Magnesium alloy cylinder segment ring rolling process optimization method based on lightweight physical interaction network

Abstract

The application provides a magnesium alloy cylinder segment ring rolling process optimization method based on a lightweight physical interaction network, and relates to the fields of rare earth magnesium alloy plastic forming and intelligent manufacturing.S1, basic data set is obtained through the design of Box-Behnken combined with a constraint type maximin-OLHS;S2, an enhanced data set is constructed by using an uncertainty active sampling method;S3, feature reconstruction is performed on the enhanced process parameter data set to obtain a ring rolling process data set;S4, a multi-dimensional loss function is used to optimize the ring rolling process model;S5, the ring rolling process model is embedded into an NSGA-II algorithm to obtain an optimal process parameter solution set.The application can solve the problems that the simulation and experiment cost of the rare earth magnesium alloy cylinder segment ring rolling process optimization is high, the sample quantity is limited, the existing data expansion method lacks pertinence, the conventional network structure is too heavy, and the loss function does not consider the physical rationality and multi-objective optimization demand.

Description

Technical Field

[0001] This invention relates to the field of rare earth magnesium alloy plastic forming and intelligent manufacturing, specifically to an optimization method for magnesium alloy cylindrical ring rolling process based on a lightweight physical interaction network. Background Technology

[0002] Rare earth magnesium alloys possess low density, high specific strength, and excellent potential for lightweight applications, making them promising candidates for use in aerospace and high-end equipment manufacturing. In the ring rolling process of rare earth magnesium alloy cylinders, rolling time and maximum wall thickness difference are crucial indicators for evaluating forming efficiency and quality. Excessive rolling time reduces processing efficiency and may affect temperature evolution and microstructure uniformity; excessive maximum wall thickness difference reduces cylinder dimensional accuracy and service reliability. Therefore, it is necessary to establish an accurate mapping relationship between process parameters and target responses, and further achieve multi-objective process optimization. However, existing research on the optimization of ring rolling and forging forming process parameters still has the following shortcomings: First, the number of samples is usually limited. The ring rolling process involves the coordinated control of the movement of multiple rolls and complex thermo-mechanical coupling effects. A single finite element calculation is time-consuming, and experimental verification is costly, resulting in an extremely limited number of effective samples that can be obtained.

[0003] Second, existing data augmentation methods do not fully consider which samples are most valuable for model improvement. Existing studies often use random sampling or simple Latin hypercube sampling when constructing training datasets, lacking proactive sampling strategies for regions with high model uncertainty and insufficient design space coverage.

[0004] Third, conventional network structures are relatively complex, and overly complex networks can easily lead to overfitting and computational burden. Existing deep learning models are mostly designed with large-scale network structures to pursue prediction accuracy, which are prone to overfitting in low-dimensional, small-sample process parameter scenarios, while also increasing the computational resource requirements for model training and inference.

[0005] Fourth, conventional regression loss functions do not fully consider physical rationality and the subsequent Pareto multi-objective optimization requirements. Existing loss functions, such as mean squared error, only aim to minimize the deviation between the predicted value and the true value, lacking constraints on the physical consistency of the prediction results, and also making it difficult to guarantee the ranking reliability of the prediction model when used as the fitness function of a multi-objective optimization algorithm.

[0006] In summary, the optimization of rare earth magnesium alloy cylinder ring rolling process faces challenges such as high simulation and experimental costs, limited sample size, lack of specificity in existing data augmentation methods, overly complex conventional network structures, and loss functions that fail to consider both physical rationality and multi-objective optimization requirements. Therefore, there is an urgent need for a data augmentation and lightweight predictive optimization method suitable for scenarios with limited computational resources, small sample sizes, and low-dimensional process parameter inputs. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, the present invention aims to provide a method for optimizing the ring rolling process of magnesium alloy cylinders based on a lightweight physical interaction network. This method addresses the problems encountered in optimizing the ring rolling process of rare earth magnesium alloy cylinders, such as high simulation and experimental costs, limited sample size, lack of specificity in existing data expansion methods, excessive weight of conventional network structures, and loss functions that do not take into account both physical rationality and multi-objective optimization requirements.

[0008] Specifically, the present invention provides an optimization method for the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network, which includes the following steps: S1. Obtain the basic dataset through a hybrid experimental design combining Box-Behnken and constrained maximin-OLHS; S2. An uncertain active sampling method is used to construct a simulation training subset and train a lightweight agent model to build an augmented dataset; S21. By sampling the basic dataset with replacement, several simulation training subsets are generated; and the corresponding simulation lightweight agent models are trained respectively to obtain several simulation lightweight agent models with prediction differences. S22. Generate a candidate sample pool within the feasible region of the preset process parameters, calculate the selection value of the candidate points, and form a simulation dataset. S221. Randomly sample within the preset feasible region of process parameters to generate a candidate sample pool; S222. Calculate the uncertainty and spatial coverage distance of candidate points in the candidate sample pool, construct a sampling value function, and calculate the sampling value of candidate points in the candidate sample pool. S223. Construct a simulation sample input set, and sequentially calculate the minimum distance between candidate points and the current simulation sample input set. Combine the sampling value of the candidate points to calculate the selection value of the candidate points. Using a greedy diversity principle, iteratively select candidate points to add to the simulation sample input set, and finally form the target number of simulation sample input sets. S224. Conduct experiments on the simulation sample input set to obtain the simulation response dataset, and pair the two to form a simulation dataset. S23. Merge the simulation dataset with the basic dataset to obtain the enhanced dataset, which includes the enhanced process parameter dataset and the enhanced response dataset. S3. Using normalization, physical coupling relationship and explicit construction, feature reconstruction is performed on the enhanced process parameter dataset to obtain the ring rolling process dataset; S4. Construct a ring rolling process model and train it using a ring rolling process dataset. Introduce a low-rank interaction layer to control the model complexity of the ring rolling process model. At the same time, use a multi-dimensional loss function to optimize the ring rolling process model and obtain a trained ring rolling process model. S5. Embed the trained ring rolling process model into the NSGA-II algorithm to obtain the optimal process parameter solution set that balances forming efficiency and wall thickness uniformity, for use in actual production decision-making.

[0009] Preferably, S1 includes: S11. A structured design is used to collect process parameters at different levels. A constrained parameter space is used to supplement the continuous space of process parameters. The maximum and minimum distance criteria are combined to ensure the dispersion of process parameter samples, thus obtaining a basic process parameter dataset. S111. Using Box-Behnken structured design, process parameters that can effectively cover low-level, medium-level and high-level regions are obtained, and the first basic process parameter dataset is constructed. S112. Using constrained maximin optimal Latin hypercube sampling, the process parameter space is supplemented to construct a second basic process parameter dataset. : ; in, To supplement the sample set for the candidate OLHS, For the feasible region of process parameters, This is the first basic process parameter dataset. The merged sample set is the result of combining the Box-Behnken samples with the OLHS supplementary samples. These are any two distinct points in the merged sample set. These are any two distinct sample points in the normalized merged sample set.

[0010] S113. Merge the first basic process parameter dataset constructed in S111 with the second basic process parameter dataset constructed in S112 to obtain the basic process parameter dataset. S12. Conduct experiments on the basic process parameter dataset to obtain a basic response dataset that corresponds one-to-one with the basic process parameter dataset. Merge the basic process parameter dataset and the basic response dataset into a basic dataset.

[0011] Preferably, S21 includes: S211. By sampling the basic dataset with replacement, training perturbations are created without increasing the number of real simulations, and several differentiated simulation training subsets are constructed. The expected number of different samples in each simulation training subset for: ; in, This represents the number of times the sample will be drawn.

[0012] S212. Using the several simulation training subsets obtained in S211, train the corresponding simulation lightweight agent model to obtain several simulation lightweight agent models with prediction differences.

[0013] Preferably, S222 includes: S2221. For candidate points in the candidate sample pool, input them into several simulated lightweight proxy models with prediction differences trained in S212, and calculate the uncertainty of the candidate points as follows: ; in, This represents the number of lightweight proxy models; Number the lightweight proxy model; For the first The lightweight proxy model for the first Predicted rolling time values ​​for each candidate point; For the first The lightweight proxy model for the first Predicted maximum wall thickness difference for each candidate point; for The lightweight proxy model for the first The variance of the rolling time prediction results for each candidate point; for The lightweight proxy model for the first The variance of the prediction results for the maximum wall thickness difference at each candidate point; The sample variance of rolling time in the base dataset. The sample variance of the largest wall thickness difference in the base dataset; This is a very small constant used to prevent the denominator from being zero.

[0014] S2222. Determine the spatial coverage distance of candidate points in the candidate pool by calculating the minimum normalized distance from candidate points to the basic dataset. : ; in, For the first Normalized coordinates of candidate points, Among the candidate points, the first one is... Normalized values ​​of each process parameter; It is the normalized process parameter vector of the i-th existing sample in the base dataset; The i-th existing sample in the basic dataset The normalized value of each process parameter.

[0015] S2223. Normalize the uncertainty and spatial coverage distance of the candidate points respectively, and calculate the sampling value of the candidate points. for: ; in, For sampling value coefficients, Uncertainty evaluation values ​​for m candidate points; is the normalized spatial coverage distance of the m-th candidate point.

[0016] Preferably, S223 includes: S2231. Select the candidate point with the highest sampling value as the first supplementary sample point, and add the supplementary sample point to the simulation input dataset: S2232. Calculate the minimum distance between the remaining candidate points in the candidate sample pool and the set of simulation input datasets. ; in, For the (b+1)th round of selection, the minimum distance from the m-th unselected candidate point to the currently selected simulation input sample set; b is the number of selected simulation input samples or the current selection round number; This is the set of b simulation input samples that have been selected so far; for Any selected simulation input sample; Selected simulation input samples Normalized coordinates.

[0017] S2233. Determine the selection value by combining the minimum distance of the set of remaining candidate points with the sampling value obtained in S2223. ; in, To select the value coefficient, Given that b simulation input samples have already been selected, this is the selection value of the m-th unselected candidate point when selecting the (b+1)-th simulation input sample. The sampling value of the m-th candidate point; The minimum distance between the normalized sets.

[0018] S2234. Select the remaining candidate points with the highest selection value in the candidate sample pool into the simulation input dataset, and repeatedly calculate the selection value of the remaining candidate points in the candidate sample pool until a sufficient number of simulation input data are selected.

[0019] Preferably, S3 includes: S31. Normalize the enhanced process parameter dataset to obtain normalized features: ; in, This is the normalized value of the j-th process parameter for the i-th sample; These are the corresponding original process parameter values; and These are the lower and upper limits of the j-th process parameter, respectively; It is a very small constant; S32. Based on the physical coupling relationship between process parameters during ring rolling, and combined with the enhanced process parameter dataset, construct physical derived features. : ; ; in, The linear velocity of the driving roller surface; This is the core roller feed speed ratio; This refers to the roller diameter ratio; This is the curvature coupling index. Let be the working radius of the drive roller for the i-th sample; Let be the average rotational speed of the drive roller for the i-th sample; Let be the average feed rate of the core roller for the i-th sample; Let be the working radius of the core roller for the i-th sample.

[0020] S33. The parameters of the enhanced process parameter dataset are coupled pairwise using an explicit construction method to obtain second-order interactive features. S34. The normalized features, physical derived features, and second-order interaction features are concatenated to obtain the ring rolling input dataset of the ring rolling process model. S35. Merge the ring rolling input dataset and the enhanced response dataset to obtain the ring rolling process dataset.

[0021] Preferably, S4 includes: S41. A lightweight physical interaction guided regression network LPIGR-Net is used to construct a ring rolling process model. A low-rank interaction layer is introduced to express the coupling relationship between parameters with a small number of low-rank multiplicative interaction terms to control the model complexity. Gating is used to suppress invalid features and enhance the training stability under small sample conditions. S42. To address the differences in the dimensions of the dual-objective response, the physical rationality of the prediction results, the consistency of the ranking of the dual objectives, and the need for lightweighting the model during the training of the ring rolling process model, a physical-Pareto lightweight loss function is constructed to train the ring rolling process model.

[0022] Preferably, S42 includes: S421. Standardize the enhanced response dataset and construct a scale-balanced loss by combining the Charbonnier loss with the dual-objective response values ​​of the ring rolling process model. : ; in, , This is the standardized predicted rolling time. This is the standardized actual rolling time. This is the predicted value of the maximum wall thickness difference after standardization. This represents the true value of the maximum wall thickness difference after standardization. The weighting coefficient for the rolling time target. The weighting coefficients for the target of maximum wall thickness difference. This is the Charbonnier robust smoothing coefficient.

[0023] S422. Penalize the dual-objective response value of the ring rolling process model where the rolling time and maximum wall thickness difference do not conform to physical meaning, and construct a physical rationality constraint loss: ; in, To increase the number of samples in the dataset This is the predicted maximum wall thickness difference for the i-th sample.

[0024] S423. Based on the enhanced response dataset, construct a set of true dominant sample pairs among sample pairs, and use the Softplus ranking function to penalize the response values ​​of the ring rolling process model that violates the bi-objective superiority relationship, thus constructing a smooth ranking loss: S424. Based on the parameter size, gated channel activation level, and low-rank interactive branch magnitude of LPIGR-Net, a lightweight regularized loss is constructed: ; in, For the set of all trainable parameters, To hide the number of channels, represents the weighting coefficients of the gated sparse regularization term; These are the weight coefficients for the low-rank interactive branch regularization term; For model parameters Regular terms; The number of samples used in training; For the first The gating vector corresponding to each sample; For the gated vector Norm; It is a low-rank interaction order; Number the low-rank interactive branches; For the first The first trainable weight parameter in a low-rank interaction branch, For the first The second trainable weight parameter in a low-rank interaction branch, For the first The third trainable weight parameter in a low-rank interaction branch; S425. Using the physical-Pareto lightweight loss function, a multidimensional loss function is constructed by integrating the scale balance loss, physical rationality constraint loss, smoothing ranking loss, and lightweight regularization loss.

[0025] ; in, The weighting coefficients for the loss due to physical rationality constraints. The weighting coefficients for the order consistency loss are: The weighting coefficients of lightweight regularization loss.

[0026] Preferably, S423 includes: S4231. Based on the true dual-objective response values ​​of any two samples in the enhanced response dataset, and according to the dual-objective minimization optimization direction of rolling time and maximum wall thickness difference, construct a set of true dominance sample pairs based on the true dominance relationship between sample pairs. S4232. The Softplus sorting function is used to sort and penalize the response values ​​of the ring rolling process model that violate the true dominance sample set in the prediction results of the ring rolling process model, and a smooth sorting loss is constructed.

[0027] ; in, For the number of truly dominant sample pairs, This is the standardized rolling time prediction value for the i-th sample. For the sample Standardized rolling time prediction For the sample The predicted value of the maximum wall thickness difference. For the sample The predicted value of the maximum wall thickness difference. The first temperature coefficient, This is the second temperature coefficient.

[0028] Preferably, the low-rank physical interaction layer can be represented as: ; in, The interaction enhancement features output by the low-rank physical interaction layer. The initial hidden features are the input to the embedding layer's output. For 18-dimensional ring rolling input features, It is a low-rank interactive order. For low-rank interactive branch numbering, For the first The first learnable projection vector of the low-rank interaction branches. For the first The second learnable projection vector of the low-rank interaction branch. For the first The learnable weight coefficients of the low-rank interaction branches, where T is the vector transpose.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows: First, this invention uses a hybrid experimental design that combines Box-Behnken and constrained maximin-OLHS to simultaneously ensure structured representativeness and spatial coverage with a limited number of samples.

[0030] Second, this invention uses the Bootstrap uncertainty active hybrid sampling method to estimate the prediction uncertainty of candidate samples through a lightweight surrogate model and combines spatial coverage distance to screen supplementary sample points, so that limited simulation or experimental resources are given priority to areas with high model uncertainty and insufficient sample coverage, thereby improving the utilization rate of simulation resources and avoiding sample aggregation.

[0031] Third, this invention proposes the LPIGR-Net lightweight physical interaction-guided regression network, which combines physical derived features, second-order interaction features, low-rank interaction layers, and gated residual layers. This enables the model to effectively learn the nonlinear mapping relationship between process parameters and rolling time and maximum wall thickness difference even under small sample conditions. This structure avoids using overly complex network structures in low-dimensional, small-sample process parameter scenarios, effectively reducing the computational load for model training and inference.

[0032] Fourth, this invention proposes PPL-Loss, which unifies scale-balanced regression, physical rationality, Pareto ranking consistency, and lightweight constraints into a single loss function. Scale-balanced regression ensures that target responses of different dimensions are treated fairly during training; physical rationality constraints guide the model predictions to conform to the physical laws of the ring rolling process; and Pareto ranking consistency constraints enable the model predictions to correctly reflect the dominance relationships between different combinations of process parameters in subsequent NSGA-II multi-objective optimization. This loss function not only gives the prediction model better point prediction capabilities but also makes it more suitable as a fitness function for multi-objective optimization algorithms. Attached Figure Description

[0033] Figure 1 The flowchart shows the optimization method for magnesium alloy cylindrical segment ring rolling process based on lightweight physical interaction network of the present invention. Figure 2 This is a flowchart illustrating the overall technical route of the present invention; Figure 3 This is a joint distribution diagram of the Box-Behnken samples and the maxmin-OLHS supplementary samples in the parameter space of this invention; Figure 4 This is a flowchart of the Bootstrap uncertainty sampling method BUAS of the present invention; Figure 5 This is a schematic diagram of the lightweight proxy model structure of the Bootstrap uncertainty sampling method of the present invention; Figure 6 This is a schematic diagram of the lightweight physical interaction guided regression network LPIGR-Net structure of the present invention; Figure 7 This is a flowchart of the multi-objective process optimization based on LPIGR-Net and NSGA-II of the present invention. Detailed Implementation

[0034] The following is for reference Figure 1 and Figure 2 The embodiments of the present invention will be described.

[0035] S1. Obtain the basic dataset through a hybrid experimental design combining Box-Behnken and constrained maximin-OLHS.

[0036] S11. A structured design is used to collect process parameters at different levels, and constrained maximin optimal Latin hypercube sampling is used to supplement the continuous space of process parameters. The maximum-minimum distance criterion is combined to ensure the dispersion of process parameter samples, thus obtaining a basic process parameter dataset.

[0037] S111. Using Box-Behnken structured design, process parameters that can effectively cover low-level, medium-level and high-level regions are obtained, and the first basic process parameter dataset is constructed. S112. Using constrained maximin optimal Latin hypercube sampling, the process parameter space is supplemented to construct a second basic process parameter dataset. : ; in, To supplement the sample set for the candidate OLHS, For the feasible region of process parameters, This is the first basic process parameter dataset. The merged sample set is the result of combining the Box-Behnken samples with the OLHS supplementary samples. These are any two distinct points in the merged sample set. These are any two distinct sample points in the normalized merged sample set.

[0038] Specifically, relying solely on Box-Behnken design may result in insufficient coverage of the continuous parameter space. Therefore, this invention introduces constrained maximin optimal Latin hypercube sampling to supplement the process parameter space.

[0039] S113. Merge the first basic process parameter dataset constructed in S111 with the second basic process parameter dataset constructed in S112 to obtain the basic process parameter dataset. : ; S12. Conduct experiments on the basic process parameter dataset to obtain a basic response dataset that corresponds one-to-one with the basic process parameter dataset. Merge the basic process parameter dataset and the basic response dataset into a basic dataset.

[0040] Given limited computing resources, the basic dataset consists of 50 to 100 sets.

[0041] In a preferred embodiment, the basic dataset consists of 100 sets. Figure 3 The figure shows the joint distribution of some Box-Behnken samples and constrained maximin-optimal Latin hypercube supplementary samples in the parameter space, where hollow circles represent Box-Behnken samples and solid triangles represent maximin-OLHS supplementary samples.

[0042] S2. An uncertain active sampling method is used to construct a simulation training subset and train a lightweight agent model to build an augmented dataset.

[0043] This invention proposes a Bootstrap Uncertainty Active Sampling Method (BUAS) to select the most valuable sample points for inclusion from the candidate process parameter space. The flowchart of the Bootstrap Uncertainty Sampling Method (BUAS) is shown below. Figure 4 As shown.

[0044] S21. By sampling the basic dataset with replacement, several simulation training subsets are generated; and the corresponding simulation lightweight agent models are trained respectively to obtain several simulation lightweight agent models with prediction differences.

[0045] S211. By sampling the basic dataset with replacement, training perturbations are created without increasing the number of real simulations, thus constructing several differentiated simulation training subsets.

[0046] Each subset is derived from the original Samples were drawn from the samples This can be repeated, but sample duplication is allowed within it. The expected number of samples in each simulation training subset is different. for: ; in, This represents the number of times the sample will be drawn.

[0047] S212. Using the several Bootstrap simulation training subsets obtained in S211, train the corresponding simulation lightweight agent models to obtain several simulation lightweight agent models with prediction differences.

[0048] In a preferred embodiment, such as Figure 5 As shown, lightweight proxy models with the same structure but different training subsets and slightly different hidden dimensions are used, and each is trained using the Bootstrap training subset. This allows multiple models to form a moderate difference in predictions, which is then used for subsequent uncertainty estimation of candidate points.

[0049] S22. Generate a candidate sample pool within the feasible region of the preset process parameters, calculate the selection value of the candidate points, and form a simulation dataset.

[0050] S221. Random sampling is performed within the preset feasible domain of process parameters to generate a candidate sample pool.

[0051] Random sampling was performed using any of the following methods: Sobol sequence, Latin hypercube sampling, or uniform grid random sampling.

[0052] S222. Calculate the uncertainty and spatial coverage distance of candidate points in the candidate sample pool, construct a sampling value function, and calculate the sampling value of candidate points in the candidate sample pool.

[0053] S2221. For candidate points in the candidate sample pool, input them into several lightweight simulation proxy models with prediction differences trained in S212 to calculate the uncertainty of the candidate points. for: ; in, This represents the number of lightweight proxy models; Number the lightweight proxy model; For the first The lightweight proxy model for the first Predicted rolling time values ​​for each candidate point; For the first The lightweight proxy model for the first Predicted maximum wall thickness difference for each candidate point; for The lightweight proxy model for the first The variance of the rolling time prediction results for each candidate point; for The lightweight proxy model for the first The variance of the prediction results for the maximum wall thickness difference at each candidate point; The sample variance of rolling time in the base dataset. The sample variance of the largest wall thickness difference in the base dataset; This is a very small constant used to prevent the denominator from being zero.

[0054] S2222. Determine the spatial coverage distance of candidate points in the candidate pool by calculating the minimum normalized distance from candidate points to the basic dataset. : ; in, For the first Normalized coordinates of candidate points, For the first Among the candidate points, the first one is... Normalized values ​​of each process parameter; It is the normalized process parameter vector of the i-th existing sample in the base dataset; The i-th existing sample in the basic dataset The normalized value of each process parameter.

[0055] Specifically, These correspond to the four original process parameters.

[0056] The larger the value, the farther the candidate point is from the existing samples, and the more valuable it is for improving the spatial coverage of the dataset.

[0057] S2223. Normalize the uncertainty and spatial coverage distance of the candidate points respectively, and calculate the sampling value of the candidate points. for: ; in, For sampling value coefficients, This is the normalized uncertainty evaluation value for the m-th candidate point; is the normalized spatial coverage distance of the m-th candidate point.

[0058] Preferably, when At the same time, the sampling value of candidate points can take into account both model uncertainty and sample space coverage.

[0059] S223. Construct a simulation sample input set, and calculate the minimum distance between candidate points and the current simulation sample input set in turn. Combine the sampling value of the candidate points to calculate the selection value of the candidate points. Adopt the greedy diversity principle to iteratively select candidate points to add to the simulation sample input set, and finally form the target number of simulation sample input sets.

[0060] S2231. Construct the simulation sample input set, and select the candidate points with the highest sampling value from S2223 into the simulation sample input set: ; in, Number the first selected candidate point. This indicates searching within the candidate sample pool for samples that have sampling value. The largest candidate point number; This is the first selected candidate process parameter sample; This is the set containing the first simulation input sample.

[0061] S2232. Calculate the minimum distance between the remaining candidate points in the candidate sample pool and the current simulation sample input set. : ; in, For the (b+1)th round of selection, the minimum distance from the m-th unselected candidate point to the currently selected simulation input sample set; b is the number of selected simulation input samples or the current selection round number; This is the set of b simulation input samples that have been selected so far; for Any selected simulation input sample; Selected simulation input samples Normalized coordinates.

[0062] S2233. Determine the selection value by combining the minimum distance of the set of remaining candidate points with the sampling value obtained in S2223. : ; in, To select the value coefficient, Given that b simulation input samples have already been selected, this is the selection value of the m-th unselected candidate point when selecting the (b+1)-th simulation input sample. The sampling value of the m-th candidate point; The minimum distance between the normalized sets.

[0063] S2234. Select the remaining candidate points with the highest selection value from the candidate sample pool into the simulation sample input set. Repeat the calculation of the selection value of the remaining candidate points in the current candidate sample pool until the target number of simulation sample input sets is selected. ; in, Number the candidate points selected in round b+1; This indicates that the m-th candidate point has not yet been selected into the current simulation input sample set. This is a sample of candidate process parameters selected in round b+1. Given the currently selected set of b simulation input samples, This is the set of simulation input samples after adding the (b+1)th simulation input sample.

[0064] S224. Conduct experiments on the simulation sample input set to obtain the simulation response dataset, and pair the two to form a simulation dataset.

[0065] ; in, For simulation datasets, For the first One simulated input sample, For the corresponding simulation response data, This represents the number of simulation samples.

[0066] S23. Merge the simulation dataset with the basic dataset to obtain the enhanced dataset. for: ; Specifically, the enhanced datasets include enhanced process parameter datasets and enhanced response datasets.

[0067] S3. Using normalization, physical coupling relationships, and explicit construction, the enhanced process parameter dataset is reconstructed to obtain the ring rolling process dataset.

[0068] like Figure 6 As shown, the lightweight physical interaction guided regression network LPIGR-Net proposed in this invention has the core design idea of: original process parameters + physical derived features + second-order interaction features + low-rank interaction modeling + gated residual learning. This network does not rely on a complex network structure and explicitly models the coupling relationship of "radius-speed-feed-roll diameter" in the ring rolling process, which reduces the amount of computation and enhances the model's adaptability to small samples.

[0069] Specifically, the enhanced datasets include enhanced process parameter datasets and enhanced response datasets.

[0070] S31. Normalize the enhanced process parameter dataset to obtain normalized features: ; in, This is the normalized value of the j-th process parameter for the i-th sample; These are the corresponding original process parameter values; and These are the lower and upper limits of the j-th process parameter, respectively; It is a very small constant.

[0071] S32. Based on the physical coupling relationship between process parameters during ring rolling, and combined with the enhanced process parameter dataset, construct physical derived features. : ; Specifically, the surface linear velocity of the drive roller is determined by both the drive roller radius and rotational speed. The core roller feed speed ratio reflects the relative relationship between the core roller feed speed and the surface linear velocity of the drive roller. The roller diameter ratio reflects the geometric matching relationship between the core roller and the drive roller. The curvature coupling index characterizes the comprehensive influence of the curvature of the drive roller and the core roller on the deformation contact state.

[0072] ; in, For the first The physical derived feature vector of each sample; The linear velocity of the driving roller surface; This is the core roller feed speed ratio; This refers to the roller diameter ratio; This is the curvature coupling index. Let be the working radius of the drive roller for the i-th sample; Let be the average rotational speed of the drive roller for the i-th sample; Let be the average feed rate of the core roller for the i-th sample; Let be the working radius of the core roller for the i-th sample.

[0073] S33. By explicitly constructing the parameters of the enhanced process parameter dataset pairwise, second-order interaction features are obtained: ; in, For the first The second-order interaction feature vector of each sample, These are the four normalized process parameters for the i-th sample; Indicates the first The normalized process parameters and the first The pairwise multiplicative interaction terms between normalized process parameters; Indicates the first The squared terms of a normalized process parameter.

[0074] S34. The normalized features, physical derived features, and second-order interaction features are concatenated to obtain the ring rolling input dataset of the ring rolling process model.

[0075] This invention reconstructs 4-dimensional process parameters into 18-dimensional input through step S31. The core purpose is not simply to increase dimensionality, but to explicitly express the physical coupling relationships in the ring rolling process beforehand, making it easier for the model to learn the mapping relationship between parameters and rolling time and maximum wall thickness difference under small sample conditions. Without significantly increasing model complexity, explicitly introducing the physical mechanisms and parameter coupling relationships in the ring rolling process into the model improves the model's prediction accuracy, stability, and interpretability under small sample conditions. Specifically, the original 4-dimensional input only includes the drive roll radius, drive roll speed, core roll feed rate, and core roll radius. However, the rolling time and maximum wall thickness difference in the ring rolling process are not determined solely by these parameters, but are jointly influenced by surface linear velocity, feed rate matching, roll diameter ratio, curvature coupling, and second-order interactions between parameters. Therefore, concatenating the original parameters, physically derived features, and second-order interaction features to form an 18-dimensional input is equivalent to providing the network with key rules such as "radius × speed," "feed / linear velocity," "roll diameter matching," and "parameter multiplicative interaction" beforehand, reducing the difficulty for the model to learn complex coupling relationships from limited samples. This approach enhances the model's ability to express the essential laws of ring rolling, reduces reliance on large-scale samples and complex deep networks, minimizes the risk of overfitting, and enables more reliable prediction of rolling time and maximum wall thickness difference when used as the fitness function for NSGA-II, thus obtaining a more credible Pareto optimal process parameter solution set. LPIGR-Net uses "original normalized process parameters, physically derived features, and second-order interaction features" as inputs, combined with low-rank interaction layers and gated residual layers to learn the nonlinear mapping relationship between process parameters and the dual-objective response.

[0076] S35. Merge the ring rolling input dataset and the enhanced response dataset to obtain the ring rolling process dataset.

[0077] S4. Construct a ring rolling process model and train it using a ring rolling process dataset. Introduce a low-rank interaction layer to control the model complexity of the ring rolling process model. At the same time, use a multi-dimensional loss function to optimize the ring rolling process model and obtain a trained ring rolling process model.

[0078] S41. A lightweight physical interaction guided regression network LPIGR-Net is used to construct a ring rolling process model. A low-rank interaction layer is introduced to express the coupling relationship between parameters with a small number of low-rank multiplicative interaction terms, thereby controlling the model complexity. Furthermore, gating is used to suppress ineffective features and enhance the training stability under small sample conditions.

[0079] Specifically, the ring rolling input features are used as input to the ring rolling process model, and feature mapping is performed sequentially through the input embedding layer, the low-rank physical interaction layer, and the gated residual layer to obtain the ring rolling process model for predicting rolling time and maximum wall thickness difference.

[0080] Specifically, the low-rank physical interaction layer can be represented as: ; in, The interaction enhancement features output by the low-rank physical interaction layer. The initial hidden features are the input to the embedding layer's output. For 18-dimensional ring rolling input features, It is a low-rank interactive order. For low-rank interactive branch numbering, For the first The first learnable projection vector of the low-rank interaction branches. For the first The second learnable projection vector of the low-rank interaction branch. For the first The learnable weight coefficients of the low-rank interaction branches, where T is the vector transpose.

[0081] S42. To address the differences in the dimensions of the dual-objective response, the physical rationality of the prediction results, the consistency of the ranking of the dual objectives, and the need for lightweighting the model during the training of the ring rolling process model, a physical-Pareto lightweight loss function is constructed to train the ring rolling process model.

[0082] To ensure that LPIGR-Net not only has high prediction accuracy but also meets physical constraints and is compatible with subsequent NSGA-II multi-objective optimization, this invention designs the PPL-Loss loss function. Ordinary regression loss typically only focuses on the error between predicted and true values. However, in the optimization of rare earth magnesium alloy cylinder ring rolling processes, simply having a small prediction error is insufficient; it also requires accurate prediction, physical reasonableness, suitability for Pareto optimization, and a lightweight model. Therefore, the PPL-Loss design is guided by scale balance, robust regression, physical constraints, Pareto ranking consistency, and lightweight design.

[0083] S421. Standardize the enhanced response dataset and construct a scale-balanced loss by combining the Charbonnier loss with the dual-objective response values ​​of the ring rolling process model. : ; in, To increase the number of samples in the dataset, This is the standardized predicted rolling time. This is the standardized actual rolling time. This is the predicted value of the maximum wall thickness difference after standardization. This represents the true value of the maximum wall thickness difference after standardization. The weighting coefficient for the rolling time target. The weighting coefficients for the target of maximum wall thickness difference. This is the Charbonnier robust smoothing coefficient.

[0084] Specifically, the prediction output of LPIGR-Net is The actual output is Because of differences in units and numerical ranges, the output is standardized. The standardized predicted value is... The actual value is We use Charbonnier loss instead of ordinary squared error. Compared with MSE, Charbonnier loss approximates squared loss when the error is small, and its growth is more gradual when the error is large, making it more robust to outliers.

[0085] S422. Penalize the dual-objective response value of the ring rolling process model where the rolling time and maximum wall thickness difference do not conform to physical meaning, and construct a physical rationality constraint loss. for: ; in, To increase the number of samples in the dataset, This is the predicted maximum wall thickness difference for the i-th sample.

[0086] Specifically, It is a linear rectifier function. and When the predicted value is zero, the loss term is 0; when any predicted value is negative, the loss term incurs a penalty.

[0087] S423. Based on the enhanced response dataset, construct a set of true dominant sample pairs among sample pairs, and use the Softplus ranking function to penalize the response values ​​of the ring rolling process model that violates the bi-objective superiority relationship, thus constructing a smooth ranking loss: S4231. Based on the true bi-objective response values ​​of any two samples in the enhanced response dataset, and according to the bi-objective minimization optimization direction of rolling time and maximum wall thickness difference, construct a set of true dominance sample pairs based on the true dominance relationship between sample pairs: Specifically, in the ring rolling process, it is desirable for samples to simultaneously have shorter rolling times and smaller maximum wall thickness differences. Based on this expectation, a set of true dominant sample pairs is constructed: Specifically, for any two samples in the augmented response dataset and The actual bi-objective response values ​​are as follows: ; in, and Samples and The corresponding rolling time, and Samples and The corresponding maximum wall thickness difference.

[0088] Since the optimization of the ring rolling process aims to minimize both rolling time and maximum wall thickness difference, therefore, when the sample The rolling time is no greater than that of the sample. And the sample The maximum wall thickness difference is not greater than that of the sample. And at least one target is strictly smaller than the sample. When determining the sample Outperforms the sample in the context of dual objectives. , denoted as: ; Based on the above determination rules, construct the set of true dominant sample pairs: ; in, Let be the set of dominant sample pairs determined by the true bi-objective response values. To increase the number of samples in the response dataset. For any All of these represent samples It outperforms the sample in terms of real response. This set is used to provide a true benchmark for predicting ranking penalties in subsequent calculations.

[0089] S4232. The Softplus sorting function is used to sort and penalize the response values ​​of the ring rolling process model that violate the true dominance sample set in the prediction results of the ring rolling process model, and a smooth sorting loss is constructed.

[0090] Specifically, for the true dominant sample pairs The prediction results of the ring rolling process model should also maintain the same dual-objective superiority / inferiority relationship, that is, the predicted samples... The rolling time and maximum wall thickness difference should not exceed the sample size. : ; in, and Samples and The corresponding rolling time, and Samples and The corresponding maximum wall thickness difference.

[0091] If the model prediction result is: ; and For the sample and The corresponding predicted rolling time, and Samples and The predicted value of the corresponding maximum wall thickness difference.

[0092] This indicates that the model failed to maintain the dual-objective superiority / inferiority relationship between the real sample pairs, predicting the better sample in the real response as the relatively worse one, which may mislead the subsequent NSGA-II multi-objective optimization process. Therefore, it is necessary to penalize this type of ranking violation.

[0093] Specifically, to maintain consistency in the scales of the two objectives—rolling time and maximum wall thickness difference—standardized predicted response values ​​are used in actual calculations. For the true dominant sample pairs... If the model predicts the correct ranking, then the following should be satisfied: ; in, and This is the standardized predicted rolling time. and This is the predicted value of the maximum wall thickness difference after standardization; and This is a temperature coefficient used to adjust the intensity of the sorting penalty.

[0094] For a single true dominance sample pair When it appears ; This indicates that the predicted results violate the true superiority / inferiority relationship between the two objectives. To ensure the ranking penalty has continuous differentiability, the Softplus function is used for smoothing the penalty. for: ; Furthermore, the Pareto ranking consistency loss is obtained by averaging across all truly dominant sample pairs. for: ; in, For the number of truly dominant sample pairs, This is the standardized rolling time prediction value for the i-th sample. For the sample Standardized rolling time prediction For the sample The predicted value of the maximum wall thickness difference. For the sample The predicted value of the maximum wall thickness difference. The first temperature coefficient, This is the second temperature coefficient.

[0095] In this way, the Pareto ranking consistency loss first determines the bi-objective superiority / inferiority relationship between samples based on the actual response values, and then checks whether the model prediction results maintain this superiority / inferiority relationship. When a truly superior sample is incorrectly predicted as inferior in the prediction results, the loss function penalizes this ranking error, thereby guiding LPIGR-Net to simultaneously learn the response values ​​and the Pareto ranking structure between samples. The ring rolling process model trained in this way can more reliably serve as a fitness evaluation model for the NSGA-II multi-objective optimization algorithm.

[0096] S424. Based on the parameter size, gated channel activation level, and low-rank interactive branch magnitude of LPIGR-Net, a lightweight regularized loss is constructed: Specifically, the lightweight regularization loss includes the model weight regularization term. Gated sparse regularization terms and low-rank interaction branch regularization terms Among them, the model weight regularization term Used to constrain the overall parameter magnitude of LPIGR-Net to prevent the model parameters from becoming too large; gated sparse regularization term The activation strength of the gate vector is constrained to ensure the network prioritizes valid channels and suppresses redundant feature propagation; low-rank interaction branch regularization term. Used to constrain the magnitude of low-rank multiplicative interaction terms, preventing low-rank interaction layers from overfitting local coupling relationships between parameters under small sample conditions. Lightweight regularization loss. for:

[0097] in, For the set of all trainable parameters, To hide the number of channels, represents the weighting coefficients of the gated sparse regularization term; These are the weight coefficients for the low-rank interactive branch regularization term; For model parameters Regular terms; The number of samples used in training; For the first The gating vector corresponding to each sample; For the gated vector Norm; It is a low-rank interaction order; Number the low-rank interactive branches; For the first The first trainable weight parameter in a low-rank interaction branch, For the first The second trainable weight parameter in a low-rank interaction branch, For the first The third trainable weight parameter in a low-rank interaction branch.

[0098] Through the aforementioned lightweight regularization constraints, LPIGR-Net can control the model parameter size and channel activation intensity while maintaining nonlinear coupling expression capabilities, reducing the risk of overfitting in small samples and decreasing the computational burden when used as an NSGA-II fitness evaluation model.

[0099] S425. Using the physical-Pareto lightweight loss function, a multidimensional loss function is constructed by integrating the scale balance loss, physical rationality constraint loss, smoothing ranking loss, and lightweight regularization loss.

[0100] ; in, The weighting coefficients for the loss due to physical rationality constraints. The weighting coefficients for the order consistency loss are: The weighting coefficients of lightweight regularization loss.

[0101] In a preferred embodiment, .

[0102] S5. Embed the trained ring rolling process model into the NSGA-II algorithm to obtain the optimal process parameter solution set that balances forming efficiency and wall thickness uniformity, for use in actual production decision-making.

[0103] After training, LPIGR-Net was used as a fast surrogate model for optimizing the process parameters of rare earth magnesium alloy cylindrical ring rolling, and embedded into the NSGA-II multi-objective optimization algorithm to achieve efficient evaluation and screening of candidate process parameter combinations. Specifically, within the feasible domain of given process parameters, an initial population was first generated, with the working radius of the drive roll, the average speed of the drive roll, the average feed rate of the mandrel, and the working radius of the mandrel as the design variables to be optimized. Subsequently, each candidate individual in the population was input into the trained LPIGR-Net to quickly predict its corresponding rolling time and maximum wall thickness difference, and the above prediction results were used as the basis for the dual-objective fitness evaluation of NSGA-II. NSGA-II, based on the non-dominated sorting and crowding distance mechanism, performed hierarchical optimization and diversity preservation of candidate process parameter combinations, and continuously updated the population through evolutionary operations such as selection, crossover, and mutation, so that the optimization process gradually converged towards shorter rolling time and smaller maximum wall thickness difference. After multiple iterations, a Pareto optimal process parameter solution set that balances forming efficiency and wall thickness uniformity was finally obtained, providing a decision-making basis for the selection of process parameters in the ring rolling process of rare earth magnesium alloy sections. The overall optimization process is as follows: Figure 7 As shown.

[0104] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network, characterized in that, The steps include: S1. Obtain the basic dataset through a hybrid experimental design combining Box-Behnken and constrained maximin-OLHS; S2. An uncertainty-based active sampling method is used to construct a simulation training subset and train a lightweight proxy model, thereby constructing an augmented dataset, specifically: S21. By sampling the basic dataset with replacement, several simulation training subsets are generated; and the corresponding simulation lightweight agent models are trained respectively to obtain several simulation lightweight agent models with prediction differences. S22. Generate a candidate sample pool within the preset feasible region of process parameters, calculate the selection value of candidate points, and construct a simulation dataset, specifically as follows: S221. Randomly sample within the preset feasible region of process parameters to generate a candidate sample pool; S222. Calculate the uncertainty and spatial coverage distance of candidate points in the candidate sample pool, construct a sampling value function, and calculate the sampling value of candidate points in the candidate sample pool. S223. Construct a simulation sample input set, and sequentially calculate the minimum distance between candidate points and the current simulation sample input set. Combine the sampling value of the candidate points to calculate the selection value of the candidate points. Using a greedy diversity principle, iteratively select candidate points to add to the simulation sample input set, and finally form the target number of simulation sample input sets. S224. Conduct experiments on the simulation sample input set to obtain the simulation response dataset, and pair the two to form a simulation dataset. S23. Merge the simulation dataset with the basic dataset to obtain the enhanced dataset, which includes the enhanced process parameter dataset and the enhanced response dataset. S3. Using normalization, physical coupling relationship and explicit construction, feature reconstruction is performed on the enhanced process parameter dataset to obtain the ring rolling process dataset; S4. Construct a ring rolling process model and train it using a ring rolling process dataset. Introduce a low-rank interaction layer to control the model complexity of the ring rolling process model. At the same time, use a multi-dimensional loss function to optimize the ring rolling process model and obtain a trained ring rolling process model. S5. Embed the trained ring rolling process model into the NSGA-II algorithm to obtain the optimal process parameter solution set that balances forming efficiency and wall thickness uniformity, for use in actual production decision-making.

2. The method for optimizing the magnesium alloy cylindrical section ring rolling process based on a lightweight physical interaction network according to claim 1, characterized in that: S1 includes: S11. A structured design is used to collect process parameters at different levels. A constrained parameter space is used to supplement the continuous space of process parameters, and the maximum-minimum distance criterion is combined to ensure the dispersion of process parameter samples, resulting in a basic process parameter dataset, specifically including: S111. Using Box-Behnken structured design, process parameters that can effectively cover low-level, medium-level and high-level regions are obtained, and the first basic process parameter dataset is constructed. S112. Using constrained maximin optimal Latin hypercube sampling, the process parameter space is supplemented to construct a second basic process parameter dataset. : ； in, To supplement the sample set for the candidate OLHS, For the feasible region of process parameters, This is the first basic process parameter dataset. The merged sample set is the result of combining the Box-Behnken samples with the OLHS supplementary samples. These are any two distinct points in the merged sample set. These are any two distinct sample points in the normalized merged sample set; S113. Merge the first basic process parameter dataset constructed in S111 with the second basic process parameter dataset constructed in S112 to obtain the basic process parameter dataset. S12. Conduct experiments on the basic process parameter dataset to obtain a basic response dataset that corresponds one-to-one with the basic process parameter dataset. Merge the basic process parameter dataset and the basic response dataset into a basic dataset.

3. The method for optimizing the magnesium alloy cylindrical section ring rolling process based on a lightweight physical interaction network according to claim 1, characterized in that: S21 includes: S211. By sampling the basic dataset with replacement, training perturbations are created without increasing the number of real simulations, and several differentiated simulation training subsets are constructed. The expected number of different samples in each simulation training subset for: ； in, Number of draws; S212. Using the several simulation training subsets obtained in S211, train the corresponding simulation lightweight agent model to obtain several simulation lightweight agent models with prediction differences.

4. The method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network according to claim 1, characterized in that: S222 includes: S2221. For candidate points in the candidate sample pool, input them into several simulated lightweight proxy models with prediction differences trained in S212, and calculate the uncertainty of the candidate points as follows: ； in, This represents the number of lightweight proxy models; Number the lightweight proxy model; For the first The lightweight proxy model for the first Predicted rolling time values ​​for each candidate point; For the first The lightweight proxy model for the first Predicted maximum wall thickness difference for each candidate point; for The lightweight proxy model for the first The variance of the rolling time prediction results for each candidate point; for The lightweight proxy model for the first The variance of the prediction results for the maximum wall thickness difference at each candidate point; The sample variance of rolling time in the base dataset. The sample variance of the largest wall thickness difference in the base dataset; It is a very small constant used to prevent the denominator from being zero; S2222. Determine the spatial coverage distance of candidate points in the candidate pool by calculating the minimum normalized distance from candidate points to the basic dataset. : ； in, For the first Normalized coordinates of candidate points, Among the candidate points, the first one is... Normalized values ​​of each process parameter; The normalized process parameter vector of the i-th existing sample in the base dataset; The i-th existing sample in the basic dataset Normalized values ​​of each process parameter; S2223. Normalize the uncertainty and spatial coverage distance of the candidate points respectively, and calculate the sampling value of the candidate points. for: ； in, For sampling value coefficients, Uncertainty evaluation values ​​for m candidate points; is the normalized spatial coverage distance of the m-th candidate point.

5. The method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network according to claim 1, characterized in that, S223 includes: S2231. Select the candidate point with the highest sampling value as the first supplementary sample point, and add the supplementary sample point to the simulation input dataset: S2232. Calculate the minimum distance between the remaining candidate points in the candidate sample pool and the set of simulation input datasets. ； in, For the (b+1)th round of selection, the minimum distance from the m-th unselected candidate point to the currently selected simulation input sample set; b is the number of selected simulation input samples or the current selection round number; This is the set of b simulation input samples that have been selected so far; for Any selected simulation input sample; Selected simulation input samples Normalized coordinates; S2233. Determine the selection value by combining the minimum distance of the set of remaining candidate points with the sampling value obtained in S2223. ； in, To select the value coefficient, Given that b simulation input samples have already been selected, this is the selection value of the m-th unselected candidate point when selecting the (b+1)-th simulation input sample. The sampling value of the m-th candidate point; The minimum distance between the normalized sets; S2234. Select the remaining candidate points with the highest selection value in the candidate sample pool into the simulation input dataset, and repeatedly calculate the selection value of the remaining candidate points in the candidate sample pool until a sufficient number of simulation input data are selected.

6. The method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network according to claim 1, characterized in that, S3 include: S31. Normalize the enhanced process parameter dataset to obtain normalized features: ； in, This is the normalized value of the j-th process parameter for the i-th sample; These are the corresponding original process parameter values; and These are the lower and upper limits of the j-th process parameter, respectively; It is a very small constant; S32. Based on the physical coupling relationship between process parameters during ring rolling, and combined with the enhanced process parameter dataset, construct physical derived features. : ； ； in, The linear velocity of the driving roller surface; This is the core roller feed speed ratio; This refers to the roller diameter ratio; Curvature coupling index; Let be the working radius of the drive roller for the i-th sample; Let be the average rotational speed of the drive roller for the i-th sample; Let be the average feed rate of the core roller for the i-th sample; Let be the working radius of the core roller for the i-th sample; S33. The parameters of the enhanced process parameter dataset are coupled pairwise using an explicit construction method to obtain second-order interactive features. S34. The normalized features, physical derived features, and second-order interaction features are concatenated to obtain the ring rolling input dataset of the ring rolling process model. S35. Merge the ring rolling input dataset and the enhanced response dataset to obtain the ring rolling process dataset.

7. The method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network according to claim 1, characterized in that, S4 include: S41. A lightweight physical interaction guided regression network LPIGR-Net is used to construct a ring rolling process model. A low-rank interaction layer is introduced to express the coupling relationship between parameters with a small number of low-rank multiplicative interaction terms to control the model complexity. Gating is used to suppress invalid features and enhance the training stability under small sample conditions. S42. To address the differences in the dimensions of the dual-objective response, the physical rationality of the prediction results, the consistency of the ranking of the dual objectives, and the need for lightweighting the model during the training of the ring rolling process model, a physical-Pareto lightweight loss function is constructed to train the ring rolling process model.

8. The method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network according to claim 4, characterized in that, S42 includes: S421. Standardize the enhanced response dataset and construct a scale-balanced loss by combining the Charbonnier loss with the dual-objective response values ​​of the ring rolling process model. : ； in, , This is the standardized predicted rolling time. This is the standardized actual rolling time. This is the predicted value of the maximum wall thickness difference after standardization. This represents the true value of the maximum wall thickness difference after standardization. The weighting coefficient for the rolling time target. The weighting coefficients for the target of maximum wall thickness difference. Charbonnier robust smoothing coefficient; S422. Penalize the dual-objective response value of the ring rolling process model where the rolling time and maximum wall thickness difference do not conform to physical meaning, and construct a physical rationality constraint loss. : ； in, To increase the number of samples in the dataset This is the predicted maximum wall thickness difference for the i-th sample. S423. Based on the enhanced response dataset, construct a set of true dominant sample pairs among sample pairs, and use the Softplus ranking function to penalize the response values ​​of the ring rolling process model that violates the bi-objective superiority relationship, thus constructing a smooth ranking loss: S424. Based on the parameter size, gated channel activation level, and low-rank interactive branch magnitude of LPIGR-Net, a lightweight regularized loss function is constructed. : ； in, For the set of all trainable parameters, To hide the number of channels, represents the weighting coefficients of the gated sparse regularization term; These are the weight coefficients for the low-rank interactive branch regularization term; For model parameters Regular terms; The number of samples used in training; For the first The gating vector corresponding to each sample; For the gated vector Norm; It is a low-rank interaction order; Number the low-rank interactive branches; For the first The first trainable weight parameter in a low-rank interaction branch, For the first The second trainable weight parameter in a low-rank interaction branch, For the first The third trainable weight parameter in a low-rank interaction branch; S425. Employing a physical-Pareto lightweight loss function, a multidimensional loss function is constructed by integrating scale balance loss, physical rationality constraint loss, smoothing ranking loss, and lightweight regularization loss. ; ； in, To smooth the sorting loss, The weighting coefficients for the loss due to physical rationality constraints. The weighting coefficients for the order consistency loss are: The weighting coefficients of lightweight regularization loss.

9. The method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network according to claim 8, characterized in that, S423 includes: S4231. Based on the true dual-objective response values ​​of any two samples in the enhanced response dataset, and according to the dual-objective minimization optimization direction of rolling time and maximum wall thickness difference, construct a set of true dominance sample pairs based on the true dominance relationship between sample pairs. S4232. The Softplus ranking function is used to impose a ranking penalty on the response values ​​of the ring rolling process model that violate the true dominance sample set in the prediction results of the ring rolling process model, and a smooth ranking loss is constructed. ； in, For the number of truly dominant sample pairs, This is the standardized rolling time prediction value for the i-th sample. For the sample Standardized rolling time prediction For the sample The predicted value of the maximum wall thickness difference. For the sample The predicted value of the maximum wall thickness difference. The first temperature coefficient, This is the second temperature coefficient.

10. The method for optimizing the ring rolling process of magnesium alloy cylinder segments based on a lightweight physical interaction network according to claim 7, characterized in that, The low-rank physical interaction layer is represented as: ； in, The interaction enhancement features output by the low-rank physical interaction layer. The initial hidden features are the input to the embedding layer's output. For 18-dimensional ring rolling input features, It is a low-rank interactive order. For low-rank interactive branch numbering, For the first The first learnable projection vector of the low-rank interaction branches. For the first The second learnable projection vector of the low-rank interaction branch. For the first The learnable weight coefficients of the low-rank interaction branches, where T is the vector transpose.

Images