Fault Detection Strategy Based on Principal Component Score Difference of $ \pmb k $ Nearest Neighbors
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摘要: 针对具有非线性和多模态特征过程的故障检测问题, 本文提出一种基于k近邻主元得分差分的故障检测策略.首先, 通过主元分析(Principal component analysis, PCA)方法计算样本的真实得分.然后, 应用样本的k近邻均值计算样本估计得分.接下来, 通过上述两种得分计算样本的得分差分矩阵和残差矩阵, 其中残差矩阵由样本的估计得分计算得到，这区别于传统方法.最后, 在差分子空间和残差子空间中分别建立新的统计指标进行故障检测.值得注意的是本文的得分差分方法能够消除数据结构对过程故障检测的影响, 同时, 新的统计量能够提高过程的故障检测率.将本文方法在两个模拟例子和Tennessee Eastman (TE)过程中进行测试, 并与传统方法如PCA、KPCA、DPCA和~FD-kNN等进行对比分析, 测试结果证明了本文方法的有效性.Abstract: In order to monitor a process with nonlinear and multimode characteristics effectively, this paper presents a novel fault detection method using principal component score difference based on k nearest neighbors. In the proposed method, firstly, real scores of samples are calculated through principal component analysis (PCA) method. Next, estimated scores of samples are calculated using the mean of k nearest neighbors through a linear transformation. After that a score difference matrix can be obtained through calculating the difference between the real scores and the estimated scores; meanwhile, a residual matrix can be also obtained by reconstructing a sample using the estimated scores. At last, two new statistics are built to monitor the variability of a sample in the score difference subspace (SDS) and residual subspace (RS), respectively. It should be noted that the proposed difference method is able to eliminate the impact of data structure on process monitoring and the new statistics can improve fault detection rate of a process. The efficiency of the proposed method in this paper is tested in two simulated cases and in the Tennessee Eastman (TE) processes. The experimental results indicate that the proposed method outperforms the conventional methods, such as PCA, KPCA, DPCA, and FD-kNN.
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Key words:
- Principal component analysis (PCA) /
- difference of scores /
- k nearest neighbors (kNN) /
- multimode process /
- Tennessee Eastman (TE) processes /
- fault detection
1) 本文责任编委 刘允刚 -
表 1 参数设置, 故障检测率和误报率
Table 1 Setting of parameters, FDR and FAR
方法 PCs k FDR FAR PCA 2 - 0 0 PC-kNN 2 3 85 0 本文方法 2 5 100 0 
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表 2 各种方法的故障检测率
Table 2 FDRs using different methods
方法 F1 F2 F3 F4 F5 PCA-T2 54.6 0.1 89.4 67.8 3.4 PCA-SPE 79.8 0.6 98.8 76.5 1.4 KPCA-T2 69.6 1.4 6.1 67.6 0.5 KPCA-SPE 83.5 1.4 65.5 83.5 2 DPCA-T2 84.1 0 93.5 75.9 4.5 DPCA-SPE 65.8 0.1 88.1 76.6 1.5 Tdiff2 87.3 1.5 92.5 72.5 4.8 qdiff 92.5 90.3 100 92.5 95.1
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表 3 各种方法的故障误报率
Table 3 FARs using different methods
方法 F1 F2 F3 F4 F5 PCA-T2 0 0 1.5 1.5 1.5 PCA-SPE 0 0 2.5 2.5 2.5 KPCA-T2 0.5 0.5 2 2 2 KPCA-SPE 0 0 2.5 2.5 2.5 DPCA-T2 0 0 3 3 3 DPCA-SPE 0 0 2.5 2.5 2.5 Tdiff2 0 0 0.5 0.5 0.5 qdiff 0 0 1 1 1
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