Radiation shielding multi-objective optimization design method based on Bayesian neural network

Abstract

The invention provides a radiation shielding multi-objective optimization design method based on a Bayesian neural network, and the method is characterized in that the method comprises the following steps: S1, obtaining sample data; s2, network construction and evaluation; s3, robust design optimization is carried out; according to the method, cognitive uncertainty in the modeling process of an agent model is quantified by using a loss function based on variational inference and KL divergence derivation, a nuclear radiation shielding calculation agent model considering uncertainty factors is obtained, and radiation shielding calculation is performed on an objective function in multi-objective optimization design through the constructed agent model. And a Pareto optimal solution set with certain robustness is obtained in combination with robust optimization design. According to the method, prior distribution is added to the weights of a neural network model, then the change conditions of the weights when data are given are obtained to measure the cognitive uncertainty in radiation shielding simulation, and the robustness of an optimization result is improved.

Description

Technical Field

[0001] The invention relates to the field of nuclear facility radiation shielding calculation, and in particular to a radiation shielding multi-objective optimization design method based on a Bayesian neural network. Background Art

[0002] With the rapid development of advanced nuclear facilities, radiation shielding and reinforcement design have become increasingly important. Lightweight and compactness are important development directions for radiation shielding of high-performance nuclear facilities, especially for mobile and compact nuclear devices, such as nuclear-powered ship reactors, space reactors and other systems. The available space of these nuclear facilities is limited, and the weight of the shielding structure is also limited. It is necessary to ensure shielding performance while taking into account mobility.

[0003] Traditional radiation shielding design is an inefficient and non-optimal process. Designers often propose initial design solutions based on actual engineering experience, and then obtain the final shielding solution after a large number of calculations and updates and iterations. This method requires designers to have rich engineering design experience and clear design ideas. It is greatly affected by human factors and it is impossible to judge whether it is the optimal solution. In addition, there are many uncertain factors in actual design and optimization problems, which inevitably disturb the shielding design parameters, resulting in fluctuations in shielding performance and making the shielding effect fail to meet design expectations.

[0004] In addition, radiation shielding calculation is also an extremely complex process. Commonly used radiation shielding calculation methods include deterministic method and Monte Carlo method: the deterministic method is to establish relevant models based on actual mathematical and physical problems, and use various numerical solution methods to calculate the approximate solution of the Boltzmann transport equation. The calculation results are relatively accurate, but the ability to handle complex scenarios is relatively lacking; the Monte Carlo method is based on statistical experiments. It obtains approximate solutions by simulating random transport processes. It can handle complex three-dimensional radiation shielding problems, but the speed of solving approximate solutions with a higher given confidence level is slow.

[0005] In combination with the design requirements of radiation shielding for nuclear facilities, in view of the current design problems of low efficiency, non-optimal solutions and interference from uncertain factors, it is urgent to propose a rapid multi-objective optimization design method for radiation shielding taking into account uncertain factors, so as to provide design guidance for the optimization problem of radiation shielding. Summary of the invention

[0006] In view of this, the present invention proposes a multi-objective optimization design method for radiation shielding based on Bayesian neural network, which combines the Bayesian neural network (BNN) considering uncertainty factors with the nuclear Monte Carlo program, constructs a BNN proxy model through the data of simulation calculation results, and uses the BNN proxy model for prediction in the multi-objective optimization process based on non-dominated sorting algorithm (NSGA-Ⅱ).

[0007] To achieve the above object, the technical solution proposed by the present invention is as follows:

[0008] A multi-objective optimization design method for radiation shielding based on a Bayesian neural network, characterized by comprising the following steps:

[0009] Step S1: Sample data acquisition. This step is to obtain training samples from the radiation simulation model. First, establish the basic model of radiation shielding simulation. Second, clarify the optimization design objectives, determine the optimization design variables and their value ranges. Then, randomly generate uniform samples and convert them into corresponding radiation shielding simulation models. Finally, perform radiation shielding calculations to obtain the radiation shielding simulation data available for training;

[0010] Step S2: Network construction and evaluation. This step is to construct a radiation shielding calculation surrogate model under uncertain conditions to accelerate the subsequent multi-objective optimization process. Preprocess the data obtained in Step S1, divide the data set into a training set, a validation set and a test set, use the training set to train the BNN network structure, use the validation set to adjust the network hyperparameters until the error meets the accuracy requirements or reaches the maximum number of iterations, obtain the trained model, and use the test set to evaluate the generalization ability of the final model;

[0011] Step S3: Robust design optimization. This step is to use the constructed Bayesian neural network, comprehensively consider the uncertain factors affecting the radiation shielding calculation results, and perform multi-objective optimization design on the shielding scheme based on the NSGA-II algorithm. Randomly generate the initial population, set the sampling value, use the BNN model obtained in Step S2 to perform sampling prediction calculations, obtain the output mean and standard deviation of the current population, and use the output results to perform robust design optimization until the convergence condition is met, and then the final Pareto optimal solution set can be obtained.

[0012] Further, the steps of obtaining sample data in Step S1 include:

[0013] Step S11: Establish the basic model of radiation shielding simulation, and the following data need to be configured:

[0014] Geometric model, including the simplified shapes, sizes and positions of each module in the nuclear facility; material information, including the material density, material nuclides, nuclide ratios and nuclide cross-section databases of each module in the nuclear facility; source term information, including the shape, type, position, direction and energy size of the source; counting information, including the type of statistical results and whether they are converted into dose rates.

[0015] Step S12: Clarify the design objectives and design variables, specifically including:

[0016] Taking the minimization of the neutron / γ-ray normalized dose rate, the total weight of the shielding structure, the total volume of the shielding structure, the economic cost, etc. as the design objectives; taking the types of materials, material thicknesses, material arrangement orders, nuclide contents, etc. of each shielding structure as design variables, and given the value ranges or discrete values of the design variables.

[0017] Step S13: Generate random uniform samples using Latin hypercube sampling, specifically including:

[0018] In the n-dimensional vector space, divide each dimension into m non-overlapping intervals with the same probability; randomly generate a number according to the uniform distribution within the m intervals of each dimension; shuffle the order of the m random numbers in each dimension, randomly select a random number from each dimension, and form an n-dimensional vector with them; repeat the extraction process until all m random numbers in each dimension are extracted.

[0019] Step S14: Convert the sample values into a radiation shielding simulation model, then perform radiation shielding calculations, and construct a radiation shielding simulation dataset, specifically including:

[0020] Update the geometric or material parameter values of the model in the radiation simulation file with the random sample values generated by Latin hypercube sampling; calculate the shielding result data through Monte Carlo particle transport software, and then combine it with the input variable values to form a radiation shielding simulation dataset available for training.

[0021] Furthermore, the steps of network construction and evaluation in step S2 include:

[0022] Step S21: Data preprocessing, specifically including:

[0023] First, perform logarithmic processing with base 10 on the shielding data, then perform normalization processing on the logarithmically processed data, and divide the dataset into a training set, a validation set, and a test set.

[0024] Step S22: Construction of a Bayesian neural network, specifically including:

[0025] The network consists of 1 input layer, m hidden layers, and 1 output layer; the number of neurons in the input layer and the number of neurons in the output layer are determined by the input variables and output variables, and the i-th (i = 1, 2,..., m) hidden layer has n i neurons; the weights and biases between adjacent layers are not a definite value, but a random variable that follows a certain probability distribution; non-linear transformation is performed between adjacent layers through an activation function, and commonly used activation functions include Sigmod, Tanh, Relu, Softmax, etc.; the optimizer is selected as Adam; the learning rate lr is set to 0.01; the variational inference method is used to approximate the posterior distribution, and there is noise noise in the likelihood function, and the loss function is derived using the KL divergence:

[0026]

[0027] Among them, q(w) is the approximate posterior distribution, P(w) is the prior distribution, and P(D|w) is the likelihood estimate.

[0028] Since the operation of sampling from a certain distribution is not differentiable and thus the network error cannot be backpropagated, the reparameterization technique is used to sample from the distribution and retain the gradient information:

[0029]

[0030] ω i = g(θ i , ε i ) = μ i + σ i · ε i

[0031] ε i ~N(0, 1)

[0032] Since backpropagating θ i may make the standard deviation less than 0, to ensure that the standard deviation is positive, sample the standard deviation:

[0033]

[0034] So far, the weights of the neural network have changed from sampling from the normal distribution (μ i , σ i ) to sampling from the normal distribution (μ i , ρ i ). After that, the Monte Carlo method is used to sample and estimate the derivative of the expectation.

[0035] Step S23: Bayesian neural network evaluation, specifically including:

[0036] Adopt the mean absolute percentage error MAPE:

[0037]

[0038] Logarithmic root mean square deviation Log-RMS:

[0039]

[0040] Coefficient of determination R-squared:

[0041]

[0042] to evaluate the model accuracy of the test set. Among them, y ois the original output value of the i-th sample in the test set, is the network prediction value of the i-th sample, is the average output value of the original data, and m is the number of samples in the test set.

[0043] Further, the steps of robust design optimization in step S3 include:

[0044] Step S31: Set the genetic algorithm parameters and randomly generate the initial parent population;

[0045] Step S32: Use the BNN neural network to predict the population output, and use the Monte Carlo method to statistically obtain the mean and standard deviation of each output result:

[0046]

[0047] where N is the number of observations, is the network prediction value of all samples in the population at the j-th observation, is the standard deviation of the network prediction values of all samples in the population at the j-th observation, is the network prediction value of the i-th sample at the j-th observation, is the average value of the network prediction results of all samples in the population at the j-th observation, and m is the number of samples in the population.

[0048] Step S33: Construct the objective function of multi-objective optimization, calculate the domination solution set S and the domination times n of each individual, and use the non-dominated sorting method to divide the initial population into R 1 layers, R 2 layers, ……, R n layers and other non-dominated levels rank. The method for judging the domination relationship is as follows:

[0049]

[0050] where F n (X) is the objective function, X 1 and X 2 are any two design parameter vectors. For any component of the objective vector Y 1 , if it is less than the corresponding component in the objective vector Y 2 , or at least one component of Y 2 is greater than the corresponding component of Y 1 , then the objective vector Y 1 is said to dominate the objective vector Y 2 , denoted as Y 1 <Y 2 , Y 1 is the non-dominated object, and Y 2 is the dominated object. If Y 1 <Y2 , the design parameter vector satisfies X 1 <X 2 .

[0051] The crowding degree d of each individual in the population is calculated as follows:

[0052]

[0053] Among them, i - 1, i, and i + 1 represent three adjacent radiation shielding schemes in the population, F is the objective function such as neutron / γ normalized dose rate, weight, volume, cost, etc., F max 、F min are respectively the maximum and minimum values of a certain objective vector in the current population.

[0054] Step S34: Use the non - dominated sorting algorithm to perform genetic operations on the population; using the non - dominated level and crowding degree, the dominance and non - dominance relationships between any two individuals i and j in the population can be obtained, and then the quality of individual fitness can be distinguished, and an elite population is selected to replace the parent population; the comparison relationship for the quality of fitness is as follows:

[0055]

[0056] Step S35: Repeat Step S32 to Step S34 until the multi - objective optimization convergence condition is met, and the final Pareto optimal solution set is obtained. The solutions on this solution set have a certain degree of robustness.

[0057] As can be seen from the above - mentioned technical solutions, compared with the prior art, the present invention discloses a multi - objective optimization design method for radiation shielding based on a Bayesian neural network, and the beneficial effects are as follows:

[0058] The present invention proposes a method of combining a Bayesian neural network with the multi - objective optimization design of nuclear radiation shielding calculations. The loss function derived based on variational inference and KL divergence is used to quantify the epistemic uncertainty in the process of surrogate model modeling, and a nuclear radiation shielding calculation surrogate model considering uncertainty factors is obtained. The objective function in the multi - objective optimization design is calculated for radiation shielding through the constructed surrogate model, and a Pareto optimal solution set with a certain degree of robustness is obtained by combining robust optimization design. This method adds a prior distribution to the weights of the neural network model, and then obtains the changes in these weights when given data to measure the epistemic uncertainty in radiation shielding simulation, improving the robustness of the optimization results. Brief Description of the Drawings

[0059] Figure 1 is a schematic diagram of a multi - objective optimization design method for radiation shielding based on a Bayesian neural network provided by the present invention;

[0060] Figure 2 Schematic diagram of the Bayesian neural network structure according to an embodiment of the present invention;

[0061] Figure 3 Prediction situation and evaluation indexes of the test set of the Bayesian neural network according to an embodiment of the present invention;

[0062] Figure 4 Flow chart of Monte Carlo sampling for calculating mean and standard deviation according to an embodiment of the present invention;

[0063] Figure 5 Schematic diagram of the NSGA-II algorithm process based on the Bayesian neural network according to an embodiment of the present invention;

[0064] Figure 6 Initial population and Pareto solution set of the non-dominated sorting algorithm based on the Bayesian neural network according to an embodiment of the present invention. Specific implementation manners

[0065] In order to more clearly understand the above objects, features and advantages of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0066] As Figure 1 shown, this example provides a multi-objective optimization design method for radiation shielding based on a Bayesian neural network, including the following steps:

[0067] Step S1: Sample data acquisition; establish a basic model for radiation shielding simulation, clarify the optimization design objectives, determine the optimization design variables and their value ranges, then randomly generate uniform samples, convert them into corresponding radiation shielding simulation models, and finally perform radiation shielding calculations to obtain radiation shielding simulation data available for training. Step S1 specifically includes:

[0068] Step S11: Establish a basic model for radiation shielding simulation and configure the following data: geometric model, including the simplified shapes, sizes and positions of each module in the nuclear facility; material information, including the material density, material nuclides, nuclide ratios and nuclide cross-section databases of each module in the nuclear facility; source term information, including the shape, type, position, direction and energy magnitude of the source; counting information, including the type of statistical results and whether they are converted into dose rates.

[0069] In this embodiment, the geometric model is a simplified model of a kilopower space reactor, which consists of a core, a neutron reflector, a shielding layer, heat pipes, an engine, and other structural components; the radiation shielding structure is composed of multiple shielding structures, using LiH and W to shield neutrons and gamma rays respectively. In addition, BeO is used as the reflector material to slow down neutrons, and the material database uses the default MCNP database; the core of the reactor is set as the cell source, the gamma ray energy is 1.33 MeV, the neutron energy is 1 MeV, and the source particle direction is isotropic; the counting card is set to the F1 mode (surface flux counting), and the normalized dose rate before and after penetrating the shielding structure is statistically calculated according to the internationally common flux-dose conversion factors NCRP-38 and ANSI / ANS-6.1.1.

[0070] Step S12: Define the design objectives and design variables, specifically including:

[0071] The design objectives are to minimize the neutron / gamma ray normalized dose rate, the total weight of the shielding structure, the total volume of the shielding structure, the economic cost, etc.; the design variables are the material types, material thicknesses, material arrangement orders, nuclide contents, etc. of each shielding structure, and the value ranges or discrete values of the design variables are given.

[0072] In this embodiment, the design objectives are to minimize the neutron normalized dose rate, the gamma ray normalized dose rate, and the total weight of the shielding structure; the design variables are the material thicknesses of each shielding structure (a total of 5), and the value range of the design variables is given as [2.0 cm, 7.0 cm].

[0073] Step S13: Use Latin hypercube sampling to generate random uniform samples, specifically including:

[0074] In an n-dimensional vector space, each dimension is divided into m non-overlapping intervals with the same probability; a number is randomly generated according to a uniform distribution within the m intervals of each dimension; the order of the m random numbers in each dimension is shuffled, and a random number is randomly selected from each dimension and they are combined into an n-dimensional vector; the extraction process is repeated until the m random numbers in each dimension are extracted.

[0075] In this embodiment, in a 5-dimensional design vector space, each dimension is divided into 3000 non-overlapping intervals with the same probability; 3000 sample data are generated using the Latin hypercube sampling method, forming a sample matrix of [3000, 5].

[0076] Step S14: Convert the sample values into a radiation shielding simulation model, then perform radiation shielding calculations, and construct a radiation shielding simulation data set, specifically including: updating the geometric or material parameter values of the model in the radiation simulation file with the random sample values generated by Latin hypercube sampling; calculating the shielding result data through Monte Carlo particle transport software, and then combining it with the input variable values to form a radiation shielding simulation data set available for training.

[0077] In this embodiment, use the random sample values generated in step S13 to update the thickness values of the shielding materials in the neutron / γ-ray radiation simulation file respectively; calculate the normalized dose rate and the total weight of the shielding structure before and after penetrating the shielding material through MCNP, and then combine them corresponding to the input variable values generated in step S13 to obtain a radiation shielding simulation data set available for training, which is a sample matrix of [3000, 8].

[0078] Step S2: Complete network construction and evaluation; construct a radiation shielding calculation surrogate model under uncertain conditions to accelerate the subsequent multi-objective optimization process. Preprocess the data obtained in step S1, divide the data set into a training set, a validation set and a test set, use the training set to train the BNN network structure, use the validation set to adjust the network hyperparameters until the error meets the accuracy requirements or reaches the maximum number of iterations, obtain the trained model, and use the test set to evaluate the generalization ability of the final model; the specific steps of step S2 include:

[0079] Step S21: Data preprocessing; first perform logarithmic processing with base 10 on the shielding data, then perform normalization processing on the logarithmically processed data, and divide the data set into a training set, a validation set and a test set.

[0080] In this embodiment, first perform logarithmic processing with base 10 on the neutron normalized dose rate and the γ-ray normalized dose rate, then perform normalization processing on all output data within [-1, 1], and divide the data set according to the ratio of training set:validation set:test set = 0.8:0.1:0.1. The normalization formula is as follows:

[0081] X std =(X - X.min(axis = 0)) / (X.max(axis = 0) - X.min(axis = 0))

[0082] X scaled = X std ×(max - min)+min

[0083] where X scaled is the normalized data, and X stdis the normalized standard value, max and min are the set normalization ranges, X.min(axis=0) represents the minimum value of all data, and X.max(axis=0) represents the maximum value of all data.

[0084] Step S22: Construct a Bayesian neural network, specifically including: The network consists of 1 input layer, m hidden layers, and 1 output layer; The number of neurons in the input layer and the output layer are determined by the input variables and output variables. The i-th (i = 1, 2,..., m) hidden layer has n i neurons; The weights and biases between adjacent layers are not a definite value, but a random variable that follows a certain probability distribution; Nonlinear transformation is performed between adjacent layers through an activation function. Commonly used activation functions include Sigmod, Tanh, Relu, Softmax, etc.; The optimizer is selected as Adam; The learning rate lr is set to 0.01; The method of variational inference is used to approximate the posterior distribution, and there is noise noise in the likelihood function. The loss function is derived from the KL divergence:

[0085] In this embodiment, as Figure 2 shown, the neural network consists of 1 input layer, 1 hidden layer, and 1 output layer. The number of neurons in each layer is [5:32:3]; The activation function between the input layer and the hidden layer is Sigmod, and the activation function between the hidden layer and the output layer is Linear; The optimizer is selected as Adam; The learning rate lr is set to 0.01; The weights and biases between adjacent layers are not a definite value, but a random variable that follows a certain probability distribution. Assume that all random variables follow N(0,1 2 ) distribution; The method of variational inference is used to approximate the posterior distribution, and the noise noise is set to 0.1. The loss function is obtained from the KL divergence:

[0086]

[0087] Among them, q(w) is the approximate posterior distribution, P(w) is the prior distribution, and P(D|w) is the likelihood estimate. The reparameterization trick is used to sample from the distribution and retain the gradient information:

[0088]

[0089] ω i = g(θ i , ε i ) = μ i + σ i · ε i

[0090] ε i ~N(0,1)

[0091] Since the backpropagation of θ i may make the standard deviation less than 0, in order to ensure that the standard deviation is positive, sample the standard deviation:

[0092]

[0093] So far, the weights of the neural network have been sampled from the normal distribution (μ i , σ i ) and become sampled from the normal distribution (μ i , ρ i ). After that, the Monte Carlo method is used to sample and estimate the derivative of the expectation.

[0094] Step S23: Bayesian neural network evaluation, specifically including:

[0095] Use the mean absolute percentage error MAPE:

[0096]

[0097] Logarithmic root mean square deviation Log-RMS:

[0098]

[0099] Coefficient of determination R-squared:

[0100]

[0101] to evaluate the model accuracy of the test set. Where y i is the original output value of the i-th sample in the test set, is the network prediction value of the i-th sample, is the average output value of the original data, and m is the number of samples in the test set.

[0102] As Figure 3 shown, when the network is trained until the test set can meet the set conditions, or the program reaches the set number of iterations (time), end the training, and use this network for subsequent multi-objective optimization result prediction.

[0103] Step S3: Robust design optimization. What this step realizes is to use the constructed Bayesian neural network, comprehensively consider the uncertainty factors affecting the radiation shielding calculation results, and perform multi-objective optimization design on the shielding scheme based on the NSGA-II algorithm. Randomly generate the initial population, set the sampling value, use the BNN model obtained in step S2 to perform sampling prediction calculations, obtain the output mean and standard deviation of the current population, and use the output results for robust design optimization until the convergence condition is met, and the final Pareto optimal solution set can be obtained.

[0104] The specific steps of step S3 include:

[0105] Step S31: Set the parameters of the genetic algorithm: the population size npop is 500, the number of evolutionary iterations epoch is 200, the crossover probability pc is 0.6, and the mutation probability mu is 0.01; randomly generate the initial parent population, which is a matrix of [500, 8].

[0106] Step S32: As Figure 4 shown, use the BNN neural network to predict the population output, and use the Monte Carlo method to statistically obtain the mean and standard deviation of each output result:

[0107]

[0108] where N is the number of observations for a single sample, set to 200; is the network prediction value of all samples in the population at the j-th observation, is the standard deviation of the network prediction values of all samples in the population at the j-th observation, is the network prediction value of the i-th sample at the j-th observation, is the average value of the network prediction results of all samples in the population at the j-th observation, and m is the number of samples in the population, which is 500.

[0109] Step S33: Construct the objective function for multi-objective optimization, calculate the domination solution set S and the domination times n of each individual, and use the non-dominated sorting method to divide the initial population into R 1 layers, R 2 layers, ……, R n layers and other non-dominated levels rank. The method for judging the domination relationship is as follows:

[0110]

[0111] where F n (X) is the objective function, X 1 and X 2 are any two design parameter vectors. For any component of the objective vector Y 1 , if it is less than the corresponding component in the objective vector Y 2 , or at least one component of Y 2 is greater than the corresponding component of Y 1 , then it is said that the objective vector Y 1 dominates the objective vector Y 2 , denoted as Y 1 <Y 2 , Y 1 is the non-dominated object, and Y 2 is the dominated object. If Y 1 <Y 2 , then the design parameter vector satisfies X 1<X 2 。

[0112] According to the non-dominated level rank and the objective function value, calculate the crowding degree d at each non-dominated level. The crowding degree of each individual in the population is calculated as follows:

[0113]

[0114] where i - 1, i, and i + 1 represent three adjacent radiation shielding schemes in the population, F is the objective function such as neutron / γ normalized dose rate, weight, volume, cost, etc., F max 、F min are respectively the maximum and minimum values of the corresponding objective vector in the current population.

[0115] Step S34: As shown in Figure 5 , use the non-dominated sorting algorithm to perform genetic operations on the parent population P g after non-dominated sorting and crowding degree calculation to generate the offspring population Q g ; after performing radiation shielding calculation on the offspring population Q g using the method of step S32, merge the offspring population Q g with the parent population P g to obtain the mixed population C g , and perform non-dominated sorting and crowding degree calculation again for the mixed population C g ; using the non-dominated level and crowding degree, the dominance and non-dominance relationships between any two individuals i and j in the population can be obtained, and then the advantages and disadvantages of individual fitness can be distinguished; select individuals with the same size as the initial population in the order of the best fitness to form the elite population P g+1 , and use the elite population P g+1 to replace the parent population P g ; the comparison relationship for the advantages and disadvantages of fitness is as follows:

[0116]

[0117] Step S35: Repeat steps S32 to S34 until the multi-objective optimization convergence condition is satisfied to obtain the Pareto optimal solution set shown in Figure 6 , and the solutions on this solution set have a certain robustness.

[0118] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, any person skilled in the art within the scope of the present invention can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features without departing from the spirit or scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A multi-objective optimization design method for radiation shielding based on Bayesian neural network, characterized in that: The following steps are involved: Step S1: Sample data acquisition; This step is to obtain training samples from the radiation simulation model; first, a basic model of radiation shielding simulation is established, then the optimization design goal is clarified, the optimization design variables and their value ranges are determined, and then uniform samples are randomly generated and converted into corresponding radiation shielding simulation models. Finally, radiation shielding calculations are performed to obtain radiation shielding simulation data for training; Step S2: Network construction and evaluation; This step constructs a radiation shielding calculation proxy model under uncertainty conditions to accelerate the subsequent multi-objective optimization process; Preprocess the data obtained in step S1, divide the data set into a training set, a validation set, and a test set, use the training set to train the BNN network structure, use the validation set to adjust the network hyperparameters, until the error meets the accuracy requirement or reaches the maximum number of iterations, obtain the trained model, and use the test set to evaluate the generalization ability of the final model; Step S3: Robust design optimization; this step uses the constructed Bayesian neural network to comprehensively consider the uncertainty factors that affect the radiation shielding calculation results, and performs multi-objective optimization design on the shielding scheme based on the NSGA-Ⅱ algorithm; randomly generates an initial population, sets the sampling value, and uses the BNN model obtained in step S2 to perform sampling prediction calculations to obtain the output mean and standard deviation of the current population. The output results are used for robust design optimization until the convergence conditions are met, and the final Pareto optimal solution set can be obtained.

2. The radiation shielding multi-objective optimization design method based on Bayesian neural network according to claim 1 is characterized in that: The step of obtaining sample data in step S1 includes: Step S11: Establish a basic model for radiation shielding simulation. The following data needs to be configured: The geometric model includes the simplified shapes, sizes and positions of the modules in the nuclear facility; Material information, including material density, material nuclides, nuclide ratios, and nuclide cross-section databases for each module in the nuclear facility; Source information, including source shape, type, location, direction, and energy; Counting information, including the type of statistical results and whether they are converted into dose rates. Step S12: clarify the design objectives and design variables, including: The design objectives are to minimize the normalized neutron / gamma-ray dose rate, the total weight of the shielding structure, the total volume of the shielding structure, and the economic cost; the material type, material thickness, material arrangement sequence, nuclide content, etc. of each shielding structure are used as design variables, and the value range or discrete value of the design variables is given; Step S13: Generate a random uniform sample using Latin hypercube sampling, specifically including: In an n-dimensional vector space, each dimension is divided into m non-overlapping intervals with equal probability; a number is randomly generated in each of the m intervals according to a uniform distribution; the order of the m random numbers in each dimension is shuffled, a random number is randomly drawn from each dimension, and they are combined into an n-dimensional vector; the extraction process is repeated until all the m random numbers in each dimension are extracted; Step S14: Convert the sample values into a radiation shielding simulation model, then perform radiation shielding calculations, and construct a radiation shielding simulation data set, specifically including: updating the geometric or material parameter values of the model in the radiation simulation file with the random sample values generated by Latin hypercube sampling; calculating the shielding result data through Monte Carlo particle transport software, and then combining it with the input variable values to form a radiation shielding simulation data set available for training.

3. The radiation shielding multi-objective optimization design method based on Bayesian neural network according to claim 1 is characterized in that: The steps of network construction and evaluation in step S2 include: Step S21: Data preprocessing, first perform logarithmic processing with base 10 on the shielding data, then perform normalization processing on the logarithmically processed data, and divide the data set into a training set, a validation set, and a test set; Step S22: Bayesian neural network construction, specifically including: the network consists of 1 input layer, m hidden layers, and 1 output layer; the number of neurons in the input layer and the number of neurons in the output layer are determined by the input variables and the output variables, and the i-th layer (i=1,2,…,m) has n hidden layers. i neurons; the weight and bias between two adjacent layers are not a fixed value, but a random variable that obeys a certain probability distribution; nonlinear transformation is performed between two adjacent layers through activation functions; Adam is used as the optimizer; the learning rate lr is set to 0.01; the variational inference method is used to approximate the posterior distribution, and there is noise in the likelihood function. The loss function is derived using KL divergence: Among them, q(w) is the approximate posterior distribution, P(w) is the prior distribution, and P(D|w) is the likelihood estimate; Step S23: Bayesian neural network evaluation, specifically including: using the mean absolute percentage error MAPE: Logarithmic root mean square deviation Log-RMS: Coefficient of determination R-squared: To evaluate the model accuracy of the test set; where y i is the original output value of the i-th sample in the test set, is the network prediction value of the i-th sample, is the average output value of the original data, and m is the number of samples in the test set.

4. The radiation shielding multi-objective optimization design method based on Bayesian neural network according to claim 1 is characterized in that: The steps of robust design optimization in step S3 include: Step S31: Set the genetic algorithm parameters and randomly generate an initial parental population; Step S32: Use the BNN neural network to predict the population output, and use the Monte Carlo method to statistically obtain the mean and standard deviation of each output result: Where N is the number of observations, is the network prediction value of all samples in the population at the jth observation, is the standard deviation of the network prediction values ​​of all samples in the population at the jth observation, is the network prediction value of the i-th sample at the j-th observation, is the average value of the network prediction results of all samples in the population at the jth observation, and m is the number of samples in the population; Step S33: Construct the objective function of multi-objective optimization, calculate the dominant solution set S and the number of dominated solutions n of each individual, and use the non-dominated sorting method to divide the initial population into R1 layer, R2 layer, ..., R n The method for determining the dominance relationship of the non-dominated hierarchy rank is as follows: Among them, X1 and X2 are any two design parameter vectors; for any component of the target vector Y1, if it is less than the corresponding component in the target vector Y2, or at least one component of Y2 is greater than the corresponding component of Y1, then the target vector Y1 is said to dominate the target vector Y2, denoted as Y1 < Y2, Y1 is the non-dominated object, and Y2 is the dominated object; if Y1 < Y2, then the design parameter vector satisfies X1 < X2; The crowding degree d of each individual in the population is calculated as follows: Among them, i-1, i, i+1 represent three adjacent radiation shielding schemes in the population, F is the objective function such as neutron / γ normalized dose rate, weight, volume, cost, F max 、F min are the maximum and minimum values ​​of a target vector in the current population respectively; Step S34: Use the non-dominated sorting algorithm to perform genetic operations on the population; using the non-dominated level and crowding degree, the domination and non-domination relationships between any two individuals i and j in the population can be obtained, and then the superiority and inferiority of the individual fitness can be distinguished, and the elite population is selected to replace the parental population; the comparison relationship formula for the superiority and inferiority of fitness is as follows: Step S35: Repeat steps S32 to S34 until the multi-objective optimization convergence condition is satisfied, and obtain the final Pareto optimal solution set. The solutions on the solution set have a certain degree of robustness.

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