Incipient fault detection of nonlinear chemical processes based on weighted probability related KPCA

doi:10.16085/j.issn.1000-6613.2019-0397

Abstract

Abstract:

The traditional kernel principal component analysis (KPCA) is a widely used nonlinear chemical process fault detection method, but it is often difficult to detect the incipient fault in the process effectively because it does not make full use of the probability distribution information of process data. Aiming at the limitations of the traditional KPCA method, a new incipient fault detection method of nonlinear chemical process based on weighted probability related KPCA (WPRKPCA) was proposed. Different from the traditional KPCA method monitoring the change of kernel components, the WPRKPCA uses Kullback Leibler divergence (KLD) to measure the variations of the probability distribution of the kernel components, and then establishes a statistical monitoring model based on KLD components to fully exploit the probability information contained in the process data. Taking into account the difference of fault information carried by different KLD components, the WPRKPCA designs an exponential weighting strategy based on kernel density estimation (KDE). The different weights are assigned to enhance the incipient fault detection sensitivity of the monitoring model according to the difference of fault information described by the KLD component. The simulation results on a numerical example and the continuous stirred reactor (CSTR) system showed that the WPRKPCA has better performance than the traditional KPCA for the detection of incipient faults.

Key words: process systems, incipient fault, kernel principal component analysis, the Kullback Leibler divergence, chemical reactors, numerical simulation

摘要：

传统核主元分析法（KPCA）是一种广泛应用的非线性化工过程故障检测方法，但是其未充分利用过程数据的概率分布信息，往往难以有效检测过程中的微小故障。针对传统KPCA方法的局限性，本文提出了一种基于加权概率相关核主元分析（WPRKPCA）的非线性化工过程微小故障检测方法。与传统KPCA方法监控核成分的变化不同，该方法利用Kullback Leibler散度（KLD）度量核成分的概率分布变化，进而建立基于KLD成分的统计监控模型，以充分挖掘过程数据所包含的概率信息。进一步考虑到不同KLD成分承载故障信息的差异性，该方法设计了一种基于核密度估计的指数加权策略，根据KLD成分描述故障信息程度的差异分配相应的权值，以加强监控模型对微小故障检测的灵敏性。在一个数值例子和连续搅拌反应器（CSTR）系统上的仿真结果表明，本文所提方法具有比传统KPCA方法更好的微小故障检测性能。

关键词: 过程系统, 微小故障, 核主元分析, KL散度, 化学反应器, 数值模拟

CLC Number:

TP277

Peipei CAI,Xiaogang DENG,Yuping CAO,Jiawei DENG. Incipient fault detection of nonlinear chemical processes based on weighted probability related KPCA[J]. Chemical Industry and Engineering Progress, 2019, 38(12): 5247-5256.

蔡配配,邓晓刚,曹玉苹,邓佳伟. 基于WPRKPCA的非线性化工过程微小故障检测[J]. 化工进展, 2019, 38(12): 5247-5256.

Figures/Tables 13

References 32

1	ZHANG S M, ZHAO C H. Stationarity test and Bayesian monitoring strategy for fault detection in nonlinear multimode process[J]. Chemical & Intelligent Laboratory Systems, 2017, 168: 45-61.
2	GE Z Q. Review on data-driven modeling and monitoring for plant-wide industrial process[J]. Chemical & Intelligent Laboratory Systems, 2017, 171: 16-25.
3	文成林, 吕菲亚, 包哲静,等. 基于数据驱动的微小故障诊断方法综述[J]. 自动化学报, 2016, 42(9): 1285-1299.
	WEN C L, LÜ F Y, BAO Z J, et al. A review of data driven-based incipient fault diagnosis[J]. Acta Automatica Sinica, 2016, 42(9): 1285-1299.
4	AMAR M, GONDAL I, WILSON C. Vibration spectrum imaging: a novel bearing fault classification approach[J]. IEEE Transactions on Industrial Electronics, 2015, 62(1): 494-502.
5	LUO L J, BAO S Y, MAO J F, et al. Industrial process monitoring based on knowledge data integrated sparse model and two-level deviation plots[J]. Industrial & Engineering Chemistry Research, 2018, 57(2): 611-622.
6	ZHU J L, GE Z Q, SONG Z H. Distributed parallel PCA for modeling and monitoring of large-scale plant-wide processes with big data[J]. IEEE Transactions on Industrial Informatics, 2017, 13(4): 1877-1885.
7	QI L J, DU W Y, ZHANG Y W. Semi-supervised kernel partial least squares fault detection and identification approach with application to HGPWLTP[J]. Journal of Chemometrics, 2016, 30(7): 377-385.
8	CAI L F, TIAN X M, CHEN S. A process monitoring method based on noisy independent component analysis[J]. Neurocomputing, 2014, 127(1): 231-246.
9	DONG Y N, QIN S J. A novel dynamic PCA algorithm for dynamic data modeling and process monitoring[J]. Journal of Process Control, 2018, 67: 1-11
10	CHERRY G A, QIN S J. Multi-block principal component analysis based on a combined index for semiconductor fault detection and diagnosis[J]. IEEE Transactions on Semiconductor Manufacturing, 2006, 19(2): 159-172.
11	LEE J M, YOO C K, LEE I B. Fault detection of batch processes using multiway kernel principal component analysis[J]. Computers & Chemical Engineering, 2004, 28(9): 1837-1847.
12	WOLD S. Exponentially weighted moving principal components analysis and projections to latent structures[J]. Chemometrics & Intelligent Laboratory Systems, 1994, 23(1): 149-161.
13	JI H Q, HE X, SHANG J, et al. Incipient fault detection with smoothing techniques in statistical process monitoring[J]. Control Engineering Practice, 2017, 62: 11-21.
14	尚骏, 陈茂银, 周东华. 基于变元统计分析的微小故障检测[J]. 上海交通大学学报, 2015, 49(6): 799-805.
	SHANG Jun, CHEN Maoyin, ZHOU Donghua. Incipient fault detection using transformed component statistical analysis[J]. Journal of Shanghai Jiaotong University, 2015, 49(6): 799-805
15	HARMOUCHE J, DELPHA C, DIALLO D. Incipient fault detection and diagnosis based on Kullback-Leibler divergence using principal component analysis: Part Ⅰ[J]. Signal Processing, 2014, 94: 278-287.
16	HARMOUCHE J, DELPHA C, DIALLO D. Incipient fault detection and diagnosis based on Kullback-Leibler divergence using principal component analysis: Part Ⅱ[J]. Signal Processing, 2015, 109(1): 334-344.
17	CHEN H T, JIANG B, LU N Y. An improved incipient fault detection method based on Kullback Leibler divergence[J]. ISA Transaction, 2018, 79: 127-136
18	GE Z Q, YANG C J, SONG Z H. Improved kernel PCA-based monitoring approach for nonlinear processes[J]. Chemical Engineering Science, 2009, 64(9): 2245-2255.
19	CHEN H T, JIANG B, LU N Y, et al. Multi-mode kernel principal component analysis-based incipient fault detection for pulse width modulated inverter of China railway high-speed 5[J]. Advances in Mechanical Engineering, 2017, 9(10): 1-12.
20	CHEN H T, JIANG B, DING S X, et al. Probability-relevant incipient fault detection and diagnosis methodology with applications to electric drive systems[J]. IEEE Transactions on Control Systems Technology, 2018,27(6): 1-8.
21	DENG X G, TIAN X M, CHEN S, et al. Fault discriminant enhanced kernel principal component analysis incorporating prior fault information for monitoring nonlinear processes[J]. Chemom. Intell. Lab. Syst., 2017, 162: 21-34.
22	DENG X G, WANG L. Modified kernel principal component analysis using double-weighted local outlier factor and its application to nonlinear process monitoring[J]. ISA Transactions, 2018, 72: 218-228.
23	FAN J C, QIN S J, WANG Y Q. Online monitoring of nonlinear multivariate industrial processes using filtering KICA-PCA[J]. Control Engineering Practice, 2014, 22(1): 205-216.
24	DENG X G, TIAN X M, CHEN S, et al. Nonlinear process fault diagnosis based on serial principal component analysis[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(3): 560-572.
25	LEE J M, YOO C K, CHOI S W, et al. Nonlinear process monitoring using kernel principal component analysis[J]. Chemical Engineering Science, 2004, 59(1): 223-234.
26	SCHOLKOPF B, SMOLA A, MULLER K R. Nonlinear component analysis as a kernel eigenvalue problem[J]. Neural Computation, 1998, 10(5): 1299-1319.
27	KULLBACK S, LEIBLER R A. On information and sufficiency[J]. The Annals of Mathematical Statistics, 1951, 22(1): 79-86.
28	BASSEVILLE M. Distance measures for signal processing and pattern recognition[J]. Signal Processing, 1989, 18(4): 349-369.
29	ROSENBLATT M. Curve estimates[J]. Annals of Mathematical Statistics, 1971, 42(6):1815-1842.
30	PRAZEN E. On estimation of a probability density function and mode[J]. Ann. Math. Statis., 1962, 33(3): 1065-1076.
31	DONG D, MCAVOY T J. Nonlinear principal component analysis-based on principal curves and neural networks[J].Computers & Chemical Engineering, 1996, 20(1): 65-78.
32	SONG B, SHI H B. Temporal-spatial global locality projections for multimode process monitoring[J]. IEEE Access, 2018, 6: 9740-9749.

方法统计量	KPCA		PRKPCA		WPRKPCA
方法统计量	T²/%	SPE/%	T²/%	SPE/%	T²/%	SPE/%
故障1	12.33	1.67	67	62	67	74.67
故障2	1.33	11.67	46.67	99	53.67	99
均值	6.83	6.67	56.84	80.5	60.34	86.84

方法统计量	KPCA		PRKPCA		WPRKPCA
方法统计量	T²/%	SPE/%	T²/%	SPE/%	T²/%	SPE/%
故障1	12.33	1.67	67	62	67	74.67
故障2	1.33	11.67	46.67	99	53.67	99
均值	6.83	6.67	56.84	80.5	60.34	86.84

故障	故障描述	幅值
F1	进料流速Q_F阶跃变化	+0.8L·min^-1
F2	进料浓度C_AF斜坡变化	+2×10^-5mol·L^-1·min^-1
F3	催化剂逐渐失活	+1.45K·min^-1
F4	换热器结垢	-38J·min^-2·K^-1
F5	反应器温度传感器出现偏差	+0.9K
F6	冷凝器中温度测量中的传感器偏差	+1.3K

故障	故障描述	幅值
F1	进料流速Q_F阶跃变化	+0.8L·min^-1
F2	进料浓度C_AF斜坡变化	+2×10^-5mol·L^-1·min^-1
F3	催化剂逐渐失活	+1.45K·min^-1
F4	换热器结垢	-38J·min^-2·K^-1
F5	反应器温度传感器出现偏差	+0.9K
F6	冷凝器中温度测量中的传感器偏差	+1.3K

方法统计量	PCA		KLD-PCA		PRPCA		KPCA		PRKPCA		WPRKPCA
方法统计量	T²	SPE	T²	SPE	T²	SPE	T²	SPE	T²	SPE	T²	SPE
F1	2.43	1.43	93.86	2.29	89	2.71	3.14	2.71	94.43	59.71	95.14	80
F2	41.43	1.00	87.71	0	88.29	0	41.57	4.29	88.57	85.29	91.43	87.43
F3	13.29	7.29	76.43	67	75.71	65.71	20	6.71	76.86	73.86	78.29	75
F4	1.43	2.14	15.71	76	20.29	70	1.71	20.14	16.57	76.71	30.14	86.71
F5	2.86	1.43	96.71	1.00	96.71	1.29	3.14	1.14	96.71	74.57	96.71	87.71
F6	1.57	1.43	2.29	97.71	4.14	97.71	1.29	20.86	2.29	98.14	7	98.43
均值	10.50	2.45	62.12	40.67	62.36	38.74	11.81	9.31	62.57	78.05	66.45	85.88