基于多元统计法的工业故障检测技术研究
毕业论文关键词：多元统计分析，故障诊断，主元分析法（PCA），田纳西-伊斯曼过程（TE过程）
Title Research on fault diagnosis based on multivariate statistical method
Abstract Fault diagnosis has become an important part in automation monitor and control system. It’s an interdisciplinary subject, widely involved in many other applications, such as artificial intelligence, statistics and system integration. With the development of science and technology, traditional method of fault diagnosis could not meet our increasing needs because the system has become more and more complicate. This paper is based on Multiple Statistics Analysis and mainly uses the Principle component analysis in the fault diagnosis. In this paper we will see: 1. Through the overview of the development of fault diagnosis, introduction of the traditional method in fault diagnosis, we could have a complete understanding in this field. 2. Introduce the principle component analysis and least square method and analyze the advantage and disadvantage of both method. 3. Use PCA as the major method and synthesize the SPE and T2 statistical method in fault diagnosis. 4. Introduce the TE process, which is the chief object when we apply the multiple statistics analysis.
Keywords: Fault diagnosis, Multiple statistics analysis, PCA, TE process.
目次
1 绪论 . 1
1.1 故障检测技术介绍 1
1.2 多元统计过程控制 4
1.3 本文主要内容 6
2 主成分分析法 ... 7
2.1 主成分分析的概念及基本思想 7
2.2 主成分分析的数学模型及几何意义 8
2.3 主成分分析的推导 .. 10
2.4 主成分分析的计算步骤 .. 13
3 多元统计法在工业故障检测的运用 . 14
3.1 过程统计控制图 .. 14
3.2 Hotelling T2
图 . 15
3.3 平方预测误差SPE 16
3.4 贡献图 .. 16
4 田纳西-伊斯曼过程的仿真实验 17
4.1 田纳西伊斯曼过程介绍 ... 17
4.2 田纳西伊斯曼过程监控分析 ... 20
4.3 运用PCA 的TE 过程故障研究 21
4.4 本章小结 .. 27