CIESC Journal ›› 2025, Vol. 76 ›› Issue (1): 283-295.DOI: 10.11949/0438-1157.20240689
• Process system engineering • Previous Articles Next Articles
Shaoji WANG1,2(), Kuangrong HAO1,2(
), Lei CHEN1,2
Received:
2024-06-20
Revised:
2024-07-27
Online:
2025-02-08
Published:
2025-01-25
Contact:
Kuangrong HAO
通讯作者:
郝矿荣
作者简介:
王绍吉(2000—),男,硕士研究生,2221995@mail.dhu.edu.cn
基金资助:
CLC Number:
Shaoji WANG, Kuangrong HAO, Lei CHEN. Research on temperature forecasting of polyester fiber esterification process based on federated learning[J]. CIESC Journal, 2025, 76(1): 283-295.
王绍吉, 郝矿荣, 陈磊. 基于联邦学习的聚酯纤维酯化过程温度预测研究[J]. 化工学报, 2025, 76(1): 283-295.
工厂 | 起始时间 | 终止时间 | 总样本量 | 训练集样本量 | 验证集样本量 | 测试集样本量 | 变量维度 |
---|---|---|---|---|---|---|---|
工厂A | 2012-03-01 00:00:00 | 2012-04-22 01:50:00 | 14999 | 10499 | 1499 | 3001 | 20 |
工厂B | 2016-11-07 00:00:00 | 2016-11-20 21:19:00 | 20000 | 14000 | 2000 | 4000 | 20 |
工厂C | 2022-02-01 00:05:00 | 2022-02-01 20:32:00 | 2000 | 1400 | 200 | 400 | 20 |
Table 1 Details of the PE dataset
工厂 | 起始时间 | 终止时间 | 总样本量 | 训练集样本量 | 验证集样本量 | 测试集样本量 | 变量维度 |
---|---|---|---|---|---|---|---|
工厂A | 2012-03-01 00:00:00 | 2012-04-22 01:50:00 | 14999 | 10499 | 1499 | 3001 | 20 |
工厂B | 2016-11-07 00:00:00 | 2016-11-20 21:19:00 | 20000 | 14000 | 2000 | 4000 | 20 |
工厂C | 2022-02-01 00:05:00 | 2022-02-01 20:32:00 | 2000 | 1400 | 200 | 400 | 20 |
模型 | 架构 | 参数维度 | 总参数量 |
---|---|---|---|
GRU | GRU层 | GRU(20, 128) | 57729 |
全连接层 | Linear(128, 1) | ||
LSTM | LSTM层 | LSTM(20, 128) | 76929 |
全连接层 | Linear(128, 1) | ||
RNN | RNN层 | RNN(20, 128) | 19329 |
全连接层 | Linear(128, 1) | ||
MLP | 全连接层-1 | Linear(240, 128) | 39169 |
全连接层-2 | Linear(128, 64) | ||
全连接层-3 | Linear(64, 1) | ||
CNN | 卷积层-1 | Conv1d(12, 16, kernel_size=2, stride=1) | 9265 |
卷积层-2 | Conv1d(16, 32, kernel_size=1, stride=1) | ||
池化层 | Maxpool1d(kernel_size=2, stride=2, padding=0, dilation=1) | ||
全连接层-1 | Linear(128, 64) | ||
全连接层-2 | Linear(64, 1) |
Table 2 Details of the model architecture and parameters
模型 | 架构 | 参数维度 | 总参数量 |
---|---|---|---|
GRU | GRU层 | GRU(20, 128) | 57729 |
全连接层 | Linear(128, 1) | ||
LSTM | LSTM层 | LSTM(20, 128) | 76929 |
全连接层 | Linear(128, 1) | ||
RNN | RNN层 | RNN(20, 128) | 19329 |
全连接层 | Linear(128, 1) | ||
MLP | 全连接层-1 | Linear(240, 128) | 39169 |
全连接层-2 | Linear(128, 64) | ||
全连接层-3 | Linear(64, 1) | ||
CNN | 卷积层-1 | Conv1d(12, 16, kernel_size=2, stride=1) | 9265 |
卷积层-2 | Conv1d(16, 32, kernel_size=1, stride=1) | ||
池化层 | Maxpool1d(kernel_size=2, stride=2, padding=0, dilation=1) | ||
全连接层-1 | Linear(128, 64) | ||
全连接层-2 | Linear(64, 1) |
算法 | 特殊超参数搜索范围 |
---|---|
Localised | — |
FedAvg | — |
FedAvg_FT | — |
APFL | — |
APPLE | — |
FedProx | |
FedRep | |
FML | |
FedAPEN、FedPatsf | |
Table 3 Special hyperparameters and search ranges of algorithms
算法 | 特殊超参数搜索范围 |
---|---|
Localised | — |
FedAvg | — |
FedAvg_FT | — |
APFL | — |
APPLE | — |
FedProx | |
FedRep | |
FML | |
FedAPEN、FedPatsf | |
公共超参数 | 搜索范围 |
---|---|
通讯轮数 | [ |
学习率 | [0.001,0.01] |
动量 | [0.5,0.9] |
批大小 | [ |
窗口大小 | [ |
隐藏层层数 | [ |
隐藏层大小 | [ |
本地训练轮数 | [ |
Table 4 Common hyperparameters and search ranges for algorithms
公共超参数 | 搜索范围 |
---|---|
通讯轮数 | [ |
学习率 | [0.001,0.01] |
动量 | [0.5,0.9] |
批大小 | [ |
窗口大小 | [ |
隐藏层层数 | [ |
隐藏层大小 | [ |
本地训练轮数 | [ |
算法 | GRU | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.0029 | 0.0400 | 0.0283 |
FedAvg | 0.0032 | 0.0407 | 0.0291 |
FedAvg_FT | 0.0036 | 0.0435 | 0.0318 |
FedProx | 0.0099 | 0.0799 | 0.0676 |
FedRep | 0.0037 | 0.0484 | 0.0402 |
FML | 0.0029 | 0.0391 | 0.0283 |
APFL | 0.0034 | 0.0420 | 0.0305 |
APPLE | 0.0036 | 0.0418 | 0.0306 |
FedAPEN | 0.0024 | 0.0403 | 0.0292 |
本文 | 0.0026 | 0.0359 | 0.0262 |
Table 5 GRU model forecasting comparison of different algorithms on PE dataset
算法 | GRU | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.0029 | 0.0400 | 0.0283 |
FedAvg | 0.0032 | 0.0407 | 0.0291 |
FedAvg_FT | 0.0036 | 0.0435 | 0.0318 |
FedProx | 0.0099 | 0.0799 | 0.0676 |
FedRep | 0.0037 | 0.0484 | 0.0402 |
FML | 0.0029 | 0.0391 | 0.0283 |
APFL | 0.0034 | 0.0420 | 0.0305 |
APPLE | 0.0036 | 0.0418 | 0.0306 |
FedAPEN | 0.0024 | 0.0403 | 0.0292 |
本文 | 0.0026 | 0.0359 | 0.0262 |
算法 | LSTM | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.0041 | 0.0466 | 0.0364 |
FedAvg | 0.0029 | 0.0373 | 0.0276 |
FedAvg_FT | 0.0029 | 0.0399 | 0.0301 |
FedProx | 0.0072 | 0.0726 | 0.0615 |
FedRep | 0.0035 | 0.0443 | 0.0338 |
FML | 0.0035 | 0.0439 | 0.0326 |
APFL | 0.0029 | 0.0399 | 0.0301 |
APPLE | 0.0041 | 0.0498 | 0.0371 |
FedAPEN | 0.0025 | 0.0358 | 0.0264 |
本文 | 0.0027 | 0.0352 | 0.0257 |
Table 6 LSTM model forecasting comparison of different algorithms on PE dataset
算法 | LSTM | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.0041 | 0.0466 | 0.0364 |
FedAvg | 0.0029 | 0.0373 | 0.0276 |
FedAvg_FT | 0.0029 | 0.0399 | 0.0301 |
FedProx | 0.0072 | 0.0726 | 0.0615 |
FedRep | 0.0035 | 0.0443 | 0.0338 |
FML | 0.0035 | 0.0439 | 0.0326 |
APFL | 0.0029 | 0.0399 | 0.0301 |
APPLE | 0.0041 | 0.0498 | 0.0371 |
FedAPEN | 0.0025 | 0.0358 | 0.0264 |
本文 | 0.0027 | 0.0352 | 0.0257 |
算法 | RNN | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.0027 | 0.0359 | 0.0245 |
FedAvg | 0.0024 | 0.0353 | 0.0241 |
FedAvg_FT | 0.0027 | 0.0383 | 0.0278 |
FedProx | 0.0070 | 0.0727 | 0.0610 |
FedRep | 0.0031 | 0.0416 | 0.0320 |
FML | 0.0027 | 0.0385 | 0.0275 |
APFL | 0.0026 | 0.0374 | 0.0260 |
APPLE | 0.0028 | 0.0378 | 0.0267 |
FedAPEN | 0.0027 | 0.0368 | 0.0276 |
本文 | 0.0024 | 0.0348 | 0.0235 |
Table 7 RNN model forecasting comparison of different algorithms on PE dataset
算法 | RNN | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.0027 | 0.0359 | 0.0245 |
FedAvg | 0.0024 | 0.0353 | 0.0241 |
FedAvg_FT | 0.0027 | 0.0383 | 0.0278 |
FedProx | 0.0070 | 0.0727 | 0.0610 |
FedRep | 0.0031 | 0.0416 | 0.0320 |
FML | 0.0027 | 0.0385 | 0.0275 |
APFL | 0.0026 | 0.0374 | 0.0260 |
APPLE | 0.0028 | 0.0378 | 0.0267 |
FedAPEN | 0.0027 | 0.0368 | 0.0276 |
本文 | 0.0024 | 0.0348 | 0.0235 |
算法 | MLP | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.014 | 0.0867 | 0.0714 |
FedAvg | 0.0058 | 0.0572 | 0.0445 |
FedAvg_FT | 0.0045 | 0.0533 | 0.0421 |
FedProx | 0.015 | 0.0928 | 0.0835 |
FedRep | 0.0069 | 0.0652 | 0.0551 |
FML | 0.0085 | 0.0729 | 0.0632 |
APFL | 0.0045 | 0.0561 | 0.0481 |
APPLE | 0.0067 | 0.0665 | 0.0542 |
FedAPEN | 0.0055 | 0.0561 | 0.0455 |
本文 | 0.0042 | 0.0487 | 0.0388 |
Table 8 MLP model forecasting comparison of different algorithms on PE dataset
算法 | MLP | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.014 | 0.0867 | 0.0714 |
FedAvg | 0.0058 | 0.0572 | 0.0445 |
FedAvg_FT | 0.0045 | 0.0533 | 0.0421 |
FedProx | 0.015 | 0.0928 | 0.0835 |
FedRep | 0.0069 | 0.0652 | 0.0551 |
FML | 0.0085 | 0.0729 | 0.0632 |
APFL | 0.0045 | 0.0561 | 0.0481 |
APPLE | 0.0067 | 0.0665 | 0.0542 |
FedAPEN | 0.0055 | 0.0561 | 0.0455 |
本文 | 0.0042 | 0.0487 | 0.0388 |
算法 | CNN | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.032 | 0.168 | 0.151 |
FedAvg | 0.031 | 0.154 | 0.133 |
FedAvg_FT | 0.034 | 0.176 | 0.155 |
FedProx | 0.026 | 0.144 | 0.126 |
FedRep | 0.032 | 0.163 | 0.144 |
FML | 0.039 | 0.192 | 0.170 |
APFL | 0.035 | 0.179 | 0.157 |
APPLE | 0.036 | 0.169 | 0.151 |
FedAPEN | 0.036 | 0.177 | 0.154 |
本文 | 0.024 | 0.142 | 0.120 |
Table 9 CNN model forecasting comparison of different algorithms on PE dataset
算法 | CNN | ||
---|---|---|---|
MSE | RMSE | MAE | |
Localised | 0.032 | 0.168 | 0.151 |
FedAvg | 0.031 | 0.154 | 0.133 |
FedAvg_FT | 0.034 | 0.176 | 0.155 |
FedProx | 0.026 | 0.144 | 0.126 |
FedRep | 0.032 | 0.163 | 0.144 |
FML | 0.039 | 0.192 | 0.170 |
APFL | 0.035 | 0.179 | 0.157 |
APPLE | 0.036 | 0.169 | 0.151 |
FedAPEN | 0.036 | 0.177 | 0.154 |
本文 | 0.024 | 0.142 | 0.120 |
变量 | 贡献度 |
---|---|
酯化釜温度调节 | 1.0 |
气相管线温度 | 0.25 |
分离塔顶部温度 | 0.09 |
酯化分离水回流量控制 | 0.06 |
酯化釜液位 | 0.05 |
热水循环泵频率调节 | 0.04 |
水回流泵出口压力 | 0.03 |
Table 10 Contributions of variables to the forecasting of esterification temperature
变量 | 贡献度 |
---|---|
酯化釜温度调节 | 1.0 |
气相管线温度 | 0.25 |
分离塔顶部温度 | 0.09 |
酯化分离水回流量控制 | 0.06 |
酯化釜液位 | 0.05 |
热水循环泵频率调节 | 0.04 |
水回流泵出口压力 | 0.03 |
消融算法 | MSE | RMSE | MAE |
---|---|---|---|
FedPatsf_Tune | 0.0026 | 0.0358 | 0.0246 |
FedPatsf_Lw | 0.0025 | 0.0355 | 0.0244 |
FedPatsf_Joint | 0.0028 | 0.0369 | 0.0260 |
FedPatsf | 0.0024 | 0.0348 | 0.0235 |
Table 11 The FedPatsf algorithm ablation experiment
消融算法 | MSE | RMSE | MAE |
---|---|---|---|
FedPatsf_Tune | 0.0026 | 0.0358 | 0.0246 |
FedPatsf_Lw | 0.0025 | 0.0355 | 0.0244 |
FedPatsf_Joint | 0.0028 | 0.0369 | 0.0260 |
FedPatsf | 0.0024 | 0.0348 | 0.0235 |
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