IDPC-RVM based online prediction of quality variables for multimode batch processes

doi:10.11949/0438-1157.20220096

Abstract

Abstract:

Batch processes have multimode characteristics. The high-dimensional characteristics of process data and the selection of mode center in the existing batch process mode partitioning method directly affects the rationality of the mode partitioning results, which in turn affects the accuracy of online prediction of batch process quality variables. To cope with this challenge, an online prediction method of batch processes quality variables based on improved density peaks clustering relevance vector machine (IDPC-RVM) is proposed. First, based on the DPC algorithm, the sample similarity is measured by considering the high-dimensional characteristics of the process data, and the mode centers of the batch process are accurately obtained by the mode centers selection strategy with the unbalanced sample density. Then, the optimal number of modes is obtained without prior knowledge according to the mode partitioning index (MPI), and the transition modes are identified to complete the mode partitioning of batch processes. Finally, the RVM prediction model of each mode data is established to realize the online prediction of batch process quality variables. The experimental results of penicillin fermentation process show that compared with RVM, SCFCM-RVM and DPC-RVM methods, the RMSE of the proposed method for the prediction of penicillin concentration was reduced to 0.0093, and the R² was increased to 0.9995, which effectively improving the prediction accuracy.

Key words: batchwise, improved density peaks clustering, mode partitioning, model, prediction

摘要：

间歇过程具有多模态特性，现有的间歇过程模态划分方法中过程数据高维特征和模态中心的选取直接影响模态划分结果的合理性，进而影响间歇过程质量变量在线预测的精度。为提高间歇过程质量变量在线预测的精度，提出了一种基于改进密度峰值聚类相关向量机(improved density peaks clustering-relevance vector machine，IDPC-RVM)的间歇过程质量变量在线预测方法。首先，在密度峰值聚类算法基础上，考虑过程数据的高维特征进行样本相似性度量，并通过样本密度不平衡下的模态中心选取策略准确获取间歇过程模态中心；其次，利用模态划分指标在无须先验知识的情况下获取间歇过程最优模态数目，并识别过渡模态完成间歇过程的模态划分；最后，建立各模态数据的RVM预测模型，实现间歇过程质量变量的在线预测。青霉素发酵过程的实验结果表明，与RVM、SCFCM-RVM和DPC-RVM方法相比，对青霉素浓度预测的均方根误差(RMSE)降低至0.0093，判定系数(R²)提升至0.9995，有效地提高了预测精度。

关键词: 间歇式, 改进密度峰值聚类, 模态划分, 模型, 预测

CLC Number:

TP 274

Xinjie ZHOU, Jianlin WANG, Xingcong AI, Enguang SUI, Rutong WANG. IDPC-RVM based online prediction of quality variables for multimode batch processes[J]. CIESC Journal, 2022, 73(7): 3120-3130.

周新杰, 王建林, 艾兴聪, 随恩光, 王汝童. 基于IDPC-RVM的多模态间歇过程质量变量在线预测[J]. 化工学报, 2022, 73(7): 3120-3130.

Figures/Tables 14

Fig.1 Clusters distribution with unbalanced sample density

Fig.2 Mode partitioning flowchart of batch processes for improved DPC

Fig.3 Flow chart of online prediction of quality variables in multimode batch processes based on IDPC-RVM

Table 1 Variables of penicillin fermentation process

过程变量	单位	过程变量	单位
通风率	L/h	二氧化碳浓度	mmol/L
搅拌功率	W	pH
底物流加速率	L/h	反应器温度	K
底物流温度	K	产热量	kcal/h
底物浓度	g/L	加酸流速	ml/h
溶解氧浓度	mol/L	加碱流速	ml/h
生物质浓度	g/L	加冷却水流速	L/h
青霉素浓度	g/L	加热水流速	L/h
反应器体积	L

Fig.4 Sample density of penicillin fermentation process

Fig.5 Decision graph

Fig.6 Partitioning results of batch 3 with different number of modes

Fig.7 Discrimination of the optimal number of modes

Fig.8 Steady modes with different methods

Table 2 Final mode partitioning results of different methods

方法	SM #1	TM #1	SM #2	TM #2	SM #3	TM #3	SM #4
SCFCM	1~38	39~48	49~93	94~110	111~146	147~226	227~400
DPC	1~40	—	41~283	—	284~343	—	344~400
IDPC	1~28	29~49	50~98	99~117	118~177	178~199	200~400

Fig.9 Prediction results of test batch 1 with different methods

Fig.10 Prediction error at each sampling point in test batch 1

Fig.11 RMSE of different batches

Table 3 Mean RMSE and mean R2 of different methods

方法	平均RMSE	平均R²
RVM	0.0592	0.9815
SCFCM-RVM	0.0167	0.9986
DPC-RVM	0.0382	0.9924
IDPC-RVM	0.0093	0.9995

References 31

1	Chang P, Lu R W. Process monitoring of batch process based on overcomplete broad learning network[J]. Engineering Applications of Artificial Intelligence, 2021, 99: 104139.
2	Chu F, Wang J C, Zhao X, et al. Transfer learning for nonlinear batch process operation optimization[J]. Journal of Process Control, 2021, 101: 11-23.
3	Chu F, Cheng X, Jia R D, et al. Final quality prediction method for new batch processes based on improved JYKPLS process transfer model[J]. Chemometrics and Intelligent Laboratory Systems, 2018, 183: 1-10.
4	Yamaguchi T, Yamashita Y. Quality prediction for multi-grade batch process using sparse flexible clustered multi-task learning[J]. Computers & Chemical Engineering, 2021, 150: 107320.
5	Zhu J L, Gao F R. Improved nonlinear quality estimation for multiphase batch processes based on relevance vector machine with neighborhood component variable selection[J]. Industrial & Engineering Chemistry Research, 2018, 57(2): 666-676.
6	Tipping M E. Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 2001, 1(3): 211-244.
7	Qiu K P, Wang J L, Wang R T, et al. Soft sensor development based on kernel dynamic time warping and a relevant vector machine for unequal-length batch processes[J]. Expert Systems with Applications, 2021, 182: 115223.
8	Zhao H T. Order-information-based phase partition and fault detection for batch processes[J]. Industrial & Engineering Chemistry Research, 2018, 57(23): 7905-7921.
9	Guo J Y, Yuan T M, Li Y. Fault detection of multimode process based on local neighbor normalized matrix[J]. Chemometrics and Intelligent Laboratory Systems, 2016, 154: 162-175.
10	Zhu J L, Wang Y Q, Zhou D H, et al. Batch process modeling and monitoring with local outlier factor[J]. IEEE Transactions on Control Systems Technology, 2019, 27(4): 1552-1565.
11	Chang P, Qiao J F, Lu R W, et al. Multiphase batch process monitoring based on higher-order cumulant analysis[J]. The Canadian Journal of Chemical Engineering, 2020, 98(2): 513-524.
12	Wang J L, Qiu K P, Liu W M, et al. Unsupervised-multiscale-sequential-partitioning and multiple-SVDD-model-based process-monitoring method for multiphase batch processes[J]. Industrial & Engineering Chemistry Research, 2018, 57(51): 17437-17451.
13	Dong W W, Yao Y, Gao F R. Phase analysis and identification method for multiphase batch processes with partitioning multi-way principal component analysis (MPCA) model[J]. Chinese Journal of Chemical Engineering, 2012, 20(6): 1121-1127.
14	Ye X F, Wang P L, Yang Z Y. Time sequential phase partition and modeling method for fault detection of batch processes[J]. IEEE Access, 2017, 6: 1249-1260.
15	Zhao C H, Sun Y X. Step-wise sequential phase partition (SSPP) algorithm based statistical modeling and online process monitoring[J]. Chemometrics and Intelligent Laboratory Systems, 2013, 125: 109-120.
16	Li W Q, Zhao C H, Gao F R. Sequential time slice alignment based unequal-length phase identification and modeling for fault detection of irregular batches[J]. Industrial & Engineering Chemistry Research, 2015, 54(41): 10020-10030.
17	Yu W K, Zhao C H, Zhang S M. A two-step parallel phase partition algorithm for monitoring multiphase batch processes with limited batches[J]. IFAC-PapersOnLine, 2017, 50(1): 2750-2755.
18	Liu J X, Liu T, Zhang J. Window-based stepwise sequential phase partition for nonlinear batch process monitoring[J]. Industrial & Engineering Chemistry Research, 2016, 55(34): 9229-9243.
19	Zhao C H, Gao F R. Statistical modeling and online fault detection for multiphase batch processes with analysis of between-phase relative changes[J]. Chemometrics and Intelligent Laboratory Systems, 2014, 130: 58-67.
20	Lu N Y, Gao F R, Wang F L. Sub-PCA modeling and on-line monitoring strategy for batch processes[J]. AIChE Journal, 2004, 50(1): 255-259.
21	张雷, 张小刚, 陈华. 基于Gath-Geva算法和核极限学习机的多阶段间歇过程软测量[J]. 化工学报, 2018, 69(6): 2576-2585.
	Zhang L, Zhang X G, Chen H. Soft sensors for multi-stage batch processes based on Gath-Geva algorithm and kernel extreme learning machine[J]. CIESC Journal, 2018, 69(6): 2576-2585.
22	Luo L J, Bao S Y, Mao J F, et al. Phase partition and phase-based process monitoring methods for multiphase batch processes with uneven durations[J]. Industrial & Engineering Chemistry Research, 2016, 55(7): 2035-2048.
23	Luo L J, Bao S Y, Mao J F, et al. Fuzzy phase partition and hybrid modeling based quality prediction and process monitoring methods for multiphase batch processes[J]. Industrial & Engineering Chemistry Research, 2016, 55(14): 4045-4058.
24	Luo L J. Monitoring uneven multistage/multiphase batch processes using trajectory-based fuzzy phase partition and hybrid MPCA models[J]. The Canadian Journal of Chemical Engineering, 2019, 97(1): 178-187.
25	刘伟旻, 王建林, 邱科鹏, 等. 基于DHSC的多模态间歇过程测量数据异常检测方法[J]. 化工学报, 2017, 68(11): 4201-4207.
	Liu W M, Wang J L, Qiu K P, et al. Method for detecting abnormal data in multimode batch processes based on dynamic hypersphere structure change[J]. CIESC Journal, 2017, 68(11): 4201-4207.
26	Rodriguez A, Laio A. Clustering by fast search and find of density peaks[J]. Science, 2014, 344(6191): 1492-1496.
27	Flores K G, Garza S E. Density peaks clustering with gap-based automatic center detection[J]. Knowledge-Based Systems, 2020, 206: 106350.
28	Xu M L, Li Y H, Li R X, et al. EADP: an extended adaptive density peaks clustering for overlapping community detection in social networks[J]. Neurocomputing, 2019, 337: 287-302.
29	Guo R X, Zhang N, Wang J Q, et al. Phase partition and identification based on a two-step method for batch process[J]. Transactions of the Institute of Measurement and Control, 2018, 40(16): 4472-4483.
30	邵昌昇, 楼巍, 严利民. 高维数据中的相似性度量算法的改进[J]. 计算机技术与发展, 2011, 21(2): 1-4.
	Shao C S, Lou W, Yan L M. Optimization of algorithm of similarity measurement in high-dimensional data[J]. Computer Technology and Development, 2011, 21(2): 1-4.
31	Birol G, Ündey C, Çinar A. A modular simulation package for fed-batch fermentation: penicillin production[J]. Computers & Chemical Engineering, 2002, 26(11): 1553-1565.

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