 and 0.6, it is considered that there is a moderate correlation between the variables.

[0142] When the absolute value of the correlation coefficient is greater than 0.6, the variables are considered to be strongly correlated.

[0143] By using sensitivity analysis to screen key uncertain input parameters, we can easily and directly identify the input parameters with a significant impact while maintaining confidence levels.

[0144] In another embodiment of the present invention, a system for analyzing the uncertainty and sensitivity of severe reactor accidents is provided. This system can be used to implement the above-mentioned method for analyzing the uncertainty and sensitivity of severe reactor accidents. Specifically, the system for analyzing the uncertainty and sensitivity of severe reactor accidents includes a type module, an input module, a debugging module, a calculation module, and an analysis module.

[0145] The type module identifies the accident conditions and reactor types under study, and determines the applicable integrated severe accident analysis procedure.

[0146] The input module, based on the integrated severe accident analysis program obtained from the type module, determines the target output parameters, and selects uncertainty input parameters based on the target output parameters and the physical model characteristics of the integrated severe accident analysis program ISAA, and specifies the baseline value, distribution type and range;

[0147] The debugging module, based on the baseline values ​​of the uncertain input parameters obtained from the input module, uses a severe accident analysis program to model and debug the overall system and accident conditions of the nuclear power plant, and analyzes the baseline conditions to obtain the conservative calculation results of the program; based on the uncertain input parameters selected by the input module and the modeling and debugging of the baseline conditions, uncertainty analysis is carried out, and the input parameter matrix is ​​randomly sampled using the Latin hypercube sampling method and modified into the modeling card for batch calculation;

[0148] The calculation module extracts the calculation results and verifies them using the normality test method. When the calculation results conform to the normal distribution, the Ewen factor method, parametric statistics, and nonparametric statistics are used to calculate the one-sided tolerance upper limit of the target output parameters when the confidence level and probability level are both 95%. The calculation results of different methods and the calculation results of the debugging model benchmark working condition are compared and analyzed to obtain a target output result that is closer to the actual situation.

[0149] The analysis module performs sensitivity analysis on the uncertain input parameters and target output of the input module based on the uncertainty analysis results obtained from the calculation module, obtains the sensitivity index analysis results, and acquires the importance information of the uncertain input parameters.

[0150] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of methods for analyzing the uncertainty and sensitivity of severe reactor accidents, including:

[0151] The study identifies the accident conditions and reactor type, and determines the applicable Integrated Severe Accident Analysis (ISAA) program. Based on the ISAA program, target output parameters are determined, and uncertainty input parameters are selected based on these parameters and the physical model characteristics of the ISAA program, specifying baseline values, distribution types, and ranges. Using the baseline values ​​of the uncertainty input parameters, the ISAA program is used to model and debug the overall nuclear power plant system and accident conditions, and the baseline conditions are analyzed to obtain conservative calculation results for comparison with uncertainty and sensitivity analyses. Uncertainty analysis is then conducted based on the selected uncertainty input parameters and the modeling and debugging of the baseline conditions, utilizing Latin hyperspectral imaging. The cubic sampling method is used to randomly sample the input parameter matrix and modify it into the modeling card for batch calculation. The obtained calculation results are extracted and tested using the normality test method. When the obtained calculation results conform to the normal distribution, the Ewen factor method, parametric statistics, and nonparametric statistics are used to calculate the one-sided tolerance upper limit of the target output parameter when the confidence level and probability level are both 95%. The calculation results of different methods and the calculation results of the benchmark working condition are compared and analyzed to obtain the target output result that is closer to the actual situation. Based on the obtained uncertainty analysis results, sensitivity analysis is performed on the uncertain input parameters and target output to obtain the sensitivity index analysis results and obtain the importance information of the uncertain input parameters.

[0152] In another embodiment of the present invention, a storage medium is also provided, specifically a computer-readable storage medium (memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0153] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the method for uncertainty and sensitivity analysis of severe reactor accidents in the above embodiments; one or more instructions in the computer-readable storage medium are loaded by the processor and executed as follows:

[0154] The study identifies the accident conditions and reactor type, and determines the applicable Integrated Severe Accident Analysis (ISAA) program. Based on the ISAA program, target output parameters are determined, and uncertainty input parameters are selected based on these parameters and the physical model characteristics of the ISAA program, specifying baseline values, distribution types, and ranges. Using the baseline values ​​of the uncertainty input parameters, the ISAA program is used to model and debug the overall nuclear power plant system and accident conditions, and the baseline conditions are analyzed to obtain conservative calculation results for comparison with uncertainty and sensitivity analyses. Uncertainty analysis is then conducted based on the selected uncertainty input parameters and the modeling and debugging of the baseline conditions, utilizing Latin hyperspectral imaging. The cubic sampling method is used to randomly sample the input parameter matrix and modify it into the modeling card for batch calculation. The obtained calculation results are extracted and tested using the normality test method. When the obtained calculation results conform to the normal distribution, the Ewen factor method, parametric statistics, and nonparametric statistics are used to calculate the one-sided tolerance upper limit of the target output parameter when the confidence level and probability level are both 95%. The calculation results of different methods and the calculation results of the benchmark working condition are compared and analyzed to obtain the target output result that is closer to the actual situation. Based on the obtained uncertainty analysis results, sensitivity analysis is performed on the uncertain input parameters and target output to obtain the sensitivity index analysis results and obtain the importance information of the uncertain input parameters.

[0155] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0156] Example

[0157] Please see Figure 3 The selected accident condition is a severe accident caused by a large-break loss of water at both ends of the reactor, and the Hualong One pressurized water reactor (HPR1000) is chosen as the reactor type for the study of physical phenomena. The system nodes of the HPR1000 nuclear power plant are divided as follows: Figure 3 As shown, the numerical model includes the primary loop system, part of the secondary loop (SG secondary side), and active and passive safety devices. Loops B and C of the three coolant system loops are omitted in the nodal diagram. The control unit CV100-140 represents the reactor pressure vessel; it connects to the steam generator inlet chamber CV201 and the pressurizer CV500 via the heat pipe section CV200; after heat exchange with the secondary loop, it returns to the core descent section CV134 via the outlet CV209 and the cold pipe section CV237. Safety devices are controlled by functions to activate their conditions. The CMT reservoir (CV503) is connected to the cold pipe section CV237, injecting boron-containing water into the core via the descent section CV134. The Low-Pressure Safety Injection (LHSI) pump draws water from the Internal Refueling Tank (IRWST) and injects water into the core in the same manner as the CMT. The containment spray (CSP) pump is interconnected with the LHSI pump in the system piping for backup; if one pump fails, the other ensures the continued operation of both systems. The Cavity Injection System (CIS) and the Passive Containment Heat Transfer System (PCS) each have an independent heat exchange tank, namely CV811 and CV810. The CIS tank (CV811) injects water into the annular flow channel (CV600) between the pressure vessel and the insulation layer by gravity. The PCS system relies on gravity and the density difference of water to form a natural circulation between the tank (CV810) and the heat exchangers (CV800, 801, 802).

[0158] In this embodiment, it is assumed that a double-end shear failure occurs in the cold tube section CV237, leading to core decooling and a severe meltdown accident. It is also assumed that one LHSI, one CSP pump, three CMTs, a passive CIS, and a passive PCS can be put into normal operation and achieve core cooling. The uncertainty analysis program of this invention was used to study the uncertainty of hydrogen generated by core oxidation during the accident process.

[0159] The optimal estimation procedure is selected based on the characteristics of the accident conditions studied and the reactor type, taking into account the applicability of the optimal estimation procedure and the physical phenomena it can simulate, such as... Figure 2 As shown.

[0160] The target output parameters need to consider key indicators under nuclear power plant accident conditions, existing research literature, and physical parameters that may cause serious consequences. In this embodiment, the mass of hydrogen produced is selected as the target output parameter because the production and distribution of hydrogen directly determine whether rapid combustion or explosion will occur within the containment vessel, thereby compromising the integrity of the containment vessel, and is a key target outcome.

[0161] Based on the characteristics and physical significance of the physical model of the target output and the optimal estimation procedure, model input parameters corresponding to key physical phenomena under the accident conditions are selected, including uncertain input parameters such as radiation, heat conduction, heat convection, metal oxidation, and decay heat models in the core heat transfer and oxidation models, and their baseline values, distribution types, and ranges are specified. The baseline values ​​are the values ​​of each uncertain input parameter in the baseline condition modeling. The distribution types are mainly uniform, normal, log-normal, and triangular distributions. The range is determined by the fluctuation range of the baseline values ​​of the uncertain input parameters and engineering and modeling experience. The uncertainty analysis only analyzes the target output results and does not consider the number of selected input parameters; therefore, there is no limitation on the number of input parameters. This example selects 17 relevant model parameters based on the output parameter hydrogen production mass and the physical model of the optimal estimation procedure.

[0162] Table 6 Uncertainty Input Parameters

[0163]

[0164]

[0165] The modeling node diagram is divided based on the power plant design parameters and structural diagrams, as shown below. Figure 3As shown, the primary loop system and part of the secondary loop system of the studied reactor type were numerically modeled using the optimal estimation procedure, including the reactor coolant system and the passive emergency core cooling system. The simulated values ​​were compared with the actual steady-state operating parameters of the power plant. If they did not match, the established numerical model was adjusted. The actual steady-state operating parameters compared included pressurizer pressure, coolant inlet and outlet temperatures, coolant flow rate, and steam generator steam flow rate.

[0166] For 17 uncertain input parameters of four distribution types, N samples are randomly drawn using the LHS method and then randomly combined to obtain the input parameter matrix. The sample size N is determined by the minimum calculated sample size under a certain probability level and a certain confidence level corresponding to the Wilks formula. In this embodiment, the selected probability level and confidence level are both 95%, and the selected sampling size N is the 208 sample size corresponding to the sixth-order Wilks formula.

[0167] Modify the obtained input parameter matrix to the corresponding input position in the optimal estimation program modeling card, perform the calculation using the optimal estimation program, and use the Aptplot program to extract the target output parameter change curve over time, as shown in the figure. Figure 4 As shown. Determine the stable time point of the target output parameters and extract the corresponding values ​​after the hydrogen production mass stabilizes.

[0168] The one-sided tolerance upper limit of the target output is calculated using various uncertainty analysis methods, such as... Figure 5 As shown, different analytical methods can be compared to avoid introducing excessive conservatism and to ensure that other actions of nuclear power plants are carried out under the premise of ensuring safety.

[0169] This example uses Spearman correlation coefficient, Pearson correlation coefficient, partial correlation coefficient (PCC), and standardized regression coefficient (SRC) to analyze and quantify the impact of different input parameters on key events in the accident process, specifically their impact on hydrogen production quality. Ultimately, the degree of influence of each parameter on hydrogen production is obtained, such as... Figure 6 and Figure 7 As shown.

[0170] The main conclusions drawn from the calculation and analysis are as follows:

[0171] (1) Under a double-end shear large-break accident, the total amount of hydrogen in the pressure vessel of a 1000 MWe reactor is between 182.784 and 329.581 kg, which shows a normal distribution.

[0172] (2) Among the selected uncertainty parameters, the cladding oxidation fracture temperature RT-ZrO2, the maximum velocity of melt ejection MaxFR-Mat, the core region fragment size EDPD-CORE, and the fragment porosity POR-DB in the ISAA program show a relatively significant correlation with the outputs of interest. Calculations show that the uncertainty band for hydrogen is quite wide, which is related to the phenomenological complexity of severe accidents. On the other hand, this also suggests that future work should combine uncertainty analysis to further revise and improve the numerical model of the integrated analysis program, thereby minimizing uncertainty. For example, the model parameters of the ISAA program analyzed in this invention, such as RT-ZrO2 and MaxFR-Mat, are empirical constants; further development and improvement of related models are needed in the future.

[0173] In summary, the present invention provides a method and system for uncertainty and sensitivity analysis of severe reactor accidents, which effectively solves the problems of extremely high complexity and uncertainty in severe accident analysis. It can quantify the uncertainties in severe accident analysis procedures and power plant state parameters, which is beneficial to the safety design of nuclear power plants and the development of severe accident analysis. It can more realistically simulate accident conditions and provide methodological guidance for general technicians to study the process and characteristics of severe accidents.

[0174] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0175] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0176] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0177] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0178] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0179] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0180] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0181] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0182] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0183] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0184] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for uncertainty and sensitivity analysis of severe reactor accidents, characterized in that, Includes the following steps: S1. Determine the accident conditions and reactor type to be studied, and identify the applicable integrated severe accident analysis procedure; S2. Based on the integrated severe accident analysis program obtained in step S1, determine the target output parameters, and select the uncertainty input parameters based on the target output parameters and the physical model characteristics of the integrated severe accident analysis program ISAA, and specify the baseline value, distribution type and range. S3. Based on the baseline values ​​of the uncertainty input parameters obtained in step S2, the overall system of the nuclear power plant and the accident conditions are modeled and debugged using the severe accident analysis program, and the baseline conditions are analyzed to obtain the conservative calculation results of the program, which are used for the analysis and comparison of uncertainty and sensitivity analysis in steps S4 to S7. S4. Based on the uncertainty input parameters selected in step S2 and the modeling and debugging of the baseline working condition in step S3, uncertainty analysis is carried out. The input parameter matrix is ​​randomly sampled using the Latin hypercube sampling method and modified into the modeling card for batch calculation. S5. Extract the calculation results obtained in step S4, and test the calculation results according to the normality test method; S6. When the calculation result obtained in step S5 conforms to the normal distribution, the one-sided tolerance upper limit of the target output parameter is obtained by using the Irwin factor method, parametric statistical method and nonparametric statistical method to calculate the target output parameter when the confidence level and probability level are both 95%. The calculation results of different methods and the calculation results of the baseline working condition in step S3 are compared and analyzed to obtain a target output result that is closer to the actual situation. S7. Based on the uncertainty analysis results obtained in steps S4 to S6, perform sensitivity analysis on the uncertainty input parameters and target output in step S2 to obtain the sensitivity index analysis results and acquire the importance information of the uncertainty input parameters.

2. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 1, characterized in that, In step S2, the uncertain input parameters include radiation, heat conduction, heat convection, metal oxidation, decay heat model, fuel rod collapse, molten material repositioning, molten pool heat transfer, and the release and migration of fission products in the core heat transfer and oxidation model.

3. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 1, characterized in that, In step S4, the input parameters with different distributions are randomly stratified and sampled using the Latin hypercube sampling method, including normal distribution, log-normal distribution, uniform distribution, and triangular distribution. The sampled input parameters are randomly combined to generate input files corresponding to those in step S3 in batches. The system script is then used to call the integrated severe accident analysis program to perform batch calculations. The sample size is determined by the Wilks formula.

4. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 1, characterized in that, In step S5, the Epps-Pulley test is used to test the normality of the population. The calculated result is substituted into the test formula and compared with the p-quantile of the test value. If the test value is less than the p-quantile corresponding to a specific sample size and significance level, then the population sample conforms to a normal distribution.

5. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 1, characterized in that, In step S6, the Irwin factor method specifically involves: Find the Irwin factors at a certain probability level and a certain confidence level from the Irwin factor table, and determine the upper limit of the one-sided tolerance value x of the target output. U The calculation is as follows: in, denoted as the sample mean, k as the corresponding Irwin factor, and s as the sample standard deviation.

6. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 1, characterized in that, In step S6, the parameter statistical method specifically involves: Calculate the population mean and population variance, find the corresponding values ​​in the p-quantile table of the standard normal distribution, and calculate the upper limit of one-sided tolerance (x) at a certain probability level and a certain confidence level. U as follows: x U =+u p ×σ Where μ represents the population mean, σ represents the population standard deviation, and u p The p-quantile of the standard normal distribution; The population mean and population standard deviation are calculated as follows: Where υ is the degree of freedom, t 1-a (υ) represents the quantile of the t-distribution at confidence level 1-a when the degrees of freedom are υ. For χ with degrees of freedom υ 2 The quantile of the significance level α of the distribution.

7. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 1, characterized in that, In step S6, when the calculation result of the normality test method does not conform to the normality distribution, nonparametric statistical method is used to calculate and sort all output parameters. Based on the confidence level β, probability level γ, and number of sampling N, the order of the Wilks formula is determined, and the corresponding one-sided tolerance upper limit is obtained directly from the order.

8. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 1, characterized in that, In step S7, Spearman correlation coefficient, Pearson correlation coefficient, partial correlation coefficient (PCC), and standardized regression coefficient (SRC) are used to quantify the impact of different input parameters on key events in the accident process. The judgment coefficient R is then adjusted accordingly. 2 Determine the accuracy of the fitting results.

9. The method for uncertainty and sensitivity analysis of severe reactor accidents according to claim 8, characterized in that, Corrected judgment coefficient R 2 for: Among them, y j The output parameters are calculated for uncertainty. To adjust the output parameter y j The fitted model is estimated, where N is the sample size.

10. A system for uncertainty and sensitivity analysis of severe reactor accidents, characterized in that, include: The type module identifies the accident conditions and reactor type under study, and determines the applicable integrated severe accident analysis procedure; The input module, based on the integrated severe accident analysis program obtained from the type module, determines the target output parameters, and selects uncertainty input parameters based on the target output parameters and the physical model characteristics of the integrated severe accident analysis program ISAA, and specifies the baseline value, distribution type and range; The debugging module, based on the baseline values ​​of uncertain input parameters obtained from the input module, uses a severe accident analysis program to model and debug the overall system of the nuclear power plant and accident conditions, and analyzes the baseline conditions to obtain the conservative calculation results of the program. Uncertainty analysis is carried out based on the uncertain input parameters selected by the input module and the modeling and debugging of the benchmark working condition. The input parameter matrix is ​​randomly sampled using the Latin hypercube sampling method and modified into the modeling card for batch calculation. The calculation module extracts the calculation results and verifies them using the normality test method. When the calculation results conform to the normal distribution, the Ewen factor method, parametric statistics, and nonparametric statistics are used to calculate the one-sided tolerance upper limit of the target output parameters when the confidence level and probability level are both 95%. The calculation results of different methods and the calculation results of the debugging model benchmark working condition are compared and analyzed to obtain a target output result that is closer to the actual situation. The analysis module performs sensitivity analysis on the uncertain input parameters and target output of the input module based on the uncertainty analysis results obtained from the calculation module, obtains the sensitivity index analysis results, and acquires the importance information of the uncertain input parameters.

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