| 一种改进的马氏距离相对变换主元分析方法及其故障检测应用 |
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| 引用本文： | 石怀涛,刘建昌,薛鹏,张珂,吴玉厚,张丽秀,谭帅.一种改进的马氏距离相对变换主元分析方法及其故障检测应用[J].自动化学报,2013,39(9):1533-1542. |
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| 作者姓名： | 石怀涛 刘建昌 薛鹏 张珂 吴玉厚 张丽秀 谭帅 |
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| 作者单位： | 1.沈阳建筑大学交通与机械工程学院 沈阳 110168; |
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| 摘 要： | 目前, 主元分析方法(PCA)在数据处理、模式识别、过程监测等领域得到了越来越广泛的应用, 但仍存在部分关键问题亟待解决. 本文为了提高PCA方法的故障检测性能, 进行了一系列的改进, 首先, 本文引入相对变换的概念, 使用马氏距离相对变换直接消除量纲, 通过理论推导证明了马氏距离相对变换可以对数据不进行标准化直接进行数据变换, 而且给出了在相对空间内数据进行PCA变换的合理解释, 表明了基于马氏距离相对变换的PCA故障检测方法可以有效的消除变量量纲对数据的影响, 提高数据的可分性. 其次, 改进了SPE监控指标, 提出一种基于马氏距离的平方预测误差指标, 更有效地实现对工业过程的故障检测. 最后, 将两种改进方法相结合, 提出改进的马氏距离相对变换PCA故障检测方法, 并以轧钢过程活套系统为背景, 实际数据仿真结果表明: 与PCA以及其它改进方法相比, 本文提出的方法具有更好的故障检测性能和实时性, 能准确、有效地检测出活套故障.
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| 关 键 词： | 马氏距离相对变换主元分析 改进SPE 故障检测 单故障 多故障 活套故障 |
| 收稿时间： | 2012-01-06 |
Improved Relative-transformation Principal Component Analysis Based on Mahalanobis Distance and Its Application for Fault Detection |
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| SHI Huai-Tao,LIU Jian-Chang,XUE Peng,ZHANG Ke,WU Yu-Hou,ZHANG Li-Xiu,TAN Shuai.Improved Relative-transformation Principal Component Analysis Based on Mahalanobis Distance and Its Application for Fault Detection[J].Acta Automatica Sinica,2013,39(9):1533-1542. |
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| Authors: | SHI Huai-Tao LIU Jian-Chang XUE Peng ZHANG Ke WU Yu-Hou ZHANG Li-Xiu TAN Shuai |
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| Affiliation: | 1.College of Transportation and Mechanical Engineering, Shen-yang Jianzhu University, Shenyang 110168, China;2.College of Information Science and Engineering, Northeastern University, Shen-yang 110819, China;3.Baoshan Iron and Steel Co., Ltd., Shang- hai 200941, China |
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| Abstract: | Principal component analysis (PCA) has been widely used in process industries, which could maintain the maximum fault detection rate. Although many issues have been addressed in PCA, some essential problems remain unresolved. This study improves PCA for fault detection performance in the following ways. Firstly, a relative transformation scheme based on Mahalanobis distance (MD) is introduced to eliminate the effect of dimension of data instead of dimensionless standardization, and improve the accuracy and real-time performance of fault detection. The theoretical derivation proves that relative transformation based on MD can directly eliminate the effect of dimension and give reasonable explanation of PCA in the relative space, the analysis and simulation results show its superiority and effectiveness. Secondly, an improved squared prediction error (SPE) statistic is given to improve the fault detection performance of standardized PCA, which can make the standardized PCA-based fault detection method more suitable for the actual industrial process. Finally, two improved methods are combined to detect the fault more effectively. The proposed methods are applied to detect single fault and multi-fault of looper system in hot continuous rolling process, simulation results demonstrate the effectiveness of these improvements for fault detection performance in terms of sensitiveness, accuracy and real-time performance of fault detection. |
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| Keywords: | Relative-transformation PCA based on Mahalanobis distance improved squared prediction error (SPE) fault detection single fault multi-fault looper system |
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