Comparison of Multivariate Analysis methods with Application to Fault
Diagnosis for non-Gaussian process
Xu Jiapeng, Wen Chenglin
Institute of Systems Science and Control Engineering, school of Automation,
Hangzhou Dianzi University, Hangzhou Zhejiang 310018, China
E-mail: imxjp@sina.com, E-mail: wencl@hdu.edu.cn
Abstract: Traditional fault diagnosis methods of multivariate analysis (MVA) usually require that sampling data of separated
latent variables must be subject to normal distribution, which is usually difficult to meet the actual industrial p rocesses. This
paper firstly introduces a method of fault diagnosis based on Q statistic. It requires that sampling data must be subject to normal
distribution. Then this paper introduces a method of fault diagnosis based on information incremental matrix (IIM), whose
sampling data h aven’t the limitation of n ormal distribution. The method is mainly composed of defining covariance matrix,
calculating information incremental matrix, information incremental mean and dynamic threshold, and so on. Finally, this paper
gives a example of numerical simulation and a example of Tennessee Eastman Process (TEP), to verify the detection
performance of two fault diagnosis methods, i.e., Q statistic and IIM, in false and missed alarm. The results show that Q statistic
method have poor detection performance in the case that sampling data are not subject to normal distribution, while the method
of fault diagnosis based on IIM is better.
Key words
fault d iagnosis;non-Gaussian process; Q statistic; information incremental matrix
1 Introduction
In industrial systems, many of the actual processes
contain both Gaussian and non-Gaussian process [1], so the
sampling data acquired from industrial systems are usually
not subject to normal distribution. Currently, most
data-driven fault diagnosis methods based on MVA require
that sampling data are subject to normal distribution, such as
Principal Component Analysis (PCA), Relative Principal
Component Analysis (RPCA) [2], Designated Component
Analysis (DCA) [3]. Ding introduced a fault diagnosis
method based on Q statistic in the literature [4], which is a
method of MVA like the PCA. The method firstly
establishes a mon itoring mod e l based on extensive historical
data, then it can determine whether the new observational
data deviate monitoring model, to judge whether the system
is faulty. This method requires that the sample data are
subject to normal distribution and it is only applicable to
invariant model. However, most of industrial processes are
slow time-variant [5].
Addressing the above problems, the literature [6, 7] gave
a fault diagnosis method based on IIM. This fault diagnosis
method neither has a limi tation that sampling data must be
subject to normal distribution, nor needs extensive historical
data to build model offline. In the case of IIM, the most
interesting side is that sampling data haven’t limi tation of
Gaussian distribution, whereas the method of Q statistic is
looking for the Gaussian distribution. Thus, IIM may reveal
more meaningful information in the non-Gaussian data than
Q statistic. The IIM method de fines and calculates the
covariance matrix based on current and previous time
sampling data, updating covariance matrix when new
observational data is gained. Then covariance matrix of the
current time subtract the covariance matrix of the previous
time, resulting in infor matio n incremental matrix. Finally,
calculating the information incremental mean and dynamic
*
This work is supported by National Natural Science Foundation (NNSF)
of China under Grant 61304109, 61203094, 61174112, 61433001.
threshold based on the infor mation incremental matrix, the
method can determine the system whether there is a failure.
2Faultdia
g
nosis method based on Q statistic
(Algorithm 1 [4])
Consider a process with m variables, let
11 1
22 2
12
11
11
mn
n
mm m
xx xn
xx xn
xx xn
!
#+
#+
(
#+
#+
#+
%,
XR
(1)
Where n is the number of samples. The mean vector of
n
X
is constructed as:
nnn
n
lXb
1
(2)
Where
&
n
n
Rl (
T
1,1,1
.
Q statistic is
T
nn
Q ))xb xb
(3)
Assuming the sampling data subject to normal distribution,
Box [7] proved that the Q distribution can be approximated
as
hgQ
2
~
(4)
Where
)(
2
h
is the chi-squared distribution with h degrees
of freedom and
S
Q
h
)(2
2
(5)
)(2
g
Q
S
(6)
Where
)()()))(((
222
QQQQS
))
.For our
purpose of fault detection,
S
,
)(Q
can be estimated using
Proceedings of the 34th Chinese Control Conference
Jul
y
28-30, 2015, Han
g
zhou, China
6362
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