Heat-force-shielding integrated multi-level structure optimization design method based on PINN

Abstract

The invention provides a heat-force-shielding integrated multi-level structure optimization design method based on a PINN, and the method is characterized in that the method comprises the following steps: S1, model building and data preparation; s2, PINN neural network training is carried out; s3, designing and optimizing a multi-level structure; according to the method, a multi-level shielding structure model is constructed according to the irradiation shielding capability of a component, a structural thermal performance analysis model is established by taking the component as a heat source, a proxy model is generated by utilizing PINN training, multi-target optimization is performed through an NSGA-III algorithm, and finally a Pareto optimal solution set is obtained. Compared with a traditional shielding optimization method, structural multi-level customization design is carried out according to shielding protection requirements, through thermodynamic analysis and shielding calculation, the PINN algorithm and the NSGA-III algorithm are combined, the thermal performance of the structure is considered, the shielding capacity is guaranteed, and meanwhile the lightweight capacity and optimization efficiency of the structure are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of radiation shielding calculation for nuclear facilities, and specifically to an optimization design method for a multi-level structure based on PINN that integrates thermal-mechanical-shielding. Background Technology

[0002] In the design of complex structures such as nuclear energy equipment and spacecraft, the coordinated optimization of radiation shielding, thermal management, and mechanical performance has long been a technical bottleneck. Traditional shielding design optimization methods typically do not consider the thermodynamic properties of structural components. However, this approach has led to numerous problems in practice. For example, variations in material thickness not only affect radiation attenuation but also alter heat conduction paths. Furthermore, the normal operation of components requires not only effective radiation shielding but also ensuring their operation at appropriate operating temperatures.

[0003] Furthermore, existing radiation shielding designs often employ high atomic number materials to meet shielding performance requirements, failing to implement differentiated shielding strategies based on the radiation tolerance of different components. This approach easily leads to insufficient shielding in critical areas or material redundancy in non-critical areas, further impacting the design's lightweight nature and functionality. Although some research has attempted to use multi-level structures, the lack of a systematic modeling framework means that existing multi-level structure designs still rely on empirical methods to adjust material layout, failing to effectively quantify the balance between lightweight design and shielding effectiveness.

[0004] Secondly, the multiphysics simulation calculation process for radiation and thermal analysis is extremely cumbersome, with each simulation calculation potentially taking several hours, severely limiting the efficiency of design iteration. Considering the design requirements for radiation shielding of nuclear facilities and the thermal performance of components, and addressing the current design problems of poor coordination, low efficiency, and insufficient targeted protection, there is an urgent need to propose a multi-level structural optimization design method based on PINN that integrates thermal, mechanical, and shielding functions. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a multi-level structural optimization design method based on PINN (Physical Induction Network) that integrates thermal, mechanical, and shielding functions. This method utilizes a multi-level structural design to implement gradient protection for the radiation shielding requirements of different components. By integrating radiation shielding, thermal management, and mechanical performance optimization within a unified framework, and combining the PINN neural network and the NSGA-III algorithm, cross-domain collaborative optimization is achieved. This results in a balance between multiple objectives, including lightweight design, optimized shielding effectiveness, and control of component operating temperature.

[0006] To achieve the above objectives, the technical solution proposed by this invention is as follows:

[0007] A method for optimizing the design of a multi-level structure based on PINN (Physical Insulation-Shielding Integration) is characterized by the following steps:

[0008] Step S1: Model Building and Data Preparation; This step is used to determine the multi-level shielding structure and analyze its thermodynamic performance, and to obtain the sample data required for training the PINN neural network. A multi-level shielding structure model is constructed based on the radiation shielding capability of the components, and a structural thermodynamic performance analysis model is established based on the heating characteristics of the components; structural properties are analyzed and design variables and optimization objectives are defined; structural parameter samples are randomly generated within a set range; particle transport programs and thermo-mechanical multiphysics simulation programs are called to perform calculations and obtain integrated thermo-mechanical-shielding sample data.

[0009] Step S2: PINN Neural Network Training; This step is used to construct a multi-level structural surrogate model integrating thermal, mechanical, and shielding functions, supporting subsequent multi-objective optimization. The data obtained in Step S1 is preprocessed, dividing the dataset into training, validation, and test sets. Based on the structural thermal performance analysis model, physical equation constraints and loss functions are defined, and some physical parameters are used as mesh parameters for training. The network structure is trained using the training set, and the network parameters are adjusted using the validation set until the error meets the accuracy requirements or reaches the maximum number of iterations, resulting in a well-trained model. The generalization ability of the final model is then evaluated using the test set.

[0010] Step S3: Multi-level structure design optimization; This step utilizes the constructed PINN neural network surrogate model, combined with the NSGA-Ⅲ algorithm, to perform multi-objective optimization design of the shielding scheme. Within a set range, an initial population is randomly generated; the objective function value is calculated using the surrogate model obtained in Step S2; the population is sorted by non-dominated hierarchy; offspring populations are generated through genetic operations and merged with parents, and non-dominated hierarchy is sorted again, with elite populations selected based on reference points and niches; after repeated iterations until the convergence condition is met, the Pareto optimal solution set is finally obtained.

[0011] Furthermore, the model building and data preparation steps in step S1 include:

[0012] Step S11: Establish a multi-level shielding structure model; the following data needs to be configured:

[0013] The geometric model includes the simplified shape, size, and location of the structure to be shielded and its internal components; source term information includes the shape, type, location, orientation, and energy level of the source; count information includes the type of statistical results and whether they are converted into dose rate; material information includes the material density, nuclide type, nuclide percentage, and nuclide cross-section database of each module in the nuclear facility; and radiation tolerance information includes the initial radiation tolerance and target radiation tolerance of each component.

[0014] Step S12: Establish a structural thermodynamic performance analysis model; the following data needs to be configured:

[0015] Component information, including heating power and thermal resistance; material information, including material density, coefficient of thermal expansion, thermal conductivity, and Young's modulus of the structure and components; environmental information, including ambient temperature, whether it is a vacuum environment, and whether it is a natural air convection environment.

[0016] Step S13: Define the design variables and optimization objectives, and generate random uniform samples, specifically including:

[0017] The optimization objectives are the minimum neutron / gamma-ray normalized dose rate of the components, the total weight of the shielding structure, the average surface temperature of the components, and the thermal stress at the contact surfaces of the components. The design variables are the material type, thickness, arrangement order, and nuclide content of each shielding structure, with given value ranges or discrete values. A simulation model is established based on the multi-level structural model from step S11. Latin hypercube sampling (LHS) is used, dividing each dimension into m intervals in an n-dimensional space. Values ​​are randomly generated according to a uniform distribution, shuffled, and arranged into an n-dimensional vector; this sampling is repeated until the desired samples are generated.

[0018] Step S14: Call the particle transport program and the thermo-mechanical multiphysics simulation program to perform calculations and obtain integrated thermo-mechanical-shielding sample data, specifically including:

[0019] The geometric or material parameters in the radiation simulation file and the thermo-mechanical multiphysics simulation file are updated using random samples generated by LHS; the thermo-mechanical-shielding integrated sample dataset is generated for training by calculating with Monte Carlo particle transport software and multiphysics coupling program and combining with the input variable values.

[0020] Furthermore, the PINN neural network training step in step S2 includes:

[0021] Step S21: Data preprocessing; The particle simulation data and thermo-coupling data are processed separately. The shielded data undergoes logarithmic transformation to base 10, and the processed data is normalized. The mean and standard deviation of the thermo-coupling data are calculated, and standardized according to the standardization formula, the expression of which is:

[0022]

[0023] Where μ is the mean and σ is the standard deviation. The complete dataset is ultimately divided into training, validation, and test sets.

[0024] Step S22: Define physical equation constraints and loss functions; based on the structural thermodynamic performance analysis model, use physical formulas to describe heat transfer and stress caused by temperature differences in the equipment, providing physical constraints for the neural network. The thermal resistance and thermal stress calculations of the heat transfer path use classical formulas, and correction factors are used to describe coupling effects, shielding layer effects, and radiation corrections. For example, the formula for conductive thermal resistance:

[0025]

[0026] Among them, R th1 Where L is the thermal resistance, k is the thermal conductivity of the material, and A is the thermal transfer area.

[0027] Convection thermal resistance formula:

[0028]

[0029] Among them, R th2 For convective thermal resistance, h m Let A be the convective heat transfer coefficient, and A be the heat transfer area.

[0030] Temperature difference calculation formula:

[0031] ΔT=P·R

[0032] Where P is the heating power.

[0033] Thermal stress calculation formula:

[0034] σ=EαΔT

[0035] Where σ is thermal stress, E is Young's modulus of the material, α is the coefficient of thermal expansion of the material, and ΔT is the temperature gradient.

[0036] Step S24: PINN Neural Network Construction; the network consists of one input layer, m hidden layers, and one output layer. The number of neurons in the input and output layers is determined by the input and output variables. The i-th layer (i = 1, 2, ..., m) contains ni neurons, and adjacent layers undergo nonlinear transformations through activation functions. The optimizer is Adam, with a learning rate of 0.01. The actual output is divided into two parts: data-driven and physical equation-driven. The coupling coefficient will also be used as an adjustment factor, and the weights and biases will be iteratively updated. During training, the goal is to minimize the error performance function until training is complete or the error meets the conditions. The commonly used error performance function is the mean squared error (MSE), whose expression is:

[0037]

[0038] Among them, y i For the actual output, The desired output is given by n, where n is the number of samples.

[0039] Step S24: Neural network evaluation, specifically including: using the Mean Absolute Percentage Error MAPE:

[0040]

[0041] Logarithmic Root Mean Square Deviation Log-RMS:

[0042]

[0043] Determine the coefficient of determination R-squared: Determine the coefficient of determination R-squared:

[0044] [[ID=IP19]]

[0045] 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.

[0046] Furthermore, the steps of robust design optimization in step S3 include:

[0047] Step S31: Set the genetic algorithm parameters and randomly generate the initial parental population; [[ID=3.]

[0048] Step S32: Use the surrogate model built in step S2 to predict the population output;

[0049] Step S33: Construct the objective function of multi-objective optimization, calculate the domination solution set S and the domination times n of each individual; 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:

[0050]

[0051] and satisfy:

[0052]

[0053] 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 it is said that the target vector Y1 dominates 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;

[0054] Step S34: Reference Point Association and Niche Selection; Based on the dimension M of the objective function, reference points are uniformly distributed in the target space, and the distance of each individual to a reference point in the target space is calculated. Individuals are assigned to the nearest reference point, and the number of associated individuals ρ for each reference point is counted. Starting from the highest priority level R1, individuals are selected sequentially to join the next generation population; if partial selection is required at a certain level, individuals associated with sparse reference points are retained first; if multiple individuals are associated with the same reference point, they are selected randomly to avoid duplication.

[0055] Step S34: Genetic operations generate a progeny population; select high-quality individuals from the parent population based on non-dominant level and reference point sparsity. Simultaneously, select random individuals to perform simulated binary crossover and polynomial mutation.

[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. The solutions on the solution set have a certain degree of robustness. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of an integrated multi-level structure optimization design method based on PINN thermal-mechanical-shielding provided by the present invention;

[0058] Figure 2 This is a schematic diagram of the multi-level chip-circuit-casing structure provided by the present invention;

[0059] Figure 3 This is a schematic diagram of the simulation model analysis process of the thermo-mechanical performance of the multi-level structure according to an embodiment of the present invention;

[0060] Figure 4 This is a schematic diagram of the NSGA-Ⅲ multi-objective optimization algorithm based on the PINN neural network of this invention; Detailed Implementation

[0061] The following is in conjunction with the appendix Figure 1-4 The technical solution of the present invention will be described in detail below.

[0062] like Figure 1 As shown, this embodiment provides an optimized design method for a multi-level structure based on PINN's integrated thermal-mechanical-shielding system. It includes the following steps:

[0063] Step S1: Model building and data preparation;

[0064] This step is used to determine the multi-level shielding structure and analyze its thermodynamic performance, obtaining the sample data required for training the PINN neural network. A multi-level shielding structure model is constructed based on the radiation shielding capability of the components, and a structural thermodynamic performance analysis model is established based on the heat generation of the components. Structural properties are analyzed, and design variables and optimization objectives are defined. Structural parameter samples are randomly generated within a set range. Particle transport programs and thermo-mechanical multiphysics simulation programs are called to perform calculations, obtaining integrated thermo-mechanical-shielding sample data.

[0065] The steps of model building and data preparation in step S1 include:

[0066] Step S11: Establish a multi-level shielding structure model; the following data needs to be configured:

[0067] The geometric model includes the simplified shape, size, and location of the structure to be shielded and its internal components; source term information includes the shape, type, location, orientation, and energy level of the source; count information includes the type of statistical results and whether they are converted into dose rate; material information includes the material density, nuclide type, nuclide percentage, and nuclide cross-section database of each module in the nuclear facility; and radiation tolerance information includes the initial radiation tolerance and target radiation tolerance of each component.

[0068] like Figure 2 As shown in the example, the geometric model is a simplified model of the intelligent control module. The outer shell is composed of an aluminum alloy layer, a tungsten shielding layer, and a carbon fiber layer. The chip A on the front of the upper PCB board and the six smaller chips B on the front of the lower PCB board are key chips with weak radiation resistance, which require targeted protection. Their radiation resistance dose needs to meet certain requirements. A tungsten chip shielding cover is provided on the surface of A, and a tungsten cover is provided on the upper PCB board B for local circuit layer shielding.

[0069] Step S12: Establish a structural thermodynamic performance analysis model; the following data needs to be configured:

[0070] Component information, including heating power and thermal resistance; material information, including material density, coefficient of thermal expansion, thermal conductivity, and Young's modulus of the structure and components; environmental information, including ambient temperature, whether it is a vacuum environment, and whether it is a natural air convection environment.

[0071] Step S13: Define the design variables and optimization objectives, and generate random uniform samples, specifically including:

[0072] The optimization objectives are the minimum neutron / gamma-ray normalized dose rate of the components, the total weight of the shielding structure, the average surface temperature of the components, and the thermal stress at the contact surfaces of the components. The design variables are the material type, thickness, arrangement order, and nuclide content of each shielding structure, with given value ranges or discrete values. A simulation model is established based on the multi-level structural model from step S11. Latin hypercube sampling (LHS) is used, dividing each dimension into m intervals in an n-dimensional space. Values ​​are randomly generated according to a uniform distribution, shuffled, and arranged into an n-dimensional vector; this sampling is repeated until the desired samples are generated.

[0073] Step S14: Call the particle transport program and the thermo-mechanical multiphysics simulation program to perform calculations and obtain integrated thermo-mechanical-shielding sample data. Specifically, this includes: updating the geometric or material parameters in the radiation simulation file and the thermo-mechanical multiphysics simulation file with random samples generated by LHS; and generating an integrated thermo-mechanical-shielding sample dataset for training by calculating with Monte Carlo particle transport software and multiphysics coupling program and combining it with the input variable values.

[0074] like Figure 3 The diagram illustrates the thermal field distribution of a specific structural dimension. By selecting specific points or surfaces, optimized target temperatures and thermal stresses can be obtained. Then, through parametric modeling, the distribution of the geometric temperature and stress fields under different combinations of structural thicknesses is obtained. Finally, the temperature and stress value datasets at the target locations are collected. The shielding simulation objective function data is collected by setting corresponding counter cards.

[0075] Step S2: Training the PINN neural network;

[0076] This step is used to construct a multi-level structural proxy model integrating thermal, mechanical, and shielding functions, which supports subsequent multi-objective optimization.

[0077] The data obtained in step S1 is preprocessed and the dataset is divided into a training set, a validation set, and a test set. Based on the structural thermodynamic performance analysis model, physical equation constraints and loss functions are defined, and some physical parameters are used as mesh parameters for training. The network structure is trained using the training set, and the network parameters 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.

[0078] The steps for training the PINN neural network in step S2 include:

[0079] Step S21: Data preprocessing; The particle simulation data and thermo-coupling data are processed separately. The shielded data undergoes logarithmic transformation to base 10, and the processed data is normalized. The mean and standard deviation of the thermo-coupling data are calculated, and standardized according to the standardization formula, the expression of which is:

[0080]

[0081] Where μ is the mean and σ is the standard deviation. The complete dataset is ultimately divided into training, validation, and test sets.

[0082] Step S22: Define physical equation constraints and loss functions; based on the structural thermodynamic performance analysis model, use physical formulas to describe heat transfer and stress caused by temperature differences in the equipment, providing physical constraints for the neural network. The thermal resistance and thermal stress calculations of the heat transfer path use classical formulas, and correction factors are used to describe coupling effects, shielding layer effects, and radiation corrections. For example, the formula for conductive thermal resistance:

[0083]

[0084] Where R is the thermal resistance, L is the heat transfer length, k is the thermal conductivity of the material, A is the heat transfer area, and ω1 is the thermal resistance coupling coefficient, which is used to simplify the influence of other uncertainties in the conduction heat transfer path.

[0085] Convection thermal resistance formula:

[0086]

[0087] Among them, h m ω is the convective heat transfer coefficient, A is the heat transfer area, and ω2 is the convective thermal resistance coupling coefficient, used to simplify the influence of other uncertainties in the convective heat transfer path.

[0088] Temperature difference calculation formula:

[0089] ΔT=P·R

[0090] Where P is the heating power.

[0091] Thermal stress calculation formula:

[0092] σ=ω3·EαΔT

[0093] Where σ is thermal stress, E is Young's modulus of the material, α is the coefficient of thermal expansion of the material, ΔT is the temperature gradient, and ω3 is the thermal stress coupling coefficient.

[0094] Step S24: Construction of the PINN neural network; the network consists of one input layer, m hidden layers, and one output layer. The number of neurons in the input and output layers is determined by the input and output variables. The i-th layer (i = 1, 2, ..., m) contains ni neurons, and adjacent layers undergo nonlinear transformations through activation functions. The optimizer used is Adam, and the learning rate is set to 0.01. The actual output of this paper is divided into two parts: data-driven and physical equation-driven. The coupling coefficient will also be used as an adjustment factor and continuously updated along with the weights and biases. During training, the goal is to minimize the error performance function until training is complete or the error meets the conditions. The commonly used error performance function is the mean squared error (MSE), whose expression is:

[0095]

[0096] Among them, y i For the actual output, The desired output is given by n, where n is the number of samples.

[0097] Step S24: Neural network evaluation, specifically including: using Mean Absolute Percentage Error (MAPE).

[0098]

[0099] Log-RMS deviation:

[0100]

[0101] Determinance coefficient R-squared:

[0102]

[0103] 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.

[0104] Step S3: Multi-level structure design optimization;

[0105] Figure 4It is a schematic diagram of the NSGA-Ⅲ multi-objective optimization algorithm process based on the PINN neural network. This step uses the constructed PINN neural network surrogate model and combines the NSGA-Ⅲ algorithm to conduct multi-objective optimization design for the shielding scheme. Within the set range, an initial population is randomly generated; the surrogate model obtained in step S2 is used to calculate the objective function values; non-dominated ranking is performed on the population; the offspring population is generated through genetic operations and merged with the parent population, and non-dominated ranking is carried out and the elite population is selected based on the reference point and niche; after repeated iterations until the convergence condition is met, the Pareto optimal solution set is finally obtained.

[0106] The steps of the multi-level structure design in step S3 include:

[0107] Step S31: Set the genetic algorithm parameters, give the initialization parameters of the genetic algorithm such as the number of generations of evolution, population size, crossover probability, mutation probability, etc., and randomly generate the initial parent population;

[0108] Step S32: Use the surrogate model built in step S2 to predict the population output, perform radiation shielding calculation and thermal-mechanical coupling calculation on the initial population scheme with the constructed PINN neural network, and obtain four target values: the maximum transmittance of the shield, the total weight of the structure, the surface temperature of the components, and the thermal stress on the component contact surface;

[0109] Step S33: Construct the objective function for multi-objective optimization, calculate the domination solution set S and the number of domination times n of each individual; use the non-dominated sorting method to divide the initial population into non-dominated levels rank such as R1 layer, R2 layer,..., Rn layer, and the method for judging the domination relationship is as follows:

[0110]

[0111] And it satisfies:

[0112]

[0113] Among them, X_1 and X_2 are any two design parameter vectors; for any component of the target vector Y_1, if it is less than the corresponding component in the target 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 target vector Y_1 dominates the target 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;

[0114] Step S34: Reference Point Association and Niche Selection; Based on the dimension M of the objective function, uniformly set reference points in the target space and calculate the distance of each individual to the reference point in the target space. Assign individuals to the nearest reference point and count the number of associated individuals ρ for each reference point. Starting from the highest priority level R1, select individuals sequentially to add to the next generation population; if partial selection is required at a certain level, prioritize retaining individuals associated with sparse reference points (smaller ρ); if multiple individuals are associated with the same reference point, select randomly to avoid duplication. Maintain the same number of individuals as the initial population size to form an elite population, and replace the parent population with the elite population;

[0115] Step S34: Genetic operations generate offspring population; select high-quality individuals from the parent population according to non-dominant level and reference point sparsity. Simultaneously, select random individuals and perform genetic operations such as simulated binary crossover (SBX) and polynomial mutation to generate offspring population;

[0116] Step S35: Determine whether the number of generations has reached the maximum number of iterations. If the condition is met, output the elite population; otherwise, the elite population generates a new offspring population through genetic operations, replacing the original offspring population, and repeat steps S32-S34.

[0117] The above description is only a preferred embodiment of the present invention, and therefore cannot be used to limit the scope of the present invention. All equivalent changes and modifications made within the scope of the present invention and the content of the specification should still fall within the scope of the present invention.

Claims

1. A method for optimizing the design of a multi-level structure based on PINN (Physical Insulation-Shielding Integration), characterized in that, Includes the following steps: Step S1: Model building and data preparation; This step is used to determine the multi-level shielding structure and analyze its thermal performance, and obtain the sample data required for training the PINN neural network; construct a multi-level shielding structure model based on the radiation shielding capability of the components, and establish a structural thermal performance analysis model based on the heating of the components; analyze the structural properties and clarify the design variables and optimization objectives, and randomly generate structural parameter samples within the set range. The particle transport program and the thermo-mechanical multiphysics simulation program were called to perform calculations and obtain sample data integrating thermo-mechanical-shielding. Step S2: Training the PINN neural network; This step is used to construct a multi-level structural proxy model integrating thermal-mechanical-shielding, which supports subsequent multi-objective optimization; the data obtained in step S1 is preprocessed and the dataset is divided into training set, validation set and test set; Based on the structural thermodynamic performance analysis model, physical equation constraints and loss functions are defined, and some physical parameters are used as mesh parameters for training. The network structure is trained using the training set, and the network parameters 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: Multi-level structure design optimization; This step utilizes the constructed PINN neural network surrogate model, combined with the NSGA-Ⅲ algorithm, to perform multi-objective optimization design of the shielding scheme; within a set range, an initial population is randomly generated; the objective function value is calculated using the surrogate model obtained in step S2; the population is sorted by non-dominated hierarchy; offspring populations are generated through genetic operations and merged with parents, and non-dominated hierarchy is sorted again, with elite populations selected based on reference points and niches; after repeated iterations until the convergence condition is met, the Pareto optimal solution set is finally obtained.

2. The PINN-based integrated thermal-mechanical-shielding multi-level structure optimization design method according to claim 1, characterized in that: The steps of model building and data preparation in step S1 include: Step S11: Establish a multi-level shielding structure model; the following data needs to be configured: The geometric model includes the simplified shape, size, and location of the structure to be shielded and its internal components; source term information includes the shape, type, location, orientation, and energy level of the source; count information includes the type of statistical results and whether they are converted into dose rate; material information includes the material density, nuclide type, nuclide percentage, and nuclide cross-section database of each module in the nuclear facility; and radiation tolerance information includes the initial radiation tolerance and target radiation tolerance of each component. Step S12: Establish a structural thermodynamic performance analysis model; the following data needs to be configured: Component information, including heating power and thermal resistance; material information, including material density, coefficient of thermal expansion, thermal conductivity, and Young's modulus of the structure and components; environmental information, including ambient temperature, whether it is a vacuum environment, and whether it is a natural air convection environment. Step S13: Define the design variables and optimization objectives, and generate random uniform samples, specifically including: The optimization objectives are the minimum neutron / gamma-ray normalized dose rate of the components, the total weight of the shielding structure, the average surface temperature of the components, and the thermal stress at the contact surfaces of the components. The design variables are the material type, thickness, arrangement order, and nuclide content of each shielding structure, with given value ranges or discrete values. A simulation model is established based on the multi-level structure model in step S11. Latin hypercube sampling (LHS) is used, in an n-dimensional space, each dimension is divided into m intervals, and values ​​are randomly generated according to a uniform distribution, shuffled, and formed into an n-dimensional vector. The sampling is repeated until the required samples are generated. Step S14: Call the particle transport program and the thermo-mechanical multiphysics simulation program to perform calculations and obtain integrated thermo-mechanical-shielding sample data, specifically including: The geometric or material parameters in the radiation simulation file and the thermo-mechanical multiphysics simulation file are updated using random samples generated by LHS; the thermo-mechanical-shielding integrated sample dataset is generated for training by calculating with Monte Carlo particle transport software and multiphysics coupling program and combining with the input variable values.

3. The PINN-based integrated thermal-mechanical-shielding multi-level structure optimization design method according to claim 1, characterized in that: The steps for training the PINN neural network in step S2 include: Step S21: Data preprocessing; The particle simulation data and thermo-coupling data are processed separately. The shielded data undergoes logarithmic transformation to base 10, and the processed data is normalized. The mean and standard deviation of the thermo-coupling data are calculated, and standardized according to the standardization formula, the expression of which is: Where μ is the mean and σ is the standard deviation; the complete dataset is finally divided into training set, validation set, and test set; Step S22: Define physical equation constraints and loss functions; based on the structural thermodynamic performance analysis model, use physical formulas to describe heat transfer and stress caused by temperature difference in the equipment, providing physical constraints for the neural network; the thermal resistance and thermal stress of the heat transfer path are calculated using classical formulas, and correction factors are used to describe coupling effects, shielding layer effects, and radiation corrections. The formula for conduction thermal resistance is: Where R is the thermal resistance, L is the heat transfer length, k is the thermal conductivity of the material, and A is the heat transfer area; Thermal stress calculation formula: σ=EαΔT Where σ is thermal stress, E is Young's modulus of the material, α is the coefficient of thermal expansion of the material, and ΔT is the temperature gradient; Step S24: PINN Neural Network Construction; The network consists of one input layer, m hidden layers, and one output layer. The number of neurons in the input and output layers is determined by the input and output variables. The i-th layer (i = 1, 2, ..., m) contains ni neurons, and adjacent layers undergo nonlinear transformations through activation functions. The optimizer used is Adam, with a learning rate of 0.

01. The actual output is divided into two parts: data-driven and physical equation-driven. During training, the goal is to minimize the error performance function, gradually adjusting the weights and biases until training is complete or the error meets the conditions. The error performance function is the mean squared error (MSE), and its expression is: Among them, y i For the actual output, The desired output is given by n, where n is the number of samples. Step S24: Neural network evaluation, specifically including: using Mean Absolute Percentage Error (MAPE). Log-RMS deviation: Determinance coefficient R-squared: 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.

4. The PINN-based integrated thermal-mechanical-shielding multi-level structure optimization design method according to claim 1, characterized in that: The steps of the multi - level structure design in step S3 include: Step S31: Set the genetic algorithm parameters and randomly generate an initial parent population; Step S32: Use the surrogate model built in step S2 to predict the population output; Step S33: Construct the objective function for multi-objective optimization, calculate the dominant solution set S and the number of times each individual is dominated n; use the non-dominated sorting method to divide the initial population into layers R1, R2, ..., R... n For non-dominated hierarchical levels like rank, the method for determining dominance relationships is as follows: And satisfy: Where, 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; Step S34: Reference point association and niche selection; According to the dimension M of the objective function, uniformly set reference points in the objective space and calculate the distances corresponding to the reference points of each individual in the objective space. Assign individuals to the reference point with the closest distance, and count the number of associated individuals ρ for each reference point. Starting from the highest - priority level R1, select individuals to join the next - generation population in turn; if partial selection is required at a certain level, preferentially retain individuals associated with sparse reference points; if multiple individuals are associated with the same reference point, randomly select to avoid duplication; Step S34: Genetic operations to generate the offspring population; Select high - quality individuals from the parent population according to the non - dominated level and reference - point sparsity; at the same time, select random individuals to perform simulated binary crossover and polynomial mutation; 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 robustness.

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