Multi-objective optimization method for performance of plate-shaped fuel

Abstract

The invention discloses a multi-objective optimization method for performance of plate-shaped fuel. The method comprises the following steps: 1, carrying out model related setting in a fuel performance analysis program; 2, determining decision variables, optimization objectives and constraint conditions required by the multi-objective optimization method; 3, determining the number of individuals of each generation of population and the maximum number of iterations; 4, selecting a required multi-objective optimization algorithm, and performing population initialization operation; 5, introducing an elitist strategy, performing non-dominated sorting and distributing fitness; 6, calculating a non-dominated set optimization individual congestion degree and a constraint violation degree; 7, inputting the population individuals into a fuel performance analysis program, and respectively carrying out irradiation thermal hydraulic coupling calculation to obtain an optimization target value; 8, performing operations such as selection, crossover and variation on the current population individuals, and evolving to generate a filial generation population; 9, repeating the steps 5-8 until the algorithm judges that the optimization process is converged or the maximum number of iterations is reached; and 10, outputting an optimal solution set, namely design parameter information of p groups of dispersion particle diameters and pellet matrix thickness containing the optimized target value.

Description

Technical Field

[0001] The invention belongs to the technical field of fuel element performance optimization, and specifically relates to a multi-objective optimization method for plate fuel performance, which is suitable for optimizing the performance of plate fuel elements under parameters such as different dispersed particle sizes. Background Art

[0002] In a nuclear reactor system, the fuel assembly is the most core component, in which a chain reaction is carried out to generate heat to realize the operation of the nuclear reactor. Compared with rod-shaped fuel, plate-shaped fuel has a compact structure, high fuel consumption and high thermal conductivity, and can achieve a higher power density. Due to its structural characteristics, the coolant flow channel is narrow. Considering the effects of multiple physical fields such as irradiation, the flow and heat transfer are complex and the operating conditions are harsh. Plate-shaped fuel elements may face problems such as flow channel blockage, unstable flow, flow-induced vibration, core cracking and bubbling, which may cause accidents such as coolant evaporation and sudden rise in plate temperature. Therefore, optimizing the performance of fuel elements is very important for improving the safety and reliability of reactors.

[0003] The conventional optimization design of plate-shaped fuel elements relies on experience and trial and error methods, and lacks a systematic optimization process. In actual engineering, there are often multiple optimization problems that are as optimal as possible within a given range. The optimization of one of the objectives must be at the expense of other objectives. There is no unique optimal parameter that satisfies all objectives at the same time. This is a typical multi-objective optimization problem. As an effective optimization tool, the multi-objective optimization algorithm can consider multiple optimization objectives at the same time. At present, the research on multi-objective optimization methods in the nuclear field includes fuel replacement optimization, fuel element design, radiation shielding design, etc., but it is rarely used in nuclear fuel design. Comprehensively considered, its geometric design and microscopic particle size are crucial to fuel performance. Optimizing the plate-shaped fuel element parameters as the standard and finding suitable plate-shaped fuel element geometric parameters are of great significance for improving the thermal-hydraulic properties of fuel elements.

[0004] In view of the above background, this patent proposes a method for optimizing the particle parameters of plate-shaped fuel elements by combining a fuel performance analysis program simulation. Summary of the invention

[0005] In order to achieve key performance optimization of plate fuel elements under complex service conditions, the purpose of the present invention is to provide a multi-objective optimization method for plate fuel performance. The multi-objective optimization method can balance multiple desired optimization objectives and obtain a set of better solutions with better comprehensive performance.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A multi-objective optimization method for plate fuel performance is proposed. Based on the fuel performance analysis program, by combining the multi-objective optimization genetic algorithm, the fuel performance analysis program outputs the optimization target performance value for the multi-objective optimization process under different particle diameters and volume fractions, thus realizing the multi-objective optimization of fuel thermal performance under joint simulation.

[0008] The method comprises the following steps:

[0009] Step 1: Determine the material thermal mechanical model in the fuel performance analysis program, establish the fuel element pellet cladding geometry model, perform meshing settings, set solid domain constraint boundary conditions, coolant temperature, and flow heat transfer boundary conditions;

[0010] Step 2: Determine the decision variables, optimization objectives and constraints required for the multi-objective optimization method: the decision variables are the diameter of the dispersed fuel particles and the thickness of the fuel pellet matrix; the constraints are the relationship between the particle volume fraction and the diameter; the optimization objectives are to reduce the pellet peak temperature, reduce the Mises stress, and reduce the pellet volume strain;

[0011] Step 3: Considering the computational efficiency of the fuel performance analysis program and the complexity of the plate fuel element model in the fuel performance analysis program, the number of individuals p in each generation of population is determined, and the maximum number of iterations is set to c;

[0012] Step 4: Select the required multi-objective optimization algorithm: Non-dominated Sorting Genetic Algorithm NSGA-Ⅱ, and perform population initialization operation according to the range of decision variables;

[0013] Step 5: Introduce the elite strategy, perform non-dominated sorting and allocate fitness;

[0014] Step 6: According to the non-dominated sorting genetic algorithm operator, calculate the crowding degree and constraint violation degree of the non-dominated set optimization individual;

[0015] Step 7: Input the population individuals of different decision variables into the fuel performance analysis program, perform irradiation thermal-hydraulic coupling calculations respectively, and obtain the optimized target performance value;

[0016] Step 8: For the non-dominated sorting genetic algorithm, according to the non-dominated sorting genetic algorithm operator, the selection, crossover and mutation operations are performed on the individuals of the current population to evolve and generate the offspring population;

[0017] Step 9: Repeat steps 5 to 8 until the non-dominated sorting genetic algorithm determines that the optimization process converges, or reaches the maximum number of iterations c;

[0018] Step 10: Output the optimal solution set, i.e., the design parameter information of p groups of dispersed fuel particle diameters and fuel pellet matrix thicknesses containing the optimization target values, and select the optimal solution that meets the requirements.

[0019] The present invention has the following advantages and innovations:

[0020] 1) Based on the high-precision fuel performance analysis program, it can optimize the design parameters of plate-shaped fuel elements;

[0021] 2) In the field of fuel performance optimization, different from traditional optimization methods, the multi-objective optimization method is adopted, which can balance multiple optimization objectives and obtain a set of better solutions with better performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of the multi-objective optimization method for plate fuel performance of the present invention.

[0023] Figure 2 Schematic diagram of a representative microscopic unit of plate-shaped fuel. DETAILED DESCRIPTION

[0024] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0025] The present invention discloses a multi-objective optimization method for plate fuel performance combined with a fuel performance analysis program. The optimization method flow is shown in the attached Figure 1 The representative unit structure of the plate-shaped fuel is shown in the attached figure. Figure 2 shown.

[0026] The method comprises the following steps:

[0027] Step 1: Perform model calculation related settings in the fuel performance analysis program BEEs-Plates. BEEs-Plates is a plate fuel performance analysis program developed by the Thermal Hydraulics Research Laboratory of Xi'an Jiaotong University based on the open source finite element analysis platform MOOSE (The Multi-physics Object Oriented Simulation Environment). The program includes thermal mechanical models such as three-dimensional heat conduction, fuel densification, thermal expansion, irradiation growth, and stress-strain calculation. At the same time, a zero-dimensional point reactor neutron mechanics and a one-dimensional coolant flow heat transfer model are established. On the basis of the above, the BEEs-Plates program also adds a representative unit module of dispersed plate fuel particles, which can consider the microscopic characteristics of dispersed fuel particles, study the microscopic behavioral characteristics of fuel particles, and realize cross-dimensional multi-physics field coupling solution with the three-dimensional fuel model. In this optimization method, a microscopic fuel particle model is used for program simulation calculations.

[0028] The setting process of the fuel performance analysis program is as follows: determine the material thermomechanical model, including the material property model of U3Si2 and Al and the behavior model of radiation swelling. Establish the geometric model of the micro-unit and macroscopic whole of the dispersed plate fuel element; set the solid domain constraints, coolant inlet velocity and inlet temperature, and flow outlet pressure boundary conditions; use structured grids for grid division, and layer them according to the plate width direction to improve the calculation robustness;

[0029] Step 2: Determine the decision variables, optimization objectives and constraints required for the multi-objective optimization method. The multi-objective optimization method is widely used in engineering problems that focus on multi-parameter optimization. Its main parameters are decision variables and ranges, optimization objective functions, the number of individuals in each generation, and iteration termination conditions.

[0030] For the method of the present invention, in the particle microscopic model, the fuel particles are filled in the fuel matrix at equal intervals, and the decision variables can be set to the diameter d of the dispersed fuel particles, the thickness w of the fuel pellet matrix, etc. The optimization constraint is the constraint relationship between the particle volume fraction and the particle diameter. According to the particle diameter and the matrix thickness, the volume of the particle and the matrix can be calculated respectively, and then the volume fraction of the particle in the matrix can be calculated. The volume fraction needs to be limited to the range of 0.25 to 0.45. The optimization objectives are set to reduce the pellet peak temperature, reduce the Mises stress, and reduce the pellet volume strain;

[0031] Step 3: Set the iterative process parameters in the multi-objective optimization process. The optimization iteration process mainly includes setting the optimization algorithm population for each generation and the iteration termination conditions. Considering the computational efficiency of the fuel performance analysis program and the complexity of the plate fuel element model in the fuel performance analysis program, the number of individuals p in each generation of the population is determined, and the maximum number of iterations can be set to c. If the change in each optimization result is less than the set threshold, the optimization algorithm is judged to have converged, then the iteration can be terminated and the population optimization result can be output;

[0032] Step 4: Select a multi-objective optimization algorithm suitable for the current problem, such as the non-dominated sorting genetic algorithm NSGA-Ⅱ, the decomposition-based multi-objective evolutionary algorithm MOEA / D, etc. According to the number of individuals p in the population mentioned in the previous step, randomly generate individuals x1, x2, ..., x in all decision variable spaces. p , perform population initialization operation. The decision variable space is the possible value range formed by the upper and lower limits of the decision variables;

[0033] Step 5: The algorithm introduces the elite strategy. In addition to the first initialization, the newly generated offspring population is merged with the parent population to form a whole and then non-dominated sorting is performed. This can include more feasible solutions and expand the solution space. Perform non-dominated sorting to sort the individuals in the population and generate a set of individuals in the population with different non-dominated levels from high to low;

[0034] Step 6: Calculate the crowding and constraint violation of the non-dominated set optimization individuals. NSGA-Ⅱ adopts the concept of crowding to improve the diversity and uniformity of the solution set. The algorithm first determines the nearest points on both sides of the population individuals in the objective function coordinate system, and then uses the area or volume value formed by the nearby points as the crowding value. For the solution set individual x, the constraint violation is represented by CV(x), which means the difference between the decision variable and the constraint value. CV(x) is non-negative, and the larger its value, the higher the constraint violation of the solution;

[0035] Step 7: Input the decision variable parameters of the population individuals generated in the previous steps into the fuel performance analysis program BEEs-Plates, specifically the diameter d of the dispersed fuel particles and the thickness w of the fuel pellet matrix. When running BEEs-Plates, the input parameters affect the fuel mechanical mechanics and temperature modules, which are transmitted from the microscopic to the macroscopic plate-shaped fuel as a whole through the representative unit model, and then coupled with the one-dimensional coolant module for iterative calculation. For individuals with different parameters, a series of pellet peak temperature, Mises stress, and pellet volume strain values ​​can be calculated and passed back to the multi-objective optimization algorithm as the optimization target value;

[0036] Step 8: For the non-dominated sorting genetic algorithm, according to the non-dominated sorting genetic algorithm operator, the current population individuals are selected, crossed, and mutated to evolve and generate offspring populations. Selection is performed through the roulette selection method, and the selection probability and survival probability of individuals are determined according to the proportion of chromosome fitness values; crossover is to replace and reorganize part of the parent individual structure to generate new individuals, and the methods include crossover, recombination, and rearrangement; mutation is the operation of random changes in gene coding based on small perturbations when offspring are generated, which can be divided into binary mutation, real number mutation, and sequence mutation. All three genetic operator operations are performed in a probabilistic manner, which enhances the global search performance.

[0037] Step nine: Repeat steps five to eight until the non-dominated sorting genetic algorithm determines that the optimization process has converged, or reaches the maximum number of iterations c. The non-dominated sorting genetic algorithm mainly uses a fitness evaluation method based on Pareto sorting. Through continuous evolution and iteration, it can gradually approach the Pareto optimal solution set of multi-objective optimization problems. If the value of the optimal solution set tends to stabilize with the iteration, and the difference between the parent and offspring individuals is less than the set limit, the non-dominated sorting genetic algorithm determines that the optimization process has converged. The maximum number of iterations c can be set freely, for example, in the range of 8 to 20 times;

[0038] Step 10: The algorithm ends the iteration and outputs the optimal solution set, which contains the parameter information of p groups of dispersed particle diameters d and core block matrix thickness w corresponding to the optimization target value. The solution sets with different performances form the Pareto frontier in the target space, with optimization targets with different tendencies. The individual solutions in the solution set can be used as a reference for researchers to select the optimal solution with appropriate performance.

[0039] The above content is a further detailed description of the present invention in combination with a specific preferred embodiment. It cannot be determined that the specific embodiments of the present invention are limited to this. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the present invention and the scope of patent protection determined by the submitted claims.

Claims

1. A multi-objective optimization method for plate fuel performance, characterized in that: On the basis of the fuel performance analysis program, by combining the multi-objective optimization genetic algorithm, the fuel performance analysis program outputs the optimized target performance value for the multi-objective optimization process under different particle diameters and volume fractions, realizing the multi-objective optimization of fuel thermal performance under joint simulation; The method comprises the following steps: Step 1: Determine the material thermal mechanical model in the fuel performance analysis program, establish the fuel element pellet cladding geometry model, perform meshing settings, set solid domain constraint boundary conditions, coolant temperature, and flow heat transfer boundary conditions; Step 2: Determine the decision variables, optimization objectives and constraints required for the multi-objective optimization method: the decision variables are the diameter of the dispersed fuel particles and the thickness of the fuel pellet matrix; the constraints are the relationship between the particle volume fraction and the diameter; the optimization objectives are to reduce the pellet peak temperature, reduce the Mises stress, and reduce the pellet volume strain; Step 3: Considering the computational efficiency of the fuel performance analysis program and the complexity of the plate fuel element model in the fuel performance analysis program, the number of individuals p in each generation of population is determined, and the maximum number of iterations is set to c; Step 4: Select the required multi-objective optimization algorithm: Non-dominated Sorting Genetic Algorithm NSGA-Ⅱ, and perform population initialization operation according to the range of decision variables; Step 5: Introduce the elite strategy, perform non-dominated sorting and allocate fitness; Step 6: According to the non-dominated sorting genetic algorithm operator, calculate the crowding degree and constraint violation degree of the non-dominated set optimization individual; Step 7: Input the population individuals of different decision variables into the fuel performance analysis program, perform irradiation thermal-hydraulic coupling calculations respectively, and obtain the optimized target performance value; Step 8: For the non-dominated sorting genetic algorithm, according to the non-dominated sorting genetic algorithm operator, the current population individuals are subjected to selection, crossover, and mutation operations to evolve and generate offspring populations; Step 9: Repeat steps 5 to 8 until the non-dominated sorting genetic algorithm determines that the optimization process converges, or reaches the maximum number of iterations c; Step 10: Output the optimal solution set, i.e., the design parameter information of p groups of dispersed fuel particle diameters and fuel pellet matrix thicknesses containing the optimization target values, and select the optimal solution that meets the requirements.

2. A multi-objective optimization method for plate fuel performance according to claim 1, characterized in that: In step eight, selection is performed through the roulette wheel selection method, and the selection probability and survival probability of the individual are determined according to the ratio of the chromosome fitness value; crossover is to replace and recombine part of the structure of the parent individual to produce a new individual, and the methods include crossover, recombination and rearrangement; mutation is the operation of random changes in gene coding based on small disturbances when offspring are generated, which is divided into binary mutation, real number mutation and serial mutation; the three genetic operator operations are all performed in a probabilistic manner, which enhances the global search performance.

3. A multi-objective optimization method for plate-shaped fuel performance according to claim 1, characterized in that: In step nine, the non-dominated sorting genetic algorithm adopts a fitness evaluation method based on Pareto sorting, and gradually approaches the Pareto optimal solution set of the multi-objective optimization problem through continuous evolution and iteration; if the value of the optimal solution set tends to be stable with the iteration, and the difference between the parent and offspring individuals is less than the set limit, the non-dominated sorting genetic algorithm determines that the optimization process has converged.

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