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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (7): 1297-1306    DOI: 10.3785/j.issn.1008-973X.2023.07.004
    
Fault detection method based on dynamic inner concurrent projection to latent structure
Xiang-yu KONG1(),Ya-lin CHEN1,2,Jia-yu LUO1,Zhi-yan YANG3
1. College of Missile Engineering, Rocket Force University of Engineering, Xi’an 710025, China
2. AVIC Chengdu Caic Electronics Limited Company, Chengdu 610091, China
3. China Electronic Product Reliability and Environmental Testing Research Institute, Guangzhou 511370, China
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Abstract  

The online monitoring dynamic inner projection to latent structures (OM-DiPLS) model was proposed aiming at the problems of false alarm and missing quality data of some periods in actual industrial process fault detection. The model can be updated when quality data of some periods were missing by introducing quality data of time delay. An online monitoring dynamic internal concurrent latent structure projection (OM-DiCPLS) model was proposed based on the OM-DiPLS model in order to better monitor the unpredictable information in the quality variables. The process data and quality data were projected into the covariant subspace with relevant inputs and outputs, the input principal subspace with unrelated outputs but relevant processes, the input residual subspace, the unpredictable output principal subspace and the output residual subspace. Process monitoring was realized by constructing corresponding statistics for each subspace. The Tennessee-Eastman process simulation experiment shows that the proposed algorithm effectively improves the effective detection rate of quality-related faults and reduces the false alarm rate of quality-unrelated faults.

Key words： partial least square      key performance indicator      dynamic modeling      process monitoring      fault detection     
Received: 21 May 2022      Published: 17 July 2023
CLC:  TP 277  
Fund:  国家自然科学基金资助项目（62273354，61673387，61833016）；陕西省自然科学基金资助项目（2020JM-356）
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Xiang-yu KONG
Ya-lin CHEN
Jia-yu LUO
Zhi-yan YANG
Cite this article:

Xiang-yu KONG,Ya-lin CHEN,Jia-yu LUO,Zhi-yan YANG. Fault detection method based on dynamic inner concurrent projection to latent structure. Journal of ZheJiang University (Engineering Science), 2023, 57(7): 1297-1306.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.07.004     OR     https://www.zjujournals.com/eng/Y2023/V57/I7/1297


基于动态内并行潜结构投影的故障检测方法

针对实际工业过程故障检测时存在误报警现象及易缺失部分时段质量数据的问题，提出在线监测动态内潜结构投影(OM-DiPLS)模型. 该模型通过引入时延的质量数据，使得在缺失部分时段质量数据时能够实现模型的更新. 为了更好地监控质量变量中不可预测的信息，基于OM-DiPLS模型提出在线监测动态内并行潜结构投影模型. 该模型将过程数据和质量数据投影到输入输出相关的协变子空间、输出无关但过程相关的输入主子空间、输入残差子空间、不可预测的输出主子空间及输出残差子空间，通过对各子空间构造相应的统计量，实现过程监测. 田纳西-伊斯曼过程仿真的实验表明，利用所提算法有效提高了质量相关故障的有效检测率，降低了质量无关故障的误报率.


关键词： 偏最小二乘,  关键性能指标,  动态建模,  过程监测,  故障检测 
子空间 统计量 计算 控制限
${S_{{\rm{CVS}}} }$ $T_{\rm{c}}^2$ ${\boldsymbol{v} }_k{\boldsymbol{\varLambda} } _k^{ - 1}{ {\boldsymbol{v} }_k^{\rm{T} } }$ ${J_{ {\rm{th} },T_{\rm{c}}^2} }{\text{ = } }\dfrac{ {A({n^2} - 1)} }{ {n(n - A)} }{F_{A,n - A,\alpha } }$
${S_{{\rm{IPS}}} }$ $ T_x^2 $ ${\boldsymbol{v} }_x{\boldsymbol{\varLambda} } _x^{ - 1}{ {\boldsymbol{v} }_x^{\rm{T} } }$ ${J_{{\rm{th}},T_x^2} } = \dfrac{ { {A_x}({n^2} - 1)} }{ {n(n - {A_x})} }{F_{ {A_x},n - {A_x},\alpha } }$
${S_{{\rm{OPS}}} }$ $ T_y^2 $ ${\boldsymbol{v} }_y{\boldsymbol{\varLambda} } _y^{ - 1}{ {\boldsymbol{v} }_y^{\rm{T}}}$ ${J_{{\rm{th}},T_y^2} }{\text{ = } }\dfrac{ { {A_y}({n^2} - 1)} }{ {n(n - {A_y})} }{F_{ {A_y},n - {A_y},\alpha } }$
${S_{{\rm{IRS}}} }$ $ {Q_x} $ ${\left\| { { {{\boldsymbol{\tilde x}}}_x} } \right\|^2}$ ${J_{{\rm{th}},{Q_x} } } = g\chi _{h,\alpha }^2$
${S_{{\rm{ORS}}} }$ $ {Q_y} $ ${\left\| { { {{\boldsymbol{\tilde y}}}_y} } \right\|^2}$ ${J_{{\rm{th}},{Q_y} } } = g\chi _{h,\alpha }^2$
Tab.1 Statistical indicators of OM-DiCPLS model
故障
编号 		DTPLS OMDC-PLS OM-DiCPLS
${S_{\rm{D}}}$ ${S_{{\rm{WD}}} }$ ${S_{{\rm{WG}}} }$ ${S_{{\rm{DT}}} }$ ${S_{{\rm{CVS}}} }$ ${S_{{\rm{IPS}}} }$ ${S_{{\rm{IRS}}} }$ ${S_{{\rm{OPS}}} }$ ${S_{{\rm{ORS}}} }$ ${S_{{\rm{CVS}}} }$ ${S_{{\rm{IPS}}} }$ ${S_{{\rm{IRS}}} }$ ${S_{{\rm{OPS}}} }$ ${S_{{\rm{ORS}}} }$
1 99.75 99.50 99.88 99.88 99.38 99.63 100.0 98.50 06.13 100.0 99.88 100.0 100.0 99.62
2 99.50 98.75 98.50 99.13 98.63 98.88 100.0 97.88 02.88 99.25 99.37 100.0 98.99 99.37
5 36.89 24.06 16.00 46.88 33.13 29.25 4.13 26.75 02.13 28.55 19.87 100.0 58.24 52.45
6 100.0 98.62 99.50 100.0 99.38 99.38 100.0 97.88 53.13 99.37 99.62 100.0 100.0 99.87
7 58.97 97.24 100.0 99.50 61.00 100.0 100.0 39.13 04.13 47.92 100.0 100.0 80.25 67.92
8 93.22 96.87 91.38 93.63 98.75 97.50 100.0 89.25 04.63 97.99 97.48 100.0 98.36 98.87
10 32.12 18.42 11.75 66.13 63.00 29.25 44.78 32.13 01.88 48.18 11.95 99.75 76.86 72.08
12 86.83 96.12 89.00 92.88 97.63 98.63 97.83 82.38 16.75 95.85 97.61 100.0 99.87 98.74
13 92.35 93.86 94.88 95.63 94.63 95.38 100.0 90.25 14.25 93.58 94.88 99.87 97.48 97.36
Tab.2 Detection rates of quality-related fault %
Fig.1 Monitoring effect of quality-related fault (12)
Fig.2 Monitoring effect of OM-DiCPLS method for fault (2)
故障
编号 		DTPLS OMDC-PLS OM-DiCPLS
${S_{\rm{D}}}$ ${S_{{\rm{WD}}} }$ ${S_{{\rm{WG}}} }$ ${S_{{\rm{DT}}} }$ ${S_{{\rm{CVS}}} }$ ${S_{{\rm{IPS}}} }$ ${S_{{\rm{IRS}}} }$ ${S_{{\rm{OPS}}} }$ ${S_{{\rm{ORS}}} }$ ${S_{{\rm{CVS}}} }$ ${S_{{\rm{IPS}}} }$ ${S_{{\rm{IRS}}} }$ ${S_{{\rm{OPS}}} }$ ${S_{{\rm{ORS}}} }$
3 13.84 11.65 6.13 5.75 14.88 5.00 01.74 10.20 00.50 07.42 03.89 98.87 50.69 45.66
4 24.22 14.04 95.63 99.88 14.75 52.00 100.0 09.00 01.25 07.04 25.91 100.0 58.87 50.44
9 14.09 10.78 07.88 7.63 15.88 6.38 02.17 06.38 00.50 08.68 03.77 99.50 49.56 44.40
11 29.36 31.33 69.13 71.13 27.50 64.13 89.35 07.38 00.75 11.70 47.92 100.0 62.52 65.53
14 99.62 100.0 100.0 91.13 4.75 99.88 100.0 06.50 01.00 03.27 100.0 100.0 41.51 38.99
15 14.34 10.03 05.88 8.25 11.25 9.88 01.74 11.00 00.75 08.30 03.90 97.99 46.79 40.63
Tab.3 False alarm rates of quality-unrelated fault %
Fig.3 Monitoring effect of quality-unrelated fault (4)
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