CIESC Journal ›› 2025, Vol. 76 ›› Issue (9): 4613-4629.DOI: 10.11949/0438-1157.20250145
• Special Column: Modeling and Simulation in Process Engineering • Previous Articles Next Articles
Xu GUO(
), Jining JIA, Kejian YAO(
)
Received:2025-02-17
Revised:2025-04-14
Online:2025-10-23
Published:2025-09-25
Contact:
Kejian YAO
通讯作者:
姚克俭
作者简介:郭旭(1999—),男,硕士研究生,zjutGuox@outlook.com
CLC Number:
Xu GUO, Jining JIA, Kejian YAO. Modeling of batch distillation process based on optimized CNN-BiLSTM neural network[J]. CIESC Journal, 2025, 76(9): 4613-4629.
郭旭, 贾继宁, 姚克俭. 基于优化CNN-BiLSTM神经网络的间歇精馏过程建模[J]. 化工学报, 2025, 76(9): 4613-4629.
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| 参数 | 数值 |
|---|---|
| 色谱柱温度/℃ | 180 |
| 进样口温度/℃ | 180 |
| 热导池温度/℃ | 200 |
| 桥电流/mA | 110 |
| 氢气压力/MPa | 0.01 |
| 进样体积/μl | 1 |
| 色谱柱类型 | Porapak-Q |
Table 1 Operating parameters for FULI GC9790Ⅱ gas chromatograph
| 参数 | 数值 |
|---|---|
| 色谱柱温度/℃ | 180 |
| 进样口温度/℃ | 180 |
| 热导池温度/℃ | 200 |
| 桥电流/mA | 110 |
| 氢气压力/MPa | 0.01 |
| 进样体积/μl | 1 |
| 色谱柱类型 | Porapak-Q |
Fig.1 Process flow diagram for batch distillation1—reboiler; 2—reflux drum; 3—reflux pump; 4—distillate pump; 5—distillate storage tank; 6—feed storage tank; 7—feeding pump; V—electric heating switch; PI—pressure indicator; TI—temperature indicator; M—metering pump motor; V1—V17—control valves; LI—level indicator; R—reflux ratio controller; FIC—flow controller; TIC—temperature controller
| 批次 | 加热功率/kW | 原料乙醇质量分数 | 回流比 | 备注 |
|---|---|---|---|---|
| 1 | 1.75~2.50 | 0.429 | 1.0 | 调节加热功率使蒸汽率为5.6 L/h |
| 2 | 1.70~2.50 | 0.492 | 1.0 | |
| 3 | 1.65~2.50 | 0.589 | 1.0 | |
| 4 | 1.70~2.50 | 0.652 | 1.0 | 调节加热功率使蒸汽率为6.5 L/h |
| 5 | 1.73~2.50 | 0.490 | 1.5 | 调节加热功率使蒸汽率为5.6 L/h |
| 6 | 1.70~2.50 | 0.590 | 1.5 | |
| 7 | 1.75~2.25 | 0.650 | 1.5 | 调节加热功率使蒸汽率为6.5 L/h |
| 8 | 1.75~2.50 | 0.493 | 2.0 | 调节加热功率使蒸汽率为5.6 L/h |
| 9 | 1.70~2.50 | 0.592 | 2.0 | |
| 10 | 1.78~2.25 | 0.654 | 2.0 | 调节加热功率使蒸汽率为6.5 L/h |
| 11 | 1.77~2.50 | 0.486 | 2.5 | 调节加热功率使蒸汽率为5.6 L/h |
| 12 | 1.72~2.50 | 0.614 | 2.5 | |
| 13 | 1.75~2.25 | 0.685 | 2.5 | 调节加热功率使蒸汽率为6.5 L/h |
| 14 | 2.0~2.25 | 0.674 | 2.5 | 调节加热功率使蒸汽率为8.5 L/h |
| 15 | 1.65~2.50 | 0.683 | 2.5 | 调节加热功率使蒸汽率为5.6 L/h |
| 16 | 1.80~2.25 | 0.677 | 3.0 | 调节加热功率使蒸汽率为6.5 L/h |
| 17 | 1.75~2.50 | 0.726 | 3.5 | 调节加热功率使蒸汽率为6.5 L/h |
| 18 | 1.60~2.50 | 0.483 | 3.3 | 恒定回流比生产操作,调节加热功率使蒸汽率为5.0 L/h |
| 19 | 1.60~2.50 | 0.463 | 1.0 ~ 3.0 | 阶跃回流比生产操作,调节加热功率使蒸汽率为5.0 L/h |
Table 2 Explanation of operating conditions for each batch of data
| 批次 | 加热功率/kW | 原料乙醇质量分数 | 回流比 | 备注 |
|---|---|---|---|---|
| 1 | 1.75~2.50 | 0.429 | 1.0 | 调节加热功率使蒸汽率为5.6 L/h |
| 2 | 1.70~2.50 | 0.492 | 1.0 | |
| 3 | 1.65~2.50 | 0.589 | 1.0 | |
| 4 | 1.70~2.50 | 0.652 | 1.0 | 调节加热功率使蒸汽率为6.5 L/h |
| 5 | 1.73~2.50 | 0.490 | 1.5 | 调节加热功率使蒸汽率为5.6 L/h |
| 6 | 1.70~2.50 | 0.590 | 1.5 | |
| 7 | 1.75~2.25 | 0.650 | 1.5 | 调节加热功率使蒸汽率为6.5 L/h |
| 8 | 1.75~2.50 | 0.493 | 2.0 | 调节加热功率使蒸汽率为5.6 L/h |
| 9 | 1.70~2.50 | 0.592 | 2.0 | |
| 10 | 1.78~2.25 | 0.654 | 2.0 | 调节加热功率使蒸汽率为6.5 L/h |
| 11 | 1.77~2.50 | 0.486 | 2.5 | 调节加热功率使蒸汽率为5.6 L/h |
| 12 | 1.72~2.50 | 0.614 | 2.5 | |
| 13 | 1.75~2.25 | 0.685 | 2.5 | 调节加热功率使蒸汽率为6.5 L/h |
| 14 | 2.0~2.25 | 0.674 | 2.5 | 调节加热功率使蒸汽率为8.5 L/h |
| 15 | 1.65~2.50 | 0.683 | 2.5 | 调节加热功率使蒸汽率为5.6 L/h |
| 16 | 1.80~2.25 | 0.677 | 3.0 | 调节加热功率使蒸汽率为6.5 L/h |
| 17 | 1.75~2.50 | 0.726 | 3.5 | 调节加热功率使蒸汽率为6.5 L/h |
| 18 | 1.60~2.50 | 0.483 | 3.3 | 恒定回流比生产操作,调节加热功率使蒸汽率为5.0 L/h |
| 19 | 1.60~2.50 | 0.463 | 1.0 ~ 3.0 | 阶跃回流比生产操作,调节加热功率使蒸汽率为5.0 L/h |
| 序号 | 特征 | MIC | 特征 | MIC | ||
|---|---|---|---|---|---|---|
| X | Y1 | X | Y2 | |||
| 1 | 塔釜温度 | 馏出液乙醇浓度 | 0.3 | 塔釜温度 | 塔釜乙醇浓度 | 0.7 |
| 2 | 塔节一温度 | 馏出液乙醇浓度 | 0.3 | 塔节一温度 | 塔釜乙醇浓度 | 0.7 |
| 3 | 塔节三温度 | 馏出液乙醇浓度 | 0.5 | 塔节三温度 | 塔釜乙醇浓度 | 0.4 |
| 4 | 塔节五温度 | 馏出液乙醇浓度 | 0.7 | 塔节五温度 | 塔釜乙醇浓度 | 0.2 |
| 5 | 塔节六温度 | 馏出液乙醇浓度 | 0.5 | 塔节六温度 | 塔釜乙醇浓度 | 0.2 |
| 6 | 塔顶温度 | 馏出液乙醇浓度 | 0.4 | 塔顶温度 | 塔釜乙醇浓度 | 0.2 |
| 7 | 产品温度 | 馏出液乙醇浓度 | 0.4 | 产品温度 | 塔釜乙醇浓度 | 0.1 |
| 8 | 冷凝水流量 | 馏出液乙醇浓度 | 0.08 | 冷凝水流量 | 塔釜乙醇浓度 | 0.1 |
| 9 | 馏出液体积 | 馏出液乙醇浓度 | 0.2 | 馏出液体积 | 塔釜乙醇浓度 | 0.2 |
| 10 | 原料浓度 | 馏出液乙醇浓度 | 0.4 | 原料浓度 | 塔釜乙醇浓度 | 0.2 |
| 11 | 回流比 | 馏出液乙醇浓度 | 0.4 | 回流比 | 塔釜乙醇浓度 | 0.1 |
| 12 | 塔釜液位 | 馏出液乙醇浓度 | 0.2 | 塔釜液位 | 塔釜乙醇浓度 | 0.4 |
| 13 | 塔釜压力 | 馏出液乙醇浓度 | 0.4 | 塔釜压力 | 塔釜乙醇浓度 | 0.1 |
| 14 | 塔节二压力 | 馏出液乙醇浓度 | 0.4 | 塔节二压力 | 塔釜乙醇浓度 | 0.1 |
| 15 | 塔节四压力 | 馏出液乙醇浓度 | 0.5 | 塔节四压力 | 塔釜乙醇浓度 | 0.1 |
| 16 | 塔节七压力 | 馏出液乙醇浓度 | 0.4 | 塔节七压力 | 塔釜乙醇浓度 | 0.1 |
Table 3 MIC values of input variables for ethanol prediction in the distillate and tower bottom
| 序号 | 特征 | MIC | 特征 | MIC | ||
|---|---|---|---|---|---|---|
| X | Y1 | X | Y2 | |||
| 1 | 塔釜温度 | 馏出液乙醇浓度 | 0.3 | 塔釜温度 | 塔釜乙醇浓度 | 0.7 |
| 2 | 塔节一温度 | 馏出液乙醇浓度 | 0.3 | 塔节一温度 | 塔釜乙醇浓度 | 0.7 |
| 3 | 塔节三温度 | 馏出液乙醇浓度 | 0.5 | 塔节三温度 | 塔釜乙醇浓度 | 0.4 |
| 4 | 塔节五温度 | 馏出液乙醇浓度 | 0.7 | 塔节五温度 | 塔釜乙醇浓度 | 0.2 |
| 5 | 塔节六温度 | 馏出液乙醇浓度 | 0.5 | 塔节六温度 | 塔釜乙醇浓度 | 0.2 |
| 6 | 塔顶温度 | 馏出液乙醇浓度 | 0.4 | 塔顶温度 | 塔釜乙醇浓度 | 0.2 |
| 7 | 产品温度 | 馏出液乙醇浓度 | 0.4 | 产品温度 | 塔釜乙醇浓度 | 0.1 |
| 8 | 冷凝水流量 | 馏出液乙醇浓度 | 0.08 | 冷凝水流量 | 塔釜乙醇浓度 | 0.1 |
| 9 | 馏出液体积 | 馏出液乙醇浓度 | 0.2 | 馏出液体积 | 塔釜乙醇浓度 | 0.2 |
| 10 | 原料浓度 | 馏出液乙醇浓度 | 0.4 | 原料浓度 | 塔釜乙醇浓度 | 0.2 |
| 11 | 回流比 | 馏出液乙醇浓度 | 0.4 | 回流比 | 塔釜乙醇浓度 | 0.1 |
| 12 | 塔釜液位 | 馏出液乙醇浓度 | 0.2 | 塔釜液位 | 塔釜乙醇浓度 | 0.4 |
| 13 | 塔釜压力 | 馏出液乙醇浓度 | 0.4 | 塔釜压力 | 塔釜乙醇浓度 | 0.1 |
| 14 | 塔节二压力 | 馏出液乙醇浓度 | 0.4 | 塔节二压力 | 塔釜乙醇浓度 | 0.1 |
| 15 | 塔节四压力 | 馏出液乙醇浓度 | 0.5 | 塔节四压力 | 塔釜乙醇浓度 | 0.1 |
| 16 | 塔节七压力 | 馏出液乙醇浓度 | 0.4 | 塔节七压力 | 塔釜乙醇浓度 | 0.1 |
| 模型 | 训练次数 | 学习速率 | 阈值 | 正则化参数 | 学习率下降因子 | 学习率下降开始迭代次数 | 最小输入批次 | 时间步长 |
|---|---|---|---|---|---|---|---|---|
| BP | 1000 | 0.001 | — | — | — | — | — | — |
| SVR | — | — | 0.0001 | 10 | — | — | — | — |
| LSTM | 1000 | 0.001 | — | — | 0.01 | 400 | 100 | 4 |
| BiLSTM | 1000 | 0.001 | — | — | 0.01 | 400 | 100 | 4 |
| CNN-BiLSTM | 1000 | 0.001 | — | — | 0.01 | 400 | 100 | 4 |
Table 4 Training parameters of different models
| 模型 | 训练次数 | 学习速率 | 阈值 | 正则化参数 | 学习率下降因子 | 学习率下降开始迭代次数 | 最小输入批次 | 时间步长 |
|---|---|---|---|---|---|---|---|---|
| BP | 1000 | 0.001 | — | — | — | — | — | — |
| SVR | — | — | 0.0001 | 10 | — | — | — | — |
| LSTM | 1000 | 0.001 | — | — | 0.01 | 400 | 100 | 4 |
| BiLSTM | 1000 | 0.001 | — | — | 0.01 | 400 | 100 | 4 |
| CNN-BiLSTM | 1000 | 0.001 | — | — | 0.01 | 400 | 100 | 4 |
| 折编号 | 训练集批次 | 验证集批次 | 验证集样本数 | 训练集总样本数 |
|---|---|---|---|---|
| 第1折 | 4~17 | 1~3 | 71 | 530 |
| 第2折 | 1~3 & 7~17 | 4~6 | 79 | 530 |
| 第3折 | 1~6 & 10~17 | 7~9 | 108 | 530 |
| 第4折 | 1~9 & 13~17 | 10~12 | 99 | 530 |
| 第5折 | 1~12 & 16~17 | 13~15 | 90 | 530 |
| 第6折 | 1~15 | 16~17 | 68 | 530 |
Table 5 Explanation of six-fold cross-validation on the training set
| 折编号 | 训练集批次 | 验证集批次 | 验证集样本数 | 训练集总样本数 |
|---|---|---|---|---|
| 第1折 | 4~17 | 1~3 | 71 | 530 |
| 第2折 | 1~3 & 7~17 | 4~6 | 79 | 530 |
| 第3折 | 1~6 & 10~17 | 7~9 | 108 | 530 |
| 第4折 | 1~9 & 13~17 | 10~12 | 99 | 530 |
| 第5折 | 1~12 & 16~17 | 13~15 | 90 | 530 |
| 第6折 | 1~15 | 16~17 | 68 | 530 |
| 算法 | ISAO算法 |
|---|---|
| 输入 | 种群个数N,维度dim,测试函数fobj,迭代总次数tmax,迭代次数t |
| 输出 | 适应度值 |
| Begin | 初始化:生成种群X |
| 1. | while (t<tmax)do |
| 2. | For N do |
| 3. | 通过SAO算法计算种群个体的位置并计算适应度值 |
| 4. | 规范种群个体的边界 |
| 5. | 通过本文提出的位置更新策略更新个体位置并评估其适应度值 |
| 6. | if 新适应度值小于旧适应度值 |
| 7. | 新适应度所对应的种群个体将替代旧种群个体 |
| 8. | End if |
| 9. | End for |
| 10. | 更新精英池 |
| 11. | t=t+1 |
| 12. | End while |
| End |
Table 6 Pseudocode of the ISAO algorithm[24]
| 算法 | ISAO算法 |
|---|---|
| 输入 | 种群个数N,维度dim,测试函数fobj,迭代总次数tmax,迭代次数t |
| 输出 | 适应度值 |
| Begin | 初始化:生成种群X |
| 1. | while (t<tmax)do |
| 2. | For N do |
| 3. | 通过SAO算法计算种群个体的位置并计算适应度值 |
| 4. | 规范种群个体的边界 |
| 5. | 通过本文提出的位置更新策略更新个体位置并评估其适应度值 |
| 6. | if 新适应度值小于旧适应度值 |
| 7. | 新适应度所对应的种群个体将替代旧种群个体 |
| 8. | End if |
| 9. | End for |
| 10. | 更新精英池 |
| 11. | t=t+1 |
| 12. | End while |
| End |
| 项目 | 评价指标 | BP | SVR | LSTM | BiLSTM | CNN-BiLSTM |
|---|---|---|---|---|---|---|
| 馏出液乙醇质量分数 | RMSE | 0.125 | 0.127 | 0.108 | 0.106 | 0.0677 |
| MAE | 0.0535 | 0.0529 | 0.0454 | 0.0425 | 0.0321 | |
| R2 | 0.751 | 0.746 | 0.822 | 0.863 | 0.956 | |
| 塔釜乙醇质量分数 | RMSE | 0.0649 | 0.0954 | 0.0539 | 0.0472 | 0.0250 |
| MAE | 0.0326 | 0.0477 | 0.0221 | 0.0196 | 0.0163 | |
| R2 | 0.917 | 0.899 | 0.949 | 0.969 | 0.983 |
Table 7 The average value of evaluation metrics of the training set on six-fold cross-validation for different models
| 项目 | 评价指标 | BP | SVR | LSTM | BiLSTM | CNN-BiLSTM |
|---|---|---|---|---|---|---|
| 馏出液乙醇质量分数 | RMSE | 0.125 | 0.127 | 0.108 | 0.106 | 0.0677 |
| MAE | 0.0535 | 0.0529 | 0.0454 | 0.0425 | 0.0321 | |
| R2 | 0.751 | 0.746 | 0.822 | 0.863 | 0.956 | |
| 塔釜乙醇质量分数 | RMSE | 0.0649 | 0.0954 | 0.0539 | 0.0472 | 0.0250 |
| MAE | 0.0326 | 0.0477 | 0.0221 | 0.0196 | 0.0163 | |
| R2 | 0.917 | 0.899 | 0.949 | 0.969 | 0.983 |
| 项目 | 批次 | 指标 | BP | SVR | LSTM | BiLSTM | CNN-BiLSTM |
|---|---|---|---|---|---|---|---|
| 馏出液乙醇质量分数 | 18 | RMSE | 0.00850 | 0.00850 | 0.00470 | 0.00470 | 0.00610 |
| 18 | MAE | 0.00670 | 0.00670 | 0.00380 | 0.00420 | 0.00530 | |
| 18 | R2 | 0.159 | 0.149 | 0.745 | 0.741 | 0.566 | |
| 19 | RMSE | 0.0207 | 0.0214 | 0.0139 | 0.0131 | 0.00540 | |
| 19 | MAE | 0.0198 | 0.0206 | 0.0130 | 0.0122 | 0.00460 | |
| 19 | R2 | -16.772 | -17.983 | -6.986 | -6.098 | 0.208 | |
| 塔釜乙醇质量分数 | 18 | RMSE | 0.0415 | 0.0486 | 0.0333 | 0.0173 | 0.0165 |
| 18 | MAE | 0.0385 | 0.0472 | 0.0315 | 0.0145 | 0.0141 | |
| 18 | R2 | 0.852 | 0.798 | 0.905 | 0.971 | 0.974 | |
| 19 | RMSE | 0.0338 | 0.0420 | 0.0307 | 0.0278 | 0.0258 | |
| 19 | MAE | 0.0251 | 0.0347 | 0.0283 | 0.0236 | 0.0216 | |
| 19 | R2 | 0.874 | 0.805 | 0.896 | 0.915 | 0.927 |
Table 8 Test results of two batches of test set data on different neural network models
| 项目 | 批次 | 指标 | BP | SVR | LSTM | BiLSTM | CNN-BiLSTM |
|---|---|---|---|---|---|---|---|
| 馏出液乙醇质量分数 | 18 | RMSE | 0.00850 | 0.00850 | 0.00470 | 0.00470 | 0.00610 |
| 18 | MAE | 0.00670 | 0.00670 | 0.00380 | 0.00420 | 0.00530 | |
| 18 | R2 | 0.159 | 0.149 | 0.745 | 0.741 | 0.566 | |
| 19 | RMSE | 0.0207 | 0.0214 | 0.0139 | 0.0131 | 0.00540 | |
| 19 | MAE | 0.0198 | 0.0206 | 0.0130 | 0.0122 | 0.00460 | |
| 19 | R2 | -16.772 | -17.983 | -6.986 | -6.098 | 0.208 | |
| 塔釜乙醇质量分数 | 18 | RMSE | 0.0415 | 0.0486 | 0.0333 | 0.0173 | 0.0165 |
| 18 | MAE | 0.0385 | 0.0472 | 0.0315 | 0.0145 | 0.0141 | |
| 18 | R2 | 0.852 | 0.798 | 0.905 | 0.971 | 0.974 | |
| 19 | RMSE | 0.0338 | 0.0420 | 0.0307 | 0.0278 | 0.0258 | |
| 19 | MAE | 0.0251 | 0.0347 | 0.0283 | 0.0236 | 0.0216 | |
| 19 | R2 | 0.874 | 0.805 | 0.896 | 0.915 | 0.927 |
| 项目 | 批次 | 指标 | CNN-BiLSTM | SAO-CNN-BiLSTM | ISAO-CNN-BiLSTM |
|---|---|---|---|---|---|
| 馏出液乙醇质量分数 | 18 | RMSE | 0.00610 | 0.00540 | 0.000900 |
| 18 | MAE | 0.00530 | 0.00440 | 0.000700 | |
| 18 | R2 | 0.255 | 0.566 | 0.981 | |
| 19 | RMSE | 0.0129 | 0.00170 | 0.00110 | |
| 19 | MAE | 0.0100 | 0.00120 | 0.00100 | |
| 19 | R2 | 0.193 | 0.811 | 0.998 | |
| 塔釜乙醇质量分数 | 18 | RMSE | 0.0165 | 0.0125 | 0.00290 |
| 18 | MAE | 0.0141 | 0.0118 | 0.00250 | |
| 18 | R2 | 0.974 | 0.986 | 0.999 | |
| 19 | RMSE | 0.0258 | 0.00940 | 0.00350 | |
| 19 | MAE | 0.0216 | 0.00710 | 0.00240 | |
| 19 | R2 | 0.927 | 0.985 | 0.998 |
Table 9 Comparison of model evaluation metrics
| 项目 | 批次 | 指标 | CNN-BiLSTM | SAO-CNN-BiLSTM | ISAO-CNN-BiLSTM |
|---|---|---|---|---|---|
| 馏出液乙醇质量分数 | 18 | RMSE | 0.00610 | 0.00540 | 0.000900 |
| 18 | MAE | 0.00530 | 0.00440 | 0.000700 | |
| 18 | R2 | 0.255 | 0.566 | 0.981 | |
| 19 | RMSE | 0.0129 | 0.00170 | 0.00110 | |
| 19 | MAE | 0.0100 | 0.00120 | 0.00100 | |
| 19 | R2 | 0.193 | 0.811 | 0.998 | |
| 塔釜乙醇质量分数 | 18 | RMSE | 0.0165 | 0.0125 | 0.00290 |
| 18 | MAE | 0.0141 | 0.0118 | 0.00250 | |
| 18 | R2 | 0.974 | 0.986 | 0.999 | |
| 19 | RMSE | 0.0258 | 0.00940 | 0.00350 | |
| 19 | MAE | 0.0216 | 0.00710 | 0.00240 | |
| 19 | R2 | 0.927 | 0.985 | 0.998 |
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