An extended logical analysis of data approach to fault detections of industrial hybrid systems

doi:10.11949/0438-1157.20200328

Abstract

Abstract:

It is difficult to deal with industrial hybrid systems involving both continuous and discrete variables using conventional data-driven fault detection methods. While logical analysis of data (LAD) methods are able to effectively explore hidden rules in discrete and continuous data by means of logical analysis for variable associations. However, conventional LAD has the problem of losing trend change information when extracting features of continuous variables. And when processing industrial data with high-dimensional, multivariate features, it will cause a lot of redundancy in the extracted rules. Motivated by these observations, this paper presents an extended logical analysis of data (ELAD) approach to fault detections of industrial hybrid systems. Therein, correlated variables are selected according to the association degree with key variables and additive variable trends are employed to characterize process status changes, creating an explicable fault detection model. The proposed method is applied to the steam drum process of an industrial coal gasification plant in detecting the influence of key hybrid variables on the fault of steam drum level. The results verify the feasibility and effectiveness of the contribution.

Key words: logical analysis of data, hybrid process, interpretable rules, grey association degree, fault detection

摘要：

常规的数据驱动故障检测方法难以处理同时包含连续和离散变量的工业混杂系统，数据逻辑分析（logical analysis of data， LAD）方法通过对历史数据中变量组合的逻辑分析，能够有效地挖掘离散和连续变量数据中存在的隐含规则。然而，常规的LAD在提取连续变量特征时存在对趋势变化信息丢失的问题，并且在处理具有高维度、多变量特征的工业数据时会导致提取的规则存在大量冗余。为此，本文提出一种基于扩展数据逻辑分析（extended logical analysis of data， ELAD）的工业混杂系统故障检测方法，根据与关键变量的关联度选取相关变量，增加变量的趋势信息以进行过程状态变化的表征，生成可解释的故障检测模型。应用于工业煤气化汽包过程，有效地检测了关键混杂变量对汽包液位故障的影响，实验结果验证了所提方法的可行性和有效性。

关键词: 数据逻辑分析, 混杂系统, 可解释规则, 灰色关联度, 故障检测

CLC Number:

TQ 028.8

Zhongjian SUN,Bo YANG,Chu QI,Hongguang LI. An extended logical analysis of data approach to fault detections of industrial hybrid systems[J]. CIESC Journal, 2020, 71(11): 5237-5245.

孙中建,杨博,齐楚,李宏光. 面向工业混杂系统故障检测的扩展数据逻辑分析方法[J]. 化工学报, 2020, 71(11): 5237-5245.

Figures/Tables 15

Table 1 Logical analysis of data algorithms

Step	Algorithm
1	Input: $B +, B - ? 0,1 n, P, C 0 = ?, ? D$
2	for d=1,2,…,D
3	if d<D, C_d=0, end if
4	for T through C_d_-1
5	p= maximum index of T;
6	for s=p+1,p+2,…,n
7	for l_new through {l_s, l_s′}
8	T′=T\|\|l_new
9	for i=1,2,…,d
10	$T ″$ =remove i^th literal from T′;
11	if $T ″ ? C d - 1$ , go to 19, end if
12	end for
13	if $1 ∈ T' (B +)$
14	if $1 ? T' (B -)$
15	P=P∪{T′};
16	else if d<D
17	C_d=C_d∪{T′};
18	end if
19	end if
20	end for
21	end for
22	end for
23	end for
24	Output: P

Table 1 Logical analysis of data algorithms

Step	Algorithm
1	Input: $B +, B - ? 0,1 n, P, C 0 = ?, ? D$
2	for d=1,2,…,D
3	if d<D, C_d=0, end if
4	for T through C_d_-1
5	p= maximum index of T;
6	for s=p+1,p+2,…,n
7	for l_new through {l_s, l_s′}
8	T′=T\|\|l_new
9	for i=1,2,…,d
10	$T ″$ =remove i^th literal from T′;
11	if $T ″ ? C d - 1$ , go to 19, end if
12	end for
13	if $1 ∈ T' (B +)$
14	if $1 ? T' (B -)$
15	P=P∪{T′};
16	else if d<D
17	C_d=C_d∪{T′};
18	end if
19	end if
20	end for
21	end for
22	end for
23	end for
24	Output: P

Fig.1 The flow chart of ELAD

Fig.2 The unit window and slide length

Fig.3 Patterns in selecting

Fig.4 The steam drum process diagram

Table 2 Correlated variables and its description

变量	描述	变量	描述
F₁	汽包补水流量	F₃	汽包排污流量
L₁	汽包液位	DV	补水流量阀
P₁	汽包压力	T₂	汽包出口蒸汽温度
T₁	锅炉水补水温度	T₃	去汽化炉循环水温度
D₁	汽包循环水密度	F₄	去汽化炉循环水流量
F₂	汽包出口蒸汽流量	F₅	去汽化炉顶部盘管循环水流量

Fig.5 The grey association analysis between variables

Table 3 Correlated variable data

补水流量F₁	汽包液位L₁	汽包压力P₁	…	补水温度T₁	循环水流量F₄	补水流量阀DV	状态
9.80	71.09	4.19	…	176.82	20.19	1	正常
9.80	71.10	4.19	…	176.81	20.20	1	正常
9.78	71.16	4.19	…	176.80	20.20	1	故障
9.75	71.18	4.19	…	176.79	20.18	1	故障
…	…	…	…	…	…	…	…
0	71.04	4.22	…	171.39	20.23	0	正常
0	71.04	4.22	…	171.39	20.21	0	正常
…	…	…	…	…	…	…	…
8.62	62.94	4.17	…	178.29	20.12	1	故障
8.70	62.95	4.17	…	178.29	20.16	1	故障

Fig.6 Visualizations of the dataset

Table 4 Number of training and testing datasets

状态	训练集	测试集	总计
正常	7633	1837	9470
故障	367	163	530
总计	8000	2000	10000

Table 5 Coverages of events

基本事件	基本事件含义	覆盖率
P(1)	DV=1	1.000
P(2)	k=1	0.790
P(3)	L₁>71.105	0.757
P(4)	L₁′>0.039	0.995
P(5)	F₁>3.423	0.847
P(6)	F₁′≤0.027	0.251
P(7)	D₁′≤0.0093	0.362
P(8)	F₁>3.1788	0.981
P(9)	L₁′>0.0987	0.460
P(10)	F₁′>1.5455	0.038
P(11)	L₁≤63.005	0.243
P(12)	L₁′>0.0701	0.790
P(13)	T₂′>81.987	0.240
P(14)	F₄≤20.225	0.619
P(15)	F₁>6.2149	0.594
P(16)	L₁′>0.1093	0.305
P(17)	T₂′>99.6787	0.046

Table 6 Coverages of rules

规则	基本事件	基本事件含义	覆盖率
R(1)	P(1)∩P(2)∩P(3)∩P(4)	DV=1, k=1, L₁>71.105, L₁′>0.039	0.752
R(2)	P(3)∩P(5)∩P(6)∩P(7)	L₁>71.105, F₁>3.423, F₁′≤0.027, D₁′≤0.0093	0.074
R(3)	P(1)∩P(2)∩P(3)∩P(8)	DV=1, k=1, L₁>71.105, F₁>3.1788	0.738
R(4)	P(1)∩P(2)∩P(9)∩P(10)	DV=1, k=1, L₁′>0.0987, F₁′>1.5455	0.019
R(5)	P(11)∩P(12)	L₁≤63.005, L₁′>0.0701	0.237
R(6)	P(13)∩P(14)	T₂′>81.987, F₄≤20.225	0.065
R(7)	P(11)∩P(15)	L₁≤63.005, F₁>6.2149	0.237
R(8)	P(11)∩0P(16)∩P(17)	L₁≤63.005, L₁′>0.1093, T₂′>99.6787	0.022

Table 7 Fault Probabilities

规则		模式		故障
R₁	0.039	M₁	0.039	P=0.053
R₂	0.004	M₁	0.039
R₃	0.037	M₂	0.039
R₄	0.002	M₂	0.039
R₅	0.011	M₃	0.014
R₆	0.002	M₃	0.014
R₇	0.014	M₄	0.014
R₈	0.001	M₄	0.014

Table 8 Accuracies of patterns

检测模式	准确率/%
M₁	99.9
M₂	100
M₃	99.4
M₄	99.7

Table 9 Performance comparisons with traditional classifiers

方法	平均规则数目	准确率/%
LAD	12	97.3
ELAD	4	99.8
kNN	－	86.8
SVM	－	96.4

References 39

1	Zhou G, Biswas G, Feng W. A comprehensive diagnosis of hybrid systems for discrete and parametric faults using hybrid I/O automata[J]. Ifac Papersonline, 2015, 48(21): 143-149.
2	Barton P I, Lee C K. Modeling, simulation, sensitivity analysis, and optimization of hybrid systems[J]. ACM Transactions on Modeling and Computer Simulation, 2002, 12(4): 256-289.
3	Maurya M R, Rengaswamy R, Venkatasubramanian V. A signed directed graph and qualitative trend analysis-based framework for incipient fault diagnosis[J]. Chemical Engineering Research & Design, 2007, 85(10): 1407-1422.
4	李晗, 萧德云. 基于数据驱动的故障诊断方法综述[J]. 控制与决策, 2011, 26(1): 1-9, 16.
	Li H, Xiao D Y. Survey on data driven fault diagnosis methods[J]. Journal of Control and Decision, 2011, 26(1): 1-9, 16.
5	Ming L, Zhao J. Review on chemical process fault detection and diagnosis[C]//6th International Symposium on Advanced Control of Industrial Processes, New Jersey: IEEE, 2017: 457-462.
6	Bezerra C G, Costa B S J, Guedes L A, et al. An evolving approach to unsupervised and Real-Time fault detection in industrial processes[J]. Expert Systems with Applications, 2016, 63: 134-144.
7	Sadeghi R, Hamidzadeh J. Automatic support vector data description[J]. Soft Computing, 2018, 22(1): 147-158.
8	Yu J, Yan X. Whole process monitoring based on unstable neuron output information in hidden layers of deep belief network[J]. IEEE Transactions on Cybernetics, 2019, PP(99): 1-10.
9	Heracleous C, Panayiotou C G, Polycarpou M M. Fault diagnosis of uncertain hybrid systems[J]. IFAC-PapersOnLine, 2018, 51(24): 123-130.
10	Lebbal M E H, Chafouk H, Hoblos G, et al. Faults detection and isolation for non linear hybrid systems[J]. IFAC Proceedings Volumes, 2006, 39(13): 986-991.
11	Krell M M, Straube S. Backtransformation: a new representation of data processing chains with a scalar decision function[J]. Advances in Data Analysis and Classification, 2017, 11(2): 415-439.
12	Ragab A, El-Koujok M, Amazouz M, et al. Fault detection and diagnosis in the Tennessee Eastman process using interpretable knowledge discovery[C]// 2017 Annual Reliability and Maintainability Symposium, New Jersey: IEEE, 2017: 1-7.
13	Lopez-Soto D, Yacout S, Angel-Bello F. Root cause analysis of familiarity biases in classification of inventory items based on logical patterns recognition[J]. Computers and Industrial Engineering, 2016, 93(C): 121-130.
14	Kogan A, Lejeune M A. Combinatorial methods for constructing credit risk ratings[M]// Lee C F, Lee J. Handbook of Financial Econometrics and Statistics. New York: Springer, 2015: 439-483.
15	Kronek L P, Reddy A A. Logical analysis of survival data: prognostic survival models by detecting high-degree interactions in right-censored data[J]. Bioinformatics, 2008, 24(16): i248-i253.
16	Mortada M A, Yacout S, Lakis A. Fault diagnosis in power transformers using multi-class logical analysis of data[J]. Journal of Intelligent Manufacturing, 2014, 25(6): 1429-1439.
17	Shaban Y, Yacout S, Balazinski M, et al. Cutting tool wear detection using multiclass logical analysis of data[J]. Machining Science and Technology, 2017, 21(4): 526-541.
18	Jocelyn S, Chinniah Y, Ouali M S, et al. Application of logical analysis of data to machinery-related accident prevention based on scarce data[J]. Reliability Engineering and System Safety, 2017, 159: 223-236.
19	Ragab A, El-Koujok M, Poulin B, et al. Fault diagnosis in industrial chemical processes using interpretable patterns based on Logical Analysis of Data[J]. Expert Systems with Applications, 2017, 95: 368-383.
20	Jie Y, Yan X. Mutual information-dynamic stacked sparse autoencoders for fault detection[J]. Industrial & Engineering Chemistry Research, 2019, 58(47): 21614-21624.
21	Boros E, Crama Y, Hammer P L, et al. Logical analysis of data: classification with justification[J]. Annals of Operations Research, 2011, 188(1): 33-61.
22	Boros E, Hammer P L, Ibaraki T, et al. Logical analysis of numerical data[J]. Mathematical Programming, 1997, 79(1): 163-190.
23	Han J, Kim N, Yum B J, et al. Pattern selection approaches for the logical analysis of data considering the outliers and the coverage of a pattern[J]. Expert Systems with Applications, 2011, 38(11): 13857-13862.
24	Chikalov I, Lozin V, Lozina I, et al. Logical analysis of data: Theory, methodology and applications[M]//Three Approaches to Data Analysis. Springer Berlin Heidelberg, 2013: 147-192.
25	Crama Y, Hammer P L, Ibaraki T. Cause-effect relationships and partially defined Boolean functions[J]. Annals of Operations Research, 1988, 16(1): 299-325.
26	Crama Y, Hammer P L. Boolean Functions: Theory, Algorithms, and Applications[M].New York: Cambridge University Press, 2011: 511-526.
27	Boros E, Hammer P L, Ibaraki T, et al. An implementation of logical analysis of data[J]. IEEE Transactions on Knowledge and Data Engineering, 2000, 12(2): 292-306.
28	Bonates T O, Hammer P L, Kogan A. Maximum patterns in datasets[J]. Discrete Applied Mathematics, 2008, 156(6): 846-861.
29	Velliangiri S, Alagumuthukrishnan S. A review of dimensionality reduction techniques for efficient computation[J]. Procedia Computer Science, 2019, 165: 104-111.
30	Singh T, Patnaik A, Chauhan R. Optimization of tribological properties of cement kiln dust-filled brake pad using grey relation analysis[J]. Materials and Design, 2016, 89: 1335-1342.
31	Li G D, Yamaguchi D, Nagai M. A grey-based decision-making approach to the supplier selection problem[J]. Mathematical & Computer Modelling, 2007, 46(3/4): 573-581.
32	Qiu B, Wang F, Li Y, et al. Research on method of simulation model validation based on improved grey relational analysis[J]. Physics Procedia, 2012, 25: 1118-1125.
33	Chan J W K, Tong T K L. Multi-criteria material selections and end-of-life product strategy: grey relational analysis approach[J]. Materials and Design, 2007, 28(5): 1539-1546.
34	李海林, 郭崇慧. 基于形态特征的时间序列符号聚合近似方法[J]. 模式识别与人工智能, 2011, 24(5): 665-672.
	Li H L, Guo C H. Symbolic aggregate approximation based on shape features[J]. Pattern Recognition and Artificial Intelligence, 2011, 24(5): 665-672.
35	Chen N, Xue Y, Ding J, et al. Symbolizing for wind speed time series[J]. Automation of Electric Power Systems, 2017, 41(11): 33-38.
36	Lu B, Castillo I, Chiang L, et al. Industrial PLS model variable selection using moving window variable importance in projection[J]. Chemometrics and Intelligent Laboratory Systems, 2014, 135: 90-109.
37	Tang H, Liu S. Basic theory of fuzzy Bayesian networks and its application in machinery fault diagnosis[C]//Fourth International Conference on Fuzzy Systems and Knowledge Discovery, New Jersey: IEEE Computer Society, 2007: 132-137.
38	Chelson P O. Reliability computation using fault tree analysis[R]. Jet Propulsion Laboratory 32-1542, 1971.
39	Straube S, Krell M M. How to evaluate an agent's behavior to infrequent events?-Reliable performance estimation insensitive to class distribution[J]. Frontiers in Computational Neuroscience, 2014, 8: 43-43.

[1]	Yihao ZHANG, Zhenlei WANG. Fault detection using grouped support vector data description based on maximum information coefficient [J]. CIESC Journal, 2023, 74(9): 3865-3878.
[2]	Yuanzhe SHAO, Zhonggai ZHAO, Fei LIU. Quality-related non-stationary process fault detection method by common trends model [J]. CIESC Journal, 2023, 74(6): 2522-2537.
[3]	Bing SONG, Chengfeng ZHENG, Hongbo SHI, Yang TAO, Shuai TAN. Research on quality-related fault detection method based on VAE-OCCA [J]. CIESC Journal, 2023, 74(4): 1630-1638.
[4]	Minghui YANG, Xiaoyue LIU, Xiaogang DENG, Mingyan LIAO, Chunwang HOU. Incipient fault detection for dynamic chemical processes based on weighted probability CVDA [J]. CIESC Journal, 2022, 73(9): 3963-3972.
[5]	Jiawang YONG, Qianqian ZHAO, Nenglian FENG. Fault diagnosis of proton exchange membrane fuel cell based on nonlinear dynamic model [J]. CIESC Journal, 2022, 73(9): 3983-3993.
[6]	Jinyu GUO, Zhe WANG, Yuan LI. Fault detection method based on kernel entropy independent component analysis [J]. CIESC Journal, 2022, 73(8): 3647-3658.
[7]	Kun WANG, Hongbo SHI, Shuai TAN, Bing SONG, Yang TAO. Local time difference constrained neighborhood preserving embedding algorithm for fault detection [J]. CIESC Journal, 2022, 73(7): 3109-3119.
[8]	Jinyu GUO, Wentao LI, Yuan LI. Application of adaptive algorithm of online reduced KECA in fault detection [J]. CIESC Journal, 2021, 72(8): 4227-4238.
[9]	LI Yuan, YANG Dongsheng, ZHAO Liying, ZHANG Cheng. Fault detection using hierarchical variational Gaussian mixture model and principal polynomial analysis [J]. CIESC Journal, 2021, 72(3): 1616-1626.
[10]	Xiaohui WANG, Yanjiang WANG, Xiaogang DENG, Zheng ZHANG. Industrial process fault detection using weighted deep support vector data description [J]. CIESC Journal, 2021, 72(11): 5707-5716.
[11]	Mingyue DENG, Jianchang LIU, Peng XU, Shubin TAN, Liangliang SHANG. New fault detection and diagnosis strategy for nonlinear industrial process based on KECA [J]. CIESC Journal, 2020, 71(5): 2151-2163.
[12]	Yu HAN, Junfang LI, Qiang GAO, Yu TIAN, Guogang YU. Fault detection based on fault discrimination enhanced kernel entropy component analysis algorithm [J]. CIESC Journal, 2020, 71(3): 1254-1263.
[13]	XU Jing,WANG Zhenlei,WANG Xin. Fault detection for chemical process based on nonlinear dynamic global-local preserving projections [J]. CIESC Journal, 2020, 71(12): 5655-5663.
[14]	Wei CHAI, Longhang GUO, Binbin CHI. Interval model for predicting effluent quality variables of wastewater treatment plants [J]. CIESC Journal, 2019, 70(9): 3449-3457.
[15]	Lei YU, Xiaogang DENG, Yuping CAO, Kaiqi LU. Fault detection method of unequal-length batch process based on VGDTW-MCVA [J]. CIESC Journal, 2019, 70(9): 3441-3448.