Simulation Method for Rare-earth Extraction and Separation Processes Based on Multi-branch Regression Generative Adversarial Networks
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摘要: 针对基于萃取机理的稀土萃取工艺流程模拟难以符合实际萃取生产工况的问题, 提出一种基于多分支回归生成对抗网络的稀土萃取分离流程模拟方法, 实现稀土萃取分离各级萃取槽稀土元素组分含量的精准计算. 首先, 针对稀土萃取生产现场有效样本数量较少, 采用生成对抗网络(GAN)构造生成对抗模型, 依据稀土萃取工艺串级分离特点, 使用多分支深层网络构造GAN的生成器, 逐级学习萃取级间数据深层特征; 提出判别器与回归器的浅层特征共享机制, 回归器复用判别器首层卷积特征以提升预测性能, 并通过回归一致性约束以生成更真实的样本; 根据多分支网络结构特点, 设计一种递归渐近式对抗训练策略, 固定前一分支子GAN模型学习到的网络参数并作为下一分支子GAN的共同特征, 各分支子GAN内部生成器、判别器、回归器三者循环对抗训练, 在保证模型稳定收敛的同时, 精准捕捉级间耦合特征. 仿真结果表明了本文所提方法的有效性.Abstract: To address the problem that the simulation of rare-earth extraction process based on extraction mechanism hardly conforms to actual extraction production conditions, a simulation method for rare-earth extraction and separation processes based on multi-branch regression generative adversarial networks is proposed to achieve accurate calculation of rare-earth element component concentrations in each extraction stage. First, in view of the limited number of effective samples in the rare-earth extraction production site, a GAN is adopted to construct a generative adversarial model. According to the cascade separation characteristics of the rare-earth extraction process, a multi-branch deep network is used to construct the generator of the GAN, learning the deep features of inter-stage extraction data level by level. A shallow feature sharing mechanism between the discriminator and the regressor is proposed, the regressor reuses the first-layer convolutional features of the discriminator to improve prediction performance, and a regression consistency constraint is introduced to generate more realistic samples. In view of the structural characteristics of the multi-branch networks, a recursive progressive adversarial training strategy is designed, the network parameters learned by the previous branch sub-GAN model are fixed and serve as common features for the next branch sub-GAN. Within each branch sub-GAN, the generator, discriminator, and regressor undergo cyclic adversarial training, ensuring stable model convergence while accurately capturing inter-stage coupling features. Simulation results demonstrate the effectiveness of the proposed method.
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图 1 稀土串级萃取分离工艺流程图
Fig. 1 Flow diagram of rare-earth cascade extraction and separation process
图 5 判别器(D)和回归器(R)网络结构图
Fig. 5 Network structure diagram of discriminator (D) and regressor (R)
图 8 输入变量$c$与输出数据${y_{25(1)}}$分布趋势图
Fig. 8 Distribution trend chart of input variable $c$ and output data ${y_{25(1)}}$
图 10 测试集上各萃取级真实值与模拟值的概率密度分布对比
Fig. 10 Comparison of probability density distributions between real values and simulated values for each extraction level on the test set
图 11 各分支真实值与预测值散点拟合图
Fig. 11 Scatter plot of real values and predicted values for each branch
图 14 第25级各模型预测绝对误差及误差分布统计对比
Fig. 14 Comparison of prediction absolute error and error distribution statistics for each model at 25th stage
图 17 不同梯度惩罚系数下的组分分布核密度估计曲线对比
Fig. 17 Comparison of kernel density estimation curves for component distributions under different gradient penalty coefficients
图 18 超参数$\lambda $对生成组分含量样本质量的影响
Fig. 18 The influence of the hyperparameter $\lambda $ on the quality of the generated component content samples
表 1 工艺输入变量
Table 1 Process input variables
输入变量 物理意义描述 $c_1$ La元素组分含量 $c_2$ Ce元素组分含量 $c_3$ Pr元素组分含量 $c_4$ Nd元素组分含量 $c_5$ Ce/La元素间分离系数 $c_6$ Pr/Ce元素间分离系数 $c_7$ Nd/Pr元素间分离系数 $c_8$ 主产品出口模式 $c_9$ 进料模式 $c_{10}$ 萃取剂流量 $c_{11}$ 洗涤剂流量 $c_{12}$ 进料级数 $c_{13}$ 有机相出口分数 $c_{14}$ 水相出口分数 
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表 2 各模型最佳超参数设置
Table 2 Optimal hyperparameter settings for each model
模型 关键参数 SVR 惩罚系数 $C=1$, 核系数 $\gamma=0.1$, 不敏感区宽度 $\epsilon=0.01$ XGBoost 学习率 $lr=0.05$, 子采样率 $S=0.8$, 最大深度: 5 BPNN 隐藏层单元数: 64, 学习率 $lr=0.001$ LSTM 隐层神经元数: 128, 学习率 $lr=0.01$, Dropout: 0.2 GRU 隐层神经元数: 128, 学习率 $lr=0.01$, Dropout: 0.2 CGAN 生成器学习率 $lr_G=0.000 2$, 判别器学习率 $lr_D=0.000 2$, L1范数权重 $\lambda_{L1}=10$ MB-DNN 隐层神经元数: 64, 学习率 $lr=0.001$, Dropout: 0.2 MB-RDN 隐层神经元数: 64, 学习率 $lr=0.001$, Dropout: 0.2 MB-RGAN 生成器学习率 $lr_G=0.000 1$, 判别器学习率 $lr_D=0.000 1$, 回归器学习率 $lr_R=0.001$, $\lambda_{GP}=10$, $\lambda_1=\lambda_2=1$
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表 3 不同模型在测试集上的性能指标对比
Table 3 Comparison of performance metrics of different models on the test set
模型 组分 平均MAE 平均RMSE 平均$R^2$ SVR 有机相 0.050 0 0.062 9 0.833 1 水相 0.057 7 0.075 1 0.841 2 XGBoost 有机相 0.036 9 0.051 4 0.879 0 水相 0.048 4 0.069 4 0.858 9 LSTM 有机相 0.035 9 0.049 8 0.902 9 水相 0.043 1 0.062 7 0.886 5 GRU 有机相 0.030 0 0.042 3 0.921 1 水相 0.036 3 0.053 7 0.916 0 BPNN 有机相 0.033 1 0.045 4 0.907 9 水相 0.041 5 0.058 1 0.902 0 CGAN 有机相 0.028 8 0.042 0 0.926 4 水相 0.033 9 0.052 6 0.918 0 MB-DNN 有机相 0.032 8 0.045 3 0.915 6 水相 0.039 3 0.057 5 0.904 8 MB-RDN 有机相 0.030 3 0.042 3 0.921 1 水相 0.038 3 0.055 3 0.909 7 MB-RGAN 有机相 0.017 6 0.027 7 0.968 5 水相 0.021 5 0.036 2 0.961 9
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表 4 模型计算复杂度与推理效率对比
Table 4 Comparison of model computational complexity and inference efficiency
模型 参数量 单样本推理耗时(ms) SVR N/A 1.01 XGBoost N/A 15.08 LSTM 148 682 18.99 GRU 114 634 19.64 BPNN 18 762 5.37 CGAN 57 354 4.99 MB-DNN 104 426 5.80 MB-RDN 172 682 7.79 MB-RGAN(Generator) 18 890 N/A MB-RGAN(Total) 461 233 26.10
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表 5 消融实验变体模型设置
Table 5 Setting of the ablation experiment variant models
模型编号 变体名称 核心变动描述 损失函数/训练策略 Model A w/o Branch 移除多分支结构, 仅在网络末端输出预测值 WGAN-GP + 回归一致性/递归训练 Model B w/o Regressor 移除回归器R, 移除回归一致性约束 仅使用WGAN-GP对抗损失 Model C w/o Sharing 移除首层特征共享, D与R独立提取特征 WGAN-GP + 回归一致性/递归训练 Model D w/o Recursive 移除递归训练, 所有层同时更新 全局端到端(End-to-End)训练 Model E w/o WGAN-GP 移除梯度惩罚项, 设定$\lambda_{GP}=0$ 无约束Wasserstein损失/递归训练 本文模型 MB-RGAN 完整模型, 保留所有改进模块 WGAN-GP + 回归一致性/递归训练
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表 6 不同变体模型的消融实验结果对比
Table 6 Comparison of ablation experiment results for different variant models
模型变体 组分 平均MAE 平均RMSE 平均$R^2$ Model A 有机相 0.025 9 0.039 6 0.938 0 水相 0.032 2 0.050 5 0.928 4 Model B 有机相 0.036 6 0.059 2 0.688 9 水相 0.039 7 0.059 5 0.902 1 Model C 有机相 0.024 6 0.038 1 0.934 0 水相 0.031 8 0.049 3 0.929 1 Model D 有机相 0.021 3 0.032 6 0.957 5 水相 0.028 8 0.045 2 0.943 9 Model E 有机相 0.032 5 0.046 8 0.895 0 水相 0.039 2 0.059 4 0.882 0 MB-RGAN 有机相 0.017 6 0.027 7 0.968 5 水相 0.021 5 0.036 2 0.961 9
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