基于混合型判别分析的工业过程监控及故障诊断

陈晓露; 王瑞璇; 王晶; 周靖林

doi:10.16383/j.aas.c180089

基于混合型判别分析的工业过程监控及故障诊断

doi: 10.16383/j.aas.c180089

陈晓露^1,,
王瑞璇^1,,
王晶^1, ,,
周靖林^1,

1.
北京化工大学信息科学与技术学院北京 100029

基金项目:

国家自然科学基金 61573050

国家自然科学基金 61473025

东北大学流程工业综合自动化国家重点实验室开放课题基金 PAL-N201702

详细信息

作者简介:
陈晓露  北京化工大学信息科学与技术学院控制科学与工程专业博士研究生.主要研究方向复杂工业过程的建模与故障诊断, 数据因果关系分析和智能学习算法. E-mail: 18810493810@163.com

王瑞璇  北京化工大学信息科学与技术学院控制工程专业硕士研究生.主要研究方向为复杂工业过程的过程监控和故障诊断.E-mail: wangruixuan11@126.com

周靖林  北京化工大学信息科学与技术学院教授. 1999年获得了大庆石油学院的工程学士学位, 2002年获得了长沙湖南大学硕士学位, 2005年获得了中国科学院自动化研究所博士学位.英国谢菲尔德大学自动控制与系统工程系的学者.主要研究内容为随机分布控制, 故障检测与诊断, 变结构控制及其应用. E-mail: jinglinzhou@mail.buct.edu.cn

通讯作者:
王晶北京化工大学信息科学与技术学院教授. 1994年和1998年分别获得了东北大学自动化专业的学士学位和控制理论与控制工程专业博士学位. 2014年在美国特拉华大学担任访问教授.主要研究方向为非线性、多变量、受约束的工业过程的先进控制方法的应用, 复杂的工业过程的建模, 优化和控制, 化学反应器中聚合物微观质量的非线性模型控制, 过程监控和复杂工业过程的故障诊断.本文通信作者.E-mail: jwang@mail.buct.edu.cn

计量
- 文章访问数: 1769
- HTML全文浏览量: 239
- PDF下载量: 330
- 被引次数: 0
出版历程
- 收稿日期: 2018-02-06
- 录用日期: 2018-10-26
- 刊出日期: 2020-08-26

Industrial Process Monitoring and Fault Diagnosis Based on Hybrid Discriminant Analysis

1.
College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029

Funds:

National Natural Science Foundation of China 61573050

National Natural Science Foundation of China 61473025

The Open-project Grant Funded by the State Key Laboratory of Synthetical Automation for Process Industry at the Northeastern University PAL-N201702

More Information

Author Bio:
CHEN Xiao-Lu  Ph.D. candidate in control science and engineering at the College of Information Science and Technology, Beijing University of Chemical Technology. Her research interest covers the modeling and fault diagnosis of complex industrial processes, data causality analysis and intelligent learning algorithm

WANG Rui-Xuan  Master student in control engineering at the College of Information Science and Technology, Beijing University of Chemical Technology. Her research interest covers the process monitoring and fault diagnosis of the complex industrial process

ZHOU Jing-Lin  Professor at the College of Information Science and Technology, Beijing University of Chemical Technology. He received his bachelor, master and Ph.D. degrees from Daqing Petroleum Institute, Hunan University, and the Institute of Automation, Chinese Academy of Sciences, in 1999, 2002, and 2005, respectively. He was an academic visitor in the Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, U.K. His research interest covers stochastic distribution control, fault detection and diagnosis, variable structure control and their applications

Corresponding author: WANG Jing Professor at the College of Information Science and Technology, Beijing University of Chemical Technology. She received bachelor degree in industry automation, the Ph.D. degree in control theory and control engineering from the Northeastern University, in 1994 and 1998, respectively. She was a visiting professor at the University of Delaware, USA in 2014. Her research interest covers orient, application of advanced control schemes to nonlinear, multivariable, constrained industrial processes, modeling, optimization and control for complex industrial process, nonlinear model-based control of polymer microscopic quality in chemical reactor, process monitoring and fault diagnosis for complex industrial process. Corresponding author of this paper

摘要

摘要: 工业过程数据具有规模性大、复杂性高、变量多、关联性强等特点.如何从数据出发准确并快速地发现故障并处理, 保证过程高效运行意义重大.本文针对复杂的工业过程, 提出了一种多方法结合的混合型过程监控与故障诊断方法, 完成数据分类, 构建故障模型库, 故障在线诊断及可视化相关处理.首先通过常规主成分分析(Principal component analysis, PCA)方法对历史数据进行初筛, 区分出正常和故障信息, 然后利用聚类方法对故障数据集进行分类, 接着利用局部线性指数判别分析方法(Local linear exponential discriminant analysis, LLEDA)建立故障模型库进而进行故障诊断.本文将基于监督学习的LLEDA方法拓展到无监督学习, 便于复杂工业大量无标签数据的处理.最后利用典型的田纳西伊士曼(Tennessee Eastman, TE)过程对所提出的方法进行有效性验证.
- 复杂工业过程 /
- 混合型故障诊断 /
- 局部线性指数判别分析 /
- 可视化
Abstract: Industrial process data has the characteristics of large scale, high complexity, multivariable and strong correlation. There is great signiflcance on how to flnd out and deal with the fault from data accurately and quickly, which can help ensure the e–cient operation of the process. The paper proposed a hybrid multi-method process monitoring and fault diagnosis framework for the complex industrial process. The framework include the data classiflcation, model library establishment, timely diagnosis. Firstly, the historical data is simply screened by principal component analysis (PCA) methods to distinguish normal and fault information. Then the clustering method is used to classify the fault data set, and the fault model libraries are established by local linear exponential discriminant analysis (LLEDA) method. Finally, the fault diagnosis is carried out. The LLEDA method based on supervised learning is extended to unsupervised learning, which facilitates the processing of a large number of unlabeled data in complex industries. Finally, a typical Tennessee Eastman process is used to verify the efiectiveness of the proposed method.
- Industrial process /
- hybrid fault diagnosis /
- local linear exponential discriminant analysis (LLEDA) /
- visualization
Recommended by Associate Editor MU Chao-Xu
注释:

1) 本文责任编委穆朝絮

HTML全文

图 1 混合型故障检测和诊断方法

Fig. 1 Hybrid fault detection and diagnostic framework

下载: 全尺寸图片幻灯片

图 2 混合型故障检测和诊断信息流程

Fig. 2 The flow diagram of Hybrid fault detection and diagnostic information

下载: 全尺寸图片幻灯片

图 3 TE过程流程图

Fig. 3 The flow diagram of TE process

下载: 全尺寸图片幻灯片

图 4 基于PCA的故障检测图

Fig. 4 The fault detection diagram based on PCA

下载: 全尺寸图片幻灯片

图 5 层次聚类分析

Fig. 5 Hierarchical cluster analysis

下载: 全尺寸图片幻灯片

图 6 故障数据的平行坐标可视化图

Fig. 6 Parallel coordinate visualization of fault data

下载: 全尺寸图片幻灯片

图 7 LLEDA方法中邻近点个数对识别率的影响

Fig. 7 The influence of the neighboring points's number on recognition rate in LLEDA method

下载: 全尺寸图片幻灯片

图 8 FDA、LLE + FDA和LLEDA方法下不同特征矢量对应的故障4, 8和13的识别率

Fig. 8 Recognition rate of fault 4, 8 and 13 corresponding to different eigenvectors under the FDA, LLE + FDA and LLEDA methods

下载: 全尺寸图片幻灯片

图 9 在EDA和LLEDA方法下故障数据的投影

Fig. 9 Projection of fault data under EDA and LLEDA methods

下载: 全尺寸图片幻灯片

图 10 LLEDA方法下故障4, 8和13的诊断结果

Fig. 10 Diagnostic results of fault 4, 8 and 13 under the LLEDA method

下载: 全尺寸图片幻灯片

表 1 TE故障汇总

Table 1 TE fault summary

编号	描述	类型
IDV (0)	正常操作	-
IDV (1)	A/C进料比率, B成分不变	阶跃
IDV (2)	B成分, A/C进料比不变	阶跃
IDV (3)	D的进口温度	阶跃
IDV (4)	反应器冷却水的入口温度	阶跃
IDV (5)	冷凝器冷却水的入口温度	阶跃
IDV (6)	A进料损失	阶跃
IDV (7)	C存在压力损失-可用性降低	阶跃
IDV (8)	A、B、C进料成分	随机变量
IDV (9)	D的进料温度	随机变量
IDV (10)	C的进料温度	随机变量
IDV (11)	反应器冷却水的入口温度	随机变量
IDV (12)	冷凝器冷却水的入口温度	随机变量
IDV (13)	反应动态	慢漂移
IDV (14)	反应器冷却水阀门	粘住
IDV (15)	冷凝器冷却水阀门	粘住
IDV (16)	未知	未知
IDV (17)	未知	未知
IDV (18)	未知	未知
IDV (19)	未知	未知
IDV (20)	未知	未知
IDV (21)	阀固定在稳态位置	未知的恒定位置

下载: 导出CSV

表 2 基于PCA方法的故障识别率

Table 2 Fault recognition rate based on PCA method

故障识别率	故障1	故障2	故障3	故障4	故障5	故障6	故障7	故障8	故障9	故障10	故障11	故障12	故障13	故障14	故障15	故障16	故障17	故障18	故障19	故障20	故障21
T²	0.5212	0.995	0.9825	0.0225	0.41	0.2625	0.99	1	0.975	0.0362	0.4163	0.9875	0.9513	0.9988	0.0488	0.2325	0.8013	0.8912	0.0675	0.3738	0.3775
SPE	0.8163	0.9988	0.9925	0.2675	1	0.5025	1	1	0.9825	0.235	0.7638	0.99	0.9625	1	0.2625	0.6937	0.975	0.9375	0.5913	0.735	0.6687

下载: 导出CSV

表 3 不同方法下故障4, 8和13的识别率

Table 3 Recognition rate of fault 4, 8 and 13 under different methods

特征向量数	识别率	FDA	LLE + EDA	LLEDA
2	Fault 8	0.525	0.675	0.85
	Fault 4	1	1	1
	Fault 13	0.2275	0.37	0.265
3	Fault 8	0.525	0.67	0.955
	Fault 4	1	1	1
	Fault 13	0.215	0.375	0.125
4	Fault 8	0.5475	0.66	0.945
	Fault 4	1	1	1
	Fault 13	0.225	0.365	0.4
5	Fault 8	0.585	0.655	0.93
	Fault 4	1	1	1
	Fault 13	0.585	0.655	0.93
6	Fault 8	0.5925	0.68	0.9025
	Fault 4	1	1	1
	Fault 13	0.2525	0.345	0.5725
7	Fault 8	0.605	0.6475	0.8875
	Fault 4	1	1	1
	Fault 13	0.265	0.3925	0.6025
8	Fault 8	0.615	0.6775	0.8775
	Fault 4	1	1	1
	Fault 13	0.2475	0.375	0.62
9	Fault 8	0.6525	0.675	0.8925
	Fault 4	1	1	1
	Fault 13	0.2425	0.255	0.615
10	Fault 8	0.6625	0.7175	0.9125
	Fault 4	1	1	1
	Fault 13	0.26	0.2325	0.7325

下载: 导出CSV

参考文献(44)

[1]	Ge Z Q, Song Z H, Gao F R. Review of recent research on data-based process monitoring. Industrial & Engineering Chemistry Research, 2013, 52(10): 3543-3562 http://cn.bing.com/academic/profile?id=4e283210b5bf9dbde9c5dbb2fd6682d6&encoded=0&v=paper_preview&mkt=zh-cn
[2]	Yin S, Ding S X, Xie X C, Luo H. A review on basic data-driven approaches for industrial process monitoring. IEEE Transactions on Industrial Electronics, 2014, 61(11): 6418-6428 doi: 10.1109/TIE.2014.2301773
[3]	Yin S, Gao H J, Kaynak O. Data-driven control and process monitoring for industrial applications-part Ⅰ. IEEE Transactions on Industrial Electronics, 2014, 61(11): 6356-6359 doi: 10.1109/TIE.2014.2312885
[4]	Yin S, Gao H J, Kaynak O. Data-driven control and process monitoring for industrial applications-Part Ⅱ. IEEE Transactions on Industrial Electronics, 2015, 62(1): 583-586
[5]	文成林, 吕菲亚, 包哲静, 刘妹琴.基于数据驱动的微小故障诊断方法综述.自动化学报, 2016, 42(9): 1285-1299 doi: 10.16383/j.aas.2016.c160105 Wen Cheng-Lin, Lv Fei-Ya, Bao Zhe-Jing, Liu Mei-Qin. A review of data driven-based incipient fault diagnosis. Acta Automatica Sinica, 2016, 42(9): 1285-1299 doi: 10.16383/j.aas.2016.c160105
[6]	Yin S, Li X W, Gao H J, Kaynak O. Data-based techniques focused on modern industry: an overview. IEEE Transactions on Industrial Electronics, 2015, 62(1): 657-667 http://cn.bing.com/academic/profile?id=8bda8b6d4f3f65fc737e0b39f6cf54e2&encoded=0&v=paper_preview&mkt=zh-cn
[7]	Jiang Y C, Yin S. Recursive total principle component regression based fault detection and its application to vehicular cyber-physical systems. IEEE Transactions on Industrial Informatics, 2018, 14(4): 1415-1423 doi: 10.1109/TII.2017.2752709
[8]	Zhang K, Peng K X, Shardt Y A W. A comparison of different statistics for detecting multiplicative faults in multivariate statistics-based fault detection approaches. IEEE Access, 2018, 6: 43808-43823 doi: 10.1109/ACCESS.2018.2862940
[9]	Qi X, Luo R Y. Sparse principal component analysis in hilbert space. Scandinavian Journal of Statistics, 2015, 42(1): 270-289 doi: 10.1111/sjos.12106
[10]	Le Thi H A, Phan D N. DC programming and DCA for sparse Fisher linear discriminant analysis. Neural Computing and Applications, 2017, 28(9): 2809-2822 doi: 10.1007/s00521-016-2216-9
[11]	Zheng J, Song Z. Semisupervised learning for probabilistic partial least aquares regression model and soft sensor application. Journal of Process Control, 2018, 64: 123-131 doi: 10.1016/j.jprocont.2018.01.008
[12]	Ge Z Q, Xie L, Kruger U, Song Z H. Local ICA for multivariate statistical fault diagnosis in systems with unknown signal and error distributions. AIChE Journal, 2012, 58(8): 2357-2372 doi: 10.1002/aic.12760
[13]	曹玉苹, 黄琳哲, 田学民.一种基于DIOCVA的过程监控方法.自动化学报, 2015, 41(12): 2072-2080 doi: 10.16383/j.aas.2015.c150058 Cao Yu-Ping, Huang Lin-Zhe, Tian Xue-Min. A process monitoring method using dynamic input-output canonical variate analysis. Acta Automatica Sinica, 2015, 41(12): 2072-2080 doi: 10.16383/j.aas.2015.c150058
[14]	Ming A B, Zhang W, Qin Z Y, Chu F L. Fault feature extraction and enhancement of rolling element bearing in varying speed condition. Mechanical Systems and Signal Processing, 2016, 76-77: 367-379 doi: 10.1016/j.ymssp.2016.02.021
[15]	Yu J. Nonlinear bioprocess monitoring using multiway kernel localized fisher discriminant analysis. Industrial & Engineering Chemistry Research, 2011, 50(6): 3390-3402 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=8da00c7b51a00f2a44fa5711f9bafe08
[16]	王晶, 刘莉, 曹柳林, 靳其兵.基于核Fisher包络分析的间歇过程故障诊断.化工学报, 2014, 65(4): 1317-1326 doi: 10.3969/j.issn.0438-1157.2014.04.023 Wang Jing, Liu Li, Cao Liu-Lin, Jin Qi-Bing. Fault diagnosis based on kernel Fisher envelope surface for batch processes. CIESC Journal, 2014, 65(4): 1317-1326 doi: 10.3969/j.issn.0438-1157.2014.04.023
[17]	Zhang J P, Li S Z, Wang J. Manifold learning and applications in recognition. Intelligent Multimedia Processing with Soft Computing. Berlin, Heidelberg: Springer, 2005. 281-300
[18]	Zhong B, Wang J, Zhou J L, Wu H Y, Jin Q B. Quality-related statistical process monitoring method based on global and local partial least-squares projection. Industrial & Engineering Chemistry Research, 2016, 55(6): 1609-1622 http://cn.bing.com/academic/profile?id=ca4efe313af1ff8f640505725bbaeabc&encoded=0&v=paper_preview&mkt=zh-cn
[19]	Luo L J. Process monitoring with global-local preserving projections. Industrial & Engineering Chemistry Research, 2014, 53(18): 7696-7705 http://cn.bing.com/academic/profile?id=a4d644efa75500fa9e28a52cbae466bf&encoded=0&v=paper_preview&mkt=zh-cn
[20]	苏祖强, 汤宝平, 邓蕾, 尹爱军.有监督LLTSA特征约简旋转机械故障诊断.仪器仪表学报, 2014, 35(8): 1766-1771 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yqyb201408012 Su Zu-Qiang, Tang Bao-Ping, Deng Lei, Yin Ai-Jun. Rotating machinery fault diagnosis with supervised-linear local tangent space alignment for dimension reduction. Chinese Journal of Scientific Instrument, 2014, 35(8): 1766-1771 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yqyb201408012
[21]	Wang J, Zhong B, Zhou J L. Quality-relevant fault monitoring based on locality-preserving partial least-squares statistical models. Industrial & Engineering Chemistry Research, 2017, 56(24): 7009-7020 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=e8e68686669984bd3be064894dda9d73
[22]	Liu Z, Wang L Y, Zhang Y, Chen C L P. A SVM controller for the stable walking of biped robots based on small sample sizes. Applied Soft Computing, 2016, 38: 738-753 doi: 10.1016/j.asoc.2015.10.029
[23]	阚英男.基于网格近似法的数控机床贝叶斯可靠性评估研究[博士学位论文], 吉林大学, 中国, 2015 Kan Ying-Nan. Research on Bayesian Reliability Assessment for NC Machine Tools based on Grid Approximation[Ph. D. Dissertation], Jilin University, China, 2015
[24]	赵孝礼, 赵荣珍, 孙业北, 何敬举.基于正则化核最大边界投影维数约简的滚动轴承故障诊断.振动与冲击, 2017, 36(14): 104-110 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zdycj201714017 Zhao Xiao-Li, Zhao Rong-Zhen, Sun Ye-Bei, He Jing-Ju. Fault diagnosis of rolling bearings based on the dimension reduction using the regularized kernel maximum margin projection. Journal of Vibration and Shock, 2017, 36(14): 104-110 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zdycj201714017
[25]	Adil M, Abid M, Khan A Q, Mustafa G, Ahmed N. Exponential discriminant analysis for fault diagnosis. Neurocomputing, 2016, 171: 1344-1353 doi: 10.1016/j.neucom.2015.07.099
[26]	Wang R X, Wang J, Zhou J L, Wu H Y. An improved kernel exponential discriminant analysis for fault identification of batch process. In: Proceedings of the 6th Data Driven Control and Learning Systems. Chongqing, China: IEEE, 2017. 16-21
[27]	Han J W, Kamber M, Pei J. Data Mining: Concepts and Techniques (Third Edition). San Francisco: Morgan Kaufmann, 2011. 1-18
[28]	Chapelle O. Training a support vector machine in the primal. Neural Computation, 2007, 19(5): 1155-1178 doi: 10.1162/neco.2007.19.5.1155
[29]	Boutros T, Liang M. Detection and diagnosis of bearing and cutting tool faults using hidden Markov models. Mechanical Systems and Signal Processing, 2011, 25(6): 2102-2124 doi: 10.1016/j.ymssp.2011.01.013
[30]	Du J, Wang S P, Zhang H Y. Layered clustering multi-fault diagnosis for hydraulic piston pump. Mechanical Systems and Signal Processing, 2013, 36(2): 487-504 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=bcf4dcb0467db1182112f614189b8570
[31]	Yiakopoulos C T, Gryllias K C, Antoniadis I A. Rolling element bearing fault detection in industrial environments based on a K-means clustering approach. Expert Systems with Applications, 2011, 38(3): 2888-2911 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=2f731db23bb777aaf856a77635f47169
[32]	Cheng G, Cheng Y L, Shen L H, Qiu J B, Zhang S. Gear fault identification based on Hilbert-Huang transform and SOM neural network. Measurement, 2013, 46(3): 1137-1146 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=0af6ae4339a6d5b13f4c46596315b72c
[33]	熊浩, 张晓星, 廖瑞金, 常涛, 孙才新.基于动态聚类的电力变压器故障诊断.仪器仪表学报, 2007, 28(3): 456-459 doi: 10.3321/j.issn:0254-3087.2007.03.014 Xiong Hao, Zhang Xiao-Xing, Liao Rui-Jin, Chang Tao, Sun Cai-Xin. Fault diagnosis of power transformer using dynamic clustering algorithm. Chinese Journal of Scientific Instrument, 2007, 28(3): 456-459 doi: 10.3321/j.issn:0254-3087.2007.03.014
[34]	范志鹏.基于小波与聚类分析相结合的旋转机械的故障诊断[硕士学位论文], 江西理工大学, 中国, 2011 Fang Zhi-Peng. Fault Diagnosis of Rotating Machinery Based on Wavelet and Clustering Analysis[Master Thesis], Jiangxi University of Science and Technology, China, 2011
[35]	高宇.基于SOM神经网络的风电电子装置故障诊断.电力系统及其自动化学报, 2010, 22(3): 142-145 doi: 10.3969/j.issn.1003-8930.2010.03.026 Gao Yu. Fault diagnosis of wind turbine power electronic devices based on SOM neural network. Proceedings of the CSU-EPSA, 2010, 22(3): 142-145 doi: 10.3969/j.issn.1003-8930.2010.03.026
[36]	Wang R X, Wang J, Zhou J L, Wu H Y. Fault diagnosis based on the integration of exponential discriminant analysis and local linear embedding. The Canadian Journal of Chemical Engineering, 2018, 96(2): 463-483 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1002/cjce.22921
[37]	Hu Z F, Pan G, Wang Y M, Wu Z H. Sparse principal component analysis via rotation and truncation. IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(4): 875-890 http://cn.bing.com/academic/profile?id=707be0cd4a6c10ba73e8c3866b2d0b3d&encoded=0&v=paper_preview&mkt=zh-cn
[38]	Saxena A, Prasad M, Gupta A, Bharill N, Patel O P, Tiwari A, et al. A review of clustering techniques and developments. Neurocomputing, 2017, 267: 664-681 doi: 10.1016/j.neucom.2017.06.053
[39]	Roweis S T, Saul L K. Nonlinear dimensionality reduction by locally linear embedding. Science, 2000, 290(5500): 2323-2326 doi: 10.1126/science.290.5500.2323
[40]	Zhao H, Liu J W, Dong W, Sun X Y, Ji Y D. An improved case-based reasoning method and its application on fault diagnosis of Tennessee Eastman process. Neurocomputing, 2017, 249: 266-276 doi: 10.1016/j.neucom.2017.04.022
[41]	Yin S, Zhu X P, Kaynak O. Improved PLS focused on key-performance-indicator-related fault diagnosis. IEEE Transactions on Industrial Electronics, 2015, 62(3): 1651-1658 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f7d63a5b33852ea6ad7ed8c01346803e
[42]	惠振东. TE化工过程优化控制仿真系统研究[硕士学位论文], 北方工业大学, 中国, 2017 Hui Zhen-Dong. Research on Simulation System of TE Chemical Process Optimization Control[Master Thesis], North China University of Technology, China, 2017
[43]	Wang Y Q, Zhang J P, Zeng F M, Wang N, Chen X P, Zhang B, et al. "Learning" can improve the blood glucose control performance for type 1 diabetes mellitus. Diabetes Technology & Therapeutics, 2017, 19(1): 41-48 http://cn.bing.com/academic/profile?id=17740f9aa67710d280b753d8599d45e9&encoded=0&v=paper_preview&mkt=zh-cn
[44]	Zhao D, Shen D, Wang Y Q. Fault diagnosis and compensation for two-dimensional discrete time systems with sensor faults and time-varying delays. International Journal of Robust and Nonlinear Control, 2017, 27(16): 3296-3320 doi: 10.1002/rnc.3742