Quality-related Variable Division and Fault Detection Based on Quality-related Virtual Variable
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摘要: 质量相关故障检测作为数据驱动的多元统计过程监测的重要研究内容, 是保障复杂装备或工业过程安全高效运行的关键技术, 而确定或划分质量相关变量是该方法的核心环节. 现有质量相关故障检测方法通常高度依赖于质量变量, 一旦质量变量不可测, 其有效性便受到严重挑战. 为解决这一挑战, 本文提出基于质量关联虚拟变量(Quality-related virtual variable, QRV)的质量相关变量划分方法, 基于此建立一种独立成分分析(Independent component analysis, ICA)质量相关故障检测模型, 并开展故障检测应用研究. 首先, 构造一个QRV, 以间接反映系统的质量特性; 其次, 基于该QRV, 利用假设检验将过程变量划分为质量相关和质量无关变量组; 随后, 将该划分结果应用于基于ICA的质量相关故障检测, 利用指数加权移动平均(Exponentially weighted moving average, EWMA)修正统计量, 并构造综合检测指标; 最后, 通过数值仿真和田纳西—伊斯曼过程(Tennessee-Eastman process, TEP)实验验证了所提方法的可行性和有效性.Abstract: Quality-related fault detection, as an important research content in data-driven multivariate statistical process monitoring, is a key technology for ensuring the safe and efficient operation of complex equipments or industrial processes. Determining or dividing quality-related variables is a core aspect of this technology. Existing quality-related fault detection methods typically rely heavily on quality variables, and their effectiveness is severely challenged when quality variables are unmeasurable. To address this challenge, a quality-related variable division method based on a quality-related virtual variable (QRV) is proposed in this paper. An independent component analysis (ICA)-based model for quality-related fault detection is established using this division method, and an application study on fault detection is conducted. First, a QRV is constructed to indirectly reflect the quality characteristics of systems; Second, based on this QRV, process variables are divided into quality-related and quality-unrelated variable groups by hypothesis testing; Subsequently, this division results are applied to the ICA-based quality-related fault detection, utilizing exponentially weighted moving average (EWMA) to modify statistics and construct comprehensive detection indices; Finally, the feasibility and effectiveness of the proposed method are verified through numerical simulations and Tennessee-Eastman process (TEP) experiments.
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图 1 基于QRV的质量相关变量划分方法的整体框架
Fig. 1 Overall framework of the quality-related variable division method based on QRV
图 3 基于QRVICA的质量相关故障检测流程图
Fig. 3 Flowchart of quality-related fault detection based on QRVICA
图 10 IDV(5)中不同变量组对质量变量的回归结果
Fig. 10 Regression results of the quality variable for different variable groups in IDV(5)
表 1 质量相关故障的FARs和FDRs(%)
Table 1 FARs and FDRs of the quality-related faults (%)
算法故障
编号MI-KPCA MKICR VIP-DCPLS OMDPLS QRVICA-without-EWMA QRVICA FAR ($\hat T^2$) FDR (${{\hat{T}}^{2}}$) FAR ($\hat I^2$) FDR (${{\hat{I}}^{2}}$) FAR (${{d}_{r}}$) FDR (${{d}_{r}}$) FAR ($T^2$) FDR ($T^2$) FAR (${\varphi }_{\text{r}}$) FDR (${\varphi }_{\text{r}}$) FAR (${\varphi }_{\text{r}}$) FDR (${\varphi }_{\text{r}}$) 1 0.30 99.62 0.63 69.13 0.00 99.75 2.50 99.63 0.00 99.75 {0.00} 99.75 2 0.00 98.50 0.63 96.88 0.00 96.50 0.63 97.75 0.00 98.25 0.00 98.50 5 0.00 24.12 0.63 20.62 0.63 24.00 1.25 19.25 0.00 24.13 0.00 25.12 6 0.00 99.75 0.00 100.00 0.00 100.00 3.13 98.75 0.00 100.00 0.00 100.00 7 0.00 40.75 0.63 35.13 0.00 40.88 1.87 64.50 0.00 37.00 0.00 37.62 8 2.40 97.62 3.75 76.00 1.25 97.75 1.25 88.13 0.00 97.63 0.00 97.50 10 0.00 79.87 0.00 63.38 0.00 55.63 0.63 54.00 0.63 80.63 0.00 84.88 12 1.25 98.88 21.88 74.13 0.00 98.75 1.25 83.88 0.00 99.25 0.00 99.62 13 0.00 94.63 1.25 85.38 0.00 95.25 0.63 93.75 0.00 93.75 0.00 94.75 平均 0.44 81.53 3.27 68.96 0.21 78.72 1.46 77.74 0.07 81.15 0.00 81.97 
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表 2 质量无关故障的FARs和FDRs(%)
Table 2 FARs and FDRs of the quality-unrelated faults (%)
算法故障
编号MI-KPCA MKICR VIP-DCPLS OMDPLS QRVICA-without-EWMA QRVICA FAR ($\hat T^2$) FDR (${{\tilde{T}}^{2}}$) FAR ($\hat I^2$) FDR (${{\tilde{I}}^{2}}$) FAR (${{d}_{r}}$) FDR (${{d}_{u}}$) FAR ($T^2$) FDR ($Q$) FAR (${\varphi }_{\text{r}}$) FDR (${\varphi }_{\text u}$) FAR (${\varphi }_{\text{r}}$) FDR (${\varphi }_{\text u}$) 4 0.10 100.00 3.75 100.00 1.25 99.00 13.00 100.00 0.10 100.00 0.00 100.00 11 2.40 69.87 12.00 83.63 2.62 66.50 17.88 79.50 0.31 73.88 0.00 83.75 14 0.00 100.00 17.88 100.00 0.37 100.00 99.38 99.88 0.21 100.00 0.00 100.00 平均 0.83 89.96 11.21 94.54 1.41 88.50 43.42 93.13 0.21 91.29 0.00 94.58
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