An intelligent design optimization method for a lead-bismuth reactor

Abstract

The present invention relates to an intelligent design optimization method for a lead-bismuth reactor, which includes: establishing a mathematical model of the lead-bismuth reactor to be optimized with a design space, a design objective function, and constraint conditions, conducting Latin hypercube sampling to generate sample points, calculating core characteristic parameters to construct a training data set, and using the BP neural network algorithm to establish a surrogate model S-LFR that can predict the core characteristic parameters of the lead-bismuth reactor; using the niche genetic algorithm Micro-GA to optimize the combination of design parameters predicted by the surrogate model S-LFR, updating the training data set and the surrogate model S-LFR, and repeatedly iterating to approach the target optimization interval until the global optimal solution is obtained. The present invention realizes the collaborative optimization of multi-objective, multi-physics, and multi-variable coupling of the lead-bismuth reactor core, greatly improves the design efficiency while ensuring the calculation accuracy, can automatically search for the optimization interval according to the design objective, and obtain the optimal design scheme.

Description

Technical Field

[0001] The present invention relates to the technical field of lead-bismuth reactor design optimization, and in particular to an intelligent design optimization method for lead-bismuth reactors. Background Art

[0002] Nuclear energy, with its characteristics of being clean, low-carbon, efficient, and sustainable, is expected to play an important role in the process of realizing sustainable energy utilization. Lead-bismuth reactors have good sustainability and strong natural circulation ability, can meet the demand for reliable energy supply in extreme environments, and have unique advantages in the comprehensive utilization of nuclear energy, attracting the key attention of major nuclear energy countries. Different application scenarios and mission function requirements have different energy output requirements (power × refueling cycle) for lead-bismuth reactors. Accordingly, there are significant differences in the optimization intervals of core parameters and reactor design schemes, and optimization methods and optimization strategies matching different energy output requirements need to be given.

[0003] The optimization design of lead-bismuth reactors is a complex multi-dimensional non-linear constrained optimization problem with the coupled influence of multiple physics, multiple variables, and multiple constraints, coupling the calculation and analysis of reactor physical characteristics, thermal-hydraulic characteristics, and structural material strength. Moreover, there is a large uncertainty introduced by nuclear reaction cross-sections, calculation model approximations, and calculation method errors in the calculation. When carrying out optimization for design objectives, there are interaction effects among different design variables and they jointly affect the design objectives. It is necessary to consider the coupled influence between design objectives and design variables and also meet physical, thermal, material, and other constraint conditions.

[0004] The existing optimization design of lead-bismuth reactors mainly adopts semi-empirical design methods, which are carried out based on the decoupling assumption that multiple design objectives and design variables are independent. The number of selected design variables is small and the range is narrow, making it difficult to systematically and comprehensively consider the multi-factor coupled influence in the miniaturization and lightweight design optimization of lead-bismuth reactors. When the existing single heuristic optimization algorithm is used for this complex non-linear constrained optimization problem of lead-bismuth reactor design optimization, a large number of random statistical samplings and simulation calculations are required, and it is difficult to ensure complete convergence of the optimization search within an acceptable calculation cost, and it is easy to fall into a local optimum. Therefore, it is urgent to develop a global optimization method research with random effects and capable of efficiently carrying out multi-factor collaborative design. Summary of the Invention

[0005] To solve the complexity problem of feature engineering in lead-bismuth reactor design and the multi-objective problem of core design optimization, the purpose of the present invention is to provide a lead-bismuth reactor intelligent design optimization method based on a neural network model and a genetic algorithm, which uses a multi-parameter and multi-objective collaborative optimization algorithm to optimize the combination of reactor design parameters, and while carrying out miniaturization and lightweight design optimization of lead-bismuth reactors, ensures the calculation efficiency.

[0006] To achieve the above objectives, the present invention adopts the following technical solutions:

[0007] An intelligent design optimization method for a lead-bismuth reactor, the method comprising the following steps in sequence:

[0008] Step (1) Establish a mathematical model of the lead-bismuth reactor to be optimized based on the design space, design objective function, and constraint conditions of the lead-bismuth reactor, conduct Latin hypercube sampling to generate sample points, and generate a training data set; use the training data set to construct a BP neural network model to obtain the lead-bismuth reactor design to-be-optimized model S-LFR;

[0009] Step (2) Use the BP neural network model to predict the design objective function of the design space to obtain a prediction set; use the niche genetic algorithm to optimize and verify the prediction set obtained by the BP neural network model prediction, add the interval data set that meets the constraint conditions to the training data set to update the BP neural network model and perform region reduction; iteratively optimize repeatedly until an optimal solution with a residual error meeting the accuracy requirements and converging is obtained.

[0010] Furthermore, step (1) specifically includes the following steps:

[0011] Step (1a) Establish a mathematical model of the lead-bismuth reactor to be optimized based on the design space, constraint conditions, and design objective function of the lead-bismuth reactor;

[0012] Step (1b) Determine the structure and input / output quantities of the BP neural network, and construct a BP neural network model;

[0013] Step (1c) Use the orthogonal Latin hypercube method to sample the design parameter region to generate a sample point set, calculate the actual design objective / constraint response values of the sample points, and perform data standardization to obtain a training data set;

[0014] Step (1d) Input the training data set into the BP neural network model for training to obtain the lead-bismuth reactor design to-be-optimized model S-LFR.

[0015] Furthermore, step (2) specifically includes the following steps:

[0016] Step (2a) Use the orthogonal Latin hypercube sampling method to sample the design independent variables in the design space to obtain a prediction set;

[0017] Step (2b) Substitute the prediction set into the lead-bismuth reactor design to-be-optimized model S-LFR to obtain the predicted values of the prediction set, and obtain the corresponding physical / thermal calculation prediction results through denormalization;

[0018] Step (2c) Use the physical / thermal calculation prediction results as the objective function, and use the niche genetic algorithm to optimize the design independent variables to obtain the optimal point;

[0019] Step (2d) calculates the response value of the true physical / thermal parameters corresponding to the optimal point for evaluation;

[0020] Step (2e) continuously updates the design region and the BP neural network model using the region reduction method and the principle of preferential point addition, iteratively searches for the optimal solution repeatedly, and outputs the optimal solution with the residual meeting the accuracy requirements and converging.

[0021] Furthermore, the specific steps of step (1a) are as follows:

[0022] Step (1a1) establishes a design space based on the lead-bismuth reactor, that is, determines the independent variable object of the optimization target and the optimization range. The formula for the independent variable design space is as follows:

[0023]

[0024] Among them, x1, x2, … x n is a set of design independent variables for reactor design optimization, L j and U j correspond to the upper and lower limits of the optimization of the design independent variables respectively. X is the design parameter vector of a specific reactor design scheme, is the design space composed of the design parameter vectors. Plan the independent variables and design space for optimization according to the optimization requirements;

[0025] Step (1a2) establishes constraint conditions, that is, determines the dependent variable and the constraint conditions of the mathematical model of the lead-bismuth reactor to be optimized. Combine the independent variable design space formula obtained in (1a1) to obtain the constraint conditions of the mathematical model of the lead-bismuth reactor to be optimized. The formula is as follows:

[0026]

[0027] Among them, y1, y2, … y n is a set of physical / thermal target response values calculated from the design independent variables, F i is a function combination including the design independent variables and the physical / thermal response values, L i and U i are the upper and lower limits of the function combination. Constrain the design independent variables and the physical / thermal response values according to the design requirements;

[0028] Step (1a3) establishes a design objective function, that is, determines the function model for judging the quality of the optimization effect. The formula is as follows:

[0029]

[0030] Among them, F iIt is a function combination that includes design independent variables and physical / thermal response values. F1(X) and F2(X) respectively reflect the optimization requirements of maximization and minimization.

[0031] Step (1a4) combines the lead-bismuth reactor design space, constraint conditions, and design objective function to obtain the mathematical model of the lead-bismuth reactor to be optimized. Its formula is:

[0032]

[0033] Furthermore, the specific steps of step (1b) are as follows:

[0034] In step (1b1), the optimization objective independent variables x1, x2,... x n and the design independent variables are used to calculate the physical / thermal response values y1, y2,... y n The training set and test set are divided and standardized. The formula for standardization is:

[0035]

[0036] where z is the value of the corresponding variable after standardization, x is the variable to be standardized, μ is the mean of the data set, and σ is the variance of the data set;

[0037] In step (1b2), the optimization objective independent variables x1, x2,... x n are used as the input of the fully connected layer of the BP neural network, and the physical / thermal response values y1, y2,... y n are used as the predicted response values of the BP neural network. Set the number of hidden layers, learning rate, batch size, and regularization coefficient of the BP neural network. The activation function is set to the non-linear activation function ReLu. The formula is as follows:

[0038]

[0039] where x is the input and f(x) is the output;

[0040] The optimizer is set to Adam for weight update. Its formula is:

[0041]

[0042] where m t is the first moment estimator of the gradient, i.e., momentum, v t is the second moment estimator of the gradient, i.e., squared gradient, and are the estimators after bias correction for momentum and squared gradient, θ t is the current parameter vector, θ t+1 is the updated parameter vector, gt is the current gradient, β1 and β1 are attenuation factors, and ∈ is a very small constant to maintain numerical stability.

[0043] Furthermore, the orthogonal Latin hypercube method in step (1c) generates a sample point set for sampling the design parameter area, specifically: the lead-bismuth reactor design data set in the sampling area is evenly divided into n areas with consistent probabilities, sampling is performed in each small interval, and then all the sampled data are aggregated and randomly arranged, so as to complete the sampling that takes into account both orthogonality and uniformity. The calculation formula is as follows:

[0044]

[0045] Among them, x j (1), x j (2)…, x j (n) is a random permutation from 1 to n, U ij It obeys the uniform random distribution in the interval U[0,1], n is the number of sampling points, and d is the dimension of the sampling points.

[0046] Further, the step (1d) specifically comprises the following steps:

[0047] Step (1d1) uses the mean square error of the training set loss function and the validation set loss function as the learning curve of the BP neural network model, inputs the training data set into the BP neural network model training iteration, until the training loss function and the validation set loss function gradually decrease and converge, then the iterative training is completed to obtain the model, if the requirements are not met, returns to step (1b) to reset the BP neural network parameters and train;

[0048] Step (1d2) calculates and verifies the prediction accuracy of the BP neural network model. If the accuracy requirement is not met, return to step (1b) to reset the BP neural network parameters and train. If the accuracy requirement is met, the BP neural network model of the lead-bismuth reactor design parameters is obtained and taken as the optimization object, that is, the lead-bismuth reactor design model to be optimized S-LFR.

[0049] Further, the step (2c) specifically comprises the following steps:

[0050] Step (2c1) initializes the population, divides each group into different microhabitats, selects the breeding father through a tournament, obtains the prediction result according to the S-LFR prediction of the model to be optimized in step (2b), restores it to the predicted value of the physical / thermal response value of the lead-bismuth reactor through denormalization, and brings it into the fitness function formula to calculate the fitness of each individual;

[0051] The denormalization formula is:

[0052] y=(m×σ)+μ

[0053] Among them, m is the predicted response value of the BP neural network, y is the predicted value of the restored physical / thermal response value of the lead-bismuth reactor, μ is the mean of the original data set, and σ is the variance of the original data set;

[0054] The fitness formula is:

[0055] F = w1·c1·y1 + w2·c2·y2 + … + w N ·c N ·y N

[0056] Among them, w1, w2, ……, w N are the required weights of the physical / thermal response values of the lead-bismuth reactor, c1, c2, ……, c N are the target coefficients, taking values of 1 and -1 respectively according to the requirements of maximization and minimization, and y1, y2, … y N are the physical / thermal response values predicted by the model S-LFR to be optimized, F is the fitness, which reflects the quality of the solution and affects the optimization and elimination process;

[0057] Step (2c2) generates the offspring population through single-point crossover and mutation operations, calculates the objective / constraint function values, combines the parent and offspring populations, and performs niche elimination operations according to the fitness;

[0058] Step (2c3) iterates repeatedly until the optimal point is found or the maximum number of iterations is reached, and then outputs the optimal point;

[0059] Step (2c4) further optimizes the optimal solutions of all niches to obtain the global optimal point.

[0060] Furthermore, the specific content of the said step (2d) is: calculating the physical / thermal response value of the actual target of the optimal point, verifying whether the accuracy meets the requirements, and evaluating and judging whether the optimal point meets the constraint conditions and improving the design objective function.

[0061] Furthermore, the specific content of the said step (2e) is: adding the optimal point that meets the accuracy requirements and conforms to the constraint conditions to the training set of the BP neural network model, training to generate a new neural network model, and repeating steps (2c), (2d) and (2e), and at the same time gradually reducing the interval range of the independent variables in the design space according to the optimal value result until the optimal solution with the residual meeting the accuracy requirements and converging is output.

[0062] From the above technical solutions, it can be seen that: the beneficial effects of the present invention are as follows:

[0063] First, the present invention uses the BP neural network model to achieve rapid prediction of the physical / thermal parameters of the lead-bismuth reactor. Compared with calculating the reactor parameters through the physical / thermal hydraulic calculation and analysis program of the lead-bismuth reactor, the time consumption is greatly shortened, effectively improving the calculation efficiency;

[0064] Second, the present invention uses a niche genetic algorithm for multi-objective collaborative optimization, breaking through the limitations of traditional single-objective optimization methods and avoiding the problems of slow efficiency and poor optimization effect in the manual optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a schematic diagram of the overall framework process of the optimization method of the present invention;

[0066] Figure 2 It is a schematic diagram of the niche genetic algorithm of the present invention;

[0067] Figure 3 It is a schematic diagram of the sequence iterative optimization analysis method based on the niche genetic algorithm of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0068] The present invention will be further described below in conjunction with the drawings and specific embodiments.

[0069] In a specific embodiment of the present invention, a design optimization method for a lead-bismuth reactor is proposed. Figure 1 It is a specific flowchart. The optimization process is mainly realized by combining a BP neural network model, a niche genetic algorithm and a sequence iterative optimization method.

[0070] Step 1: Establish a mathematical model of the lead-bismuth reactor to be optimized considering the design space, design objective function and constraint conditions of the lead-bismuth reactor. Conduct Latin hypercube sampling to generate sample points and calculate the training data set generated by the sample points. Use the training data set to construct a BP neural network model to obtain the lead-bismuth reactor design to-be-optimized model S-LFR;

[0071] Step 2: Use the BP neural network model to predict the design objective function of the design space; as Figure 2 shown, use the niche genetic algorithm to optimize and verify the data set predicted by the BP neural network model; adopt the sequence iterative optimization analysis method as Figure 3 shown, add the interval data set that meets the constraint conditions to the training set to update the BP neural network model and perform region reduction; perform sequence iteration and repeated optimization until an optimal solution with residuals meeting the accuracy requirements and converging is obtained.

[0072] An intelligent design optimization method for a lead-bismuth reactor, the method comprising the following steps in sequence:

[0073] Step (1) Establish a mathematical model of the lead-bismuth reactor to be optimized considering the design space, design objective function and constraint conditions of the lead-bismuth reactor. Conduct Latin hypercube sampling to generate sample points and generate a training data set; use the training data set to construct a BP neural network model to obtain the lead-bismuth reactor design to-be-optimized model S-LFR;

[0074] In step (2), use the BP neural network model to predict the design objective function of the design space to obtain a prediction set; use the niche genetic algorithm Micro-GA to optimize and verify the evaluation of the prediction set obtained by the BP neural network model prediction, add the interval data set that meets the constraint conditions to the training data set to update the BP neural network model and perform region reduction; perform sequential iteration and repeated optimization until an optimal solution with a residual satisfying the accuracy requirement and convergence is obtained.

[0075] Furthermore, step (1) specifically includes the following steps:

[0076] In step (1a), establish a mathematical model of the lead-bismuth reactor to be optimized based on the design space, constraint conditions, and design objective function of the lead-bismuth reactor;

[0077] In step (1b), determine the structure and input / output quantities of the BP neural network, and construct a BP neural network model;

[0078] In step (1c), use the orthogonal Latin hypercube method to sample the design parameter region to generate a sample point set, calculate the actual design objective / constraint response values of the sample points, and perform data standardization to obtain a training data set;

[0079] In step (1d), input the training data set into the BP neural network model for training to obtain the lead-bismuth reactor design model to be optimized S-LFR.

[0080] Furthermore, the said step (2) specifically includes the following steps:

[0081] In step (2a), use the orthogonal Latin hypercube sampling method to sample the design independent variables within the design space to obtain a prediction set;

[0082] In step (2b), substitute the prediction set into the lead-bismuth reactor design model to be optimized S-LFR to obtain the predicted values of the prediction set, and obtain the corresponding physical / thermal calculation prediction results through denormalization;

[0083] In step (2c), use the physical / thermal calculation prediction results as the objective function, and use the niche genetic algorithm to optimize the design independent variables to obtain the optimal point;

[0084] In step (2d), calculate the true physical / thermal parameter response values corresponding to the optimal point for evaluation;

[0085] In step (2e), use the region reduction method and the principle of preferential point addition to continuously update the design region and the BP neural network model, perform sequential iteration and repeated optimization, and output an optimal solution with a residual satisfying the accuracy requirement and convergence.

[0086] Furthermore, the said step (1a) specifically includes the following steps:

[0087] Step (1a1) establishes the design space based on the lead-bismuth reactor, that is, determines the independent variable objects of the optimization objective and the optimization range. The formula for the independent variable design space is as follows:

[0088]

[0089] where x1, x2, …, x n is a set of independent variables for reactor design optimization, L j and U j correspond to the upper and lower limits of the optimization of the independent variables respectively, X is the design parameter vector of a specific reactor design scheme, is the design space composed of the design parameter vectors. Plan the independent variables and design space according to the optimization requirements;

[0090] Step (1a2) establishes the constraint conditions, that is, determines the dependent variables and the constraint conditions of the mathematical model of the lead-bismuth reactor to be optimized. Combine the formula of the independent variable design space obtained in (1a1) to obtain the constraint conditions of the mathematical model of the lead-bismuth reactor to be optimized. The formula is as follows:

[0091]

[0092] where y1, y2, …, y n is a set of physical / thermal target response values calculated from a set of design independent variables, F i is a function combination including the design independent variables and the physical / thermal response values, L i and U i are the upper and lower limits of the function combination. Constrain the design independent variables and the physical / thermal response values according to the design requirements;

[0093] Step (1a3) establishes the design objective function, that is, determines the function model for judging the quality of the optimization effect. The formula is as follows:

[0094]

[0095] where F i is a function combination including the design independent variables and the physical / thermal response values. F1(X) and F2(X) respectively reflect the optimization requirements of maximization and minimization.

[0096] Step (1a4) Combining the lead-bismuth reactor design space, the constraint conditions and the design objective function, the mathematical model of the lead-bismuth reactor to be optimized can be obtained. The formula is:

[0097]

[0098] Furthermore, step (1b) specifically includes the following steps:

[0099] Step (1b1) performs optimization on the optimization target variables x1, x2, ... x determined in step (1a1). n The physical / thermal response values ​​y1, y2, ...y are calculated by the design independent variables n Divide the training set and test set, and perform standardization. The formula for standardization is:

[0100]

[0101] Among them, z is the standardized value of the corresponding variable, x is the variable to be standardized, μ is the mean of the data set, and σ is the variance of the data set;

[0102] Step (1b2) optimizes the target variables x1, x2, …x n As the input of the BP neural network fully connected layer, the physical / thermal response values ​​y1, y2, ...y n As the BP neural network predicts the response value, set the number of hidden layers, learning rate, batch sample number, and regularization coefficient of the BP neural network, and set the activation function to the nonlinear activation function ReLu. The formula is as follows:

[0103]

[0104] Among them, x is the input quantity and f(x) is the output quantity;

[0105] The optimizer is set to Adam to update the weights, and the formula is:

[0106]

[0107] Among them, m t is the first-order moment estimator of the gradient, i.e., momentum, v t is the second-order moment estimator of the gradient, that is, the squared gradient, and is the bias-corrected estimate of momentum and squared gradient, θ t is the current parameter vector, θ t+1 is the updated parameter vector, g t is the current gradient, β1 and β1 are attenuation factors, and ∈ is a very small constant to maintain numerical stability.

[0108] Furthermore, the orthogonal Latin hypercube method in step (1c) generates a sample point set for sampling the design parameter area, specifically: the lead-bismuth reactor design data set in the sampling area is evenly divided into n areas with consistent probabilities, sampling is performed in each small interval, and then all the sampled data are aggregated and randomly arranged, so as to complete the sampling that takes into account both orthogonality and uniformity. The calculation formula is as follows:

[0109]

[0110] Among them, x j (1), x j (2)…, x j (n) is a random permutation from 1 to n, U ij obeys a uniform random distribution in the interval U[0,1], n is the number of sampling points, and d is the dimension of the sampling points.

[0111] Furthermore, the step (1d) specifically includes the following steps:

[0112] In step (1d1), the mean square error of the training set loss function and the validation set loss function is used as the learning curve of the BP neural network model. The training data set is input into the BP neural network model for training iteration until both the training loss function and the validation set loss function gradually decrease and converge, then the iterative training is completed to obtain the model. If the requirements are not met, return to step (1b) to reset the BP neural network parameters and train again;

[0113] In step (1d2), calculate the prediction accuracy of the verified BP neural network model. If the accuracy requirement is not met, return to step (1b) to reset the BP neural network parameters and train again. If the accuracy requirement is met, obtain the BP neural network model of the lead-bismuth reactor design parameters and use it as the optimization object, which is the lead-bismuth reactor design model to be optimized S-LFR.

[0114] Furthermore, the step (2c) specifically includes the following steps:

[0115] In step (2c1), initialize the population, divide each group into different niches, select breeding parents through tournament selection, obtain the prediction result according to the model S-LFR to be optimized in step (2b), restore it to the predicted value of the physical / thermal response value of the lead-bismuth reactor through inverse normalization, and substitute it into the fitness function formula to calculate the fitness of each individual;

[0116] The denormalization formula is:

[0117] y = (m×σ) + μ

[0118] Among them, m is the predicted response value of the BP neural network, y is the predicted value of the restored physical / thermal response value of the lead-bismuth reactor, μ is the mean of the original data set, and σ is the variance of the original data set;

[0119] The fitness formula is:

[0120] F = w1·c1·y1 + w2·c2·y2 + … + W N ·c N ·y N

[0121] Among them, W1, w2, ……, wN is the required weight for the physical / thermal response values of the lead-bismuth reactor, c1, c2, …, c N is the target coefficient, taking values of 1 and -1 respectively according to the requirements of maximization and minimization, y1, y2, … y N is the physical / thermal response value predicted by the model S-LFR to be optimized, F is the fitness, which reflects the quality of the reaction solution and affects the optimization and elimination process;

[0122] Step (2c2) generates the offspring population through single-point crossover and mutation operations, calculates the values of the objective / constraint functions, combines the parent and offspring populations, and performs the niche elimination operation according to the fitness;

[0123] Step (2c3) iterates repeatedly until the optimal point is found or the maximum number of iterations is reached, and then outputs the optimal point;

[0124] Step (2c4) further optimizes the optimal solutions of all niches to obtain the global optimal point.

[0125] Furthermore, the specific content of the said step (2d) is: calculating the physical / thermal response value of the actual target of the optimal point, verifying whether the accuracy meets the requirements, and evaluating and judging whether the optimal point meets the constraint conditions and improving the design objective function.

[0126] Furthermore, the specific content of the said step (2e) is: adding the optimal point that meets the accuracy requirements and conforms to the constraint conditions to the training set of the BP neural network model, training to generate a new neural network model, and repeating steps (2c), (2d) and (2e), and at the same time gradually reducing the interval range of the independent variables of the design space according to the optimal value result until the optimal solution with the residual error meeting the accuracy requirements and converging is output.

[0127] The BP neural network algorithm simulates the connection and information transmission of human brain neurons. Its main structure includes an input layer, a hidden layer and an output layer, and realizes the learning of complex non-linear mapping relationships through forward propagation and backward propagation. Its advantages are strong adaptability, the ability to handle non-linear problems, strong generalization ability, suitability for large-scale data processing and self-adaptability. It has a wide range of applications, covering many fields such as image recognition, speech processing, financial prediction, medical diagnosis, etc., and has become an indispensable important tool in the fields of machine learning and artificial intelligence.

[0128] The niche genetic algorithm divides the initial population of the genetic algorithm into several sub-populations according to the geographical isolation technology in nature, and each sub-population evolves independently. The niche genetic algorithm maintains the diversity of the population while solving multi-objective optimization problems, reduces similar solutions through the niche elimination mechanism, prevents local optimal solutions caused by local convergence, and realizes the acquisition of global optimal solutions in the case of multiple objectives.

[0129] The sequence iteration of the BP neural network model finds the optimal solution through the niche genetic algorithm. According to the optimal solution, the regional reduction technique is used to gradually narrow the training interval, and the optimal solution is added to the training set according to the principle of selecting the best points to update the BP neural network model. Through this method, the design area where the optimal solution may exist can be reduced, the prediction accuracy of the BP neural network model can be ensured, and the overall optimization search efficiency can be improved.

[0130] In summary, the present invention uses the BP neural network model and the niche genetic algorithm to achieve the rapid optimization of the multi-physical coupling of the lead-bismuth reactor design parameters. On the one hand, it can help users avoid the subjectivity problems caused by expert human factors. Compared with the single-objective method, multi-objective optimization can alleviate the conflicts between objective functions through comprehensive optimization, obtain more solutions, and more balancedly reflect the user's needs according to the decision-making, realizing the collaborative optimization of multiple parameters and multiple objectives. On the other hand, the present invention combines the niche genetic algorithm with the regional reduction technique and the principle of selecting the best points, which can more quickly and accurately carry out the design optimization of the multi-objective coupling of the lead-bismuth reactor, and effectively avoid the problem of long calculation time of the lead-bismuth reactor physical / thermal-hydraulic calculation analysis program. Compared with calculating the reactor parameters through the lead-bismuth reactor physical / thermal-hydraulic calculation analysis program, the consumption time is greatly shortened, and the calculation efficiency is effectively improved.

Claims

1. A lead-bismuth reactor intelligent design optimization method, characterized in that: The method comprises the following steps in order: Step (1) establishing a mathematical model of the lead-bismuth reactor to be optimized based on the lead-bismuth reactor design space, design objective function and constraint conditions, performing Latin hypercube sampling to generate sample points, and generating a training data set; The BP neural network model was constructed using the training data set, and the lead-bismuth reactor design optimization model S-LFR was obtained; Step (2) Use the BP neural network model to predict the design objective function of the design space to obtain a prediction set; Use the niche genetic algorithm to optimize and verify the prediction set predicted by the BP neural network model, add the interval data set that meets the constraint conditions to the training data set to update the BP neural network model and perform region reduction; Iterate the sequence to repeatedly optimize until the optimal solution is obtained in which the residual meets the accuracy requirements and converges; Step (1) specifically includes the following steps: Step (1a) establishing a mathematical model of the lead-bismuth reactor to be optimized based on the lead-bismuth reactor design space, constraint conditions and design objective function; Step (1b) determining the structure and input / output of the BP neural network and constructing a BP neural network model; Step (1c) uses the orthogonal Latin hypercube method to sample the design parameter area to generate a sample point set, calculates the actual design target / constraint response value of the sample point, and performs data standardization to obtain a training data set; Step (1d) inputting the training data set into the BP neural network model training to obtain the lead-bismuth reactor design optimization model S-LFR; The step (1a) specifically comprises the following steps: Step (1a1) establishes the design space based on the lead-bismuth reactor, that is, determines the optimization target independent variable object and the optimization range. The independent variable design space formula is as follows: in, is a set of independent design variables for reactor design optimization, and They correspond to the optimization upper and lower limits of the design independent variables, is the design parameter vector for a particular reactor design, The design space composed of design parameter vectors, the independent variables and design space to be optimized are planned according to the optimization requirements; Step (1a2) establishes constraint conditions, that is, determines the dependent variable and the constraint conditions of the mathematical model of the lead-bismuth reactor to be optimized, and combines the independent variable design space formula obtained in (1a1) to obtain the constraint conditions of the mathematical model of the lead-bismuth reactor to be optimized, and the formula is as follows: in, It is a set of design independent variables to calculate the physical / thermal target response value. is a combination of functions including design independent variables and physical / thermal response values. and They are the upper and lower limits of the function combination, respectively, and they constrain the design independent variables and physical / thermal response values ​​according to design requirements; Step (1a3) establishes the design objective function, that is, determines the function model for judging the optimization effect. The formula is as follows: in, and Respectively reflect the optimization needs of maximization and minimization; Step (1a4) combines the lead-bismuth reactor design space, constraint conditions and design objective function to obtain the mathematical model of the lead-bismuth reactor to be optimized, and its formula is: 。 2. The method according to claim 1, characterized in that: The step (2) specifically includes the following steps: Step (2a) uses the orthogonal Latin hypercube sampling method to sample the design independent variables in the design space to obtain a prediction set; Step (2b) brings the prediction set into the lead-bismuth reactor design optimization model S-LFR to obtain the prediction value of the prediction set, and obtains the corresponding physical / thermal calculation prediction results by destandardization. Step (2c) uses the physical / thermal calculation prediction results as the objective function and uses a niche genetic algorithm to optimize the design independent variables to obtain the optimal point; Step (2d) calculates the actual physical / thermal parameter response value corresponding to the optimal point for evaluation; Step (2e) uses the area reduction method and the principle of optimal point addition to continuously update the design area and BP neural network model, iterate the sequence to repeatedly optimize, and the output residual meets the accuracy requirements and converges to the optimal solution.

3. The method according to claim 1, characterized in that: The step (1b) specifically comprises the following steps: Step (1b1) is to optimize the target variable determined in step (1a1) Calculate the physical / thermal response value with the design independent variable Divide the training set and test set, and perform standardization. The formula for standardization is: in, z is the standardized value of the corresponding variable, x is the variable to be standardized, is the mean of the data set, is the variance of the data set; Step (1b2) will optimize the target independent variable As the input of the BP neural network fully connected layer, the physical / thermal response value As the BP neural network predicts the response value, set the number of hidden layers, learning rate, batch sample number, and regularization coefficient of the BP neural network, and set the activation function to the nonlinear activation function ReLu. The formula is as follows: in, is the input quantity, is the output; The optimizer is set to Adam to update the weights, and the formula is: in, is the first-order moment estimator of the gradient, i.e., momentum, is the second-order moment estimator of the gradient, that is, the squared gradient, and are bias-corrected estimates of momentum and squared gradient, is the current parameter vector, is the updated parameter vector, is the current gradient, and is the attenuation factor, is a very small constant to maintain numerical stability.

4. The method according to claim 1, characterized in that: The orthogonal Latin hypercube method in step (1c) generates a sample point set by sampling the design parameter area. Specifically, the lead-bismuth reactor design data set in the sampling area is evenly divided into n areas with consistent probabilities, sampling is performed in each small interval, and all the sampled data are aggregated and randomly arranged, so as to complete the sampling that takes into account both orthogonality and uniformity. The calculation formula is as follows: Among them, x j (1), x j (2)…, x j (n) is a random permutation from 1 to n, It obeys the uniform random distribution in the interval U[0,1], n is the number of sampling points, and d is the dimension of the sampling points.

5. The method according to claim 1, characterized in that: The step (1d) specifically comprises the following steps: Step (1d1) uses the mean square error of the training set loss function and the validation set loss function as the learning curve of the BP neural network model, inputs the training data set into the BP neural network model for training iteration, until the training loss function and the validation set loss function gradually decrease and converge, then the iterative training is completed to obtain the model, if the requirements are not met, returns to step (1b) to reset the BP neural network parameters and train; Step (1d2) calculates and verifies the prediction accuracy of the BP neural network model. If the accuracy requirement is not met, return to step (1b) to reset the BP neural network parameters and train. If the accuracy requirement is met, the BP neural network model of the lead-bismuth reactor design parameters is obtained and taken as the optimization object, i.e., the lead-bismuth reactor design model to be optimized S-LFR.

6. The method according to claim 2, characterized in that: The step (2c) specifically comprises the following steps: Step (2c1) initializes the population, divides each group into different microhabitats, selects the breeding father through a tournament, obtains the prediction result according to the S-LFR prediction of the model to be optimized in step (2b), restores it to the predicted value of the physical / thermal response value of the lead-bismuth reactor through denormalization, and brings it into the fitness function formula to calculate the fitness of each individual; The denormalization formula is: in, The BP neural network predicts the response value. is the predicted value of the physical / thermal response of the reduced lead-bismuth reactor, is the mean of the original data set, is the variance of the original data set; The fitness formula is: in, , ,……, The required weights for the physical / thermal response values ​​of the lead-bismuth reactor, , ,……, is the target coefficient, which takes values ​​of 1 and -1 according to the requirements of maximization and minimization, Predict the physical / thermal response values ​​for the S-LFR model to be optimized. It is fitness, which reflects the quality of the solution and affects the optimization and elimination process; Step (2c2) generates a child population through single-point crossover and mutation operations, calculates the objective / constraint function value and merges the parent and child populations, and performs niche elimination operations based on fitness; Step (2c3) is iterated repeatedly until the optimal point is found or the maximum number of iterations is reached and the optimal point is output; Step (2c4) then performs optimization operations on the optimal solutions of all microhabitats to obtain the global optimal point.

7. The method according to claim 2, characterized in that: The step (2d) specifically refers to: calculating the physical / thermal response value of the actual target of the optimal point, verifying whether the accuracy meets the requirements, and evaluating whether the optimal point meets the constraint conditions and improving the design objective function.

8. The method according to claim 2, characterized in that: The step (2e) specifically refers to: adding the optimal point that meets the accuracy requirements and meets the constraints to the training set of the BP neural network model, training to generate a new neural network model, and repeating steps (2c), (2d) and (2e), while gradually reducing the interval range of the independent variables in the design space according to the optimal value results, until the output residual meets the accuracy requirements and converges to the optimal solution.

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