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Incipient Sensor Fault Diagnosis Based on Average
Residual-Difference Reconstruction Contribution Plot
Jiyang Xuan, Zhengguo Xu,* and Youxian Sun
State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Department of Control Science and
Engineering, Zhejiang University, Hangzhou 310027, China
ABSTRACT: This paper presents a novel method to diagnose incipient single sensor fault for data-driven process monitoring.
As the traditional fault detection methods using statistical indices are not sensitive to incipient faults and the reconstruction-based
contribution plot (RBCP), which reduces the fault smearing effect of the traditional contribution plot (TCP) also does not take
incipient faults into consideration, a new contribution plot based on average residual-difference and reconstruction is defined to
detect incipient faults with high detection sensitivity and to overcome two main disadvantages, lack of consideration of
contribution plot in the normal condition and using the data at one sampling time, of the RBCP when incipient faults are treated.
Then, fault magnitude can be estimated after the correct identification without the need of a fault direction set, which is different
from the fault reconstruction method. The effectiveness of the proposed fault diagnosis method is verified by a Monte Carlo
numerical simulation and the benchmark quadruple-tank process.
1. INTRODUCTION
Multivariate statistical process monitoring (MSPM) techniques
have been applied successfully to monitoring chemical pro-
cesses.
1−3
The key to MSPM is to detect faults early and to
identify faults correctly, as faults can cause processes to deviate
from their normal operating conditions. Principal component
analysis (PCA) has been widely used to detect abnormal operating
conditions utilizing process information acquired from historical
process data, and it is capable of handling high dimensional, noisy,
and correlated data by projecting the data onto a lower
dimensional subspace, which explains the most pertaining features
of the process. When a fault is detected, it is necessary to find the
root cause of this fault, so MacGregor and Kourti
4
proposed the
traditional contribution plot (TCP) used for fault identification,
and this method has been widely used as well. The TCP reveals
which variable contributes most significantly to some multivariate
statistical indices, such as Hotelling’s T
2
and squared prediction
error (SPE). The assumption behind the TCP is that faulty
variables have large contributions to the fault detection indices.
There are, however, reports that the TCP involves fault smearing
effect which can lead to misdiagnosis. Alcala and Qin
5
showed that
the TCP approach failed to guarantee the correct identification of
the faulty variable. Furthermore, they proposed the reconstruc-
tion-based contribution plot (RBCP) to locate the faulty variable
without the fault smearing effect. The contribution plot method
is an effective way, and another available method for fault
identification is fault identification via reconstruction developed
by Dunia and Qin,
6,7
which can guarantee correct fault diagnosis
provided that the fault direction is known and is in the candidate
set of fault directions.
After detecting and identifying a fault, it is necessary to
estimate the fault magnitude finally, which can help operators
to know how serious the fault is. However, most of the existing
fault estimation methods are model-based, and data-driven
methods are scarce. Fault estimation based on fault reconstruc-
tion theory is a feasible way that requires a set of known fault
directions.
6−8
In addition, without the assumption that the fault
magnitude was far greater than the normal measurement, which
was an essential requirement for fault reconstruction method to
extract process fault direction, Zhang et al.
9
estimated the fault
magnitude by solving a unary quadratic equation after getting the
fault direction.
There are different types of faults in chemical processes, such
as sensor faults, actuator faults, and process faults. Incipient
faults that happen in the initial phase of these mentioned faults
are difficult to be detected, as the traditional PCA-based
statistical indices are not sensitive enough to these faults with
small magnitudes. A single sensor with an incipient bias fault is
considered in our work. In this paper, a numerical example is
first used to show that the detecting methods adopting common
PCA-based statistical indices fail to detect incipient sensor faults,
and the RBCP cannot identify incipient faults correctly. Two
drawbacks can be found in the RBCP method if we take incipient
sensor faults into consideration. First, the RBCP method does not
consider the contribution plot of the normal condition, which is
also vital as they can affect the contribution values of the observed
variables. Second, the RBCP is derived at one sampling time, so
the stochastic noises could decrease their effectiveness for
identifying incipient sensor faults. To address these problems
mentioned above, we propose a new contribution plot named
average residual-difference reconstruction contribution plot
(ARdR-CP). When dealing with sensor faults, the ARdR-CP has
the capability of detecting and identifying faults simultaneously.
After the faults are detected and identified, we directly utilize the
fault estimation equation derived from the fault reconstruction
method to estimate faults, but our fault diagnosis method does not
include the procedure of fault identificatio n via reconstruction that
needs a known fault direction set.
Received: November 14, 2013
Revised: February 8, 2014
Accepted: April 10, 2014
Published: April 10, 2014
Article
pubs.acs.org/IECR
© 2014 American Chemical Society 7706 dx.doi.org/10.1021/ie403857f | Ind. Eng. Chem. Res. 2014, 53, 7706−7713