基于WSDPC-RVR的多模态间歇过程软测量方法

doi:10.11949/0438-1157.20231009

摘要/Abstract

摘要：

间歇过程的多模态特性使得未考虑模态因素建立的软测量模型预测精度较低，现有的间歇过程模态划分方法对初始参数敏感且未考虑异常数据对模态划分结果的影响，其不合理的划分结果是制约多模态间歇过程软测量模型预测精度提升的一个重要因素。提出了一种基于密度加权和相似标签分配密度峰值聚类相关向量回归（weighted destiny and similar label allocation density peaks clustering-relevance vector regression， WSDPC-RVR）的多模态间歇过程软测量方法。首先，以不同数据点的密度贡献程度对低密度区域数据点的局部密度进行加权，准确选取聚类中心，并引入 $ε$ 近邻结合数据点间的距离与局部密度构建剩余数据点的分配策略；然后，定义模态评价指标并分析不同模态的统计特性，构建异常模态判别策略获取有效模态数量，完成间歇过程模态划分；最后，建立各有效模态的RVR软测量模型，实现间歇过程主导变量的在线预测。青霉素发酵过程的仿真实验结果表明，所提方法能够实现合理的模态划分，有效地提高了软测量模型的预测精度。

关键词: 间歇式, 密度峰值聚类, 模态划分, 模型, 发酵

Abstract:

The multimode characteristics of batch processes make the soft sensor model without considering mode factors have low prediction accuracy. The existing batch processes mode partitioning methods are sensitive to initial parameters and do not consider the influence of abnormal data on the mode partitioning results. The unreasonable partitioning results are an important factor restricting the improvement of the prediction accuracy of the multimode batch process soft sensor model. In this paper, a soft sensor method for multimode batch processes based on weighted destiny and similar label allocation density peaks clustering-relevance vector regression (WSDPC-RVR) is proposed. First, the local density of data points in low density areas is weighted according to the density contribution of different data points, the cluster center is accurately selected, and the ε-nearest neighbor is introduced to combine the distance between data points and the local density to construct an allocation strategy for the remaining data points. Then, the mode evaluation index is defined and the statistical characteristics of different modes are analyzed, and the abnormal mode discrimination strategy is constructed to obtain the number of effective modes and complete the mode partitioning of batch processes. Finally, the RVR soft sensor model of each effective mode is established to realize the online prediction of the dominant variables of batch processes. The simulation results of penicillin fermentation process show that the proposed method can achieve reasonable mode partitioning and effectively improve the prediction accuracy of the soft sensor model.

Key words: batchwise, density peaks clustering, mode partition, model, fermentation

中图分类号:

TP 274

王喆, 王建林, 李季, 周新杰, 随恩光. 基于WSDPC-RVR的多模态间歇过程软测量方法[J]. 化工学报, 2023, 74(11): 4656-4669.

Zhe WANG, Jianlin WANG, Ji LI, Xinjie ZHOU, Enguang SUI. Multimode batch process soft sensor method based on WSDPC-RVR[J]. CIESC Journal, 2023, 74(11): 4656-4669.

图/表 24

图1 Jain数据集

Fig.1 Jain data set

图2 DPC对Jain数据集的聚类结果

Fig.2 Clustering result on Jain of DPC

表1 WSDPC算法步骤

Table 1 The steps of WSDPC

输入：待聚类数据集
Step1：根据式(1)、式(2)计算数据点的局部密度 $ρ$ 和相对距离 $δ$ ；
Step2：计算样本距离，根据式(6)、式(7)得到密度贡献权重 $w i j$ ；
Step3：将 $w i j$ 代入式(5)计算 $ρ'$ ；
Step4：根据 $ρ ¯'$ 和 $σ δ$ 选出候选聚类中心集，利用式(8)计算相对距离 $δ'$ ；
Step5：根据式(9)计算决策值，选取最优聚类中心；
Step6：为最优聚类中心指定标签；
Step7：将聚类中心的标签分配给周围数据点；
Step8：对已有标签的数据点按照局部密度降序排列，依次寻找与自身距离小于 $ε$ 的未分配数据点并将该点归属于自身所在类簇；
Step9：重复Step8直至剩余未分配数据点个数不变；
Step10：根据式(10)计算未分配数据点与已有标签数据点的相似性指标，将该点分配给与其相似度最高的已有标签数据点所属类簇；
Step11：重复Step10直至聚类结束。
输出：聚类结果

表1 WSDPC算法步骤

Table 1 The steps of WSDPC

输入：待聚类数据集
Step1：根据式(1)、式(2)计算数据点的局部密度 $ρ$ 和相对距离 $δ$ ；
Step2：计算样本距离，根据式(6)、式(7)得到密度贡献权重 $w i j$ ；
Step3：将 $w i j$ 代入式(5)计算 $ρ'$ ；
Step4：根据 $ρ ¯'$ 和 $σ δ$ 选出候选聚类中心集，利用式(8)计算相对距离 $δ'$ ；
Step5：根据式(9)计算决策值，选取最优聚类中心；
Step6：为最优聚类中心指定标签；
Step7：将聚类中心的标签分配给周围数据点；
Step8：对已有标签的数据点按照局部密度降序排列，依次寻找与自身距离小于 $ε$ 的未分配数据点并将该点归属于自身所在类簇；
Step9：重复Step8直至剩余未分配数据点个数不变；
Step10：根据式(10)计算未分配数据点与已有标签数据点的相似性指标，将该点分配给与其相似度最高的已有标签数据点所属类簇；
Step11：重复Step10直至聚类结束。
输出：聚类结果

图3 WSDPC算法流程图

Fig.3 The flow chart of WSDPC

图4 基于WSDPC的间歇过程模态划分流程图

Fig.4 The flow chart of batch process mode partition based on WSDPC

图5 基于WSDPC-RVR的多模态间歇过程软测量流程图

Fig.5 The flow chart of multimode batch process soft sensor based on WSDPC-RVR

表2 人工数据集

Table 2 Synthetic data sets

数据集名称	数据个数	维数	类别数
Jain	373	2	2
Zelink1	299	2	3
Aggregation	788	2	7

图6 四种方法在Jain数据集上的聚类结果

Fig.6 The clustering result on Jain of four methods

图7 四种方法在Zelink1数据集上的聚类结果

Fig.7 The clustering result on Zelink1 of four methods

图8 四种方法在Aggregation数据集上的聚类结果

Fig.8 The clustering result on Aggregation of four methods

表3 四种方法在人工数据集上的聚类评价指标值

Table 3 The evaluation index value on synthetic data sets of four methods

数据集	FCM			DPC			IDPC			本文方法
数据集	ARI	NMI	ACC	ARI	NMI	ACC	ARI	NMI	ACC	ARI	NMI	ACC
Jain	0.5371	0.5016	0.8686	0.6438	0.5972	0.9035	0.1576	0.1902	0.7828	1.0000	1.0000	1.0000
Zelink1	-0.0021	0.0079	0.3746	-0.0010	0.1226	0.3880	0.0958	0.2410	0.5920	1.0000	1.0000	1.0000
Aggregation	0.6840	0.8251	0.2766	0.7548	0.8941	0.7868	0.8306	0.9150	0.3604	0.9840	0.9799	0.9924

表4 青霉素发酵过程变量

Table 4 Penicillin fermentation process variables

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

表5 青霉素发酵过程异常批次信息

Table 5 Fault batches explanation of penicillin process

通风率

搅拌功率

阶跃异常/+15%

阶跃异常/+12%

70~130 h

330~400 h

图9 15个正常批次的MEI值

Fig.9 MEI of all 15 normal batches

图10 2个异常批次的MEI值

Fig.10 MEI of two abnormal batches

图11 正常批次的模态划分结果

Fig.11 The mode partition result of normal batch

图12 2个异常批次的模态划分结果

Fig.12 The mode partition result of two abnormal batches

表6 异常批次1

Table 6 Abnormal batch 1

异常批次模态	正常模态
异常批次模态	1	2	3	4
1	12.40	20.46	29.21	26.72
2	21.48	4.35	13.23	12.72
3 4 5	18.40 17.80 14.12	12.49 12.70 12.46	2.38 1.99 6.73	6.79 6.72 1.35

表7 异常批次2

Table 7 Abnormal batch 2

异常批次模态	正常模态
异常批次模态	1	2	3	4
1	2.29	19.63	17.70	13.87
2	20.76	2.27	13.07	13.27
3 4 5	19.25 15.20 14.69	12.25 11.94 11.59	2.99 6.56 6.62	7.04 1.19 1.70

图13 不同方法的模态划分结果

Fig.13 The mode partition result of different methods

表8 三种方法的模态划分结果

Table 8 The mode partition result of three methods

算法	第一模态/h	第二模态/h	第三模态/h	第四模态/h
FCM	1~33	34~105	106~226	227~400
IDPC	1~39	40~94	95~175	176~400
本文方法	1~40	41~110	111~197	198~400

图14 测试批次4的青霉素浓度预测结果

Fig.14 Prediction results of test batch 4 for penicillin concentration

图15 不同批次的RMSE

Fig.15 RMSE of different batches

表9 不同软测量模型在5个测试批次的平均R2和平均RMSE

Table 9 Mean R2 and mean RMSE of different soft sensor models for 5 test batches

模型	平均R²	平均RMSE
FCM-RVR	0.9985	0.0169
IDPC-RVR	0.9983	0.0180
本文方法	0.9994	0.0104

参考文献 30

1	Lee K S, Chin I S, Lee H J, et al. Model predictive control technique combined with iterative learning for batch processes[J]. AIChE Journal, 1999, 45(10): 2175-2187.
2	Mei C L, Su Y, Liu G H, et al. Dynamic soft sensor development based on Gaussian mixture regression for fermentation processes[J]. Chinese Journal of Chemical Engineering, 2017, 25(1): 116-122.
3	Yao L, Ge Z Q. Locally weighted prediction methods for latent factor analysis with supervised and semisupervised process data[J]. IEEE Transactions on Automation Science and Engineering, 2017, 14(1): 126-138.
4	Yao L, Ge Z Q. Big data quality prediction in the process industry: a distributed parallel modeling framework[J]. Journal of Process Control, 2018, 68: 1-13.
5	熊伟丽, 葛祥振, 徐保国. 基于改进仿射传播的多模型软测量建模及应用研究[J]. 信息与控制, 2018, 47(2): 239-246.
	Xiong W L, Ge X Z, Xu B G. Multi-model soft sensor modeling and its application based on improved affinity propagation algorithm[J]. Information and Control, 2018, 47(2): 239-246.
6	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.
7	Ge Z Q, Song Z H, Gao F R. Review of recent research on data-based process monitoring[J]. Industrial & Engineering Chemistry Research, 2013, 52(10): 3543-3562.
8	赵小强, 牟淼. 基于变量分块的KDLV-DWSVDD间歇过程故障检测算法研究[J]. 仪器仪表学报, 2021, 42(2): 244-256.
	Zhao X Q, Mou M. Research on fault detection algorithm of batch process based on KDLV-DWSVDD of variable blocks[J]. Chinese Journal of Scientific Instrument, 2021, 42(2): 244-256.
9	Wang J L, Liu W M, Qiu K P, et al. Dynamic hypersphere based support vector data description for batch process monitoring[J]. Chemometrics and Intelligent Laboratory Systems, 2018, 172: 17-32.
10	王建林, 马琳钰, 邱科鹏, 等. 基于SVDD的多时段间歇过程故障检测[J]. 仪器仪表学报, 2017, 38(11): 2752-2761.
	Wang J L, Ma L Y, Qiu K P, et al. Multi-phase batch processes fault detection based on support vector data description[J]. Chinese Journal of Scientific Instrument, 2017, 38(11): 2752-2761.
11	Sun W, Meng Y, Palazoglu A, et al. A method for multiphase batch process monitoring based on auto phase identification[J]. Journal of Process Control, 2011, 21(4): 627-638.
12	Ye A X, Wang B P, Yang C Z. Time sequential phase partition and modeling method for fault detection of batch processes[J]. IEEE Access, 2017, 6: 1249-1260.
13	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.
14	邵盟雅, 吕锋, 宋学君, 等. 基于K-means最佳聚类的间歇过程故障诊断方法[J]. 控制工程, 2020, 27(9): 1642-1648.
	Shao M Y, Lv F, Song X J, et al. Intermittent process fault diagnosis method based on K-means optimal clustering[J]. Control Engineering of China, 2020, 27(9): 1642-1648.
15	Ng Y S, Srinivasan R. An adjoined multi-model approach for monitoring batch and transient operations[J]. Computers & Chemical Engineering, 2009, 33(4): 887-902.
16	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: 2035-2048.
17	Chen S T, Jiang Q C, Yan X F. Multimodal process monitoring based on transition-constrained Gaussian mixture model[J]. Chinese Journal of Chemical Engineering, 2020, 28(12): 3070-3078.
18	Hartigan J A, Wong M A. Algorithm AS 136: a K-means clustering algorithm[J]. Applied Statistics, 1979, 28(1): 100.
19	Dunn J C. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters[J]. Journal of Cybernetics, 1973, 3(3): 32-57.
20	Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms[M]. New York: Plenum Press, 1981.
21	Tan S, Wang F L, Peng J, et al. Multimode process monitoring based on mode identification[J]. Industrial & Engineering Chemistry Research, 2012, 51(1): 374-388.
22	Rodriguez A, Laio A. Clustering by fast search and find of density peaks[J]. Science, 2014, 344(6191): 1492-1496.
23	Morris K, McNicholas P D. Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures[J]. Computational Statistics & Data Analysis, 2016, 97: 133-150.
24	Shi Y, Chen Z S, Qi Z Q, et al. A novel clustering-based image segmentation via density peaks algorithm with mid-level feature[J]. Neural Computing and Applications, 2017, 28(1): 29-39.
25	Yang Y Q, Zheng K F, Wu C H, et al. Building an effective intrusion detection system using the modified density peak clustering algorithm and deep belief networks[J]. Applied Sciences, 2019, 9(2): 238.
26	Chen Y W, Hu X L, Fan W T, et al. Fast density peak clustering for large scale data based on kNN[J]. Knowledge-Based Systems, 2020, 187: 104824.
27	刘聪, 谢莉, 杨慧中. 基于改进DPC的青霉素发酵过程多模型软测量建模[J]. 化工学报, 2021, 72(3): 1606-1615.
	Liu C, Xie L, Yang H Z. Multi-model soft sensor development for penicillin fermentation process based on improved density peak clustering[J]. CIESC Journal, 2021, 72(3): 1606-1615.
28	周新杰, 王建林, 艾兴聪, 等. 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.
	Zhou X J, Wang J L, Ai X C, et al. IDPC-RVM based online prediction of quality variables for multimode batch processes[J]. CIESC Journal, 2022, 73(7): 3120-3130.
29	Wang J L, Qiu K P, Guo Y Q, et al. Soft sensor development based on improved just-in-time learning and relevant vector machine for batch processes[J]. The Canadian Journal of Chemical Engineering, 2021, 99(1): 334-344.
30	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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