基于共同趋势模型的非平稳过程质量相关故障检测方法

doi:10.11949/0438-1157.20230066

摘要/Abstract

摘要：

现有质量相关监控方法基于数据平稳的假设，而实际生产中存在大量的非平稳过程。针对上述问题，提出了一种基于共同趋势模型的非平稳过程质量相关故障检测方法。该方法首先识别出系统中的非平稳过程变量和质量变量，再利用Gonzalo-Granger分解求解共同趋势模型，从而分离非平稳数据中的平稳部分和非平稳部分，然后，整合平稳数据，以及非平稳数据的平稳子空间整合，应用慢特征分析（slow feature analysis， SFA）和典型相关分析（canonical correlation analysis， CCA）建立质量相关的监控模型，实现对非平稳质量变量的有效监控。最后通过对比实验，证明所提出方法可以有效发现非平稳过程质量相关故障。

关键词: 非平稳, 协整分析, 慢特征分析, 质量相关, 故障检测, 数值分析, 计算机模拟, 过程系统

Abstract:

Existing quality-related monitoring methods are based on the assumption that the data is stationary, but there are a large number of non-stationary processes in actual production. In order to solve these problems, a new fault detection method based on common trend model is proposed for non-stationary process quality-related faults. The method first identifies the non-stationary process variables and quality variables in the system, then use Gonzalo-Granger decomposition to solve the common trend model, so as to separate the non-stationary part and the stationary part of the non-stationary data. By integrating stationary subspaces of originally stationary data and non-stationary data, slow feature analysis (SFA) and canonical correlation analysis (CCA) are used to establish quality-related monitoring models to realize the effective monitoring of non-stationary quality variables. Finally, by comparing the previous methods with the simulation experiments, it is proved that the proposed method can effectively detect the quality-related faults in the system containing non-stationary variables.

Key words: non-stationary, cointegration analysis, slow feature analysis? quality-related? fault detection, numerical analysis, computer simulation, process system

中图分类号:

TP 181

邵远哲, 赵忠盖, 刘飞. 基于共同趋势模型的非平稳过程质量相关故障检测方法[J]. 化工学报, 2023, 74(6): 2522-2537.

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.

图/表 18

图1 QRCTSFA监控建模流程图

Fig.1 Modeling flowchart of QRCTSFA

图2 数值仿真中各变量变化情况

Fig.2 Variation of each variable in numerical simulation

图3 数值仿真协整分析情况

Fig.3 Cointegration analysis result of numerical simulation

图4 CCA监控结果

Fig.4 The online monitoring result by CCA

图5 SFA监控结果

Fig.5 The online monitoring result by SFA

图6 残差方法监控结果

Fig.6 The online monitoring result by contrast method

图7 QRCTSFA监控结果

Fig.7 The online monitoring result by QRCTSFA

表1 数值仿真三种方法质量相关监控性能

Table 1 Quality-related monitoring performance of three methods in numerical simulation

阶段	性能衡量指标	CCA	残差序列方法		QRCTSFA
阶段	性能衡量指标	$T 2$	$T q 2$	$S q 2$	$T q 2$	$S q 2$
无故障阶段	FAR/%	49.25	28.40	1.15	0.65	1.30
故障一(质量相关)	MDR/%	39.10	0	12.50	0.20	94.80
故障二(质量相关)	MDR/%	71.00	51.00	58.30	65.40	55.60
故障三(质量无关)	FAR/%	59.90	81.00	1.80	0	1.40

表1 数值仿真三种方法质量相关监控性能

Table 1 Quality-related monitoring performance of three methods in numerical simulation

阶段	性能衡量指标	CCA	残差序列方法		QRCTSFA
阶段	性能衡量指标	$T 2$	$T q 2$	$S q 2$	$T q 2$	$S q 2$
无故障阶段	FAR/%	49.25	28.40	1.15	0.65	1.30
故障一(质量相关)	MDR/%	39.10	0	12.50	0.20	94.80
故障二(质量相关)	MDR/%	71.00	51.00	58.30	65.40	55.60
故障三(质量无关)	FAR/%	59.90	81.00	1.80	0	1.40

图8 CCA对正常数据集T2监控结果

Fig.8 The monitoring result of T2 by CCA

图9 SFA对正常数据集T2监控结果

Fig.9 The monitoring result of T2 by SFA

图10 QRCTSFA对正常数据集T2监控结果

Fig.10 The monitoring result of T2 by QRCTSFA

表2 三相流实验CCA、QRCTSFA质量相关指标对T2和案例一误报率

Table 2 False alarm rates of CCA and QRCTSFA for T2 and Case 1 in three-phase flow process

阶段	性能衡量指标	CCA	QRCTSFA
阶段	性能衡量指标	$T 2$	$T q 2$	$S q 2$
正常集T2	FAR/%	100.00	0.03	0.81
案例一(故障集2.1)	FAR/%	100.00	0.21	1.20

表2 三相流实验CCA、QRCTSFA质量相关指标对T2和案例一误报率

Table 2 False alarm rates of CCA and QRCTSFA for T2 and Case 1 in three-phase flow process

阶段	性能衡量指标	CCA	QRCTSFA
阶段	性能衡量指标	$T 2$	$T q 2$	$S q 2$
正常集T2	FAR/%	100.00	0.03	0.81
案例一(故障集2.1)	FAR/%	100.00	0.21	1.20

图11 CCA对案例一监控结果

Fig.11 The monitoring result of Case 1 by CCA

图12 SFA对案例一监控结果

Fig.12 The monitoring result of Case 1 by SFA

图13 QRCTSFA对案例一监控结果

Fig.13 The monitoring result of Case 1 by QRCTSFA

图14 CCA对案例二监控结果

Fig.14 The monitoring result of Case 2 by CCA

图15 SFA对案例二监控结果

Fig.15 The monitoring result of Case 2 by SFA

图16 QRCTSFA对案例二监控结果

Fig.16 The monitoring result of Case 2 by QRCTSFA

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