A radiation shielding multi-objective optimization design method based on bayesian neural network

Abstract

The application provides a radiation shielding multi-objective optimization design method based on a Bayesian neural network, and is characterized in that the method comprises the following steps: step S1: sample data acquisition; step S2: network construction and evaluation; and step S3: robust design optimization. The method uses a loss function derived based on variational inference and KL divergence to quantify cognitive uncertainty in the modeling process of a surrogate model, obtains a nuclear radiation shielding calculation surrogate model considering uncertainty factors, performs radiation shielding calculation on a target function in multi-objective optimization design through the constructed surrogate model, and obtains a Pareto optimal solution set with certain robustness in combination with robust optimization design. The method adds a prior distribution to the weight of the neural network model, then obtains the change of the weight under given data to measure cognitive uncertainty in radiation shielding simulation, and improves the robustness of the optimization result.

Description

Technical Field

[0001] This invention relates to the field of radiation shielding calculation for nuclear facilities, and specifically to a multi-objective optimization design method for radiation shielding based on a Bayesian neural network. Background Technology

[0002] With the rapid development of advanced nuclear facilities, radiation shielding and hardening design has become increasingly important. Lightweight and compact design are important development directions for radiation shielding of high-performance nuclear facilities, especially mobile and compact nuclear devices, such as nuclear-powered marine reactors and space reactors. These nuclear facilities have limited available space and the weight of the shielding structure is also limited, requiring both shielding performance and mobility to be considered.

[0003] Traditional radiation shielding design is an inefficient and suboptimal process. Designers often propose initial design schemes based on practical engineering experience, and then obtain the final shielding solution only after extensive calculations and iterations. This method requires designers to have rich engineering design experience and a clear design concept, is greatly affected by human factors, and cannot determine whether it is the optimal solution. In addition, there are many uncertainties in actual design and optimization problems, which inevitably disturb the shielding design parameters, resulting in fluctuations in shielding performance and causing the shielding effect to fail to meet the design expectations.

[0004] Furthermore, radiation shielding calculation is an extremely complex process. Commonly used methods for radiation shielding calculation include deterministic methods and Monte Carlo methods: Deterministic methods are based on establishing relevant models based on actual mathematical physics problems and using various numerical solution methods to calculate approximate solutions to the Boltzmann transport equations. The calculation results are relatively accurate, but the ability to handle complex scenarios is relatively lacking; Monte Carlo methods are based on statistical experiments and obtain approximate solutions by simulating random transport processes. They can handle complex three-dimensional radiation shielding problems, but the speed of solving approximate solutions with a high given confidence level is relatively slow.

[0005] In light of the design requirements for radiation shielding of nuclear facilities, and addressing the current design problems of low efficiency, non-optimal solutions, and interference from uncertain factors, there is an urgent need to propose a rapid multi-objective optimization design method for radiation shielding that takes into account uncertainties, 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. It combines a Bayesian neural network (BNN) that considers uncertain factors with a kernel Monte Carlo program, and constructs a BNN surrogate model through data from simulation calculation results. The BNN surrogate model is then used for prediction in the multi-objective optimization process based on the non-dominated ranking algorithm (NSGA-II).

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

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

[0009] Step S1: Sample Data Acquisition. This step involves obtaining training samples from the radiation simulation model. First, a basic model for radiation shielding simulation is established. Second, the optimization design objective is clarified, and the optimization design variables and their value ranges are determined. Then, uniform samples are randomly generated and transformed into the corresponding radiation shielding simulation model. Finally, radiation shielding calculations are performed to obtain radiation shielding simulation data available for training.

[0010] Step S2: Network Construction and Evaluation. This step involves constructing a radiation shielding computational proxy model under uncertainty conditions to accelerate the subsequent multi-objective optimization process. The data obtained in Step S1 is preprocessed, dividing the dataset into training, validation, and test sets. The BNN network structure is trained using the training set, and the network hyperparameters are adjusted using the validation set until the error meets the accuracy requirements or the maximum number of iterations is reached, resulting in a trained model. The generalization ability of the final model is then evaluated using the test set.

[0011] Step S3: Robust Design Optimization. This step utilizes the constructed Bayesian neural network to comprehensively consider the uncertainties affecting the radiation shielding calculation results, and performs multi-objective optimization design of the shielding scheme based on the NSGA-II algorithm. An initial population is randomly generated, sampling values ​​are set, and the BNN model obtained in Step S2 is used for sampling prediction calculations to obtain the output mean and standard deviation of the current population. Robust design optimization is then performed using the output results until the convergence condition is met, thus obtaining the final Pareto optimal solution set.

[0012] Furthermore, the step of obtaining sample data in step S1 includes:

[0013] Step S11: Establish the basic model for radiation shielding simulation. The following data needs to be configured:

[0014] Geometric model, including the simplified shape, size and location of each module in the nuclear facility; material information, including the material density, material nuclides, nuclide percentage, and nuclide cross-section database of each module in the nuclear facility; source term information, including the shape, type, location, orientation, and energy magnitude of the source; and counting information, including the type of statistical results and whether they are converted into dose rates.

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

[0016] The design objectives are to minimize the normalized dose rate of neutrons / gamma rays, the total weight of the shielding structure, the total volume of the shielding structure, and the economic cost. The design variables are the material type, material thickness, material arrangement order, and nuclide content of each shielding structure, and the range or discrete values ​​of the design variables are given.

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

[0018] 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, and a random number is randomly drawn from each dimension to form an n-dimensional vector. The drawing process is repeated until all m random numbers in each dimension have been drawn.

[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] The geometric or material parameters of the model in the radiation simulation file are updated using random sample values ​​generated by Latin hypercube sampling; the shielding result data is calculated using Monte Carlo particle transport software, and then combined with the input variable values ​​to form a radiation shielding simulation dataset that can be used for training.

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

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

[0023] First, the masked data is processed by a base-10 logarithmic transformation, then the logarithmically processed data is normalized, and the dataset is divided into training set, validation set, and test set.

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

[0025] The network consists of one input layer, m hidden layers, and one output layer; the number of neurons in the input layer and the number of neurons in the output layer are determined by the input and output variables, and the i-th layer (i = 1, 2, ..., m) has n hidden layers. i There are 10 neurons; the weights and biases between adjacent layers are not fixed values, but random variables following a certain probability distribution; adjacent layers undergo nonlinear transformation through activation functions, commonly used activation functions include Sigmoid, Tanh, ReLU, and Softmax; the optimizer is Adam; the learning rate (lr) is set to 0.01; variational inference is used to approximate the posterior distribution, and since the likelihood function contains noise, the loss function is derived using KL divergence:

[0026]

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

[0028] Since the sampling operation from a certain distribution is not differentiable, and therefore cannot backpropagate network errors, a reparameterization technique is used to sample from the distribution while preserving gradient information.

[0029]

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

[0031] ε i ~N(0,1)

[0032] Due to backpropagation θ i Sometimes the standard deviation may be less than 0. To ensure that the standard deviation is positive, the standard deviation is sampled:

[0033]

[0034] At this point, the weights of the neural network have changed from a normal distribution (μ) i ,σ i Sampling from the normal distribution (μ) becomes... i ,ρ i Sampling is performed in the sample. Then, the Monte Carlo method is used to estimate the expected derivative.

[0035] Step S23: Evaluation of the Bayesian neural network, specifically including:

[0036] Using Mean Absolute Percentage Error (MAPE):

[0037]

[0038] Log-RMS deviation:

[0039]

[0040] Determinance coefficient R-squared:

[0041]

[0042] To evaluate the model accuracy on the test set. Where 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] Furthermore, 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 non-dominated levels such as R1 layer, R2 layer,..., R n layer, etc. rank, and the method for judging the domination relationship is as follows:

[0049] ​​​​​​​​​​​​​​​max F min These are the maximum and minimum values ​​of a target vector in the current population, respectively.

[0054] Step S34: Perform genetic operations on the population using the non-dominated sorting algorithm; by using the non-dominated hierarchy and crowding, the dominance and non-dominated relationship between any two individuals i and j in the population can be obtained, thereby distinguishing the fitness of individuals and selecting an elite population to replace the parent population; the comparison formula for fitness is as follows:

[0055]

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

[0057] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a multi-objective optimization design method for radiation shielding based on Bayesian neural networks, which produces the following beneficial effects:

[0058] This invention proposes a method combining Bayesian neural networks with multi-objective optimization design for nuclear radiation shielding calculations. It utilizes a loss function based on variational inference and KL divergence derivation to quantify the cognitive uncertainty in the surrogate model modeling process, obtaining a nuclear radiation shielding calculation surrogate model that considers uncertainty factors. This surrogate model is then used to perform radiation shielding calculations on the objective function in the multi-objective optimization design, and combined with robust optimization design, a Pareto optimal solution set with a certain degree of robustness is obtained. This method incorporates prior distributions into the weights of the neural network model and then obtains the changes of these weights with given data to measure the cognitive uncertainty in radiation shielding simulations, thereby improving the robustness of the optimization results. Attached Figure Description

[0059] Figure 1 This 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 This is a schematic diagram of the Bayesian neural network structure according to an embodiment of the present invention;

[0061] Figure 3 This describes the prediction performance and evaluation metrics of the Bayesian neural network on the test set in this embodiment of the invention.

[0062] Figure 4 This is a flowchart illustrating the calculation of the mean and standard deviation using Monte Carlo sampling according to an embodiment of the present invention.

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

[0064] Figure 6 These are the initial population and Pareto solution set of the non-dominated sorting algorithm based on Bayesian neural network in this embodiment of the invention. Detailed Implementation

[0065] To better understand the above-mentioned objectives, features, and advantages of the present invention, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

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

[0067] Step S1: Sample Data Acquisition; Establish the 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, transform them into the corresponding radiation shielding simulation model, 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 shape, size and position of each module in the nuclear facility; material information, including the material density, material nuclides, nuclide percentage and nuclide cross-section database of each module in the nuclear facility; source term information, including the shape, type, position, direction and energy magnitude of the source; and counting information, including the type of statistical results and whether they are converted into dose rate.

[0069] In this embodiment, the geometric model is a simplified model of the Kilopower space reactor, consisting of a core, a neutron reflector, a shielding layer, heat pipes, an engine, and other structural components. The radiation shielding structure consists of multiple shielding layers, using LiH and W to shield neutrons and gamma rays respectively. In addition, BeO is used as the reflector material to moderate neutrons, and the material database uses the MCNP default database. The reactor core is set as the grid source, with gamma ray energy of 1.33 MeV and neutron energy of 1 MeV, and the source particle orientation is isotropic. The counting card is set to F1 mode (area flux counting), and the normalized dose rate before and after penetrating the shielding structure is calculated according to the internationally accepted flux-dose conversion factor NCRP-38, 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 normalized dose rate of neutrons / gamma rays, the total weight of the shielding structure, the total volume of the shielding structure, and the economic cost. The design variables are the material type, material thickness, material arrangement order, and nuclide content of each shielding structure, and the range 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 material thickness of each shielding structure is used as the design variable (a total of 5), and the value range of the given design variable is [2.0cm, 7.0cm].

[0073] Step S13: Generate a random uniform sample using Latin hypercube sampling, specifically including:

[0074] 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, and a random number is randomly drawn from each dimension to form an n-dimensional vector. The drawing process is repeated until all m random numbers in each dimension have been drawn.

[0075] In this embodiment, in the 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, perform radiation shielding calculations, and construct a radiation shielding simulation dataset. Specifically, this includes: updating the geometric or material parameter values ​​of the model in the radiation simulation file with random sample values ​​generated by Latin hypercube sampling; calculating the shielding result data using Monte Carlo particle transport software, and then combining it with the input variable values ​​to form a radiation shielding simulation dataset that can be used for training.

[0077] In this embodiment, the thickness values ​​of the shielding material in the neutron / gamma-ray radiation simulation file are updated using the random sample values ​​generated in step S13. The normalized dose rate and the total weight of the shielding structure before and after penetration of the shielding material are calculated by MCNP and then combined with the corresponding input variable values ​​generated in step S13 to obtain a radiation shielding simulation dataset that can be used for training, which is a sample matrix of [3000, 8].

[0078] Step S2: Complete network construction and evaluation; construct a radiation shielding computational proxy model under uncertainty conditions to accelerate the subsequent multi-objective optimization process. Preprocess the data obtained in Step S1, dividing the dataset into training, validation, and test sets. Train the BNN network structure using the training set, and adjust the network hyperparameters using the validation set until the error meets the accuracy requirements or reaches the maximum number of iterations to obtain the trained model. Evaluate the generalization ability of the final model using the test set. Specifically, Step S2 includes:

[0079] Step S21: Data preprocessing; First, perform logarithmic processing on the masked data to base 10, then normalize the logarithmically processed data, and divide the dataset into training set, validation set, and test set.

[0080] In this embodiment, the neutron normalized dose rate and gamma-ray normalized dose rate are first logarithmically processed to base 10, then all output data are normalized within the range [-1, 1], and the dataset is divided into training set:validation set:test set = 0.8:0.1:0.1. The normalization formula is as follows:

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

[0082] X scaled =X std ×(max-min)+min

[0083] Among them, X scaled It is the normalized data, X std X.min represents the normalization standard value, while X.max and X.min represent the set normalization range. 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: Construction of the 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 number of neurons in the output layer are determined by the input and output variables, and the i-th layer (i = 1, 2, ..., m) has n hidden layers. i There are 10 neurons; the weights and biases between adjacent layers are not fixed values, but random variables following a certain probability distribution; adjacent layers undergo nonlinear transformation through activation functions, commonly used activation functions include Sigmoid, Tanh, ReLU, and Softmax; the optimizer is Adam; the learning rate (lr) is set to 0.01; variational inference is used to approximate the posterior distribution, and since the likelihood function contains noise, the loss function is derived using KL divergence:

[0085] In this embodiment, such as Figure 2 As shown, the neural network consists of one input layer, one hidden layer, and one output layer, with the number of neurons in each layer being [5:32:3]. The activation function between the input layer and the hidden layer is Sigmoid, and the activation function between the hidden layer and the output layer is Linear. The optimizer is Adam, and the learning rate (lr) is set to 0.01. The weights and biases between adjacent layers are not fixed values, but random variables following a certain probability distribution. It is assumed that all random variables follow N(0,1)... 2 The posterior distribution is approximated using variational inference, with noise set to 0.1. The loss function is obtained from the KL divergence.

[0086]

[0087] Where q(w) is the approximate posterior distribution, P(w) is the prior distribution, and P(D|w) is the likelihood estimate. The reparameter resampling technique is used to sample from the distribution and preserve gradient information:

[0088]

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

[0090] ε i ~N(0,1)

[0091] Due to backpropagation θ i Sometimes the standard deviation may be less than 0. To ensure that the standard deviation is positive, the standard deviation is sampled:

[0092]

[0093] At this point, the weights of the neural network have changed from a normal distribution (μ) i ,σ i Sampling from the normal distribution (μ) becomes... i ,ρ i Sampling is performed in the sample. Then, the Monte Carlo method is used to estimate the expected derivative.

[0094] Step S23: Evaluation of the Bayesian neural network, specifically including:

[0095] Using Mean Absolute Percentage Error (MAPE):

[0096]

[0097] Log-RMS deviation:

[0098]

[0099] Determinance coefficient R-squared:

[0100]

[0101] To evaluate the model accuracy on the test set. Where y i The original output value of the i-th sample in the test set. Let i be the network prediction value for 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] like Figure 3 As shown, when the network is trained to the point that the test set can meet the set conditions, or the program reaches the set number of iterations (time), the training ends and the network is used for subsequent multi-objective optimization result prediction.

[0103] Step S3: Robust Design Optimization. This step utilizes the constructed Bayesian neural network to comprehensively consider the uncertainties affecting the radiation shielding calculation results, and performs multi-objective optimization design of the shielding scheme based on the NSGA-II algorithm. An initial population is randomly generated, sampling values ​​are set, and the BNN model obtained in Step S2 is used for sampling prediction calculations to obtain the output mean and standard deviation of the current population. Robust design optimization is then performed using the output results until the convergence condition is met, thus obtaining the final Pareto optimal solution set.

[0104] Step S3 specifically includes:

[0105] Step S31: Set the genetic algorithm parameters: population size npop is 500, number of evolution iterations epoch is 200, crossover probability pc is 0.6, 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 As shown, the population output is predicted using a BNN neural network, and the mean and standard deviation of each output result are obtained using the Monte Carlo method:

[0107]

[0108] Where N is the number of observations for a single sample, set to 200; Let be the network prediction value of all samples in the population at the j-th observation. Let be the standard deviation of the network predictions for all samples of the population at the j-th observation. Let i be the network prediction value of the i-th sample at the j-th observation. is the average 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 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 non-dominated levels such as R1 layer, R2 layer,..., R n layer, etc. rank. The method for judging the domination relationship is as follows:

[0110]

[0111] Among them, F n (X) is the objective function, and X1 and X2 are any two design parameter vectors. For any component of the objective vector Y1, if it is less than the corresponding component in the objective vector Y2, or at least one component of Y2 is greater than the corresponding component of Y1, then the objective vector Y1 is said to dominate the objective 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.

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

[0113]

[0114] 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 the corresponding objective vector in the current population.

[0115] Step S34: As Figure 5 shown, 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 domination and non-domination 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 Pg+1 And using elite population P g+1 Replace parent population P g The comparison formula for fitness superiority / inferiority is as follows:

[0116]

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

[0118] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is 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 can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features without departing from the spirit or scope of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should 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 networks, characterized in that, Includes the following steps: Step S1: Sample Data Acquisition; This step obtains training samples from the radiation simulation model. First, a basic model for radiation shielding simulation is established. Second, the optimization design objective is clarified, the optimization design variables and their value ranges are determined, then uniform samples are randomly generated and transformed into the corresponding radiation shielding simulation model. Finally, radiation shielding calculations are performed to obtain radiation shielding simulation data available for training. Step S2: Network construction and evaluation; This step constructs a computational proxy model for radiation shielding under uncertainty conditions in order to accelerate the subsequent multi-objective optimization process; The data obtained in step S1 is preprocessed, and the dataset is divided into training set, validation set and test set. The BNN network structure is trained using the training set, and the network hyperparameters are adjusted using the validation set until the error meets the accuracy requirements or reaches the maximum number of iterations to obtain the trained model. The generalization ability of the final model is evaluated using the test set. Step S3: Robust Design Optimization; This step utilizes the constructed Bayesian neural network to comprehensively consider the uncertainties affecting the radiation shielding calculation results, and performs multi-objective optimization design of the shielding scheme based on the NSGA-II algorithm; an initial population is randomly generated, sampling values ​​are set, and the BNN model obtained in step S2 is used to perform sampling prediction calculations to obtain the output mean and standard deviation of the current population. Robust design optimization is performed using the output results until the convergence condition is met, and the final Pareto optimal solution set can be obtained. The network construction and evaluation steps in step S2 include: Step S21: Data preprocessing. First, perform logarithmic processing on the masked data to base 10, then normalize the logarithmically processed data, and divide the dataset into training set, validation set, and test set. Step S22: Construction of the 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 number of neurons in the output layer are determined by the input and output variables, and the i-th hidden layer has n... i There are 10 neurons; the weights and biases between adjacent layers are not fixed values, but random variables following a probability distribution; adjacent layers undergo nonlinear transformation through an activation function; the optimizer is Adam; the learning rate (lr) is set to 0.01; variational inference is used to approximate the posterior distribution, and the likelihood function contains noise; the loss function is derived using KL divergence. Where 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 Mean Absolute Percentage Error (MAPE). Log-root mean square deviation: Coefficient of determination: To evaluate the model accuracy on the test set; where y i The original output value of the i-th sample in the test set. Let i be the network prediction value for the i-th sample. is the average output value of the original data, and m is the number of samples in the test set.

2. The radiation shielding multi-objective optimization design method based on Bayesian neural network according to claim 1, characterized in that: The step of obtaining sample data in step S1 includes: Step S11: Establish the basic model for radiation shielding simulation. The following data needs to be configured: Geometric model, including the simplified shape, size, and location of each module in the nuclear facility; Material information, including material density, material nuclides, nuclide percentage, and nuclide cross-section database for each module in the nuclear facility; Source information, including the source's shape, type, location, orientation, and energy level; Count information, including the type of statistical results and whether they have been converted into dose rates; Step S12: Define the design objectives and design variables, specifically including: The design objectives are to minimize the normalized dose rate of neutrons / gamma rays, the total weight of the shielding structure, the total volume of the shielding structure, and the economic cost; the design variables are the material type, material thickness, material arrangement order, and nuclide content of each shielding structure, and the range or discrete values ​​of the design variables are 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, and a random number is randomly drawn from each dimension to form an n-dimensional vector; the drawing process is repeated until all m random numbers in each dimension have been drawn. Step S14: Convert the sample values ​​into a radiation shielding simulation model, perform radiation shielding calculations, and construct a radiation shielding simulation dataset. Specifically, this includes: updating the geometric or material parameter values ​​of the model in the radiation simulation file with random sample values ​​generated by Latin hypercube sampling; calculating the shielding result data using Monte Carlo particle transport software, and then combining it with the input variable values ​​to form a radiation shielding simulation dataset that can be used for training.

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