基于MATLAB故障诊断系统设计(8)

沈阳理工大学学士学位论文

[17] 李尔国, 俞 金等. PCA在过程故障检测与诊断中的应用[M], 华东理工大学学报, 2011, 5: 1-8

[18] 陈国金, 梁 军, 钱积新. 独立主元分析方法及其在化工过程监控和故障诊断中的应用[M], 化工学报, 2007, 12: 14-17

[19] 赵立杰, 王 纲, 李 元. 非线性主元分析故障检测与诊断方法及应用[M], 信息与控制出版社, 2010: 359-361

[20] 徐东艳, 孟晓刚. MATLAB函数库查询词典[M],

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, 2006: 55-62

中国铁道出版社沈阳理工大学学士学位论文

附录A：英文原文

Fault detection industrial processes using canonical variate

analysis and dynamic principal component analysis

1. Introduction

Large amounts of data are collected in many industrial processes. The task of fault detection is to use this data to determine when abnormal process behavior has occurred, whether associated with equipment failure, equipment wear, or extreme process faults. While techniques based on first-principles models have been around for more than two decades, their contribution to industrial practice has not been pervasive, due to the substantial cost and time required to develop a sufficiently accurate process model for a complex chemical plant. The fault detection techniques that have dominated the literature for the past decade and have been most effective in practice are based on models constructed almost entirely from process data.

The accuracy of detecting faults from data can be improved using data dimensionality reduction techniques, such as principal component analysis (PCA), dynamic principal component analysis (DPCA) and canonical variate analysis (CVA).The lower dimensional representations produced by these techniques can better generalize to new process data than representations using the entire dimensionality.

Academic and industrial process control engineers have applied PCA for abstracting structure from multidimensional chemical process data. PCA determines the most accurate lower dimensional representation of the data, in terms of capturing the data directions that have the most variance. The resulting lower dimensional model has been used for detecting out-of-control status and for diagnosing faults leading to the abnormal process operation. Several applications of PCA to real industrial data have been conducted at DuPont and other companies over the past 6 years, with much of the results available in various publications (for example, see Refs, and citations therein)

PCA can be extended to take into account serial correlations in the data by augmenting each observation vector with the previous l observations. We will refer to this approach as

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沈阳理工大学学士学位论文

dynamic PCA (DPCA), irrespective of how the number of lags are selected (the DPCA method of Ref. is one implementation of this approach).CVA is a dimensionality reduction technique in multivariate statistical analysis involving the selection of pairs of variables from the inputs and outputs that maximize a correlation statistic. Like DPCA, the method takes serial correlations into account during the dimensionality reduction procedure.

PCA has been used to detect faults from data collected from real chemical plants and computer simulations the Tennessee Eastman process. Applications of DPCA and CVA to chemical processes either in simulation or industry are much more limited. The objective of this paper is to evaluate and compare the performance of PCA, DPCA, and CVA for detecting faults in a realistic chemical process simulation. In this comparison, a CVA-based residual space statistic is proposed

for use in fault detection. As will be seen later, the proposed statistic gave better overall sensitivity and promptness than the existing PCA, DPCA, and CVA statistics applied to the Tennessee Eastman process.

The paper is organized as follows. First, PCA and DPCA are briefly described. Then, the CVA statistical method and fault detection statistics are described. Finally, PCA, DPCA, and CVA are applied to data collected from the Tennessee Eastman process simulator. The sensitivity, promptness, and robustness of the statistics are compared. 2. PCA

2.1. Definition

PCA is an optimal dimensionality reduction technique in terms of capturing the variance of the data. PCA determines a set of orthogonal vectors, called loading vectors, which can be ordered by the amount of variance explained in the loading vector directions. Given n observations of m measurement variables stacked into a training data matrix X, the loading vectors are calculated by computing the singularities of the optimization problem

vTXTXvmax v?0vTv(1.1)

Wherev?Rm, the stationary points of Eq. (1).can be computed via the SVD

1X?U?VT n?1(1.2)

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沈阳理工大学学士学位论文

Where U?Rm?n and V?Rm?n are unitary matrices and the matrix

??Rm?n contains

the nonnegative real singular values of decreasing magnitude (?1??2?....??min(m,n)?0) The loading vectors are the or normal column vectors in the matrix V, and the variance of the training set projected along the ith th column of V is equal to

?i2.

2.2 Fault detection

Normal operations can be characterized by employing Hotelling’s T2 statistic

T2?xTP?aPTx

?2(1.3)

Where P includes the loading vectors associated with the a largest singular values, contains the first a rows and columns of

?a?and x is an observation vector of dimension m.

Given a number of loading vectors, a, to include in Eq. (3), the threshold can be calculated for the T2statistic using the probability distribution.

(n2?1)aT??F?(a,n?a)

n(n?a)2(1.4)

WhereF?(a,n?a)is the upper 100a% critical point of the F-distribution with a and n-a degrees of freedom. The T2 …… 此处隐藏：6547字，全部文档内容请下载后查看。喜欢就下载吧 ……