New operation optimization method with time series based on Levenshtein distance hierarchical clustering

doi:10.11949/j.issn.0438-1157.20180855

Abstract

Abstract:

In the modern process industry process, DCS collects and stores a large amount of operational temporal data. If valuable operational experience and operational information can be extracted, the performance of the operating system can be greatly improved. However, operational experience is vague and cannot be quantified by value. Therefore, the operational data with time series is symbolized so that the operational experience is represented in a block form. And we propose a hierarchical clustering algorithm based on Levenshtein distance for time series. By clustering of historical operational data in the time series of variables, a variety of similar operating modes are obtained, and the process variables corresponding to the type of operation mode perform performance analysis to obtain and preserve the operational experience required in the actual work process, thereby guiding the process operation of production. In order to verify the proposed method, it is applied to the continuous multi component distillation operation process. The results show the effectiveness of the proposed method.

Key words: time series, Levenshtein distance, hierarchical clustering, operational optimization, distillation

摘要：

现代流程工业过程中，DCS采集并存储了大量的操作时序数据，若能将其中有价值的操作经验和操作信息提取出来，则可大大提高操作系统的性能。然而，操作经验概念较为模糊，无法具体量化。因此，将具有时序特征的操作数据符号化，使操作经验以区块化形式表示，并提出一种基于Levenshtein距离的时序层次凝聚聚类算法，通过对操纵变量的历史时序操作数据进行相似性搜索，进而获得多种相似的操作模式，并将每种类型的操作模式对应的过程变量进行性能分析，从而得到并保存实际工作过程中所需的操作经验，以达到生产过程操作优化的目的。为了验证所提出方法，将其用于连续组分精馏操作过程，实验结果表明所提出的基于Levenshtein距离层次聚类的操作优化方法的有效性。

关键词: 时间序列, Levenshtein距离, 层次聚类, 操作优化, 精馏

CLC Number:

TQ 028.8

Jian ZHU, Bo YANG, Yongjian WANG, Xiaojie TANG, Hongguang LI. New operation optimization method with time series based on Levenshtein distance hierarchical clustering[J]. CIESC Journal, 2019, 70(2): 581-589.

朱坚, 杨博, 王永健, 唐晓婕, 李宏光. 一种新型的基于Levenshtein距离层次聚类的时序操作优化方法[J]. 化工学报, 2019, 70(2): 581-589.

Figures/Tables 15

Fig.1 Subsequence of time series

Fig.2 Symbolic aggregate approximation

Table 1 Probability interval breakpoints

α	β ₁	β ₂	β ₃	β ₄	β ₅	β ₆	β ₇	β ₈	β ₉
3	-0.43	0.43
4	-0.67	0	0.67
5	-0.84	-0.25	0.25	0.84
6	-0.97	-0.43	0	0.43	0.97
7	-1.07	-0.57	-0.18	0.18	0.57	1.07
8	-1.05	-0.67	-0.32	0	0.32	0.67	1.15
9	-1.22	-0.76	-0.43	-0.14	0.14	0.43	0.76	1.22
10	-1.28	-0.84	-0.52	-0.25	0	0.25	0.52	0.84	1.28

Fig.3 Subsequence similarity search

Fig.4 Calculations of Levenstein distances

Table 2 LD- hierarchical agglomerative clustering

Algorithm	LD-hierarchical agglomerative
1	inputs: 样本集合Ω={S ₁,S ₂,…,S_m },聚类簇编辑距离度量函数LD,聚类簇数目k=1.
2	for j = 1,2,…,m
3	C_j = {x_j }
4	End for
5	for i = 1,2,…,m
6	for j = 1,2,…,m
7	M(i,j) = LD(C_i ,C_j );
8	M(j,i) = M(i,j)
9	End for
10	End for
11	设置当前簇数目q=m,
12	While q>k
13	找出Levenshtein距离最近的两个簇C_i ,C_j ;
14	合并C_i ,C_j ;
15	For j=j ^+1,j ^+2,…,q
16	将簇C_j 重编号成C_j _-1;
17	End for
18	删除距离矩阵M第j ^行和j ^列;
19	For j=1,2,…,q-1
20	M(i ^, j) = LD( $C i $ , C_j );
21	M(j, i ^) = M(i ^, j);
22	End for
23	q = q ^-1
24	End while
25	outputs: 簇划分C={C ₁,C ₂,…,C_k }

Table 2 LD- hierarchical agglomerative clustering

Algorithm	LD-hierarchical agglomerative
1	inputs: 样本集合Ω={S ₁,S ₂,…,S_m },聚类簇编辑距离度量函数LD,聚类簇数目k=1.
2	for j = 1,2,…,m
3	C_j = {x_j }
4	End for
5	for i = 1,2,…,m
6	for j = 1,2,…,m
7	M(i,j) = LD(C_i ,C_j );
8	M(j,i) = M(i,j)
9	End for
10	End for
11	设置当前簇数目q=m,
12	While q>k
13	找出Levenshtein距离最近的两个簇C_i ,C_j ;
14	合并C_i ,C_j ;
15	For j=j ^+1,j ^+2,…,q
16	将簇C_j 重编号成C_j _-1;
17	End for
18	删除距离矩阵M第j ^行和j ^列;
19	For j=1,2,…,q-1
20	M(i ^, j) = LD( $C i $ , C_j );
21	M(j, i ^) = M(i ^, j);
22	End for
23	q = q ^-1
24	End while
25	outputs: 簇划分C={C ₁,C ₂,…,C_k }

Fig.5 AGNES tree

Fig.6 Continuous multi-component distillation

Fig.7 Clustering results of operational modes

Fig.8 Comparison of clustering speed of LD and DTW

Fig.9 Visualization of operational modes clustering

Fig.10 Dynamic concentration curves of benzene and styrene corresponding to different operational modes

Table 3 Raw data interval breakpoints

Symbol	Breakpoint	W/(kmol/h)
a b c d e	-3	104.4
	-0.84	173.1
	-0.25	191.7
	0.25	207.6
	0.84	226.2
	3	294.9

Fig.11 Dynamic concentration curves of the benzene and styrene corresponding to operational mode A

x	——液相摩尔分数
W	——蒸汽流量，kmol/h

References 31

1	Piatetsky-Shapiro G . The data-mining industry coming of age[J]. IEEE Intelligent Systems, 1999, 14(6): 32-34.
2	Rossiter J A , Kouvaritakis B . Modelling and implicit modelling for predictive control[J]. International Journal of Control, 2001, (11): 1085-1095.
3	Favoreel W , De Moor B , Van Overschee P . Subspace state space system identification for industrial processes[J]. Journal of Process Control, 2000, (2): 149-155.
4	Braha D , Shmilovici A . Data mining source code for improving a cleaning process in the semiconductor industry[J]. IEEE Transactions on Semiconductor Manufacturing, 2002, 15(1): 91-101.
5	Dong L X , Xiao D M , Liu Y L . Rough set and radial basis function neural network based insulation data mining fault diagnosis for power transformer[J]. Journal of Harbin Institute of Technology, 2007, 14(2): 263-26.
6	Yang Q , Wang X . Challenging problems in data mining research[J]. Int. J. of Information Technology and Decision Making, 2006, 5(4): 597-604.
7	Agrawal R , Psaila G , Wimmers E , et al . Querying shapes of histories[C]//Proceeding of the 21st Int’l Conf. on Very Large Database(VLDB’95). San Francisco: Morgan Kaufmann Publishers, 1995: 502-514.
8	Keogh E , Lin J . Clustering of time-series subsequences is meaningless: implications for previous and future research[J]. Knowledge and Information Systems, 2005, 8(2): 154-177.
9	Berndt D J , James C . Using dynamic time warping to find patterns time series[C]//Proceedings of the AAAI-94 Workshop on Knowledge Discovery in Databases, Seattle, Washington: KDD workshop, 1994: 359-370.
10	Wang H , Su H , Zheng K , et al . An effectiveness study on trajectory similarity measures[C]//Proceeding of the 24th Australasian Database Conf.. Darlinghurst: Australia Computer Society, 2013: 13-22.
11	Akatsukaa S , Nodab M . Similarity analysis of sequential alarms in plant operation data by using Levenshtein distance[C]// Proceedings of the 6th International Conference on Process Systems Engineering(PSE ASIA). Kagaku: Kagaku Ronbunshu, 2013: 25-27.
12	Lin J , Keogh E , Lonardi S , et al . A symbolic representation of time series, with implications for streaming algrithms[C]// Proceedings of the ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery. USA: ACM, 2003: 2-11.
13	Keogh E , Chakrabarti K , Pazzani M , et al . Dimensionality reduction for fast similarity search in large time series databases[J]. Knowl. Inf. Syst., 2001, 3(3): 263-286.
14	Chakrabarti K , Keogh E E , Mehrotra S , et al . Locally adaptive dimensionality reduction for indexing large time series databases[J]. ACM Trans.Database Syst., 2002, (27): 188-228.
15	Goldin D Q , Kanellakis P C . On similarity queries for time series data: constraint specification and implementation[M]//International Conference on Principles and Practice of Constraint Programming. Berlin: Springer Press, 1995: 137-153.
16	Tan S C , San Lau P , Yu X W .Finding similar time series in sales transaction data[C]//International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems.Berlin: Springer International, 2015: 645-654.
17	Loh W K , Kim S W , Whang K Y .A subsequence matching algorithm that supports normalization transform in time series databases[J]. Data Mining and Knowledge Discovery, 2004, 9(1): 5-28.
18	Berndt D J , Clifford J . Using dynamic time warping to find patterns in time series[M]//KDD Workshop.Washington: KDD Press, 1994: 359-370.
19	Fu A W C , Keogh E , Lau L Y , et al . Scaling and time warping in time series querying[J]. The International Journal on Very Large Data Bases, 2008, 17(4): 899-921.
20	Bankό Z , Abonyi J . Correlation based dynamic time warping of multivariate time series[J]. Expert Systems with Applications, 2012, 39(17): 12814-12823.
21	戴东波, 汤春蕾, 熊赟 . 基于整体和局部相似性的序列聚类算法[J]. 软件学报, 2010, 21(4): 702-717.
	DAI D B , TANG C L , XIONG Y . Sequence clustering algorithm based on global and local similarity [J]. Journal of Software, 2010, 21(4): 702-717.
22	Levenshtein V . Binary codes capable of correcting deletions, insertions, and reversals[J]. Soviet Physics Doklady, 1966, 10(8): 707-710.
23	ILIOPOULOS C S , RAHMAN M S . New efficient algorithms for the LCS and constrained LCS problems[J]. Information Processing Letters, 2008, 106(1): 13-18.
24	Wagner R A , Fischer M J . The string-to-string correction problem[J]. Journal of the ACM, 1974, 21(1): 168-173.
25	Silva J D A , Hruschka E R . Extending k-means-based algorithms for evolving data streams with variable number of clusters[C]//International Conference on Machine Learning and Applications and Workshops(ICMLA). Hawaii: IEEE, 2011, 2: 14-19.
26	王勇, 唐靖, 饶勤菲, 等 . 高效率的 K-means 最佳聚类数确定算法[J]. 计算机应用, 2014, 34(5): 1331-1335.
	Wang Y , Tang J , Rao Q F , et al . High efficiency K-means optimal cluster number determination algorithm [J]. Journal of Computer Applications, 2014, 34(5): 1331-1335.
27	Celebi M E , Kingravi H A , Vela P A . A comparative study of efficient initialization methods for the k-means clustering algorithm[J]. Expert Systems with Applications, 2013, 40(1): 200-210.
28	Han J , Kamber M . Data Mining: Concepts and Techniques[M]. San Francisco: Morgan Kaufmann, 2001.
29	Narasimhan M , Jojic N , Bilmes J . Q-clustering[J]. Neural Information Processing Systems, 2005, 17: 1537-1544.
30	Li J F , Li J S , He H Q . A simple and accurate approach to hierarchical clustering[J]. Journal of Computational Information Systems, 2011, 7(7): 2577-2584.
31	Xu D , Tian Y . A comprehensive survey of clustering algrithms[J]. Ann. Data Sci., 2015, 2(2): 165-193.

Related Articles 15

[1]	Lizhi WANG, Qiancheng HANG, Yeling ZHENG, Yan DING, Jiaji CHEN, Qing YE, Jinlong LI. Separation of methyl propionate + methanol azeotrope using ionic liquid entrainers [J]. CIESC Journal, 2023, 74(9): 3731-3741.
[2]	Shanghao LIU, Shengkun JIA, Yiqing LUO, Xigang YUAN. Optimization of ternary-distillation sequence based on gradient boosting decision tree [J]. CIESC Journal, 2023, 74(5): 2075-2087.
[3]	Mujin LI, Song HU, Depan SHI, Peng ZHAO, Rui GAO, Jinlong LI. A process for offgas absorption and purification of 1,2-butylene oxide [J]. CIESC Journal, 2023, 74(4): 1607-1618.
[4]	Haiou YUAN, Fangjun YE, Shuo ZHANG, Yiqing LUO, Xigang YUAN. Synthesis of heat-integrated distillation sequences with intermediate heat exchangers [J]. CIESC Journal, 2023, 74(2): 796-806.
[5]	Guoxin SUN, Mengxuan GOU, Cheng ZHOU, Pei CHANG, Gaohong HE, Xiaobin JIANG. Membrane distillation crystallization coupling process for the treatment of high concentration Na⁺//NO $3 -$ , SO $4 2 -$ -H₂O solution [J]. CIESC Journal, 2022, 73(7): 3078-3089.
[6]	Huiying LIU, Shengkun JIA, Yiqing LUO, Xigang YUAN. Influence of vapor feed on optimal design of dividing wall column [J]. CIESC Journal, 2022, 73(7): 3090-3098.
[7]	Xingwei LIU, Shengkun JIA, Yiqing LUO, Xigang YUAN. Optimization of distillation column based on trust region algorithm [J]. CIESC Journal, 2022, 73(5): 2031-2038.
[8]	Xin LIU, Yang PAN, Gongping LIU, Jing FANG, Chunli LI, Hao LI. Study on the process of preliminary separation of Fischer-Tropsch synthetic water by coupling pervaporation and dividing wall column distillation [J]. CIESC Journal, 2022, 73(5): 2020-2030.
[9]	Wenting DUAN, Siyue REN, Xiao FENG, Yufei WANG. Distillation column pressure optimization integrated with the heat exchanger network [J]. CIESC Journal, 2022, 73(5): 2052-2059.
[10]	Xiaoqing SHI, Weixuan ZHU, Haotian YE, Zhizhong HAN, Hongguang DONG. Pretreatment process simulation and multi-objective optimization of C5 by reactive dividing wall column [J]. CIESC Journal, 2022, 73(3): 1246-1255.
[11]	Yunfei WU, Xiaoli LUAN, Fei LIU. Near-infrared spectroscopy online detecting for 2,6-dimethylphenol purity based on transfer learning [J]. CIESC Journal, 2022, 73(2): 782-791.
[12]	Tianyuan WANG, Chunbo CHEN, Lin SUN, Xionglin LUO. Optimal design of slow-time-varying system for multi-effect distillation desalination based on full-cycle slow fouling [J]. CIESC Journal, 2022, 73(2): 759-769.
[13]	Runtao WANG, Zejun LUO, Chu WANG, Xifeng ZHU. Synergistic effect during catalytic co-pyrolysis of bio-oil distillation residue and waste plastic [J]. CIESC Journal, 2022, 73(11): 5088-5097.
[14]	Xu LIU, Songlin XU, Yanfei WANG. Global multi-objective optimization of trimethyl orthoformate-acetic acid extractive distillation [J]. CIESC Journal, 2022, 73(10): 4518-4526.
[15]	XU Jianwei, LIANG Yingzong, LUO Xianglong, CHEN Jianyong, YANG Zhi, CHEN Ying. Integration and analysis of PRICO-membrane distillation seawater desalination system [J]. CIESC Journal, 2021, 72(S1): 437-444.