GAN-based high-remanence neodymium iron boron component and process optimization method

Abstract

The invention discloses a GAN-based high-remanence neodymium-iron-boron component and process optimization method, and relates to the field of high-remanence magnetic material design, and the method comprises the steps: obtaining the input characteristics and target characteristics of a sintered neodymium-iron-boron magnet; constructing a generative adversarial network, introducing a physical constraint term into a generator loss function of the generative adversarial network, carrying out data expansion on the high residual magnetism subset by using the trained generative adversarial network, and carrying out parallel training on a deep learning model and a traditional machine learning model based on the expanded data and the original data to form a hybrid prediction model; and inputting the target magnetic performance into the hybrid prediction model, and performing reverse prediction to obtain a corresponding magnet component and sintering process parameter combination. According to the method, the adversarial network introducing the physical constraint term is utilized to expand the high residual magnetism data, and the multi-dimensional feature analysis and the mixed model training are combined, so that the precise matching of the magnet component-process-magnetic performance is realized, the design accuracy is improved, the research and development period is shortened, and the experiment cost is reduced.

Description

Technical Field

[0001] This invention relates to the field of process optimization for high remanence magnetic materials, and particularly to a method for optimizing the composition and process of high remanence NdFeB based on GAN. Background Technology

[0002] Sintered NdFeB permanent magnets, with their excellent magnetic properties, have been widely used in strategic emerging industries such as new energy vehicles, wind power generation, medical devices, and high-end electronic equipment. With the accelerated technological iteration in downstream application fields, more stringent requirements are being placed on the overall performance of permanent magnets, demanding that they provide stronger and more stable magnetic fields within extreme space constraints. Therefore, developing high-performance sintered NdFeB permanent magnets with remanence exceeding 14 kGs has become a key industry need.

[0003] Publication No. CN 112259176 A discloses a method and system for predicting the magnetic properties of sintered SmCo magnets based on neural networks. Relying on existing experimental data, a neural network model establishes a predictive model between composition and process parameters and the magnetic properties of the magnet. After model optimization, the fitting accuracy and generalization ability of the model are greatly improved, thus obtaining reliable magnetic property prediction values ​​in a continuous space of composition and process parameters. This solves the problem of predicting the magnetic properties of sintered SmCo permanent magnets. However, it has obvious shortcomings: 1. It only uses existing experimental data for model training and optimization. The preparation of high remanence magnets requires precise control of composition and process, which is complex, costly, and has a low success rate, resulting in very little effective data accumulated. Using data with low remanence will cause the model to be biased towards the low remanence region, failing to capture the nonlinear correlation unique to high remanence, thus leading to low prediction accuracy for high remanence magnets; 2. The model only uses process parameters and composition as input, without considering the influence of microstructure characteristics on the performance of permanent magnets; 3. This invention is a single-phase prediction, predicting performance based on given composition and process, and cannot determine the process to be used to achieve a certain performance. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing the composition and process of high remanence NdFeB magnets based on GAN. This method utilizes an adversarial network with introduced physical constraints to expand the high remanence data, and combines multi-dimensional feature analysis and hybrid model training to achieve precise matching of magnet composition, process, and magnetic properties, thereby improving the accuracy of process optimization, shortening the R&D cycle, and reducing experimental costs.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: A method for optimizing the composition and process of high remanent NdFeB magnets based on GANs, the method comprising: S1: Obtain the input and target features of sintered NdFeB magnets; based on the remanence index in the target features, divide the dataset into a high remanence subset and a normal subset; S2: Construct a GAN, train it using a subset of high remanent magnets as real samples, introduce a physical constraint term into the generator loss function of the GAN, and use the trained GAN to augment the high remanent magnets subset to generate a physically reasonable augmented subset. S3: Based on the expanded subset, the high remanent magnetic subset and the regular subset, train at least one deep learning model and at least one traditional machine learning model in parallel to form a hybrid prediction model; S4: Input the target magnetic properties into the hybrid prediction model and reverse predict the corresponding combination of magnet composition and sintering process parameters.

[0006] As a preferred option, the input characteristics of sintered NdFeB magnets are determined by magnet composition, powder properties, and sintering process parameters; the target characteristics are determined by magnetic performance indicators.

[0007] As a preferred approach, before dividing the data into high remanent subsets and regular subsets, the data for input features and target features need to be preprocessed. First, the data should be cleaned, and missing data should be supplemented by the correlation of similar samples. Finally, the data should be normalized.

[0008] Specifically, the Z-score method is first used to identify and remove noise and outliers; then, the missing data is supplemented by interpolating the mean or K-nearest neighbors, utilizing the correlation between similar samples; finally, the min-max scaling technique is used to adjust all input features to the [0, 1] scale range.

[0009] As a preferred approach, after normalization, it is necessary to combine Pearson correlation coefficient analysis, recursive feature elimination, and LASSO regression methods to screen out key features that are highly correlated with the target feature.

[0010] Specifically, by combining Pearson correlation coefficient analysis, recursive feature elimination, and LASSO regression, key features highly correlated with the target features are selected from the input features to facilitate subsequent data expansion and model training. The original features may number in the dozens (multiple element contents, multiple granularity parameters, multiple temperature and time parameters). Inputting all features indiscriminately into the model would create an extremely high-dimensional search and learning space. If the input features contain a large number of irrelevant process parameters, the design of physical constraints would become complex and divergent. After selection, physical constraints can be applied more precisely to the key component features, allowing the generator to focus more on learning the reasonable distribution and correlation of these key features, thereby generating data with clearer physical meaning and higher quality.

[0011] As a preferred option, the remanence index boundary between the high remanence subset and the conventional subset is 14 kGs. The subset with Br > 14 kGs is the high remanence subset, and the subset with Br ≤ 14 kGs is the conventional subset.

[0012] Specifically, slight fluctuations exist in performance measurements during material preparation. Setting the threshold at a slightly lower level of 14.4 kGs (14 kGs) ensures that all potentially high-performance samples are included, avoiding the omission of boundary samples due to measurement errors and guaranteeing the completeness of the high remanence subset.

[0013] As a preferred embodiment, GAN includes a generator and a discriminator. The generator adopts a deep convolutional neural network structure to generate simulated high-performance magnet feature data through deconvolution operations. The discriminator also adopts a deep convolutional neural network structure to distinguish between real high-performance data and generated data.

[0014] Specifically, using a subset of high remanent magnets as real samples for training, the generator learns the distribution characteristics of real data through adversarial training between the generator and the discriminator. The generator uses a deep convolutional neural network structure based on randomly sampled noise and generates simulated high-performance magnet feature data through deconvolution operations. However, the loss function of the generator in traditional adversarial networks can easily lead to the generation of data that violates physical laws. Therefore, this invention introduces a constraint term in the calculation of the loss function. In adversarial training, the discriminator continuously negates the generator, and the generator updates itself based on this feedback, eventually generating an expanded subset whose distribution is indistinguishable from that of the real high remanent magnet subset.

[0015] As a preferred approach, after generating a physically reasonable expanded subset, the data quality of the expanded subset needs to be verified, including: Verify the similarity in distribution between the generated data and the real data; Samples with a total component content exceeding or falling below 100% and process parameters exceeding equipment limits are excluded. The correlation between the composition and process of the generated data and remanence was verified by using a pre-trained simple model, and samples with predicted remanence Br > 14 kGs were retained.

[0016] Specifically, the expansion subset should be verified by calculating the KL divergence between the real data and the generated data to check the distribution similarity between the generated data and the real data, and a strict threshold should be designed to select samples that meet the threshold. Then, the sum of the normalized content of the components of the above samples should be calculated, and whether the process parameters exceed the equipment limits should be checked. Samples with a total component content exceeding or falling below 100% and process parameters exceeding the equipment limits should be removed. Finally, the correlation between the components of the generated data and the process and remanence should be verified by a pre-trained simplified model, and samples with predicted remanence Br > 14 kGs should be retained.

[0017] As a preferred approach, after data quality verification and before parallel model training, the verified expanded subset, the original high remanent magnetization subset, and the regular subset should be merged to form a complete dataset. The complete dataset should then be divided into a training set and a test set in an 8:2 ratio, and a 5-fold cross-validation method should be used to avoid model overfitting.

[0018] Specifically, the validated expanded subset, the original high remanence subset, and the original regular subset are merged to form a complete dataset. This operation aims to significantly improve the distribution density and representativeness of high remanence features in the overall data, laying the foundation for the subsequent model to simultaneously learn general patterns and high-performance region-specific patterns. The complete dataset is divided into a training set and an independent test set at a preset ratio of 8:2, ensuring that the number of high remanence samples in the test set is statistically significant. Furthermore, multi-fold cross-validation is used for model training and parameter tuning on the training set. This series of rigorous data processing and evaluation procedures aims to fully utilize scarce high-performance data to maximize the evaluation and guarantee the model's performance.

[0019] As a preferred approach, the hybrid prediction model is based on a weighted fusion method using Shapley values, which integrates the prediction results of deep learning models and traditional machine learning models to obtain the final hybrid prediction model.

[0020] Specifically, convolutional neural networks and long short-term memory networks are simultaneously trained using the expanded dataset to capture the complex nonlinear relationships between composition, process, and magnetic properties. Support vector regression, extreme gradient boosting, and Gaussian process regression models are also trained to provide robust baseline predictions. Finally, a weighted fusion method based on Shapley values ​​is employed, considering the R-values ​​of each sub-model on the validation set. 2 Evaluation metrics such as RMSE are used to quantify their contribution, and the prediction results of deep learning and traditional machine learning models are dynamically weighted and integrated to obtain a high-precision and highly robust final performance prediction model.

[0021] Preferably, the combination of components and process parameters obtained from the reverse prediction is experimentally verified, and the new data obtained from the verification is added to the historical dataset. Steps S1 to S4 are repeated to achieve iterative optimization of the model.

[0022] The beneficial effects of this invention are as follows: Addressing the scarcity of high remanence data: This invention effectively expands high-performance magnet data through generative adversarial networks (GANs), ensuring that the similarity between the generated samples and the real data distribution is ≥95%, effectively expanding the amount of high remanence samples and providing sufficient data support for subsequent modeling; Improved prediction accuracy: The expanded data of this invention, combined with hybrid model training, can improve the prediction accuracy of magnetic properties from about 90% of the traditional method to more than 95%. Considering the huge potential composition-process space, the design accuracy is significantly improved. Reduce experimental costs: This invention reduces the number of blind experiments and shortens the R&D cycle of high remanent magnets by accurately predicting the composition-process space, and can significantly reduce experimental costs in complex composition systems. Enhancing model interpretability: This invention combines Shapley value analysis and feature importance assessment to identify key influencing factors, providing a scientific basis for process optimization and reducing reliance on human experience. Attached Figure Description

[0023] Figure 1 This is a flowchart of a process optimization method for high remanence sintered NdFeB permanent magnets based on generative adversarial networks.

[0024] Figure 2 This is a detailed flowchart of the model construction and experimental verification of the process optimization method for high remanence sintered NdFeB permanent magnets based on generative adversarial networks. Detailed Implementation

[0025] Example 1 This embodiment elaborates on the system implementation process of the process optimization method of the present invention, focusing on the key steps of data expansion and model training.

[0026] The input and target features of sintered NdFeB magnets are obtained; based on the remanence index in the target features, the dataset is divided into a high remanence subset and a normal subset.

[0027] Data is collected from multiple production batches and historical R&D records and integrated into a structured dataset. Data sources include, but are not limited to, laboratory pilot-scale records, pilot production logs, and process files of mass-produced products, ensuring that the data covers a wide process window and performance range.

[0028] The input features cover three categories and more than 20 features in total. The composition features are determined by the precise weight percentage of the main phase elements Nd, Fe, and B, as well as the content of added elements such as Dy, Co, Pr, Cu, and Al. The powder properties are determined by the volume weighted average diameter (SMD), particle size distribution parameters (D90 / D10, D50), powder oxygen content, and pressing density. The sintering process parameters are determined by the sintering temperature, sintering time, first-stage aging temperature, first-stage aging time, second-stage aging temperature, second-stage aging time, and orientation magnetic field.

[0029] The target characteristics are magnetic performance indicators, mainly determined by remanence (Br), with coercivity (Hcj), energy product (BHmax), and squareness (Hk / Hcj) as auxiliary constraints.

[0030] Data preprocessing: First, for each numerical feature, its mean and standard deviation are calculated. Data points exceeding three times the standard deviation are marked as outliers and removed after manual review based on process logs. For features with low missing rates, the K-nearest neighbor algorithm is used for imputation, finding the most similar sample based on other complete features and using the weighted average of its feature values ​​as the imputation value. A min-max normalization method is used to linearly map all feature values ​​to the [0,1] interval. Then, the Pearson correlation coefficient between all input features and the target remanence is calculated, retaining features with strong correlations. Subsequently, a recursive feature elimination method is used, with random forest regression as the base model, iteratively removing the least important features. Finally, LASSO regression is used to sparsify the remaining features, removing features with regression coefficients approaching zero, resulting in the final subset of key features.

[0031] Subsequently, based on the target characteristics, a remanence index limit of 14 kGs was set, with the subset containing Br > 14 kGs being the high remanence subset and the subset containing Br ≤ 14 kGs being the conventional subset. However, the preparation of high remanence magnets requires precise control of composition and process, which is complex, costly, and has a low success rate, resulting in very little effective data accumulated in practice, making it difficult to support data-driven accurate modeling.

[0032] Therefore, a Generative Adversarial Network (GAN) is constructed, which is trained using a subset of high-residual magnetic data as real samples. A physical constraint term is introduced into the generator loss function of the GAN, and the trained GAN is used to augment the subset of high-residual magnetic data to generate a physically reasonable augmented subset.

[0033] Generative Adversarial Networks (GANs) consist of a generator and a discriminator. The generator employs a deep deconvolutional neural network (DNN) structure. Its input is a random noise vector, which is progressively upsampled through multiple deconvolution operations, ultimately outputting a simulated key feature vector. The hidden layers use the ReLU activation function, and the output layer uses the Tanh activation function to constrain the values ​​within a reasonable range. The discriminator also employs a deep convolutional neural network (DNN) structure. Its input is a feature vector, which is extracted through multiple convolutions and downsampling. Finally, a fully connected layer and a Sigmoid activation function output a scalar to determine the probability that the input data is real data.

[0034] Specifically, because the loss function of traditional generative adversarial networks (GANs) tends to generate data that violates physical laws, a custom physical constraint loss term is introduced. This constraint term consists of a weighted sum of multiple sub-terms, mainly including: Composition and constraints: Penalize cases where the sum of the contents of each element in the generated sample deviates from 100%; Process range constraint: Penalize situations where process parameters in the generated samples exceed the reasonable range based on historical experience; Physical property correlation constraint: For known feature pairs with strong physical correlation, penalize generated samples whose correlation is opposite to the distribution of the real data.

[0035] The generator's total loss is a weighted sum of the standard adversarial loss and the aforementioned physical constraint loss, with the contributions of the two terms balanced by adjusting the weighting coefficients.

[0036] The adversarial training process between the generator and the discriminator uses the Adam optimizer with appropriate learning rate and momentum parameters. The training employs an alternating update strategy: first, the discriminator is updated to better distinguish between real and generated data; then, the generator is updated to produce more realistic and physically consistent data to fool the discriminator. The training process continues for thousands of rounds until the adversarial process reaches equilibrium, yielding an expanded subset generated by the generator.

[0037] After generating a physically reasonable expanded subset, the data quality of the expanded subset needs to be verified, namely, distribution consistency verification, physical reasonableness verification, and performance correlation verification.

[0038] Distribution consistency verification is the primary and core step in this method to ensure the quality of generated data. Its goal is to quantitatively evaluate whether the simulated data output by the generative adversarial network follows the same distribution pattern as the real-world high remanence sintered NdFeB data in a statistically significant manner.

[0039] This validation goes beyond a simple comparison of the mean or variance of a single feature; instead, it aims to confirm that the joint probability distribution of the generated dataset is highly consistent with the joint probability distribution of the real high remanence dataset in a multidimensional feature space. To achieve this goal, we introduce a key metric in information theory—the Kullback-Leibler divergence (KL divergence for short).

[0040] KL divergence essentially measures the amount of information lost when the probability distribution of generated data is used to approximate the probability distribution of real data. This lost information is numerically represented by the calculated KL divergence value. Its core mathematical property is that the value is always non-negative; the KL divergence is zero if and only if the two distributions are completely identical. A smaller value indicates a more similar distribution.

[0041] In the specific implementation of this invention, firstly, the probability density distributions of the real high remanent magnetization subset (after preprocessing and feature screening) and the large batch of candidate data generated by the generative adversarial network are estimated along the selected key feature dimensions. Since the features involve continuous variables, non-parametric methods such as kernel density estimation are typically used, or discretization binning is performed with a certain level of precision to construct their respective empirical distributions. Subsequently, the KL divergence is calculated according to the definition formula. The core of this formula is to calculate the logarithm of the ratio of the true distribution probability value to the generated distribution probability value for all possible data points, and then perform a weighted summation using the true distribution probability as the weight. Finally, a very strict acceptance threshold is set: the KL divergence value must be less than this threshold, which has a clear physical meaning.

[0042] Only generated datasets that meet this condition will be considered to have passed the distribution consistency verification. This step is crucial because it directly ensures that the adversarial network is not merely memorizing or simply replicating individual samples, but truly learning and capturing the complex, multi-factor coupled statistical regularities and data generation mechanisms hidden behind the limited real high remanence data. This is the cornerstone for all subsequent modeling work. If the generated data has a systematic bias in its distribution, no matter how sophisticated the subsequent model is, its predictions and process optimizations will be based on distortion, leading to failure in practical applications.

[0043] Physical rationality verification, following statistical distribution verification, applies a stringent rule-based filtering of the generated data, grounded in domain knowledge and physical laws. This verification primarily focuses on two levels: the law of conservation of composition and the boundary of process feasibility. First, at the composition level, as a multi-component alloy material, sintered NdFeB requires the sum of the weight percentages of all its constituent elements (including the main elements Nd, Fe, and B, and various additive elements such as Dy and Co) to be strictly equal to 100%. Any generated composition data whose sum significantly deviates from 100%, whether exceeding or falling short, directly violates the fundamental law of conservation of matter and represents a physically nonexistent and invalid composition. Second, at the process parameter level, every sintering and heat treatment parameter must be within the physical limits achievable by current industrial equipment and technology. For example, the sintering temperature is limited by the melting point of the heat-resistant material in the sintering furnace and cannot be infinitely high; the holding time at each stage is constrained by production efficiency and economic costs, and has a reasonable range; the orientation magnetic field strength is also constrained by the capability of the magnetization device. These boundary values ​​are not derived from model predictions, but are specific values ​​determined based on extensive industry research, equipment manuals, and engineering experience. The validation system checks each process parameter in the generated data one by one. If any parameter value is found to be outside its preset reasonable range (such as a negative sintering time or an unattainable cooling rate), no matter how "perfect" its statistical characteristics may be, the data will be marked as invalid and excluded.

[0044] Performance correlation verification involves a function-oriented screening process to ensure that the generated data, after the first two rounds of verification, not only possesses correct distribution characteristics and physical rationality but also meets the high remanence standard for the target features. A pre-trained, relatively simple "simple prediction model" is introduced as a surrogate evaluation tool. This simple model typically employs computationally efficient and interpretable algorithms and is specifically trained on limited real high remanence data, making it particularly sensitive to the feature-performance mapping relationship in high-performance regions. The generated data to be verified is input into this simple model, which predicts a corresponding remanence value for each generated "composition-process" combination, retaining only an expanded subset of predicted remanence values ​​greater than 14 kGs.

[0045] The expanded subset that passed the three validations was merged with the original high remanent magnetization subset and the regular subset to form the expanded complete dataset. The complete dataset was then divided into training and testing sets in an 8:2 ratio, and a 5-fold cross-validation method was adopted. This series of rigorous data processing and cross-validation processes aims to make full use of scarce high-performance data to evaluate and protect the model to the greatest extent.

[0046] Based on the expanded subset, the high remanent magnetic subset and the regular subset, at least one deep learning model and at least one traditional machine learning model are trained in parallel to form a hybrid prediction model.

[0047] This invention constructs a hybrid prediction model combining deep learning and traditional machine learning. This model aims to integrate the advantages of both types of models to fully utilize the expanded high-quality dataset and achieve high-precision learning and prediction of the complex mapping relationship between the composition, process, and magnetic properties of sintered NdFeB. Specifically, multiple types of benchmark models are trained in parallel. For deep learning models, Convolutional Neural Networks (CNNs) and Long Short-Term Memory Networks (LSTMs) are primarily used. CNNs can effectively capture local spatial correlations and interaction patterns between input features, such as the synergistic effects between different element contents or process parameters; LSTMs excel at handling data structures with temporal or sequential dependencies, and in this method, they can be used to model the cumulative and sequential effects of sintering, aging, and other staged processes on the final performance. These two types of networks, through their multi-level nonlinear transformation capabilities, are dedicated to learning and extracting high-dimensional abstract feature representations from the data, thereby fitting highly complex nonlinear relationships. Simultaneously, a set of classic and robust traditional machine learning models are trained concurrently, including Support Vector Regression (SVR), Extreme Gradient Boosting (XGBoost), and Gaussian Process Regression (GPR). SVR demonstrates good generalization ability in small sample or high-dimensional scenarios; XGBoost, as an efficient ensemble tree model, can automatically handle feature interactions and provide importance ranking, exhibiting strong adaptability to heterogeneous data; GPR provides a probabilistic framework for prediction, offering not only predicted values ​​but also estimates of the uncertainty of the predictions. This parallel architecture ensures that for the different patterns and regularities contained in the expanded dataset, there are corresponding models to capture them specifically.

[0048] After the independent training and validation of each sub-model, the crucial model fusion stage begins to obtain a final predictor that surpasses any single model. The core of the fusion strategy is based on the Shapley value principle in cooperative game theory, fairly quantifying the marginal contribution of each sub-model to the overall prediction result. In practice, instead of simply averaging the predictions of all models, a dynamic weighted fusion mechanism is designed. This involves evaluating each sub-model on a separate validation dataset based on key performance indicators (such as the coefficient of determination R). 2 The model's performance on Root Mean Square Error (RMSE) and Mean Squared Error (MSE) is analyzed, and combined with Shapley values, to simulate all possible model combinations. This analysis examines how the prediction accuracy of the entire model ensemble changes when a specific model is added or removed, thus objectively assessing the model's "contribution" to the collaboration. This contribution is then converted into the model's weight in the final ensemble prediction.

[0049] For example, if CNNs excel at capturing complex nonlinear relationships, while XGBoost demonstrates superior overall stability, they will be assigned higher weights; conversely, models that perform well on a specific subset but have slightly weaker generalization capabilities will receive lower weights. Ultimately, for any new input, the prediction result is a weighted average of the outputs of all sub-models based on their Shapley weights.

[0050] This contribution-weighted hybrid model ensemble approach offers several significant advantages. First, by integrating predictions from models based on different principles, it effectively reduces systematic biases or variances caused by differing model assumptions, significantly improving the overall accuracy and robustness of the predictions. This makes the final model more stable and reliable when facing complex variations in the composition-process parameter space. Second, this method enhances the interpretability and reliability of the prediction results.

[0051] Shapley value analysis not only reveals the contribution of each sub-model but also indirectly reflects the importance of different types of features (such as composition, powder properties, and process sequences) on the final performance, providing guidance for process optimization. Ultimately, this meticulously constructed hybrid predictive model becomes the core intelligent engine connecting "expanded high-fidelity data" with "precise reverse process optimization." It transforms the patterns inherent in the data into reliable predictive capabilities, enabling the model to recommend the optimal combination of composition and process parameters simply by inputting the target magnetic performance indicators. This truly achieves efficient and precise process optimization of high-performance sintered NdFeB permanent magnets driven by data, completely changing the traditional R&D model that relies on trial and error.

[0052] The target magnetic properties are input into the hybrid prediction model, and the corresponding combination of magnet composition and sintering process parameters is obtained by reverse prediction. Experimental verification is carried out based on the combination of composition and process parameters obtained by reverse prediction, and the new data obtained by verification is added to the historical dataset. Steps S1 to S4 are repeated to achieve iterative optimization of the model.

[0053] Example 2 This embodiment combines the general process of Embodiment 1 to demonstrate a complete case study of process optimization for high remanence NdFeB magnets.

[0054] Obtain the input and target features of sintered NdFeB magnets.

[0055] Data on sintered NdFeB production from a metallurgical company was collected. The original dataset contained 1,053 regular data entries, while only 82 high-performance data entries (remanence > 14 kGs) were collected. The input characteristics specifically include: Nd content (28-32%), Fe content (64-68%), B content (1.0-1.2%), Dy content (0-2.0%), and Co content (0-1.5%); powder properties are SMD (3.0-5.0 μm), D90 / D10 (2.5-4.5), D50 (2.0-4.0 μm), and oxygen content (≤1500 ppm); sintering process parameters are sintering temperature (1040-1150 ℃), sintering time (2-4 h), first-stage aging temperature (850-950 ℃), first-stage aging time (2-3 h), second-stage aging temperature (450-550 ℃), and second-stage aging time (4-6 h). The target characteristics are remanence (9-15.5 kGs), coercivity (8-31.19 kOe), maximum energy product (12-53 MGOe), and squareness (0.75-0.995).

[0056] Data preprocessing.

[0057] Three outlier data points were removed using the Z-score method, and 12 missing data points were supplemented by mean interpolation. Min-Max scaling was used to normalize all features to [0, 1]. Key features were selected through correlation coefficient analysis, RFE and LASSO regression: Nd content, B content, SMD, D90 / D10, sintering temperature, first-stage aging temperature and second-stage aging time, which were considered as key features for modeling input.

[0058] A generative adversarial network (GAN) is constructed and trained using a subset of high-residual magnetic data as real samples. A physical constraint term is introduced into the generator loss function of the GAN. The trained GAN is then used to augment the high-residual magnetic data subset to generate a physically reasonable augmented subset.

[0059] Generator: 3 layers of deconvolution, hidden layer activation function is ReLU, output layer is Tanh, and physical constraint term is introduced into the loss function, focusing on constraining the component sum deviation and process parameter out-of-bounds; Discriminator: 3 convolutional layers, with LeakyReLU activation function (α=0.2), and Sigmoid activation function for the output layer; Training parameters: batch size=32, 10,000 iterations, Adam optimizer (lr=0.0002, β1=0.5); Results generated: Using 80 real high-performance datasets as training samples, the training process iterated 5000 times, generating 400 augmented datasets. After verification using KL divergence (divergence < 0.05) and physical constraints, 282 augmented datasets with a distribution similarity ≥ 95% to the real dataset were selected and merged with the original 1000 datasets to form a complete dataset of 1282 datasets.

[0060] Based on the expanded subset, the high remanent magnetic subset and the regular subset, at least one deep learning model and at least one traditional machine learning model are trained in parallel to form a hybrid prediction model.

[0061] The expanded dataset was divided into a training set (1026 records) and a test set (256 records) in an 8:2 ratio, and 5-fold cross-validation was used. Taking remanence as an example, CNN, SVR, XGBoost, and GPR models were trained respectively. The weights were assigned based on the Shapley score and the model training evaluation results: CNN weight 0.4, XGBoost weight 0.3, SVR weight 0.2, and GPR weight 0.1.

[0062] Prediction results of the ensemble model on the test set: Remanence prediction R 2 =0.9682, coercivity prediction R 2 =0.9035, maximum magnetic energy product prediction R 2 =0.9516, squareness prediction R 2 =0.9346.

[0063] The target magnetic properties are input into the hybrid prediction model, and the corresponding combination of magnet composition and sintering process parameters is obtained by reverse prediction.

[0064] For the target performance (remanence ≥ 15.2 kGs, coercivity ≥ 8 kOe, maximum energy product ≥ 50 MGOe, squareness ≥ 0.95), the optimal composition-process parameters were predicted by the model. Experimental production using these parameters showed that the error between the actual magnetic properties and the predicted values ​​was ≤ 1.05%, meeting the requirements for industrial production.

Claims

1. A method for optimizing the composition and process of high remanent NdFeB magnets based on GANs, characterized in that, The method includes: S1: Obtain the input and target features of sintered NdFeB magnets; based on the remanence index in the target features, divide the dataset into a high remanence subset and a normal subset; S2: Construct a GAN, train it using a subset of high remanent magnets as real samples, introduce a physical constraint term into the generator loss function of the GAN, and use the trained GAN to augment the high remanent magnets subset to generate a physically reasonable augmented subset. S3: Based on the expanded subset, the high remanent magnetic subset and the regular subset, train at least one deep learning model and at least one traditional machine learning model in parallel to form a hybrid prediction model; S4: Input the target magnetic properties into the hybrid prediction model and reverse predict the corresponding combination of magnet composition and sintering process parameters.

2. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1, characterized in that, The input characteristics of sintered NdFeB magnets are determined by magnet composition, powder properties, and sintering process parameters; The target characteristics are determined by magnetic performance indicators.

3. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1, characterized in that, Before dividing the data into high remanent subsets and regular subsets, the data for input features and target features need to be preprocessed. First, the data is cleaned, and missing data is supplemented by the correlation of similar samples. Finally, the data is normalized.

4. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1 or 3, characterized in that, After normalization, it is necessary to combine Pearson correlation coefficient analysis, recursive feature elimination and LASSO regression methods to screen out key features that are highly correlated with the target features.

5. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1, characterized in that, The remanence index boundary between the high remanence subset and the normal subset is 14 kGs. The subset with Br > 14 kGs is the high remanence subset, and the subset with Br ≤ 14 kGs is the normal subset.

6. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1, characterized in that, The adversarial network consists of a generator and a discriminator. The generator uses a deep convolutional neural network structure to generate simulated high-performance magnet feature data through deconvolution operations. The discriminator also uses a deep convolutional neural network structure to distinguish between real high-performance data and generated data.

7. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1, characterized in that, After generating a physically valid augmented subset, the data quality of the augmented subset needs to be verified, including: Verify the similarity in distribution between the generated data and the real data; Samples with a total component content exceeding or falling below 100% and process parameters exceeding equipment limits are excluded. The correlation between the composition and process of the generated data and remanence was verified by using a pre-trained simplified model, and samples with predicted remanence Br>14kGs were retained.

8. A method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1 or 7, characterized in that, After data quality verification and before parallel model training, the verified expanded subset, the original high remanent magnetization subset, and the regular subset need to be merged to form a complete dataset. The new expanded subset is then divided into training and test sets in an 8:2 ratio, and a 5-fold cross-validation method is used to avoid model overfitting.

9. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1, characterized in that, The hybrid prediction model is a weighted fusion method based on Shapley values, which integrates the prediction results of deep learning models and traditional machine learning models to obtain the final hybrid prediction model.

10. The method for optimizing the composition and process of high remanent NdFeB based on GAN according to claim 1, characterized in that, Step S4 is followed by: conducting experimental verification based on the combination of components and process parameters obtained from the reverse prediction, adding the new data obtained from the verification to the historical dataset, and repeating steps S1 to S4 to achieve iterative optimization of the model.

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