Pengpeng LIU(
), Zhiguo WANG(
), Xiaoli LUAN, Fei LIU
Received:2025-09-28
Revised:2025-11-19
Published:2025-12-12
Contact:
Zhiguo WANG
通讯作者:
王志国
作者简介:刘鹏鹏(2001—),男,硕士研究生,liu_pengp@163.com
基金资助:CLC Number:
Pengpeng LIU, Zhiguo WANG, Xiaoli LUAN, Fei LIU. A hybrid modeling and optimization strategy for sequential simulated moving bed[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251079.
刘鹏鹏, 王志国, 栾小丽, 刘飞. 一种顺序式模拟移动床混合建模与优化策略[J]. 化工学报, DOI: 10.11949/0438-1157.20251079.
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| 设备与进料参数 | 吸附特性参数 | ||
|---|---|---|---|
| 柱分布结构 | 1-1-1-1 | 理论塔板数 | 2000 |
| 柱直径 | 2.5 cm | A的传质系数 | 4.54 min-1 |
| 柱长 | 100 cm | B的传质系数 | 0.36 min-1 |
| 空隙率 | 0.416 | A的亨利常数 | 0.450 |
| 最大允许流量 | 20 ml/min | B的亨利常数 | 0.167 |
| A的进料浓度 | 0.09 g/ml | A的吸附常数 | 1.11 |
| B的进料浓度 | 0.21 g/ml | B的吸附常数 | 0.467 |
Table 1 System parameters for SSMB
| 设备与进料参数 | 吸附特性参数 | ||
|---|---|---|---|
| 柱分布结构 | 1-1-1-1 | 理论塔板数 | 2000 |
| 柱直径 | 2.5 cm | A的传质系数 | 4.54 min-1 |
| 柱长 | 100 cm | B的传质系数 | 0.36 min-1 |
| 空隙率 | 0.416 | A的亨利常数 | 0.450 |
| 最大允许流量 | 20 ml/min | B的亨利常数 | 0.167 |
| A的进料浓度 | 0.09 g/ml | A的吸附常数 | 1.11 |
| B的进料浓度 | 0.21 g/ml | B的吸附常数 | 0.467 |
| 分类 | 序号 | tf/ min | Qf/ (ml/min) | te/ min | Qe/ (ml/min) |
|---|---|---|---|---|---|
| 训练集 | 1 | 80 | 6 | 60 | 20 |
| 2 | 60 | 8 | 60 | 20 | |
| 3 | 40 | 10 | 60 | 20 | |
| 4 | 40 | 12 | 60 | 20 | |
| 5 | 30 | 14 | 60 | 20 | |
| 6 | 30 | 16 | 60 | 20 | |
| 内插测试 | 7 | 60 | 7 | 60 | 20 |
| 8 | 50 | 9 | 60 | 20 | |
| 9 | 40 | 11 | 60 | 20 | |
| 10 | 40 | 13 | 60 | 20 | |
| 11 | 30 | 15 | 60 | 20 | |
| 外推测试 | 12 | 120 | 2 | 60 | 20 |
| 13 | 100 | 4 | 60 | 20 | |
| 14 | 30 | 18 | 60 | 20 | |
| 15 | 20 | 20 | 60 | 20 |
Table 2 Process conditions for the twin-column experiment
| 分类 | 序号 | tf/ min | Qf/ (ml/min) | te/ min | Qe/ (ml/min) |
|---|---|---|---|---|---|
| 训练集 | 1 | 80 | 6 | 60 | 20 |
| 2 | 60 | 8 | 60 | 20 | |
| 3 | 40 | 10 | 60 | 20 | |
| 4 | 40 | 12 | 60 | 20 | |
| 5 | 30 | 14 | 60 | 20 | |
| 6 | 30 | 16 | 60 | 20 | |
| 内插测试 | 7 | 60 | 7 | 60 | 20 |
| 8 | 50 | 9 | 60 | 20 | |
| 9 | 40 | 11 | 60 | 20 | |
| 10 | 40 | 13 | 60 | 20 | |
| 11 | 30 | 15 | 60 | 20 | |
| 外推测试 | 12 | 120 | 2 | 60 | 20 |
| 13 | 100 | 4 | 60 | 20 | |
| 14 | 30 | 18 | 60 | 20 | |
| 15 | 20 | 20 | 60 | 20 |
| 参数 | 数值 |
|---|---|
| 初始种群规模 | 60 |
| 最小种群规模 | 2 |
| 最大迭代次数(Gmax) | 300 |
| 记忆长度 | 10 |
| p-best比例 | 0.11 |
| 迭代间隔(Δg) | 10 |
| 相对改善阈值(εrel) | 2% |
| 重复运行次数 | 5 |
Table 3 L-SHADE algorithm parameters
| 参数 | 数值 |
|---|---|
| 初始种群规模 | 60 |
| 最小种群规模 | 2 |
| 最大迭代次数(Gmax) | 300 |
| 记忆长度 | 10 |
| p-best比例 | 0.11 |
| 迭代间隔(Δg) | 10 |
| 相对改善阈值(εrel) | 2% |
| 重复运行次数 | 5 |
网络 结构 | WSSEtotal | 网络 结构 | WSSEtotal | ||||||
|---|---|---|---|---|---|---|---|---|---|
| sigmoid | tanh | sigmoid | tanh | ||||||
| [ | 0.0452 | 0.0335 | [2,2] | 0.0417 | 0.0402 | ||||
| [ | 0.0322 | 0.0286 | [ | 0.0368 | 0.0402 | ||||
| [ | 0.0414 | 0.0376 | [ | 0.0355 | 0.0342 | ||||
| [ | 0.0363 | 0.0332 | [ | 0.0364 | 0.0358 | ||||
Table 4 Screening results for neural network architectures
网络 结构 | WSSEtotal | 网络 结构 | WSSEtotal | ||||||
|---|---|---|---|---|---|---|---|---|---|
| sigmoid | tanh | sigmoid | tanh | ||||||
| [ | 0.0452 | 0.0335 | [2,2] | 0.0417 | 0.0402 | ||||
| [ | 0.0322 | 0.0286 | [ | 0.0368 | 0.0402 | ||||
| [ | 0.0414 | 0.0376 | [ | 0.0355 | 0.0342 | ||||
| [ | 0.0363 | 0.0332 | [ | 0.0364 | 0.0358 | ||||
| 分类 | 序号 | R2 | NRMSE/% | ||||||
|---|---|---|---|---|---|---|---|---|---|
| A | B | A | B | ||||||
| 训练集 | 1 | 0.9970 | 0.9996 | 2.12 | 0.81 | ||||
| 2 | 0.9965 | 09995 | 2.32 | 0.88 | |||||
| 3 | 0.9949 | 0.9993 | 2.64 | 0.98 | |||||
| 4 | 0.9955 | 0.9994 | 2.70 | 0.98 | |||||
| 5 | 0.9941 | 0.9992 | 2.97 | 1.05 | |||||
| 6 | 0.9944 | 0.9993 | 3.05 | 1.05 | |||||
| 内插测试 | 7 | 0.9955 | 0.9992 | 2.43 | 0.97 | ||||
| 8 | 0.9946 | 0.9991 | 2.50 | 1.07 | |||||
| 9 | 0.9942 | 0.9989 | 2.88 | 1.13 | |||||
| 10 | 0.9938 | 0.9987 | 3.05 | 1.22 | |||||
| 11 | 0.9933 | 0.9983 | 3.11 | 1.24 | |||||
| 外推测试 | 12 | 0.9923 | 0.9958 | 3.70 | 1.82 | ||||
| 13 | 0.9936 | 0.9979 | 2.51 | 1.37 | |||||
| 14 | 0.9924 | 0.9966 | 3.69 | 1.79 | |||||
| 15 | 0.9922 | 0.9954 | 3.72 | 1.83 | |||||
Table 5 Fitting and prediction accuracy of the model in the twin-column experiment
| 分类 | 序号 | R2 | NRMSE/% | ||||||
|---|---|---|---|---|---|---|---|---|---|
| A | B | A | B | ||||||
| 训练集 | 1 | 0.9970 | 0.9996 | 2.12 | 0.81 | ||||
| 2 | 0.9965 | 09995 | 2.32 | 0.88 | |||||
| 3 | 0.9949 | 0.9993 | 2.64 | 0.98 | |||||
| 4 | 0.9955 | 0.9994 | 2.70 | 0.98 | |||||
| 5 | 0.9941 | 0.9992 | 2.97 | 1.05 | |||||
| 6 | 0.9944 | 0.9993 | 3.05 | 1.05 | |||||
| 内插测试 | 7 | 0.9955 | 0.9992 | 2.43 | 0.97 | ||||
| 8 | 0.9946 | 0.9991 | 2.50 | 1.07 | |||||
| 9 | 0.9942 | 0.9989 | 2.88 | 1.13 | |||||
| 10 | 0.9938 | 0.9987 | 3.05 | 1.22 | |||||
| 11 | 0.9933 | 0.9983 | 3.11 | 1.24 | |||||
| 外推测试 | 12 | 0.9923 | 0.9958 | 3.70 | 1.82 | ||||
| 13 | 0.9936 | 0.9979 | 2.51 | 1.37 | |||||
| 14 | 0.9924 | 0.9966 | 3.69 | 1.79 | |||||
| 15 | 0.9922 | 0.9954 | 3.72 | 1.83 | |||||
| 案例 | t1/ | t2/ | t3/ | QF/ | R2 | NRMSE/% | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| min | min | min | (ml/min) | A | B | A | B | ||||
| a | 8.00 | 11.45 | 1.71 | 11.65 | 0.9385 | 0.9953 | 9.27 | 1.96 | |||
| b | 5.51 | 11.76 | 0.78 | 16.52 | 0.9581 | 0.9957 | 7.88 | 1.74 | |||
| c | 11.47 | 12.11 | 0.34 | 6.91 | 0.9230 | 0.9940 | 9.33 | 2.31 | |||
| d | 12.15 | 12.03 | 0.12 | 5.77 | 0.8882 | 0.9948 | 8.33 | 2.32 | |||
Table 6 Prediction accuracy of the model at the SSMB product collection position
| 案例 | t1/ | t2/ | t3/ | QF/ | R2 | NRMSE/% | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| min | min | min | (ml/min) | A | B | A | B | ||||
| a | 8.00 | 11.45 | 1.71 | 11.65 | 0.9385 | 0.9953 | 9.27 | 1.96 | |||
| b | 5.51 | 11.76 | 0.78 | 16.52 | 0.9581 | 0.9957 | 7.88 | 1.74 | |||
| c | 11.47 | 12.11 | 0.34 | 6.91 | 0.9230 | 0.9940 | 9.33 | 2.31 | |||
| d | 12.15 | 12.03 | 0.12 | 5.77 | 0.8882 | 0.9948 | 8.33 | 2.32 | |||
| 案例 | 机理模型 | 混合模型 | 相对误差 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Pur(B)/% | Rec(B)/% | Pur(B)/% | Rec(B)/% | Pur(B)/% | Rec(B)/% | |||||
| a | 86.32 | 95.35 | 85.41 | 96.18 | 1.05 | 0.87 | ||||
| b | 90.98 | 91.39 | 90.83 | 91.94 | 0.16 | 0.60 | ||||
| c | 95.66 | 87.29 | 94.32 | 87.71 | 1.40 | 0.48 | ||||
| d | 98.69 | 81.15 | 96.84 | 81.77 | 1.87 | 0.76 | ||||
Table 7 Prediction of performance indicators by hybrid models
| 案例 | 机理模型 | 混合模型 | 相对误差 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Pur(B)/% | Rec(B)/% | Pur(B)/% | Rec(B)/% | Pur(B)/% | Rec(B)/% | |||||
| a | 86.32 | 95.35 | 85.41 | 96.18 | 1.05 | 0.87 | ||||
| b | 90.98 | 91.39 | 90.83 | 91.94 | 0.16 | 0.60 | ||||
| c | 95.66 | 87.29 | 94.32 | 87.71 | 1.40 | 0.48 | ||||
| d | 98.69 | 81.15 | 96.84 | 81.77 | 1.87 | 0.76 | ||||
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