Automatic solving method for critical heat flux density of reactor based on principle of statistics

Abstract

The invention discloses a method for automatically solving the critical heat flux density of a reactor based on a statistical principle, and belongs to the field of safety analysis of nuclear reactors. The problems that an over-fitting problem exists, a data set cannot be verified clearly through a fitting data set, and the development process is complicated when a traditional method is used for predicting independent variable combination items of a relational expression artificially given by CHF relational expression development are solved. The method comprises the following steps: collecting reactor CHF experimental data points; eliminating possible repeated experimental points and cold rod critical points to form a development database; based on a layered random sampling method, extracting data from the development database, and determining a fitting data set and a verification data set; based on the fitting data set, selecting a curve form of a single independent variable or a combination item; the independent variables and the combination items with the collinearity problem are removed; importance ranking analysis of the variables and the combination items is obtained through regression coefficient standardization; forming a final CHF relational expression; and based on the verification data set, verifying the CHF relational expression.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear reactor safety analysis, and in particular relates to an automatic solution method for reactor critical heat flux density based on statistical principles. Background Art

[0002] The phenomenon of a decrease in the heat transfer coefficient and a sudden increase in wall temperature due to a change in the boiling mechanism is called a boiling crisis. The maximum heat flux density before the boiling crisis is the critical heat flux density (CHF). Based on the flow pattern and heat transfer characteristics of the fluid at the time of critical boiling, a boiling crisis occurring in the nucleate boiling region with a low vapor content is called deviation from nucleate boiling (DNB); a boiling crisis occurring in the annular flow region with a high vapor content is called dryout. In pressurized water reactors, DNB-type CHF is common. When a CHF occurs, the fuel rod cladding overheats in a very short time and burns, posing a significant safety risk to the reactor.

[0003] In the development of nuclear power, reactor safety and economic efficiency are two key factors that must be considered. The next generation of nuclear power plants requires safer and more economical nuclear fuel assemblies. From a safety perspective, fuel assemblies must have a higher thermal-hydraulic margin to prevent the fuel pellets from melting. From an economic perspective, the core must have more uniform thermal-hydraulic properties. As a key limiting parameter in reactor design and operation, strengthening and accurately predicting the CHF is crucial. The setting of the CHF margin directly affects the safety and economic efficiency of the reactor.

[0004] With the development of water-cooled reactors, the CHF phenomenon has been extensively studied both experimentally and theoretically worldwide over the past few decades, resulting in a large amount of experimental data on CHF for circular tubes and rod bundles and a variety of CHF prediction methods. Existing CHF prediction methods mainly include empirical methods, mechanism models, and fluid modeling methods for CHF experiments. Empirical methods include empirical relationships, query tables, artificial neural networks, etc. Currently, the prediction of rod bundle CHF mainly relies on empirical relationships, and CHF relationships play a very important role in the design and accident analysis of various pressurized water reactors. Excellent CHF relationships can accurately predict the location of the boiling critical point and the CHF value, providing safety limits for core thermal hydraulic design and safety analysis.

[0005] Based on a qualitative analysis of the CHF phenomenon, hypotheses are proposed regarding the physical processes or key controlling factors involved. Mathematical methods are then used to analyze experimental data to derive a calculated equation, known as an empirical CHF equation. Due to the complexity of boiling criticality, its mechanisms remain largely unknown. A widely used approach for developing CHF equations for fuel assemblies is to determine a reasonable CHF equation form based on a large amount of reliable CHF experimental data. The equation coefficients are then solved using mathematical methods such as regression techniques, and the performance of the equation is evaluated using statistical methods. With the continuous expansion of CHF experimental databases, the parameter range covered has increased, and the number of flow path geometries has increased, leading to the development of numerous empirical CHF equations. These equations are often applicable only to specific geometries within a very limited parameter range. When applied to a wide range of parameters, their prediction accuracy is low. However, empirical equations are more convenient for CHF prediction. Traditional CHF equation development relies on manual calculations, which are not only time-consuming and labor-intensive, but also prone to errors and inconvenient for optimizing and updating the equation form. Furthermore, the lack of a statistically informed development process hinders the rational, scientific, and efficient use of existing CHF equations.

[0006] Currently, CHF relational development processes are chaotic and time-consuming, CHF relational development lacks statistical support, the number and form of independent variables in CHF relational determination is subjective and subject to collinearity, the distinction between development and validation data is unclear, and the relational generalization and predictive power for CHF operating conditions beyond experimental data are difficult to estimate. To address these challenges, a method for automated CHF relational solution and analysis based on statistical principles for data sampling, relational form determination, and validation evaluation is urgently needed. Summary of the Invention

[0007] The purpose of the present invention is to provide an automated solution method for the critical heat flux density of a reactor based on statistical principles, so as to solve the problems of the traditional method for predicting CHF relationship development lacking a statistical principle basis, artificially given independent variable combinations of the relationship, overfitting problems, unclear fitting data set verification data set, and complicated relationship development process.

[0008] The technical solution of the present invention is: a method for automatically calculating the critical heat flux density of a reactor based on statistical principles, comprising the following steps: S1. Based on the collected reactor CHF experimental data points, a preliminary database is formed; S2. Screen the data points and eliminate possible duplicate experimental points and cold rod critical points to form a development database for subsequent CHF relationship development; S3. Based on the stratified random sampling method, data were extracted from the development database to determine the fitting data set and the validation data set; S4. Based on the fitted data set, input the suspicious independent variables and combination items, estimate the curve form of the suspicious independent variables and combination items, and select the curve form of the single independent variable or combination item; S5. Based on the fitted data set, the variance inflation factor method is used to conduct collinearity diagnosis on the independent variables and combination items in the selected curve form, and the independent variables and combination items with collinearity problems are eliminated; S6. Using a stepwise regression method, based on the independent variables and combination items obtained in step S5, an optimal subset of independent variables is obtained, and the importance ranking analysis of the individual variables and combination items is obtained by standardizing the regression coefficients; S7. Form the final CHF relationship, which is as follows: , Among them, qCHFP is the predicted CHF value; The mean and root mean square difference of Mea / Pre of the fitted data set were obtained, and the outlier test was performed using the Grubbs test to eliminate experimental outliers; S8. Verify the CHF relationship based on the validation data set and obtain the mean and root mean square deviation of the Mea / Pre ratio for the validation data. A mean Mea / Pre ratio between 0.97 and 1.03 and a root mean square deviation less than 10% indicate that the method is effective.

[0009] As a further improvement of the present invention, in step S1, the basic physical quantities required in the preliminary database are: CHF experimental value qCHF, pressure P, mass flow rate G, steam content x, distance dg from the location where CHF occurs to the upper grid, experimental grid span dg0, experimental section inlet temperature Tin, and the number of the heating rod where CHF occurs.

[0010] As a further improvement of the present invention, in step S3, data is extracted using a stratified random sampling method based on three parameters: pressure P, mass flow rate G, and vapor content x.

[0011] As a further improvement of the present invention, in step S4, the input suspicious independent variables and combination terms include: pressure, mass flow rate, vapor fraction; the ratio of the distance from the location where CHF occurs to the upper grid to the experimental grid span, and the product of the pressure, mass flow rate, vapor fraction and the ratio; and the pairwise product of the pressure, mass flow rate, and vapor fraction.

[0012] As a further improvement of the present invention, in step S4, the curve form estimation includes the following basic forms: linear, logarithmic, exponential, power function, polynomial, and S-type.

[0013] As a further improvement of the present invention, in step S6, the stepwise regression method is as follows: the independent variables and combination terms obtained in step S5 are introduced into the CHF relationship one by one, and a partial F test is performed after each introduction of a suspicious independent variable or combination term, and the explanatory variables that have been selected are tested one by one. When the originally introduced explanatory variable becomes no longer significant due to the introduction of the subsequent explanatory variable, it is deleted to ensure that only significant variables are included in the regression equation before each introduction of a new variable, until no significant explanatory variables are selected into the regression equation and no insignificant explanatory variables are eliminated from the regression equation, so as to ensure that the final set of explanatory variables obtained is optimal, and ultimately the optimal independent variable subset is obtained.

[0014] As a further improvement of the present invention, in step S6, the method for standardizing the regression coefficient is as follows: the original coefficient data is subtracted from the mean of the corresponding coefficient and then divided by the standard deviation of the coefficient. The obtained regression coefficient is the standardized regression coefficient. According to the size of the standardized regression coefficient, the CHF-influencing program sorts the independent variables from large to small.

[0015] As a further improvement of the present invention, in step S7, the root mean square difference of Mea / Pre RMSE The calculation formula is as follows: , in, i Indicates the i Data identifier, n represents the sample size, Mea represents the experimental CHF value, and Pre represents the predicted CHF value.

[0016] The beneficial effects of the present invention are: 1. The present invention obtains a set of methods for automatically solving and analyzing CHF relationship equations through data sampling, relationship form determination and verification evaluation methods based on statistical principles. This method solves, to a certain extent, the problems of the existing CHF relationship equation development process being chaotic and time-consuming, the lack of statistical principle support for CHF relationship equation development, the subjective assumptions about the number and form of independent variables in CHF relationship equation determination, and the unclear determination of CHF relationship equation development data and verification data. Thus, a more reasonable and accurate CHF relationship equation can be obtained, providing a design reference basis for reactor safety under reactor accident conditions and normal operation, thereby ensuring the safety of the reactor.

[0017] 2. The present invention proposes a method for determining the independent variables of the CHF relationship and a method for fitting the relationship based on the variance inflation factor and the stepwise regression method. This method can better avoid the problems of the CHF relationship lacking physical laws and collinearity between independent variables caused by the original commonly used least squares regression method not screening the independent variables, and obtain a more scientific and reasonable CHF relationship.

[0018] 3. The present invention adopts a stratified random sampling method to determine the CHF relationship development method for the fitting data set and the verification data set, which can make the relationship cover a wider database range. At the same time, it has the benefits of improving the generalization ability of the relationship and improving the credibility of CHF working condition prediction outside the experimental data, which is not available in traditional methods. DETAILED DESCRIPTION

[0019] The present invention is further described in detail below with reference to specific embodiments.

[0020] A method for automatically calculating the critical heat flux density of a reactor based on statistical principles comprises the following steps: S1. Based on the collected reactor CHF experimental data points, each set of data is arranged from left to right in each column: CHF experimental value qCHF, pressure P, mass flow rate G, steam content x, distance dg between the occurrence position and the upper grid, experimental grid span dg0, experimental section inlet temperature Tin, and the number of the heating rod where CHF occurs. The multiple sets of collected data are arranged downward in rows to form a preliminary database.

[0021] S2. Filter the data points and eliminate possible duplicate experimental points and cold rod critical points. For duplicate experimental points, repeated detection is performed based on mass flow rate, pressure and experimental section inlet temperature to remove duplicate experimental points. The specific criteria are that the difference in mass flow rate is no more than 5%, the experimental section inlet temperature is no more than 2°C, and the pressure is no more than 0.3MPa. Then it is judged as a duplicate experimental point; the cold rod critical point is determined based on the number of the heating rod where CHF occurs. The cold rod critical point is the working condition that occurs on the outermost 16 heating rods. Based on the preliminary database of step S1, a development database is formed after eliminating duplicate data points and cold rod critical points for subsequent CHF relationship development.

[0022] S3. Based on the stratified random sampling method, data is extracted from the development database. The development database is stratified by three parameters: pressure P, mass flow rate G, and vapor content x. Data is randomly sampled in each layer to form a fitting data set and a validation data set. Stratified random sampling ensures that the fitting data set and the validation data set can cover every data interval of the collected development data set. Specifically, pressure P is divided into 2 MPa intervals, mass flow rate is divided into 1 Mg / m 2 The sampling ratio of the fitting data set and the validation data set is 7:3.

[0023] S4. Based on the fitted data set, input the suspicious independent variables and combination items, estimate the curve form of the suspicious independent variables and combination items, and select the curve form of a single independent variable or combination item.

[0024] The input suspicious independent variables and combination terms include: pressure P, mass flow rate G, vapor fraction x; the ratio of the distance from the CHF location to the upper grid to the experimental grid span dg / dg0, and the multiplication terms of pressure, mass flow rate, and vapor fraction and this ratio Pdg / dg0, Gdg / dg0, and xdg / dg0 respectively; and the pairwise multiplication terms of pressure, mass flow rate, and vapor fraction PG, Px, and Gx.

[0025] Based on the fitted data set, curve estimation is performed on the input suspicious independent variables and combinations, and the curve form of a single independent variable or combination is selected. The basic forms of curve estimation include: linear, logarithmic, exponential, power function, polynomial, and S-type.

[0026] Adjusted R-squared To evaluate the goodness of the curve estimation. The calculation formula is: , Where, p is the number of independent variables, n For sample size, SST is the total sum of squared deviations, SSE is the residual sum of squares. From this, the curve form of each variable can be selected.

[0027] S5. Based on the fitted data set, the variance inflation factor method is used to conduct collinearity diagnosis on the independent variables and combination items in the selected curve form, and the independent variables and combination items with collinearity problems are eliminated.

[0028] Variance inflation factor is used to measure the correlation between predictor variables. Indicates X j The square of the multiple correlation coefficient in the regression model with the (independent variable or combination of variables being tested) as the response variable and the remaining predictor variables as independent variables, then X j Variance inflation factor VIF j Defined as: , in, p is the total number of independent variables. When the VIF exceeds a set value, the model is considered to be collinear, and this multicollinearity can excessively affect the predicted value. For CHF prediction, this value is set to 10. This yields the set of independent variables and combinations that have been tested and eliminated using the VIF.

[0029] S6. Use stepwise regression to obtain the optimal subset of independent variables based on the independent variables and combined terms. The goal of the stepwise regression method is to obtain the final independent variable terms of the relationship equation based on the independent variables and combined terms. The implementation process of stepwise regression analysis is to calculate the partial regression sum of squares for the variables introduced into the regression equation at each step. Then, the variable with the smallest partial regression sum of squares is selected and a partial F test is performed at a predetermined level. If it is significant, the variable does not need to be removed from the regression equation, and the other variables in the equation do not need to be removed (because the partial regression sum of squares of the other variables is greater than the smallest one, so they do not need to be removed). Conversely, if it is not significant, the variable needs to be removed, and the other variables in the equation are then tested in order from the smallest to the largest partial regression sum of squares. All variables with insignificant effects are eliminated, and only those that remain are significant. Next, the partial regression sum of squares of the variables not introduced into the regression equation is calculated, and the variable with the largest partial regression sum is selected. The partial F test is also performed at a given level. If it is significant, the variable is introduced into the regression equation. This process continues until no variables in the regression equation can be eliminated and no new variables can be introduced. At this time, the stepwise regression process ends. Finally, the optimal subset of independent variables is obtained.

[0030] The significance of the independent variable is characterized by the partial F test. j The partial F test formula for the independent variable is: , in, SSR is included j The regression sum of squares of the independent variables, SSR(j) Does not include j The regression sum of squares of the independent variables, SSE is included j The residual sum of squares of the independent variables, p is the number of independent variables, n is the sample size.

[0031] Then, the importance ranking analysis of each variable and combination item is obtained by standardizing the regression coefficient. The method of standardizing the regression coefficient is: subtract the mean of the corresponding coefficient from the original coefficient data and then divide it by the standard deviation of the coefficient. The obtained regression coefficient is the standardized regression coefficient, and the formula is as follows: .

[0032] According to the size of the standardized regression coefficient, the independent variables affecting the CHF program can be sorted from large to small.

[0033] S7. Form the final CHF relationship, which is as follows: , Among them, qCHFP is the predicted CHF value; Get the MEA / PRE mean and root mean square deviation of the fitted data set, the root mean square deviation of Mea / Pre RMSE The calculation formula is as follows: , in, i Indicates the i Data identifier, n represents the sample size, Mea represents the experimental CHF value, and Pre represents the predicted CHF value.

[0034] The Grubbs test method is used to perform outlier test and eliminate experimental outliers. The statistic in the Grubbs test method is: Since the standard deviation is unknown, the s statistic is used instead of the standard deviation. .

[0035] Calculation of the s statistic in the Grubbs test: , in, and s are the sample mean and sample standard deviation, respectively.

[0036] In the Grubbs test, the calculation of the two-sided test critical value G is: , Where, is the significance level, t represents the corresponding T test, and N is the number of samples.

[0037] S8. Based on the validation data set, verify the CHF relationship and obtain the Mea / Pre mean and root mean square difference of the validation data.

[0038] Example 1 The fitting and verification results based on 1003 reactor CHF data points are shown in Table 1. It can be seen that the present invention provides good prediction results for both the fitting data set and the verification data set.

[0039] Table 1

Claims

1. A method for automatically calculating the critical heat flux density of a reactor based on statistical principles, characterized in that The following steps are involved: S1. Based on the collected reactor CHF experimental data points, a preliminary database is formed; S2. Screen the data points and eliminate possible duplicate experimental points and cold rod critical points to form a development database for subsequent CHF relationship development; S3, based on the three parameters of pressure P, mass flow rate G, and vapor fraction x, a stratified random sampling method is used to extract data from the development database to determine the fitting data set and the validation data set; S4. Based on the fitted data set, input the suspicious independent variables and combination items, estimate the curve form of the suspicious independent variables and combination items, and select the curve form of the single independent variable or combination item; S5. Based on the fitted data set, the variance inflation factor method is used to conduct collinearity diagnosis on the independent variables and combination items in the selected curve form, and the independent variables and combination items with collinearity problems are eliminated; S6. Using a stepwise regression method, based on the independent variables and combination items obtained in step S5, an optimal subset of independent variables is obtained, and the importance ranking analysis of the individual variables and combination items is obtained by standardizing the regression coefficients; S7, forming the final CHF relationship, obtaining the mean and root mean square difference of Mea / Pre of the fitted data set, performing outlier test using the Grubbs test method, and eliminating experimental outliers; S8. Based on the validation data set, verify the CHF relationship and obtain the Mea / Pre mean and root mean square difference of the validation data.

2. The method for automatically calculating the critical heat flux of a reactor based on statistical principles according to claim 1, characterized in that: In step S1, the basic physical quantities required in the preliminary database are: CHF experimental value qCHF, pressure P, mass flow rate G, vapor fraction x, distance dg from the location where CHF occurs to the upper grid, experimental grid span dg0, experimental section inlet temperature Tin, and the number of the heating rod where CHF occurs.

3. The automated method for calculating reactor critical heat flux based on statistical principles according to claim 1, characterized in that: In step S4, the input suspicious independent variables and combination terms include: pressure, mass flow rate, vapor fraction; the ratio of the distance from the location where CHF occurs to the upper grid to the experimental grid span, and the product of pressure, mass flow rate, vapor fraction and this ratio; and the product of pressure, mass flow rate, and vapor fraction in pairs.

4. The method for automatically calculating the critical heat flux of a reactor based on statistical principles according to claim 3, characterized in that: In step S4, the curve form estimation includes the following basic forms: linear, logarithmic, exponential, power function, polynomial, and S-type.

5. The automated method for calculating reactor critical heat flux based on statistical principles according to claim 1, characterized in that: In step S6, the stepwise regression method is as follows: the independent variables and combination terms obtained in step S5 are introduced into the CHF relationship one by one, and a partial F test is performed after each introduction of a suspicious independent variable or combination term, and the explanatory variables that have been selected are tested one by one. When the originally introduced explanatory variable becomes no longer significant due to the introduction of the subsequent explanatory variable, it is deleted to ensure that only significant variables are included in the regression equation before each introduction of a new variable, until no significant explanatory variable is selected into the regression equation and no insignificant explanatory variable is eliminated from the regression equation.

6. The method for automatically calculating the critical heat flux of a reactor based on statistical principles according to claim 5, characterized in that: In step S6, the regression coefficient is standardized as follows: the original coefficient data is subtracted from the mean of the corresponding coefficient and then divided by the standard deviation of the coefficient. The obtained regression coefficient is the standardized regression coefficient. According to the size of the standardized regression coefficient, the CHF-influencing program sorts the independent variables from large to small.

7. The method for automatically calculating reactor critical heat flux based on statistical principles according to claim 1, characterized in that: In step S7, the root mean square difference of Mea / Pre RMSE The calculation formula is as follows: ， in, i Indicates the i Data identifier, n represents the sample size, M represents the experimental CHF value, P Indicates the predicted CHF value.

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