沈阳理工大学学士学位论文

摘 要

随着对自动化设备的安全性、可靠性以及有效性要求的提高，故障诊断技术受到人们的重视，已成为国内外自动化控制界的热点研究方向之一。故障诊断是对控制系统进行故障检测与诊断，并对故障的原因、故障的频率、故障的危害程度及故障的趋势预测等内容进行分析判断，为确诊故障点、及早采取维修、防护等补救措施提供科学的决策依据。

随着科学技术进步，过程工业生产装置的结构日趋复杂，逐渐从单变量系统发展到以多变量系统为主，通常具有非线性、时变性、强耦合性及结构和参数的不确定性，这类系统和设备一旦发生故障，排除的时间增长，不仅造成巨大的经济损失，甚至造成人员伤亡和环境污染，因此传统的故障诊断方法已无法满足要求。

由于大多数过程工业难以建立精确的数学模型，基于数学模型的故障诊断方法在实际应用中遇到了较大的困难。多元统计过程控制的故障检测与诊断方法不依赖于系统的数学模型，因此该方法更具实用性。基于主元分析的工业过程故障诊断方法，由于充分利用了主元分析算法在处理线性数据时可对其降维的作用，使得对多变量生产过程的监测可在低维变量空间实现。本文对基于主元分析的故障诊断方法进行了系统、深入的研究。

关键字：故障诊断；主元分析；过程工业

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沈阳理工大学学士学位论文

Abstract

With the increasing requirement on safety, reliability and effectiveness of automation devices, study on the problem of fault diagnosis has received great attention and been one of the most active research topics. Fault diagnosis is doing fault monitoring and diagnosis for monitor and control system. It also analyzes fault source, frequency, severity, tendency etc., and provides scientific decision-making basis in order to confirm fault, take remedies, such as timely maintenance and defense.

With the development of science and technology, the process industrial production installment's structure is getting more and more complex, and develops gradually from the single variable system to the many-variable system primarily. Since it is usually highly nonlinear, time-varying, seriously coupling and its structure parameters are uncertain, traditional fault diagnosis method can’t satisfy the demand. Once this kind of system and equipment comes about malfunction, it will take a long time to be solved and lead to a large amount of economic loss, even human injuries or environmental problems.

It is difficult to found precise math-model in many industry processes, the fault detection method base on math model has much more difficulty actually application. The method of fault detection and diagnosis based on MSPC (Multivariate Statistics Process Control) doesn’t depend on the math model of system. The method of fault detection based on PCA (Principal Component Analysis) making full use of PCA algorithm well and it has the function of declining the dimension while handing line related data. It can make the monitor process carrying out from multivariate space into the low dimension. The main purpose of this thesis is to make further study on the fault diagnosis based on PCA.

Keywords: Principal Component Analysis; Fault detection; Process Industry

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沈阳理工大学学士学位论文

目 录

1 引 言 .................................................................................................................................... 1

1.1 故障诊断技术的研究背景 ......................................................................................... 1

1.1.1 故障诊断技术概述 .......................................................................................... 1 1.1.2 故障诊断技术的研究对象 .............................................................................. 1 1.1.3 故障诊断技术研究的必要性 .......................................................................... 2 1.2 国内外基于主元分析的故障诊断技术研究进展 ..................................................... 3

1.2.1 基于主元分析的故障诊断技术的研究历史 .................................................. 3 1.2.2 基于主元分析的故障诊断技术发展趋势 ...................................................... 4 1.3 本次设计主要工作内容 ............................................................................................. 7 2 故障诊断方法研究 .............................................................................................................. 8

2.1 基于解析模型的方法 ................................................................................................. 8

2.1.1 状态观测法 ...................................................................................................... 8 2.1.2 参数估计法 ...................................................................................................... 8 2.1.3 等价关系法 ...................................................................................................... 9 2.2 基于知识的方法 ......................................................................................................... 9

2.2.1 专家系统 .......................................................................................................... 9 2.2.2 人工神经网络 .................................................................................................. 9 2.2.3 因果分析法 .................................................................................................... 10 2.2.4 模糊理论 ........................................................................................................ 10 2.3 基于数据分析的方法 ............................................................................................... 10

2.3.1 主元分析法 .................................................................................................... 10 2.3.2 偏最小二乘法 ................................................................................................ 11 2.3.3 Fisher判别分析法 .......................................................................................... 11 2.3.4 规范变量分析法 ............................................................................................ 11 2.4.5 子空间法 ........................................................................................................ 12 2.4.6小波变换法 ..................................................................................................... 12

3 基于主元分析的故障诊断技术研究 ................................................................................ 13

3.1 主元分析的研究背景 ............................................................................................... 13

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沈阳理工大学学士学位论文

3.2 主元分析的数学思想 ............................................................................................... 13 3.3 主元分析的实现方法 ............................................................................................... 14

3.3.1 主元分析的分解方法 .................................................................................... 14 3.3.2 主元得分向量的计算方法 ............................................................................ 15 3.3.3 确定主元个数的方法 .................................................................................... 16 3.3.4 主元模型的建立 ............................................................................................ 17 3.3.5 主元分析的统计量 ........................................................................................ 18 3.4 基于主元分析的故障诊断流程 ............................................................................... 19 4 基于主元分析的故障诊断技术应用仿真研究 ................................................................ 21

4.1 应用仿真环境 ........................................................................................................... 21

4.1.1 田纳西--伊斯曼过程 ..................................................................................... 21 4.1.2 田纳西--伊斯曼过程工艺流程 ..................................................................... 21 4.2 仿真研究 ................................................................................................................... 22

4.2.1 基于主元分析的故障诊断步骤 .................................................................... 22 4.2.1 仿真概述 ........................................................................................................ 23 4.2.3 仿真结果 ........................................................................................................ 24

结 论 ........................................................................................................................................ 28 致 谢 ........................................................................................................................................ 29 参考文献 .................................................................................................................................. 30 附录A：英文原文 ................................................................................................................... 32 附录B：汉语翻译 ................................................................................................................... 39

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