基于TDMN的青霉素浓度在线软测量

doi:10.11949/0438-1157.20241275

摘要/Abstract

摘要：

针对青霉素发酵过程中的浓度难题，提出了一种基于时序差分记忆网络（temporal difference memory network，TDMN）的在线软测量方法。鉴于青霉素发酵过程数据的多批次、非平稳特性，采用滑动窗口进行预处理，利用TDMN模型捕捉局部特征，并通过增量学习实现模型的实时更新，以实现青霉素浓度在线软测量。实验结果表明，该模型在青霉素浓度预测中表现出显著的准确性，与人工神经网络（artificial neural network，ANN）、循环神经网络（recurrent neural network，RNN）和长短期记忆网络（long short-term memory，LSTM）等传统方法相比，具有更高的实时性和适应性，能够有效跟踪发酵过程中的浓度变化。通过与其他模型的比较，发现基于增量学习的方法显著降低了预测误差，提高了预测精度。该方法不仅能够动态更新模型，还能有效跟踪青霉素浓度的变化，为发酵过程状态的监测与控制提供了新的解决方案，具有重要的应用价值和行业意义。

关键词: 发酵过程, 神经网络, 非平稳, 预测, 模型

Abstract:

Aiming at the problem of concentration prediction in the penicillin fermentation process, an online soft measurement method based on temporal difference memory network (TDMN) was proposed. In view of the multi-batch and non-stationary characteristics of penicillin fermentation process data, this paper uses a sliding window for preprocessing, uses the TDMN model to capture local features, and realizes real-time update of the model through incremental learning to achieve online soft measurement of penicillin concentration. The experimental results show that the model exhibits significant accuracy in penicillin concentration prediction. Compared with traditional methods such as artificial neural network (ANN), recurrent neural network (RNN) and long short-term memory network (LSTM), it has higher real-time and adaptability, and can effectively track the concentration changes during the fermentation process. Through comparison with other models, it is found that the method based on incremental learning significantly reduces the prediction error and improves the prediction accuracy. This method can not only dynamically update the model, but also effectively track changes in penicillin concentration, providing a new solution for monitoring and controlling the status of the fermentation process, and has important application value and industry significance.

Key words: fermentation process, neural networks, non-stationary, prediction, model

中图分类号:

TP 274

李文亮, 纪成, 梁晨, 吴思辰, 陈石林, 孙巍, 翟持. 基于TDMN的青霉素浓度在线软测量[J]. 化工学报, 2025, 76(6): 2848-2858.

Wenliang LI, Cheng JI, Chen LIANG, Sichen WU, Shilin CHEN, Wei SUN, Chi ZHAI. On-line soft measurement of penicillin concentration based on TDMN[J]. CIESC Journal, 2025, 76(6): 2848-2858.

图/表 11

图1 用于批处理过程的数据预处理

Fig.1 Data per-processing for batch processing

图2 TDMN算法框架

Fig.2 TDMN algorithm framework

图3 基于TDMN的青霉素浓度在线软测量流程图

Fig.3 Flowchart of online soft measurement of penicillin concentration based on TDMN

表1 青霉素工业发酵过程中工艺变量的描述

Table 1 Description of process variables in the industrial penicillin fermentation process

变量编号	变量描述	变量编号	变量描述
1	通气速率/(L/h)	13	容器质量/kg
2	糖进料速率/(L/h)	14	pH
3	酸流量/(L/h)	15	温度/K
4	基础流率/(L/h)	16	产生的热量/kJ
5	加热/冷却水流量/(L/h)	17	尾气中二氧化碳含量/%
6	采暖水流量/(L/h)	18	PAA流/(L/h)
7	注射用水/稀释水流量/(L/h)	19	油流/(L/h)
8	气头压力/bar	20	耗氧速率/(g/min)
9	倾倒培养基流量/(L/h)	21	废气中的氧气百分比/%
10	底物浓度/(g/h)	22	析碳速率/(g/h)
11	溶解氧浓度/(mg/h)	23	青霉素浓度/(g/L)
12	容器体积/L

图4 随机序列之间MI值的分布

Fig.4 Distribution of MI value between random sequences

图5 通过比较MI和阈值来选择变量

Fig.5 Variable selection results by comparing MI and the threshold

图6 60批检测数据中青霉素浓度预测结果

Fig.6 Offline prediction results of penicillin concentration in 60 batches of test data

图7 60个检测批次不同方法性能的统计

Fig.7 Statistics on the performance of different methods in 60 test batches

表2 不同方法对60个供试批次青霉素浓度的平均预测评价指标

Table 2 Average prediction evaluation indexes of penicillin concentration of 60 test batches by different methods

模型	MAE	MSE	RMSE	R²
ANN	0.274	0.131	0.337	0.843
RNN	0.169	0.069	0.238	0.927
LSTM	0.156	0.047	0.203	0.939
TDMN	0.127	0.037	0.176	0.956

表3 四种模型在线测试结果

Table 3 Online test results of four models

模型	MAE	MSE	RMSE	R²
ANN	0.219	0.105	0.324	0.886
RNN	0.153	0.054	0.232	0.952
LSTM	0.119	0.035	0.187	0.961
TDMN	0.095	0.022	0.148	0.999

图8 60批检测数据中青霉素浓度在线预测结果

Fig.8 Online prediction results of penicillin concentration in 60 batches of test data

参考文献 33

[1]	Wang Q J, Zhang Z, Xu G R, et al. Pyrolysis of penicillin fermentation residue and sludge to produce biochar: antibiotic resistance genes destruction and biochar application in the adsorption of penicillin in water[J]. Journal of Hazardous Materials, 2021, 413: 125385.
[2]	Yang L, Zhang S H, Chen Z Q, et al. Maturity and security assessment of pilot-scale aerobic co-composting of penicillin fermentation dregs (PFDs) with sewage sludge[J]. Bioresource Technology, 2016, 204: 185-191.
[3]	Jiang Q C, Wang Z W, Yan S F, et al. Data-driven soft sensing for batch processes using neural network-based deep quality-relevant representation learning[J]. IEEE Transactions on Artificial Intelligence, 2023, 4(4): 602-611.
[4]	张梦轩, 刘洪辰, 王敏, 等. 化工过程的智能混合建模方法及应用[J]. 化工进展, 2021, 40(4): 1765-1776.
	Zhang M X, Liu H C, Wang M, et al. Intelligence hybrid modeling method and applications in chemical process[J]. Chemical Industry and Engineering Progress, 2021, 40(4): 1765-1776.
[5]	Knight M A, Hutchings M R, White P C L, et al. A mechanistic model captures livestock trading, disease dynamics, and compensatory behaviour in response to control measures[J]. Journal of Theoretical Biology, 2022, 539: 111059.
[6]	曾贲, 房霄, 孔德帅, 等. 一种数据驱动的对抗博弈智能体建模方法[J]. 系统仿真学报, 2021, 33(12): 2838-2845.
	Zeng B, Fang X, Kong D S, et al. A data-driven modeling method for game adversity agent[J]. Journal of System Simulation, 2021, 33(12): 2838-2845.
[7]	姚羽曼, 罗文嘉, 戴一阳. 数据驱动方法在化工过程故障诊断中的研究进展[J]. 化工进展, 2021, 40(4): 1755-1764.
	Yao Y M, Luo W J, Dai Y Y. Research progress of data-driven methods in fault diagnosis of chemical process[J]. Chemical Industry and Engineering Progress, 2021, 40(4): 1755-1764.
[8]	戚子豪, 钟文琪, 陈曦, 等. 基于混合建模的水泥生料分解过程动态特性研究[J]. 化工学报, 2022, 73(5): 2039-2051.
	Qi Z H, Zhong W Q, Chen X, et al. Research on dynamic characteristics of cement raw meal decomposition process based on hybrid modeling[J]. CIESC Journal, 2022, 73(5): 2039-2051.
[9]	张磊, 贺丁, 刘琳琳, 等. 基于模型的化工产品设计方法: 综述与展望[J]. 化工进展, 2021, 40(4): 1746-1754.
	Zhang L, He D, Liu L L, et al. Model-based chemical product design: review and perspectives[J]. Chemical Industry and Engineering Progress, 2021, 40(4): 1746-1754.
[10]	Shokry A, Pérez-Moya M, Graells M, et al. Data-driven dynamic modeling of batch processes having different initial conditions and missing measurements[C]//27th European Symposium on Computer Aided Process Engineering. Amsterdam: Elsevier, 2017: 433-438.
[11]	Mi X J, Lv T X, Tian Y, et al. Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system[J]. ISA Transactions, 2021, 112: 137-149.
[12]	陈琳, 周利, 吉旭. 基于深度学习的催化裂化过程建模方法[J]. 西安石油大学学报(自然科学版), 2023, 38(4): 94-103.
	Chen L, Zhou L, Ji X. Modelling method based on deep learning for fluid catalytic cracking processes[J]. Journal of Xi'an Shiyou University (Natural Science Edition), 2023, 38(4): 94-103.
[13]	Souza F A A, Araújo R, Mendes J. Review of soft sensor methods for regression applications[J]. Chemometrics and Intelligent Laboratory Systems, 2016, 152: 69-79.
[14]	He Y L, Tian Y, Xu Y, et al. Novel soft sensor development using echo state network integrated with singular value decomposition: application to complex chemical processes[J]. Chemometrics and Intelligent Laboratory Systems, 2020, 200: 103981.
[15]	Mota R, Nadri M, Hammouri H. Observer design for implicit state affine systems up to output injection[J]. IFAC Proceedings Volumes, 2011, 44(1): 697-702.
[16]	Wang W, Yang C H, Han J, et al. A soft sensor modeling method with dynamic time-delay estimation and its application in wastewater treatment plant[J]. Biochemical Engineering Journal, 2021, 172: 108048.
[17]	Wang Y L, Liu D J, Liu C L, et al. Dynamic historical information incorporated attention deep learning model for industrial soft sensor modeling[J]. Advanced Engineering Informatics, 2022, 52: 101590.
[18]	Li X Y, Yi X H, Liu Z H, et al. Application of novel hybrid deep leaning model for cleaner production in a paper industrial wastewater treatment system[J]. Journal of Cleaner Production, 2021, 294: 126343.
[19]	Yuan X F, Li L, Wang Y L. Nonlinear dynamic soft sensor modeling with supervised long short-term memory network[J]. IEEE Transactions on Industrial Informatics, 2020, 16(5): 3168-3176.
[20]	Mei P, Li M, Zhang Q, et al. Prediction model of drinking water source quality with potential industrial-agricultural pollution based on CNN-GRU-attention[J]. Journal of Hydrology, 2022, 610: 127934.
[21]	Liu C L, Wang K, Ye L J, et al. Deep learning with neighborhood preserving embedding regularization and its application for soft sensor in an industrial hydrocracking process[J]. Information Sciences, 2021, 567: 42-57.
[22]	Zheng B W, Zhou D W, Ye H J, et al. Preserving locality in vision transformers for class incremental learning[C]//2023 IEEE International Conference on Multimedia and Expo (ICME). Brisbane, Australia: IEEE, 2023: 1157-1162.
[23]	Wang Y M, Chen X Y, Wang X, et al. Radar detection self-evolution based on incremental learning in time-varying clutter environments[J]. IEEE Transactions on Instrumentation and Measurement, 2024, 73: 2523613.
[24]	Xie J J, Pan B, Xu X, et al. MiSSNet: memory-inspired semantic segmentation augmentation network for class-incremental learning in remote sensing images[J]. IEEE Transactions on Geoscience and Remote Sensing, 2024, 62: 5607913.
[25]	Ji C, Ma F Y, Wang J D, et al. Profitability related industrial-scale batch processes monitoring via deep learning based soft sensor development[J]. Computers & Chemical Engineering, 2023, 170: 108125.
[26]	Wang K, Gopaluni R B, Chen J, et al. Deep learning of complex batch process data and its application on quality prediction[J]. IEEE Transactions on Industrial Informatics, 2020, 16(12): 7233-7242.
[27]	Wang Y B, Long M S, Wang J M, et al. PredRNN[C]//Proceedings of the 31st International Conference on Neural Information Processing Systems. Long Beach, California, USA: ACM, 2017: 879-888.
[28]	Goldrick S, Duran-Villalobos C A, Jankauskas K, et al. Modern day monitoring and control challenges outlined on an industrial-scale benchmark fermentation process[J]. Computers & Chemical Engineering, 2019, 130: 106471.
[29]	Birol G, Cenk Ü, Ali Ç. A modular simulation package for fed-batch fermentation: penicillin production[J]. Computers & Chemical Engineering, 2002, 26(11): 1553-1565.
[30]	Melo A, Câmara M M, Clavijo N, et al. Open benchmarks for assessment of process monitoring and fault diagnosis techniques: a review and critical analysis[J]. Computers & Chemical Engineering, 2022, 165: 107964.
[31]	Wang Z X, He Q P, Wang J. Comparison of variable selection methods for PLS-based soft sensor modeling[J]. Journal of Process Control, 2015, 26: 56-72.
[32]	Silverman B W. Density Estimation for Statistics and Data Analysis[M]. London: Routledge, 2018
[33]	Jin H P, Chen X G, Wang L, et al. Adaptive soft sensor development based on online ensemble Gaussian process regression for nonlinear time-varying batch processes[J]. Industrial & Engineering Chemistry Research, 2015, 54(30): 7320-7345.