基于IDPC-RVM的多模态间歇过程质量变量在线预测

doi:10.11949/0438-1157.20220096

摘要/Abstract

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

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

中图分类号:

TP 274

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.

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.

图/表 14

图1 样本密度不平衡的类簇分布

Fig.1 Clusters distribution with unbalanced sample density

图2 改进DPC的间歇过程模态划分流程图

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

图3 基于IDPC-RVM的多模态间歇过程质量变量在线预测流程图

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

表1 青霉素发酵过程变量

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

图4 青霉素发酵过程样本密度

Fig.4 Sample density of penicillin fermentation process

图5 决策图

Fig.5 Decision graph

图6 批次3在不同模态数目下的划分结果

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

图7 最优模态数目判别

Fig.7 Discrimination of the optimal number of modes

图8 不同方法的稳定模态

Fig.8 Steady modes with different methods

表2 不同方法的最终模态划分结果

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

图9 测试批次1在不同方法下的预测结果

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

图10 测试批次1各采样点处的预测误差

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

图11 不同批次的RMSE

Fig.11 RMSE of different batches

表3 不同方法下的平均RMSE和平均R2

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

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