A radiation shielding multi-objective optimization design method and system

Abstract

The application discloses a kind of radiation shielding multi-objective optimization design method and system, it is related to radiation shielding optimization design technical field.The specific inclusion includes: obtaining the radiation shielding scheme sample that has been evaluated, constructs the physical enhancement sequence characteristics containing physical cumulative effect;Based on target tolerance vector, generate tolerance pair-wise dominance label;Through the joint training of overall dominance relationship loss, single-target relationship loss, target difference regression loss and left-right reverse consistency loss, multi-task dominance relationship learning model is trained;The pair-wise dominance probability between candidate schemes is predicted using the model, and the expected non-dominance is calculated and the candidate schemes are rearranged, for recommending radiation shielding scheme using limited simulation samples.

Description

Technical Field

[0001] This invention relates to the field of radiation shielding optimization design technology, and in particular to a multi-objective optimization design method and system for radiation shielding. Background Technology

[0002] Radiation shielding design is widely used in engineering applications such as reactors, nuclear fuel cycle facilities, radioactive source devices, space nuclear propulsion systems, and radiation detection equipment. Typical shielding structures often have layered or partitioned features. The thickness, density, equivalent atomic number, equivalent mass number, and material configuration of different shielding layers all affect the radiation dose, shielding weight, volume, and structural constraints. Multi-objective optimization of radiation shielding typically requires simultaneously reducing dose, controlling weight and volume, and meeting engineering safety requirements. Increasing the use of high-density materials such as lead, tungsten, and stainless steel, or increasing the shielding thickness, can usually reduce the dose but will lead to increased weight and volume; conversely, reducing weight and volume may result in failure to meet dose constraints.

[0003] Chinese patent CN102663151B discloses an optimized design method for nuclear radiation shielding materials. This method involves initializing the material mix ratio, calculating physical quantities, performing dimensionless weighted summation, and iteratively outputting the optimized material mix ratio using a genetic algorithm. Existing optimization schemes typically employ genetic algorithms, particle swarm optimization (PSO), S-index evolutionary multi-objective optimization (SMS-EMOA), or objective weighting methods to search for candidate shielding schemes, and obtain evaluation results through Monte Carlo particle transport procedures, discrete ordinate procedures, or experimental testing. With the development of machine learning surrogate models, some schemes utilize neural networks, random forests, or gradient boosting trees to predict target values ​​such as dose, weight, and volume, and then derive Pareto dominance relationships based on the predicted target values. While these methods can reduce manual trial and error to some extent, they still suffer from problems such as high simulation evaluation costs, propagation of target value surrogate errors, easy reversal of boundary candidate dominance relationships, insufficient utilization of pairwise supervision information in historical samples, and inadequate expression of the physical characteristics of layered shielding. Especially when the difference between the targets of two candidate shielding schemes is close to the Monte Carlo statistical error or engineering tolerance, simply ranking them based on the predicted target value can easily misjudge the approximately equivalent schemes within the numerical error range as a dominant relationship, and it is also difficult to express the incomparable state of multiple targets such as lower dose but greater weight.

[0004] Therefore, how to directly learn the multi-objective dominance relationship between shielding schemes using a limited sample of evaluated radiation shielding schemes, and output recommended radiation shielding schemes that are closer to the Pareto front based on the target tolerance stability, and further consider the low-confidence inference risk in some implementations, has become a technical problem that needs to be solved. Summary of the Invention

[0005] The main objective of this invention is to provide a multi-objective optimization design method and system for radiation shielding, which aims to directly learn the multi-objective dominance relationship between shielding schemes using a limited sample of evaluated radiation shielding schemes, and to output a recommended radiation shielding scheme that is closer to the Pareto front based on the objective tolerance stability; in some embodiments, low-confidence inference risk is further considered.

[0006] To achieve the above objectives, this invention proposes a multi-objective optimization design method for radiation shielding, comprising the following steps: The evaluated radiation shielding scheme samples are obtained by the computing device. Each radiation shielding scheme sample includes multi-layer shielding structure parameters and multi-objective evaluation results, including at least radiation dose. Feature extraction is performed on the parameters of the multi-layer shielding structure to construct a physical enhancement sequence feature. The physical enhancement sequence feature includes at least an accumulation feature representing the physical accumulation effect calculated based on the thickness and density of each shielding layer. Based on the preset target tolerance vector, the multi-target evaluation results of any two radiation shielding scheme samples are compared in pairs to generate tolerance-based pairwise domination labels, including the first scheme dominating the second scheme, the second scheme dominating the first scheme, and neutral incomparable relationships. The physical enhancement sequence features corresponding to any two radiation shielding scheme samples are input into an initial multi-task neural network to obtain a prediction output including at least the overall dominance probability, single-target relationship prediction result, and target difference. Based on the prediction output and the tolerance-based pairwise dominance label, the network parameters are jointly updated through overall dominance relationship loss, single-target relationship loss, target difference regression loss, and left-right inverse consistency loss to obtain a multi-task dominance relationship learning model. The overall dominance probability is used to represent three types of relationships: the input-first scheme dominates the input-later scheme, the input-later scheme dominates the input-first scheme, and the two are neutral and incomparable. The target difference is the difference between the evaluation results of the input-first scheme and the input-later scheme in each target category. The left-right inverse consistency loss is used to constrain the target difference of the same radiation shielding scheme before and after swapping the input order to be opposite numbers, the dominance direction probabilities to be swapped, and the neutral and incomparable probabilities to be consistent. Obtain a set of radiation shielding candidate schemes to be optimized, predict the pairwise dominance probabilities between each pair of radiation shielding candidate schemes in the set using the multi-task dominance relationship learning model, calculate the expected non-dominance degree of each radiation shielding candidate scheme based on the pairwise dominance probabilities, rearrange the set of radiation shielding candidate schemes according to the expected non-dominance degree, and output the rearranged recommended radiation shielding scheme through a designed software interface.

[0007] Preferably, each of the radiation shielding scheme samples includes The shielding layer, the first The original parameters of the shielding layer include thickness. ,density Equivalent atomic number and equivalent mass number ; The step of extracting features from the parameters of the multi-layer shielding structure and constructing physical enhancement sequence features includes: Regarding the first Each shielding layer has a corresponding cumulative thickness. Quality and thickness Cumulative mass thickness Equivalent atomic number ratio and density normalization ratio And use it as the physical enhancement sequence feature; The formula for calculating the cumulative thickness is as follows:

[0008] in, For the first The cumulative thickness of each shielding layer For the first The thickness of the shielding layer, From arrive The cumulative masking layer index, This is the index of the current shielding layer; The formula for calculating mass thickness is:

[0009] in, For the first The mass and thickness of each shielding layer For the first The thickness of the shielding layer, For the first The density of each shielding layer; The formula for calculating cumulative mass thickness is:

[0010] in, For the first The cumulative mass thickness of each shielding layer For the first The thickness of the shielding layer, For the first The density of each shielding layer From arrive The cumulative masking layer index, This is the index of the current shielding layer; The formula for calculating the ratio of equivalent atomic numbers is:

[0011] in, For the first The ratio of the equivalent atomic numbers of each shielding layer For the first The equivalent atomic number of each shielding layer For the first The equivalent mass number of each shielding layer To prevent division by zero constants, This is the index of the current shielding layer; The formula for calculating the density normalized ratio is:

[0012] in, For the first The density normalized ratio of each shielding layer For the first The density of each shielding layer For the first The equivalent mass number of each shielding layer To prevent division by zero constants, This is the index of the current shielding layer.

[0013] Preferably, the step of performing pairwise comparisons of the multi-objective evaluation results of any two radiation shielding scheme samples based on a preset target tolerance vector to generate tolerance-based pairwise dominant labels includes: Extract a first radiation shielding scheme sample and a second radiation shielding scheme sample from the radiation shielding scheme sample; Obtain the first multi-target evaluation result of the first radiation shielding scheme sample. And the second multi-target evaluation results of the second radiation shielding scheme sample. In this context, the multi-objective evaluation results for each object category are all evaluation results after unifying the object direction. The evaluation results after unifying the object direction are used for pairwise comparisons according to the direction of numerical decrease. This represents the sample index of the first radiation shielding scheme sample. This represents the sample index of the second radiation shielding scheme sample. Indicates the target category index; Obtain the target tolerance vector components of the target category ; When all target categories are satisfied And at least one target category satisfies When the first radiation shielding scheme sample dominates the second radiation shielding scheme sample, a tolerance-based pairwise domination tag is generated to indicate that the first scheme dominates the second scheme. When all target categories are satisfied And at least one target category satisfies When the second radiation shielding scheme sample dominates the first radiation shielding scheme sample, a tolerance-based pairwise domination tag is generated to indicate that the second scheme dominates the first scheme. If neither of the above two dominance conditions is met, the two are determined to be neutrally incomparable, and a tolerance-based pairwise dominance label for neutrally incomparable relationship is generated.

[0014] Preferably, the target tolerance vector component of the target category The error is determined by one of the following methods: statistical error determination based on Monte Carlo particle transport simulation, determination based on engineering acceptance margin, or determination based on the standard deviation of multi-objective evaluation results in the training set multiplied by a preset scaling factor.

[0015] Preferably, the initial multi-task neural network includes a shared shield layer encoder and a pairwise fusion module; The step of inputting the physical enhancement sequence features corresponding to any two radiation shielding scheme samples into the initial multi-task neural network to obtain the corresponding prediction output includes: The first physical enhancement sequence features Second physical enhancement sequence features The inputs are respectively fed into the shared shield layer encoder, and the corresponding first encoding vector is output. Second encoding vector ; The first encoded vector and the second encoding vector The input is fed into the pairwise fusion module to calculate the fusion vector. The formula for calculating the fusion vector is as follows:

[0016] in, Sample of the first radiation shielding scheme Sample of the second radiation shielding scheme The fusion vector, This is the first encoded vector. This is the second encoding vector. This is a vector of absolute values ​​of the element-by-element differences between the first and second encoded vectors. This is the element-wise product vector of the first and second encoded vectors, and the symbol "[]" indicates the vector concatenation operation.

[0017] Preferably, the initial multi-task neural network further includes a fusion vector. The overall dominance prediction head, single-objective relationship prediction head, and objective difference regression head are used for multi-task prediction. The network parameters are updated jointly by the overall dominance relationship loss, single-objective relationship loss, objective difference regression loss, and left-right inverse consistency loss, and the joint total loss function is described. The calculation formula is:

[0018] In the formula, For the joint total loss function, Output the corresponding overall dominance relationship loss for the overall dominance prediction head. The single-objective relationship prediction head outputs the corresponding single-objective relationship loss. Output the corresponding target difference regression loss for the target difference regression head. The left-right reverse consistency loss, , and These are the preset weights for the corresponding losses.

[0019] Preferably, in the step of obtaining the evaluated radiation shielding scheme samples, a weighted sampling strategy is used to construct paired training data consisting of the first radiation shielding scheme sample and the second radiation shielding scheme sample; wherein, the weighted sampling strategy increases the sampling weight for radiation shielding scheme samples located at the Pareto front boundary, dose boundary samples where the radiation dose reaches a preset dose threshold, and tolerance boundary samples where the absolute value of the target difference for any target category is not greater than the corresponding target tolerance vector component.

[0020] Preferably, the step of calculating the expected non-dominated degree of each radiation shielding candidate scheme based on the pairwise dominance probability, and rearranging the radiation shielding candidate scheme set according to the expected non-dominated degree, includes: For any first radiation shielding candidate scheme Based on its comparison with other second radiation shielding candidate schemes in the set The probability of pairwise dominance between them is used to calculate the probability tournament score. and expected non-dominated degree ; The formula for calculating the probability tournament score is as follows:

[0021] The formula for calculating the expected degree of non-domination is as follows:

[0022] In the formula, The first candidate for radiation shielding The probability of tournament scores, The first radiation shielding candidate scheme The expected degree of non-domination, This is an index of the currently calculated radiation shielding candidate schemes. To remove Index of other radiation shielding candidate schemes, This indicates the division scheme in the set. All other options Summation, This represents a prediction scheme for a multi-task dominance relationship learning model. Domination Plan The probability, This indicates the probability that the two are neutrally incomparable. Indicates the prediction scheme Domination Plan The probability, Weighting coefficients for neutral, incomparable relationships; According to the tournament score of the probability The set of radiation shielding candidate schemes is first sorted, and the top-ranked schemes are selected. Several radiation shielding candidate schemes were proposed, among which... The preset number of filters, and It is a positive integer, and then according to the expected nondominance degree. Forward The candidate radiation shielding schemes are rearranged to output the final recommended radiation shielding scheme.

[0023] Preferably, in the calculation of the probability tournament score and expected non-dominated degree Previously, conservative dominance inferences were also applied; The specific logic of the conservative dominance inference is as follows: the pairwise dominance probability includes schemes. Domination Plan probability, scheme Domination Plan The probability and the solution With the plan The probability that the scheme belongs to a neutral and incomparable relationship; if the scheme Domination Plan The probability did not reach the preset safety confidence threshold, or the scheme... Domination Plan If the difference between the probability of pairwise dominance and the neutral incomparable probability does not exceed a preset probability interval, then the pairwise dominance probability is forcibly replaced with... , , The probability of a neutral, incomparable relationship.

[0024] This application also discloses a radiation shielding multi-objective optimization design system, including a data acquisition module, a feature extraction module, a label generation module, a model training module, and an inference rearrangement module. The feature extraction module and the label generation module are respectively connected to the data acquisition module, the model training module is respectively connected to the feature extraction module and the label generation module, and the inference rearrangement module is connected to the model training module. The data acquisition module is used to acquire samples of evaluated radiation shielding schemes. Each sample of radiation shielding scheme includes multi-layer shielding structure parameters and multi-target evaluation results, including at least radiation dose. The feature extraction module is used to extract features from the parameters of the multi-layer shielding structure and construct physical enhancement sequence features. The physical enhancement sequence features include at least cumulative features that characterize the physical cumulative effect based on the thickness and density of each shielding layer. The tag generation module is used to perform a pairwise comparison of the multi-target evaluation results of any two radiation shielding scheme samples based on a preset target tolerance vector, and generate tolerance-based pairwise domination tags including the first scheme dominating the second scheme, the second scheme dominating the first scheme, and neutral incomparable relationships. The model training module is used to input the physical enhancement sequence features corresponding to any two radiation shielding scheme samples into an initial multi-task neural network, obtain a prediction output including at least the overall dominance probability, single-target relationship prediction result, and target difference, and based on the prediction output and the tolerance-based pairwise dominance label, jointly update the network parameters through overall dominance relationship loss, single-target relationship loss, target difference regression loss, and left-right inverse consistency loss to obtain a multi-task dominance relationship learning model; wherein, the overall dominance probability is used to represent three types of relationships: the input-first scheme dominates the input-later scheme, the input-later scheme dominates the input-first scheme, and the two are neutrally incomparable; the target difference is the difference between the evaluation results of the input-first scheme and the input-later scheme in each target category; the left-right inverse consistency loss is used to constrain the target difference of the same radiation shielding scheme before and after swapping the input order to be opposite numbers, the dominance direction probabilities to be swapped, and the neutrally incomparable probabilities to be consistent; The inference rearrangement module is used to obtain a set of radiation shielding candidate schemes to be optimized, predict the pairwise dominance probability between each pair of radiation shielding candidate schemes in the set of candidate schemes through the multi-task dominance relationship learning model, calculate the expected non-dominance degree of each radiation shielding candidate scheme based on the pairwise dominance probability, rearrange the set of radiation shielding candidate schemes according to the expected non-dominance degree, and output the rearranged recommended radiation shielding scheme.

[0025] The above technical solution has the following advantages: Evaluated radiation shielding scheme samples can be transformed into physically enhanced sequence features containing layered physical accumulation information, and the model input can preserve the shielding layer thickness, density, and layer order relationship. By generating tolerance-based pairwise dominance labels through the target tolerance vector, minor differences within the simulation error or engineering tolerance range can be categorized into neutral incomparable relationships, reducing dominance misjudgments at boundary candidates. Through joint training using overall dominance loss, single-target relationship loss, target difference regression loss, and left-right inverse consistency loss, the multi-task dominance learning model can simultaneously learn overall dominance, single-target differences, and self-consistent constraints after input order swapping. By predicting pairwise dominance probabilities for the candidate scheme set and calculating the expected non-dominated degree based on the pairwise dominance probabilities, candidate schemes can be reordered without directly relying on the ranking of a single target value. This scheme can improve the utilization rate of limited high-cost simulation samples and enhance the stability of recommended radiation shielding schemes as they approach the Pareto front. Attached Figure Description

[0026] The present invention will now be described in detail with reference to specific embodiments and accompanying drawings, wherein: Figure 1 This is a flowchart illustrating the multi-objective optimization design method for radiation shielding provided in an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram illustrating the principle of the multi-objective optimization design method for radiation shielding provided in an embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram of the training and inference timing provided in an embodiment of the present invention.

[0029] Figure 4 This is a schematic diagram of the structure of the radiation shielding multi-objective optimization design system provided in an embodiment of the present invention.

[0030] Figure 5 This is a hardware execution block diagram provided for an embodiment of the present invention. Detailed Implementation

[0031] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be noted that the terms "first," "second," etc., used in the present invention are used to distinguish similar objects and are not used to limit a specific order or sequence.

[0032] In typical applications such as nuclear engineering or space nuclear power shielding (e.g., reactors, nuclear fuel cycle facilities, radioactive source devices, space nuclear power systems, and radiation detection equipment), radiation shielding designs are widely presented as layered or partitioned structures. For example, the inner layer near the radiation source is typically used to moderate neutrons, the middle layer to absorb thermal neutrons, and the outer layer to attenuate gamma rays and provide structural support or meet structural strength requirements. Since the thickness, density, material equivalent atomic parameters, and presence of an cladding layer of each shielding layer all significantly affect the final radiation dose, shielding weight, and volume, increasing the density of materials such as lead, tungsten, and stainless steel, or increasing the shielding thickness, can usually reduce the dose but significantly increase weight and volume; conversely, reducing weight and volume may lead to failure to meet dose constraints. Therefore, radiation shielding design is essentially a typical multi-objective optimization problem. Existing multi-objective optimization algorithms, such as genetic algorithms, particle swarm optimization (PSO) algorithms (e.g., bare bone particle swarm optimization), or S-index evolutionary multi-objective optimization (SMS-EMOA), require iterative generation of numerous candidate solutions and repeated calls to Monte Carlo particle transport procedures for evaluation during the search process. The computational cost of high-fidelity simulation evaluation is extremely high. Furthermore, existing machine learning surrogate models typically employ a path of first predicting the target value and then deriving the Pareto dominance relationship. When the target approaches the Pareto front boundary, even small prediction errors can easily lead to a reversal of the dominance relationship. In addition, existing evaluated sample pairs contain rich pairwise comparative supervision information, but conventional methods often treat samples as independent coordinate points, failing to fully exploit the characteristics of the overall merits and demerits of solutions and the incomparability of multi-objective states.

[0033] To address the aforementioned issues, this embodiment provides a multi-objective optimization design method for radiation shielding. This method directly utilizes limited, high-cost simulation samples to learn the multi-objective dominance relationships among candidate shielding schemes, and then selects recommended radiation shielding candidate schemes by introducing a anticipated non-dominated degree rearrangement mechanism.

[0034] like Figure 1 and Figure 2 As shown, the radiation shielding multi-objective optimization design method of this embodiment includes the following steps: First, data acquisition and feature construction steps are performed. Samples of evaluated radiation shielding schemes are acquired. Each sample includes multi-layer shielding structure parameters and multi-target evaluation results, including at least radiation dose. These multi-target evaluation results are the results after target direction unification, and are used for pairwise comparisons according to the direction of numerical decrease. Specifically, for a given sample containing... A sample of radiation shielding schemes with one shielding layer, the first... The original parameters of the shielding layer include thickness. ,density Equivalent atomic number Equivalent mass number And parameters such as material type or coating markings.

[0035] Regarding the first Each shielding layer has a corresponding cumulative thickness. Quality and thickness Cumulative mass thickness Equivalent atomic number ratio and density normalization ratio And all of them are used as physical enhancement sequence features. The cumulative thickness calculation formula is as follows: ,in, For the first The cumulative thickness of each shielding layer For the first The thickness of the shielding layer, From arrive The cumulative masking layer index, This is the index of the current shielding layer; the formula for calculating the mass thickness is... ,in, For the first The mass and thickness of the shielding layer For the first The thickness of the shielding layer, For the first The density of each shielding layer; the formula for calculating the cumulative mass thickness is... ,in, For the first The cumulative mass thickness of each shielding layer For the first The thickness of the shielding layer, For the first The density of each shielding layer From arrive The cumulative masking layer index, This is the index of the current shielding layer; the formula for calculating the ratio of equivalent atomic numbers is: ,in, For the first The ratio of the equivalent atomic numbers of each shielding layer For the first The equivalent atomic number of each shielding layer For the first The equivalent mass number of each shielding layer To prevent division by zero constants, This is the index of the current shielding layer; the formula for calculating the density normalization ratio is... ,in, For the first The density normalized ratio of each shielding layer For the first The density of each shielding layer For the first The equivalent mass number of each shielding layer To prevent division by zero constants, This is the index of the current shielding layer.

[0036] Furthermore, a logarithmic transformation feature of thickness can be added during the feature extraction process. Through this feature addition method, simple structural parameters are transformed into a physically meaningful cumulative shielding effect sequence. Since the physical enhancement sequence features contain key physical information such as shielding layer order information, cumulative thickness, and mass thickness, it helps the model utilize shielding layer order and cumulative effect information, and reduces the difficulty for the model to learn the physical laws of shielding. Optionally, the aforementioned physical enhancement sequence features may further include at least one of the following features: macroscopic cross-section, mass attenuation coefficient, material category embedding, cladding layer equivalent thickness, source term orientation factor, and probe surface distance. These features characterize the radiation attenuation capability, geometric cumulative effect, or source term propagation conditions of the shielding material.

[0037] like Figure 2 and Figure 3 As shown, the next step is to train the multi-task dominance relationship learning model. The physical enhancement sequence features corresponding to any two radiation shielding scheme samples are input into the initial multi-task neural network to obtain the corresponding prediction output. The initial multi-task neural network includes a shared shielding layer encoder and a pairwise fusion module. It should be noted that the shared shielding layer encoder can be flexibly selected according to the characteristics of the actual shielding scheme; for example, a Transformer encoder, a one-dimensional convolutional network, a recurrent neural network, a graph neural network, or a masked attention network can be used. For schemes with a fixed number of shielding layers, a one-dimensional convolutional network can be preferred; while for schemes with variable numbers of layers or complex connection relationships, a graph neural network can be used. The first physical enhancement sequence features are input into the initial multi-task neural network. Second physical enhancement sequence features The inputs are fed into the shared shield layer encoder, and the corresponding first encoded vector is output. Second encoding vector Next, the first encoded vector... Second encoding vector Input into the pairwise fusion module to calculate the fusion vector .

[0038]

[0039] In the formula, This represents element-wise multiplication. Furthermore, the pairwise fusion module can also be equivalently implemented using bilinear layers, cross-attention mechanisms, convolutional pair maps, or Siamese network structures, all of which can be used to learn the relationship between two masking schemes. The initial multi-task neural network also includes a fusion vector-based... The system includes an overall dominance prediction head, a single-objective relationship prediction head, and an objective difference regression head for multi-task prediction.

[0040] Based on the predicted output of the initial multi-task neural network and the previously generated tolerance-based pairwise dominance labels, the network parameters of the initial multi-task neural network are jointly updated using overall dominance relationship loss, single-objective relationship loss, target difference regression loss, and left-right inverse consistency loss, thereby obtaining a trained multi-task dominance relationship learning model. The predicted output includes at least the overall dominance probability, the single-objective relationship prediction result, and the target difference.

[0041]

[0042] in, For the joint total loss function, The overall dominance prediction head outputs the corresponding overall dominance relationship loss. The single-objective relation prediction head outputs the corresponding single-objective relation loss. Output the corresponding target difference regression loss for the target difference regression header. For left-right reverse consistency loss, , and These are the preset weights for the corresponding losses. Optionally, the overall dominance relationship loss... Cross-entropy, focus loss, class balance loss, or ranking loss can be used; target difference regression loss. L1 loss, L2 loss, smooth L1 loss, or uncertainty-weighted regression loss can be flexibly adopted. Left-right reverse consistency loss is used to constrain the output consistency of the same radiation shielding scheme after the input order is interchanged.

[0043] Specifically, the overall dominance probability includes a first probability, a second probability, and a third probability. The first probability is the probability that the radiation shielding scheme with the input first dominates the radiation shielding scheme with the input second. The second probability is the probability that the radiation shielding scheme with the input second dominates the radiation shielding scheme with the input first. The third probability is the probability that the two radiation shielding schemes belong to a neutral and incomparable relationship. The target difference is the difference between the evaluation results of the radiation shielding scheme with the input first and the radiation shielding scheme with the input second in each target category. The left-right reverse consistency loss uses the sum of the target differences before and after swapping the input order, the difference in the probability of the corresponding dominance direction, and the difference in the probability of neutral and incomparable as a consistency penalty term, and constrains the model output by minimizing this consistency penalty term. By introducing multi-task learning and consistency constraints, it helps to reduce the dominance relationship reversal caused by simple target value regression at the boundary candidate, improves the internal self-consistency of the multi-task dominance relationship learning model, and reduces the risk of inconsistent judgments due to different input directions.

[0044] Among them, the single-target relationship label is generated based on the target difference of each target category and the corresponding target tolerance vector component. When When the first solution is generated, it is at the time... In terms of single-objective relation labels, it is superior to the second option in terms of individual objectives; when At that time, the second scheme was generated in the 1st month. A single-objective relation label that is superior to the first solution in terms of the target; otherwise, generate the second solution. Neutral relation labels on each target. Target difference labels are... ,in, Sample of the first radiation shielding scheme Sample of the second radiation shielding scheme In the Target difference labels on each target category Sample of the first radiation shielding scheme In the Multi-objective evaluation results across multiple objective categories Sample of the second radiation shielding scheme In the Multi-objective evaluation results across multiple target categories. The left-right reverse consistency loss is also used to constrain the correspondence between the overall dominance probability and the input order before and after swapping. If the first probability before the swap represents the scheme... Domination Plan The probability is then represented by the second probability scheme after the interchange. Domination Plan The probability of the two is used as a consistency penalty term; if the second probability representation scheme before the swap is used... Domination Plan The probability of the first probability after the interchange is given by the following scheme. Domination Plan The probability of the two is used as a consistency penalty term; the third probability before and after the swap both represent the scheme. With the plan The probability of belonging to a neutral and incomparable relationship is used as a consistency penalty term, and the difference between the two is used as a consistency penalty term.

[0045] Finally, the inference and non-dominated degree rearrangement steps are performed. A set of radiation shielding candidate schemes to be optimized is obtained. The pairwise dominance probabilities between any two candidates in the set are predicted using a trained multi-task dominance relationship learning model. Based on the pairwise dominance probabilities, the expected non-dominated degree of each candidate scheme is calculated, and the set of candidate schemes is rearranged according to the expected non-dominated degrees. For any first radiation shielding candidate scheme... Based on its comparison with other second radiation shielding candidate schemes in the set The pairwise dominance probabilities between them are calculated separately for the probability tournament score. and expected non-dominated degree .

[0046]

[0047]

[0048] in, The first candidate for radiation shielding The probability of tournament scores, The first candidate for radiation shielding The expected degree of non-domination, This is an index of the currently calculated radiation shielding candidate schemes. To remove Index of other radiation shielding candidate schemes, This indicates the division scheme in the set. All other options Summation, This represents a prediction scheme for a multi-task dominance relationship learning model. Domination Plan The probability, This indicates the probability that the two are neutrally incomparable. Indicates the prediction scheme Domination Plan The probability, The weighting coefficients represent neutral, incomparable relationships. By calculating the sum of the expected probabilities that each candidate solution is not dominated by any other candidate in the set, this can be used to measure how close the current candidate solution is to the non-dominated region. The system first ranks the candidates according to their probability tournament scores. The set of candidate radiation shielding schemes is first sorted, and the top-ranked schemes are selected. Several radiation shielding candidate schemes were proposed, among which... The preset number of filters, and It is a positive integer, and then according to the expected non-dominated degree. Forward The candidate radiation shielding schemes are meticulously rearranged, and the final recommended radiation shielding scheme is output. In alternative approaches, the candidate rearrangement step can also employ soft Copeland scores, i.e., soft ranking scores based on the cumulative pairwise win-loss relationships, pairwise win rate matrix ranking, top-K (Top-K) local non-dominated ranking, or hybrid rearrangement strategies combining the traditional non-dominated ranking genetic algorithm II (NSGA-II) selection operator. Furthermore, the method provided by this invention can be used as a standalone offline candidate screening tool, or directly embedded into existing optimization loops such as NSGA-II, Particle Swarm Optimization (PSO), and S-index Evolutionary Multi-Objective Optimization (SMS-EMOA). Before each round of high-fidelity simulation, radiation shielding candidate schemes whose ranking scores meet preset screening conditions are prioritized for recommendation. This method, which further converts pairwise dominance probabilities into candidate-level ranking scores, compared to traditional methods that directly rank based on predicted target values ​​or hard-label win-loss counts, not only more clearly expresses the neutral incomparable relationships of conflicting objectives but also enhances the stability of the output radiation shielding design located at the Pareto front.

[0049] Based on the above embodiment one, this embodiment two further elaborates on the specific method for determining the target tolerance vector and the weighted sampling strategy for training data.

[0050] Target tolerance vector components of the target category The target tolerance is preferably determined using one of the following three methods. The first method is based on statistical error determination using Monte Carlo particle transport simulations. The Monte Carlo method inevitably introduces relative errors when calculating deep-penetrating radiation shielding problems; for example, the statistical error of dose results is typically between 1% and 5%. Converting this statistical error into a specific target tolerance helps prevent the model from misinterpreting purely random fluctuations as a physical improvement in shielding performance. The second method is based on engineering acceptance margins. In actual nuclear facility shielding engineering design, there are usually clear volume or weight design limits, such as a weight tolerance of 10 kg. Using this engineering margin as the tolerance better meets the final industrial application requirements. The third method is based on multiplying the standard deviation of multi-objective evaluation results in the training set by a preset scaling factor, such as 0.05. Furthermore, the target tolerance can also be determined by dose acceptance criteria, engineering manufacturing errors, expert experience thresholds, or adaptive quantiles. This approach provides an adaptive, data-driven method when specific physical error indicators are lacking.

[0051] In the step of acquiring evaluated radiation shielding scheme samples, a weighted sampling strategy is used to construct paired training data consisting of first and second radiation shielding scheme samples. When randomly selecting two shielding schemes to form training pairs, the target difference of some scheme pairs is much larger than the corresponding target tolerance vector component, resulting in insufficient learning of boundary conditions by the model. Therefore, the weighted sampling strategy in this embodiment increases the sampling weight for radiation shielding scheme samples located at the Pareto front boundary, enabling the model to learn the boundary regions where different targets are mutually balanced. At the same time, the sampling weight is increased for dose boundary samples where the radiation dose reaches a preset dose threshold, thereby enhancing the model's sensitivity to screening schemes that meet the basic radiation protection safety red line. In addition, the sampling weight is also increased for tolerance boundary samples where the absolute value of the target difference for any target category is not greater than the corresponding target tolerance vector component, prompting the model to learn subtle differences in shielding structures. Through the above weighted sampling strategy, the redundancy of training set information caused by traditional random combination is reduced, and the model's ability to distinguish complex non-dominated regions is improved.

[0052] Based on the above embodiments, this third embodiment focuses on explaining in detail the conservative dominance inference mechanism performed before calculating the probability tournament score and expected non-dominance degree.

[0053] Calculating tournament scores based on probability and expected non-dominated degree Previously, the system also needed to perform conservative dominance inference. The specific logic of conservative dominance inference is as follows: pairwise dominance probabilities include schemes. Domination Plan probability, scheme Domination Plan The probability and the solution With the plan The probability that the scheme belongs to a neutral and incomparable relationship; if the scheme Domination Plan The probability did not reach the preset safety confidence threshold, which is, for example, 0.85, or the scheme... Domination Plan If the difference between the probability of pairwise dominance and the neutral incomparable probability does not exceed a preset probability interval (e.g., 0.2), the system intervenes and forcibly replaces the pairwise dominance probability with a fixed probability. , , The probability of neutral, incomparable relationships. In some alternative embodiments, the inference strategy is not limited to using a fixed probability threshold; it can also be implemented using a calibrated dynamic threshold, Bayesian confidence intervals, temperature-scaled probabilities, or ensemble model voting strategies. In engineering practice, conservative dominance inference can retain candidate solutions that are difficult to judge in the same priority level, thereby reducing the erroneous elimination of candidate solutions caused by low-confidence inference. This mechanism is used to conservatively correct the output of the multi-task dominance relationship learning model, which can reduce the risk of candidate misjudgment due to extrapolation generalization errors of surrogate models and improve the stability of the final re-ranking results.

[0054] This fourth embodiment provides a radiation shielding multi-objective optimization design system corresponding to the above-described radiation shielding multi-objective optimization design method.

[0055] like Figure 4 As shown, the system includes a data acquisition module 101, a feature extraction module 102, a label generation module 103, a model training module 104, and an inference rearrangement module 105. The data acquisition module 101 acquires evaluated radiation shielding scheme samples. Each radiation shielding scheme sample contains multi-layer shielding structure parameters and multi-objective evaluation results, including at least radiation dose. The feature extraction module 102, connected to the data acquisition module 101, extracts features from the multi-layer shielding structure parameters to construct physical enhancement sequence features. These physical enhancement sequence features include at least cumulative features representing the physical cumulative effect calculated based on the thickness and density of each shielding layer. The label generation module 103, connected to the data acquisition module 101, performs pairwise comparisons of the multi-objective evaluation results of any two radiation shielding scheme samples based on a preset target tolerance vector, generating tolerance-based pairwise dominant labels. These tolerance-based pairwise dominant labels include first scheme dominating second scheme, second scheme dominating first scheme, and neutral incomparability.

[0056] The model training module 104 is connected to the feature extraction module 102 and the label generation module 103, respectively. It is used to input the physical enhancement sequence features corresponding to any two radiation shielding scheme samples into the initial multi-task neural network, obtaining a prediction output that includes at least the overall dominance probability, the single-target relationship prediction result, and the target difference. Subsequently, based on the prediction output and the tolerance-based pairwise dominance labels, the network parameters of the initial multi-task neural network are jointly updated through the overall dominance relationship loss, the single-target relationship loss, the target difference regression loss, and the left-right inverse consistency loss, resulting in a trained multi-task dominance relationship learning model. The left-right inverse consistency loss uses the sum of the target differences before and after swapping the input order, the difference in the corresponding dominance direction probability, and the difference in the neutral incomparable probability as a consistency penalty term, and constrains the model output by minimizing this consistency penalty term.

[0057] The inference rearrangement module 105 is connected to the model training module 104. It acquires a set of radiation shielding candidate schemes to be optimized, predicts the pairwise dominance probabilities between any two candidates using a trained multi-task dominance relationship learning model, calculates the expected non-dominated degree for each candidate scheme based on the pairwise dominance probabilities, and rearranges the candidate scheme set according to the expected non-dominated degrees. Finally, it outputs the rearranged recommended radiation shielding scheme. Each module executes according to the aforementioned data acquisition, feature extraction, label generation, model training, and inference rearrangement process to achieve the prediction of pairwise dominance probabilities and the output of recommended schemes for radiation shielding candidate schemes.

[0058] like Figure 5 As shown, the system can be implemented using a processor (CPU), a graphics processing unit (GPU) or an artificial intelligence accelerator (AI accelerator), a memory, a raw sample database, a multi-task dominance relationship learning model training and inference unit, a candidate ranking result output unit, and a software interface. The memory stores evaluated radiation shielding scheme samples and a set of candidate schemes. The processor (CPU), GPU, or AI accelerator performs physical enhancement sequence feature construction, tolerance-based pairwise dominance label generation, multi-task dominance relationship learning model training, and candidate scheme rearrangement. The software interface outputs the rearranged recommended radiation shielding scheme.

Claims

1. A multi-objective optimization design method for radiation shielding, characterized in that, Includes the following steps: The evaluated radiation shielding scheme samples are obtained by the computing device. Each radiation shielding scheme sample includes multi-layer shielding structure parameters and multi-objective evaluation results, including at least radiation dose. Feature extraction is performed on the parameters of the multi-layer shielding structure to construct a physical enhancement sequence feature. The physical enhancement sequence feature includes at least an accumulation feature representing the physical accumulation effect calculated based on the thickness and density of each shielding layer. Based on the preset target tolerance vector, the multi-target evaluation results of any two radiation shielding scheme samples are compared in pairs to generate tolerance-based pairwise domination labels, including the first scheme dominating the second scheme, the second scheme dominating the first scheme, and neutral incomparable relationships. The physical enhancement sequence features corresponding to any two radiation shielding scheme samples are input into an initial multi-task neural network to obtain a prediction output including at least the overall dominance probability, single-target relationship prediction result, and target difference. Based on the prediction output and the tolerance-based pairwise dominance label, the network parameters are jointly updated through overall dominance relationship loss, single-target relationship loss, target difference regression loss, and left-right inverse consistency loss to obtain a multi-task dominance relationship learning model. The overall dominance probability is used to represent three types of relationships: the input-first scheme dominates the input-later scheme, the input-later scheme dominates the input-first scheme, and the two are neutral and incomparable. The target difference is the difference between the evaluation results of the input-first scheme and the input-later scheme in each target category. The left-right inverse consistency loss is used to constrain the target difference of the same radiation shielding scheme before and after swapping the input order to be opposite numbers, the dominance direction probabilities to be swapped, and the neutral and incomparable probabilities to be consistent. Obtain a set of radiation shielding candidate schemes to be optimized, predict the pairwise dominance probabilities between each pair of radiation shielding candidate schemes in the set using the multi-task dominance relationship learning model, calculate the expected non-dominance degree of each radiation shielding candidate scheme based on the pairwise dominance probabilities, rearrange the set of radiation shielding candidate schemes according to the expected non-dominance degree, and output the rearranged recommended radiation shielding scheme through a designed software interface.

2. The radiation shielding multi-objective optimization design method according to claim 1, characterized in that, Each of the radiation shielding scheme samples contains The shielding layer, the first The original parameters of the shielding layer include thickness. ,density Equivalent atomic number and equivalent mass number ; The step of extracting features from the parameters of the multi-layer shielding structure and constructing physical enhancement sequence features includes: Regarding the first Each shielding layer has a corresponding cumulative thickness. Quality and thickness Cumulative mass thickness Equivalent atomic number ratio and density normalization ratio And use it as the physical enhancement sequence feature; The formula for calculating the cumulative thickness is as follows: in, For the first The cumulative thickness of each shielding layer For the first The thickness of the shielding layer, From arrive The cumulative masking layer index, This is the index of the current shielding layer; The formula for calculating mass thickness is: in, For the first The mass and thickness of the shielding layer For the first The thickness of the shielding layer, For the first The density of each shielding layer; The formula for calculating cumulative mass thickness is: in, For the first The cumulative mass thickness of each shielding layer For the first The thickness of the shielding layer, For the first The density of each shielding layer From arrive The cumulative masking layer index, This is the index of the current shielding layer; The formula for calculating the ratio of equivalent atomic numbers is: in, For the first The ratio of the equivalent atomic numbers of each shielding layer For the first The equivalent atomic number of each shielding layer For the first The equivalent mass number of each shielding layer To prevent division by zero constants, This is the index of the current shielding layer; The formula for calculating the density normalized ratio is: in, For the first The density normalized ratio of each shielding layer For the first The density of each shielding layer For the first The equivalent mass number of each shielding layer To prevent division by zero constants, This is the index of the current shielding layer.

3. The radiation shielding multi-objective optimization design method according to claim 1 or 2, characterized in that, The process involves comparing the multi-objective evaluation results of any two radiation shielding scheme samples in pairs, based on a preset target tolerance vector, to generate tolerance-based pairwise dominant labels, including: Extract a first radiation shielding scheme sample and a second radiation shielding scheme sample from the radiation shielding scheme sample; Obtain the first multi-target evaluation result of the first radiation shielding scheme sample. And the second multi-target evaluation results of the second radiation shielding scheme sample. In this context, the multi-objective evaluation results for each object category are all evaluation results after unifying the object direction. These unified object direction evaluation results are used for pairwise comparisons according to the direction of numerical decrease. This represents the sample index of the first radiation shielding scheme sample. This represents the sample index of the second radiation shielding scheme sample. Indicates the target category index; Obtain the target tolerance vector components of the target category ; When all target categories are satisfied And at least one target category satisfies When the first radiation shielding scheme sample dominates the second radiation shielding scheme sample, a tolerance-based pairwise domination tag is generated to indicate that the first scheme dominates the second scheme. When all target categories are satisfied And at least one target category satisfies When the second radiation shielding scheme sample dominates the first radiation shielding scheme sample, a tolerance-based pairwise domination tag is generated to indicate that the second scheme dominates the first scheme. If neither of the above two dominance conditions is met, the two are determined to be neutrally incomparable, and a tolerance-based pairwise dominance label for neutrally incomparable relationship is generated.

4. The radiation shielding multi-objective optimization design method according to claim 3, characterized in that, The target tolerance vector component of the target category The error is determined by one of the following methods: statistical error determination based on Monte Carlo particle transport simulation, determination based on engineering acceptance margin, or determination based on the standard deviation of multi-objective evaluation results in the training set multiplied by a preset scaling factor.

5. The radiation shielding multi-objective optimization design method according to claim 1, characterized in that, The initial multi-task neural network includes a shared shield layer encoder and a pairwise fusion module; The step of inputting the physical enhancement sequence features corresponding to any two radiation shielding scheme samples into the initial multi-task neural network to obtain the corresponding prediction output includes: The first physical enhancement sequence features Second physical enhancement sequence features The inputs are respectively fed into the shared shield layer encoder, and the corresponding first encoding vector is output. Second encoding vector ; The first encoded vector and the second encoding vector The input is fed into the pairwise fusion module to calculate the fusion vector. The formula for calculating the fusion vector is as follows: in, Sample of the first radiation shielding scheme Sample of the second radiation shielding scheme The fusion vector, This is the first encoded vector. This is the second encoding vector. This is a vector of absolute values ​​of the element-by-element differences between the first and second encoded vectors. It is the element-wise product vector of the first encoding vector and the second encoding vector, and the symbol "[]" represents the vector concatenation operation.

6. The radiation shielding multi-objective optimization design method according to claim 5, characterized in that, The initial multi-task neural network also includes a fusion vector-based... The overall dominance prediction head, single-objective relationship prediction head, and objective difference regression head are used for multi-task prediction. The network parameters are updated jointly by the overall dominance relationship loss, single-objective relationship loss, objective difference regression loss, and left-right inverse consistency loss, and the joint total loss function is described. The calculation formula is: In the formula, For the joint total loss function, The overall dominance prediction head outputs the corresponding overall dominance relationship loss. The single-objective relation prediction head outputs the corresponding single-objective relation loss. Output the corresponding target difference regression loss for the target difference regression header. The left-right reverse consistency loss, , and These are the preset weights for the corresponding losses.

7. The radiation shielding multi-objective optimization design method according to claim 1, characterized in that, In the step of obtaining the evaluated radiation shielding scheme samples, a weighted sampling strategy is used to construct paired training data consisting of the first radiation shielding scheme sample and the second radiation shielding scheme sample; wherein, the weighted sampling strategy increases the sampling weight for radiation shielding scheme samples located at the Pareto front boundary, dose boundary samples where the radiation dose reaches the preset dose threshold, and tolerance boundary samples where the absolute value of the target difference for any target category is not greater than the corresponding target tolerance vector component.

8. The radiation shielding multi-objective optimization design method according to claim 1, characterized in that, The step of calculating the expected non-dominated degree of each radiation shielding candidate scheme based on the pairwise dominance probability, and rearranging the radiation shielding candidate scheme set according to the expected non-dominated degree, includes: For any first radiation shielding candidate scheme Based on its comparison with other second radiation shielding candidate schemes in the set The probability of pairwise dominance between them is used to calculate the probability tournament score. and expected non-dominated degree ; The formula for calculating the probability tournament score is as follows: The formula for calculating the expected degree of non-domination is as follows: In the formula, The first candidate for radiation shielding The probability of tournament scores, The first candidate for radiation shielding The expected degree of non-domination, This is an index of the currently calculated radiation shielding candidate schemes. To remove Index of other radiation shielding candidate schemes, This indicates the division scheme in the set. All other options Summation, This represents a prediction scheme for a multi-task dominance relationship learning model. Domination Plan The probability, This indicates the probability that the two are neutrally incomparable. Indicates the prediction scheme Domination Plan The probability, Weighting coefficients for neutral, incomparable relationships; According to the tournament score of the probability The set of radiation shielding candidate schemes is first sorted, and the top-ranked schemes are selected. Several radiation shielding candidate schemes were proposed, among which... The preset number of filters, and It is a positive integer, and then according to the expected nondominance degree. Forward The candidate radiation shielding schemes are rearranged to output the final recommended radiation shielding scheme.

9. The radiation shielding multi-objective optimization design method according to claim 8, characterized in that, In the calculation of probability tournament scores and expected non-dominated degree Previously, conservative dominance inferences were also applied; The specific logic of the conservative dominance inference is as follows: the pairwise dominance probability includes schemes. Domination Plan probability, scheme Domination Plan The probability and the solution With the plan The probability of belonging to a neutral and incomparable relationship; If the plan Domination Plan The probability did not reach the preset safety confidence threshold, or the scheme... Domination Plan If the difference between the probability of pairwise dominance and the neutral incomparable probability does not exceed a preset probability interval, then the pairwise dominance probability is forcibly replaced with... , , The probability of a neutral, incomparable relationship.

10. A radiation shielding multi-objective optimization design system, characterized in that, It includes a data acquisition module, a feature extraction module, a label generation module, a model training module, and an inference rearrangement module. The feature extraction module and the label generation module are respectively connected to the data acquisition module, the model training module is respectively connected to the feature extraction module and the label generation module, and the inference rearrangement module is connected to the model training module. The data acquisition module is used to acquire samples of evaluated radiation shielding schemes. Each sample of radiation shielding scheme includes multi-layer shielding structure parameters and multi-target evaluation results, including at least radiation dose. The feature extraction module is used to extract features from the parameters of the multi-layer shielding structure and construct physical enhancement sequence features. The physical enhancement sequence features include at least cumulative features that characterize the physical cumulative effect based on the thickness and density of each shielding layer. The tag generation module is used to perform a pairwise comparison of the multi-target evaluation results of any two radiation shielding scheme samples based on a preset target tolerance vector, and generate tolerance-based pairwise domination tags including the first scheme dominating the second scheme, the second scheme dominating the first scheme, and neutral incomparable relationships. The model training module is used to input the physical enhancement sequence features corresponding to any two radiation shielding scheme samples into an initial multi-task neural network, obtain a prediction output including at least the overall dominance probability, single-target relationship prediction result, and target difference, and based on the prediction output and the tolerance-based pairwise dominance label, jointly update the network parameters through overall dominance relationship loss, single-target relationship loss, target difference regression loss, and left-right inverse consistency loss to obtain a multi-task dominance relationship learning model; wherein, the overall dominance probability is used to represent three types of relationships: the input-first scheme dominates the input-later scheme, the input-later scheme dominates the input-first scheme, and the two are neutrally incomparable; the target difference is the difference between the evaluation results of the input-first scheme and the input-later scheme in each target category; the left-right inverse consistency loss is used to constrain the target difference of the same radiation shielding scheme before and after swapping the input order to be opposite numbers, the dominance direction probabilities to be swapped, and the neutrally incomparable probabilities to be consistent; The inference rearrangement module is used to obtain a set of radiation shielding candidate schemes to be optimized, predict the pairwise dominance probability between each pair of radiation shielding candidate schemes in the set of candidate schemes through the multi-task dominance relationship learning model, calculate the expected non-dominance degree of each radiation shielding candidate scheme based on the pairwise dominance probability, rearrange the set of radiation shielding candidate schemes according to the expected non-dominance degree, and output the rearranged recommended radiation shielding scheme.

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