A genetic algorithm-based parameter automatic optimization method for nuclear reactor system analysis program

Abstract

The application discloses a nuclear reactor system analysis program parameter optimization method based on a genetic algorithm, which can automatically adjust modeling parameters of a nuclear reactor system analysis program based on the genetic algorithm, and improves the prediction accuracy of the program. The steps are as follows: 1. generating a modeling file of the nuclear reactor system analysis program; 2. reading the optimized parameters in the nuclear reactor system analysis program modeling file, and constructing a target function of a single-target optimization algorithm; 3. generating a population of the genetic algorithm by using the optimized parameters, starting the nuclear reactor system analysis program by using the parameters in the generated population to perform calculation, and obtaining the fitness of individuals in the population; 4. performing selection, genetic and mutation operations on the generated population to generate a new generation of population; 5. continuously executing the step 3 to the step 4 until the algorithm calculation converges or the maximum number of generations is reached, obtaining the optimal solution of the single-target optimization and outputting to the input card of the system analysis program.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nuclear reactor system, and particularly relates to a nuclear reactor system analysis program parameter optimization method based on a genetic algorithm. BACKGROUND

[0002] Nuclear reactor system analysis programs play an important role in the normal operation and accident analysis of reactors. Due to the strong professional nature and modeling requirements, researchers usually need a lot of practice before they can use such programs skillfully, which is not conducive to the popularization and verification of such software. At the same time, due to the large amount of temperature, pressure, flow and other data generated in the calculation of the system analysis program, it is difficult to evaluate the calculation results.

[0003] In order to optimize and verify the parameters of the system analysis program, the Vienna University, the Karlsruhe Institute of Technology (KIT) in Germany and other institutions apply the fast Fourier transform method to the result evaluation of the system analysis program, and propose a method of evaluating the calculation accuracy of the system analysis program based on the weighted average of the dimensionless average amplitude of each parameter. This method has been applied to the verification and parameter sensitivity of the system analysis program, and good results have been achieved.

[0004] However, when using the fast Fourier transform method to analyze the parameter sensitivity of the modeling of the system analysis program, although good results can be achieved, it is difficult to avoid the subjective influence of human beings in the modeling process. At the same time, even if the researchers have professional knowledge and program modeling experience, it is impossible to guarantee that the program can obtain the optimal modeling. The goal of using the fast Fourier transform method is to obtain the smallest weighted average of the dimensionless average amplitude, so the parameter optimization problem of the system analysis program can be condensed into a single-objective optimization problem. This kind of optimization problem can be solved by using various algorithms in machine learning. SUMMARY

[0005] In order to solve the problems existing in the prior art, a nuclear reactor system analysis program parameter optimization method based on a genetic algorithm is needed, which can automatically adjust the modeling parameters of the nuclear reactor system analysis program based on the genetic algorithm, improve the prediction accuracy of the system analysis program, and reduce the dependence of researchers on related modeling knowledge and experience.

[0006] To achieve the above purpose, the present application adopts the following technical solutions:

[0007] A nuclear reactor system analysis program parameter optimization method based on a genetic algorithm can automatically adjust the modeling parameters of the nuclear reactor system analysis program based on the genetic algorithm, improve the prediction accuracy of the system analysis program, and includes the following steps:

[0008] Step 1: modeling the nuclear reactor loop system in the nuclear reactor system analysis program to generate a modeling file;

[0009] Step 2: reading the node division, pipe area, pipe length, pipe volume, resistance coefficient, friction coefficient, heat exchange model and heat exchange area in the modeling file as optimization parameters, constructing the objective function of the single-objective optimization algorithm, and the expression of the objective function of the single-objective optimization algorithm is as follows:

[0010]

[0011] In the formula: m represents the number of optimization parameters; π j represents the jth optimization parameter, j = 1, 2, …, m; AA l represents the dimensionless average amplitude of the lth calculation result of the nuclear reactor system analysis program, and the calculation results include primary loop pressure, secondary loop pressure, pressure drop, coolant inventory, flow rate, fluid temperature, cladding temperature, collapse liquid level and core power, l is the number of optimization parameters, and N represents the number of calculation results; AA tot represents the weighted average value of the dimensionless average amplitude of each calculation result; w f,l represents the weighted factor of each calculation result;

[0012] Step 3: generating a population of genetic algorithm using the optimization parameters of the nuclear reactor system analysis program, selecting the inverse of the objective function as the fitness function, starting the nuclear reactor system analysis program with the parameters in the population to perform calculation, obtaining the calculation results of the nuclear reactor system analysis program, and using these calculation results to obtain the fitness of individuals in the population, which is specifically divided into the following steps:

[0013] Step 3-1: writing the parameters corresponding to the individuals in the population into the modeling file of the nuclear reactor system analysis program, starting the nuclear reactor system analysis program to perform calculation, comparing the obtained calculation results with the experimental values in the existing public literature, and constructing the following error function:

[0014] ΔF(t) = F calc (t) - F exp (t)

[0015] In the formula, ΔF(t) represents the error between the calculation results of the nuclear reactor system analysis program and the experimental values in the existing public literature, t is the time of calculation; F calc (t) represents the calculation results of the nuclear reactor system analysis program; F exp (t) represents the experimental values in the existing public literature.

[0016] Step 3-2: Fourier transform the error function above to obtain the dimensionless average amplitude AA of the nuclear reactor system analysis program calculation results:

[0017]

[0018] wherein: represents the value of the error ΔF(t) after fast Fourier transform at frequency f n ; represents the value of the experimental value F exp (t) after fast Fourier transform at frequency f n ; the expression of fast Fourier transform is as follows:

[0019]

[0020] wherein F(t) represents the value of the variable F in the time domain; i represents the imaginary unit; f n represents the frequency, wherein M is the calculation time step number set in the nuclear reactor system analysis program, and M=2 p+1 ; p is the index of the definition time point number; τ is the calculation time step, n is the angular frequency in the Fourier transform, n=0, 1,..., 2 p ; F k is the value of the variable at the kth time point;

[0021] Step 3-3: after obtaining the dimensionless average amplitude AA of the nuclear reactor system analysis program calculation results, the AA values of each parameter are weighted, and the weighting formula is as follows:

[0022]

[0023]

[0024] wherein w f,l is the weighting factor introduced for each calculation result; this introduces engineering judgment to a certain extent, and the calculation formula of the weighting factor is as follows:

[0025]

[0026] wherein: W exp,l represents the contribution related to the experimental accuracy; W saf,l represents the contribution of the safety relevance of the parameter, W exp,l and W saf,l must be set according to engineering judgment; W norm,l represents the contribution of the nuclear reactor primary loop pressure;

[0027] Step 3-4: calculate the fitness evaluation result of the population, and the fitness evaluation function is taken as:

[0028]

[0029] Step 4: Selection, genetic and mutation operations are performed on the population, the selection operation is performed by using a non-feedback remainder random selection operator, some individuals with fitness greater than 2 can be inherited into the next generation population, the genetic operation is realized by using an arithmetic crossover operator, and the mutation operation is realized by using a non-uniform mutation operator, thereby generating a new generation of population;

[0030] Step 5: Steps 3 to 4 are repeatedly executed until the genetic algorithm converges or the maximum number of generations is reached, the optimal solution of single-objective optimization is obtained and output to the modeling file of the nuclear reactor system analysis program, and the automatic optimization of the parameters of the nuclear reactor system analysis program is completed; the convergence criterion is that the following conditions are met in the continuous five generations of population:

[0031] AA tot ≤0.1.

[0032] The present application has the following advantages and beneficial effects:

[0033] 1. The results of the system analysis program are evaluated by using fast Fourier transform, which solves the problem that the results of the system analysis program cannot be effectively evaluated due to too many parameters, and provides an important reference for the verification and use of the system analysis program.

[0034] 2. The genetic algorithm is introduced to automatically optimize the parameters of the nuclear reactor system analysis program, which can greatly reduce the dependence on the relevant professional knowledge and modeling experience of researchers, so that researchers can focus more on the problem itself.

[0035] 3. The advantages of the genetic algorithm can be fully utilized, the risk of falling into a local optimal solution is reduced, and the algorithm is also easy to realize parallelization, so that the global optimal input parameters of the nuclear reactor system analysis program research problem can be obtained.

[0036] 4. The method of the present application is suitable for most current nuclear reactor system analysis programs such as RELAP5, TRACE and ATHLET, etc.

[0037] 5. The method of the present application is not only suitable for the parameter optimization of the nuclear reactor system analysis program, but also suitable for the automatic optimization of the parameters of other nuclear reactor simulation programs involving many analysis parameters. DETAILED DESCRIPTION

[0038] The present application will be further described in detail below in combination with specific embodiments:

[0039] The application provides a nuclear reactor system analysis program parameter optimization method based on a genetic algorithm, which can automatically optimize modeling parameters of a nuclear reactor system analysis program based on the genetic algorithm, improve the prediction accuracy of the system analysis program, and reduce the dependence of researchers on related modeling knowledge and experience.

[0040] Step 1: modeling a nuclear reactor loop system in a nuclear reactor system analysis program to generate a modeling file;

[0041] Step 2: reading node division, pipe area, pipe length, volume, resistance coefficient, friction coefficient, heat exchange model and heat exchange area in the nuclear reactor system analysis program modeling file as optimized parameters, constructing a target function of a single-objective optimization algorithm, and the target function expression of the single-objective optimization algorithm is as follows:

[0042]

[0043] In the formula, m represents the number of optimized parameters; π j represents the jth optimized parameter, j = 1, 2, …, m; AA l represents a dimensionless average amplitude of the lth calculation result of the nuclear reactor system analysis program, the calculation results including primary loop pressure, secondary loop pressure, pressure drop, coolant charge, flow, fluid temperature, cladding temperature, collapse liquid level and core power, in order to ensure the accuracy of the fast Fourier transform method, calculation results at different positions need to be selected, and the number of calculation results usually needs to be 20-25; l is the number of the optimized parameter, and N represents the number of calculation results; AA tot represents a weighted average value of the dimensionless average amplitudes of the calculation results; w f,l represents a weighted factor of each calculation result;

[0044] Step 3: generating a population of the genetic algorithm using the optimized parameters of the nuclear reactor system analysis program, selecting the inverse of the target function as the fitness function, starting the nuclear reactor system analysis program using the parameters in the population to perform calculation, obtaining the calculation results of the nuclear reactor system analysis program, and using the calculation results to obtain the fitness of individuals in the population, which is specifically divided into the following steps:

[0045] Step 3-1: writing the parameters corresponding to the individuals in the population into the nuclear reactor system analysis program modeling file, starting the nuclear reactor system analysis program to perform calculation, comparing the obtained calculation results with experimental values in existing public literatures, and constructing the following error function: ΔF(t) = F calc (t) - F exp (t) In the formula, ΔF(t) represents the error between the calculation results of the nuclear reactor system analysis program and the experimental values in the existing public literatures, and t is the calculation time; F calc(t) represents the result of the nuclear reactor system analysis program; F exp (t) represents the experimental value in the published literature.

[0046] Step 3-2: Fourier transform the above error function to obtain the dimensionless average amplitude AA of the result of the nuclear reactor system analysis program:

[0047]

[0048] In the formula: represents the value of the error ΔF(t) after fast Fourier transform at the frequency f n ; represents the value of the experimental value F exp (t) after fast Fourier transform at the frequency f n ; the expression of fast Fourier transform is as follows:

[0049]

[0050] In the formula, F(t) represents the value of variable F in the time domain; i represents the imaginary unit; f n represents the frequency, where M is the number of calculation time steps set in the nuclear reactor system analysis program, and M = 2 p+1 ; p is the index of the number of time points defined; τ is the time step of calculation, n is the angular frequency in Fourier transform, n = 0, 1,..., 2 p ; F k is the value of the variable at the kth time point;

[0051] Step 3-3: After obtaining the dimensionless average amplitude AA of the result of the nuclear reactor system analysis program, the AA values of each parameter are weighted, and the weighting formula is:

[0052]

[0053]

[0054] where w f,l is the weighting factor introduced for each calculation result; this introduces engineering judgment to some extent, and the calculation formula of the weighting factor is:

[0055]

[0056] where: W exp,l represents the contribution related to the experimental accuracy; W saf,l represents the contribution of the safety relevance of the parameter, W exp,l and W saf,l must be set according to engineering judgment; W norm,lrepresents the contribution of the primary loop pressure of the nuclear reactor;

[0057] Step 3-3: After obtaining the dimensionless average amplitude AA of the calculation results of the nuclear reactor system analysis program, the AA values of each parameter are weighted, and the weighting formula is:

[0058]

[0059]

[0060] wherein w f,l is the introduced weighting factor for each calculation result; this introduces engineering judgment to some extent, and the weighting factor calculation formula is:

[0061]

[0062] wherein: W exp,l represents the contribution related to experimental accuracy; W saf,l represents the contribution of the safety relevance of the parameter, W exp,l and W saf,l must be set according to engineering judgment; W norm,l represents the contribution of the primary loop pressure of the nuclear reactor; W exp,l , W saf,l and W norm,l must be set according to engineering judgment, and the specific values can refer to Table 1;

[0063] Table 1: Weighting factors of typical thermal-hydraulic parameters

[0064]

[0065] Step 3-4: Calculate the fitness evaluation results of the population, and the fitness evaluation function is taken as:

[0066]

[0067] Step 4: Perform selection, genetic and mutation operations on the population, use the no-replay remainder random selection operator for selection operation to ensure that some individuals with fitness greater than 2 can be inherited to the next generation population, use the arithmetic crossover operator for genetic operation, and use the non-uniform mutation operator for mutation operation, thereby generating a new population;

[0068] Step 5: Repeat steps 3 to 4 until the genetic algorithm converges or reaches the specified maximum number of generations, obtain the optimal solution of single-objective optimization and output to the modeling file of the nuclear reactor system analysis program, and complete the automatic optimization of the parameters of the nuclear reactor system analysis program. The maximum number of generations specified by the genetic algorithm is 20. The convergence criterion is that in the next five generations of population, the following conditions are met:

[0069] AA tot ≤0.1.

[0070] The genetic algorithm-based nuclear reactor system analysis program parameter optimization method provided by the application can automatically optimize the modeling parameters of a nuclear reactor system analysis program based on a genetic algorithm, and reduce the requirements of the system analysis program on the relevant professional knowledge and use experience of researchers. The method can also be used to solve the automatic parameter optimization problem of other reactor simulation programs. Meanwhile, the method is not limited by the field to which the simulation program belongs, and the simulation programs in other fields that need to be optimized can use the ideas used in the application.

[0071] The above is a further detailed description of the application in combination with specific preferred embodiments, and the specific embodiments of the application cannot be limited to this. For ordinary skilled persons in the technical field to which the application belongs, without departing from the concept of the application, a number of simple deductions or substitutions can be made, and all of them should be regarded as falling within the scope of patent protection determined by the claims submitted.

Claims

1. An automatic optimization method for nuclear reactor system analysis program parameters based on genetic algorithm, characterized in that: The system can automatically adjust the modeling parameters of nuclear reactor system analysis programs based on genetic algorithms, thereby improving the prediction accuracy of nuclear reactor system analysis programs and reducing researchers' reliance on relevant modeling knowledge and experience. Specifically, it includes the following steps: Step 1: Model the nuclear reactor loop system in the nuclear reactor system analysis program and generate a modeling file; Step 2: Read the node partitioning, pipe area, pipe length, pipe volume, resistance coefficient, friction coefficient, heat transfer model, and heat transfer area from the modeling file as the parameters to be optimized, and construct the objective function of the single-objective optimization algorithm. The expression of the objective function of the single-objective optimization algorithm is as follows: In the formula: m represents the number of parameters to be optimized; π j Let AA represent the j-th optimized parameter, where j = 1, 2, ..., m; l This represents the dimensionless average amplitude of the l-th calculation result from the nuclear reactor system analysis program. The calculation result includes primary loop pressure, secondary loop pressure, pressure drop, coolant charge, flow rate, fluid temperature, cladding temperature, collapse level, and core power; l is the number of the parameter being optimized; N represents the number of calculation results; AA tot w represents the weighted average of the dimensionless average amplitudes of the various calculation results. f,l This represents the weighting factor for each calculation result; Step 3: Generate a population for the genetic algorithm using the optimized parameters from the nuclear reactor system analysis program. Select the reciprocal of the objective function as the fitness function. Start the nuclear reactor system analysis program using the parameters in the population to perform calculations and obtain the calculation results. Use these calculation results to obtain the fitness of individuals in the population. This is specifically divided into the following steps: Step 3-1: Write the parameters corresponding to individuals in the population into the nuclear reactor system analysis program modeling file, start the nuclear reactor system analysis program to perform calculations, compare the obtained calculation results with experimental values, and construct the following error function: ΔF(t)=F calc (t)-F exp (t) In the formula, ΔF(t) represents the error between the calculation result and the experimental value of the nuclear reactor system analysis program, and t is the time of calculation; F calc (t) represents the calculation result of the nuclear reactor system analysis program; F exp (t) represents the experimental value; Step 3-2: Perform a Fourier transform on the above error function to obtain the dimensionless average amplitude AA of the calculation results from the nuclear reactor system analysis program: In the formula: This indicates that the error ΔF(t) at frequency f n The value after Fast Fourier Transform; Indicates the experimental value F exp (t) at frequency f n The value after Fast Fourier Transform (FFT); the expression for Fast Fourier Transform is as follows: In the formula, F(t) represents the value of variable F in the time domain; i represents the imaginary unit; f n Indicates frequency, Where M is the number of calculation time steps set in the nuclear reactor system analysis program, and we take M = 2. p+1 p is the exponent defining the number of time points; τ is the time step size for calculation; and n is the angular frequency in the Fourier transform, n = 0, 1, ..., 2. p ;F k The value of the variable at time k; Step 3-3: After obtaining the dimensionless average amplitude AA from the nuclear reactor system analysis program, the AA values ​​of each parameter are weighted using the following formula: Where w f,l This introduces a weighting factor for each calculation result; this introduces engineering judgment to some extent. The formula for calculating the weighting factor is: Among them: W exp,l Indicates the contribution related to experimental accuracy; W saf,l W represents the contribution of the parameter to the safety correlation. exp,l and W saf,l It must be set according to the project's requirements; W norm,l This indicates the contribution of the primary circuit pressure in a nuclear reactor. Steps 3-4: Calculate the fitness evaluation results of the population. The fitness evaluation function is taken as: Step 4: Perform selection, genetic and mutation operations on the population. Use a no-replay remainder random selection operator to ensure that some individuals with fitness greater than 2 can be inherited into the next generation. The genetic operation is implemented using the arithmetic crossover operator, and the mutation operation is implemented using the non-uniform mutation operator, thereby generating a new generation of population. Step 5: Repeat steps 3 and 4 until the genetic algorithm converges or reaches the specified maximum number of generations, obtaining the optimal solution for the single-objective optimization and outputting it to the modeling file of the nuclear reactor system analysis program, thus completing the automatic optimization of the nuclear reactor system analysis program parameters; the convergence criterion is that the following conditions are met within five consecutive generations of the population: AA tot ≤0.1。

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