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Abstract—The problems of fault detection and isolation of
dynamic systems has been studied intensively in the recent
years and many successful industrial applications have been
reported. In the main these studies have been restricted to
model based techniques, with few reports of successful
implementation of data driven approaches. These data driven
approaches have been range from the application of linear
regression techniques, to neuro-fuzzy systems. This paper
reports on application of, Multivariate Statistical Process
Control (MSPC) methodologies, which can provide a
diagnostic tool for the on-line or real time monitoring and
detection of the process malfunction is proposed. Finally the
effectiveness of Partial Least Squares (PLS) in FDI of the
Three-Tank system are represented and discussed through
simulation results.
I. INTRODUCTION
uring the last two decades, there have been immense
advances in the areas of advanced process control,
specifically dealing with fault detection and isolation
(FDI). The objective of these developments is to be able to
detect and distinguish not only sudden faults (step faults)
but also incipient faults (including drift faults) occurring in
the process. The ability to detect and isolate these faults is
crucial in order to avoid loss of product and reduced
profitability and eventual inappropriate shut-down. In
addition FDI methods enhance the safe operability of the
processes, lack of attention to a suitable level of process
monitoring and FDI will obviously lead to environmental
and health issues [1] and [2]. There have been a number of
successful industrial studies and these have been reported
in research literature [2], [3], [4] and [5]. At the same time
there have also been comprehensive reviews on the
theoretical approaches to fault detection and process
monitoring [6]. In the process control industry, data driven approaches
such those based on soft computing [19] and MSPC
techniques [2], are preferred to model based approaches
for FDI. These methods are varied and a good overview
providing a classification of methods, with a good
framework under which quantitative model-based methods
using neural networks, fuzzy logic, neuro-fuzzy, etc can be
found in [7], [8], [9], [19], and [20]. Work reported in [1] and [2] developed concepts of
process performance monitoring (allied to FDI) through
MSPC for chemical processes. These methods are based
on Principal Component Analysis (PCA) and Partial Least
Squares (PLS). These studies have shown that MSPC is
efficient in providing early warning capabilities for the
R. J. Patton is with the Department of Engineering, University of
Hull, Hull, HU6 7RX UK (phone: +44 (0)1482-46-5117; fax: +44
(0)1482-46-6664; e-mail: R.J. Patton@hull.ac.uk).
S. Klinkhieo is with the Department of Engineering, University of
Hull, Hull, HU6 7RX UK (e-mail: S.Klinkhieo@2005.hull.ac.uk).
comprehensive monitoring and detection of process
malfunctions. In addition, these methods have been shown
to be particular valuable for application to processes
involving large amounts of data, as discussed by [1] and
[10] In this paper, Multivariate Statistical Process Control
(MSPC) methods are used as an effective set of tools for
FDI and the diagnosis of abnormal operating conditions of
the process variables. It should be noted that only a sudden
fault (step fault) is studied and presented in this research.
In Section II, the fundamental concept of PLS algorithms
is first represented. Section III, the study on three-tank
systems and fault diagnosis is discussed. Then, the
developed experimental platform for on-line FDI with the
three-tank system is presented in Section IV, and finally,
the PLS based FDI simulation results are reported and
analyzed.
II. MULTIVARIATE STATISTICAL PROCESS CONTROL MSPC is based on statistical projection techniques, namely
Principal Component Analysis (PCA), [11] and Projection
to Partial Least Squares, [12]. These two methods are
employed extensively for on-line or real time multivariate
monitoring and detection schemes of the process
malfunction. PLS offers certain attractive features, both in
MSPC applications and control system applications. The
basic approach of the algorithm is to identify the principal
features in the data by dividing the variable space in to
cause and effect, and performing a dimensionality
reduction on them. In a sense, PLS provides a method for
compressing the dimensionality of the data space. It then
identifies the primary features in the cause variables that
are able to describe the variation in the effect variables. A
major feature of PLS is that it will deal with correlated
data and will produce answers when Ordinary Least
Squares cannot [12] and [13]. This property is not unique
to PLS as there are alternative algorithms that can also
cope with correlated data, such as recursive least squares
and ridge regression [14]. A significant benefit that PLS
offers over these approaches is that once the model is
developed it can be used for both monitoring the condition
of a plant, but also to control it. The PLS approach relies on decomposing the input matrix,
KxMX ℜ∈ and the output matrix, KxNY ℜ∈ , to sum of
rank one component matrices, [15]. Here K is the number
of measurements or data sizes, M is the number of output
variables and N is the number of input variables. Typically, the PLS decomposition of X and Y are given is
carried out in the following manner [14]:
PLS-based FDI of a Three-Tank Laboratory System
S. Klinkhieo & R. J. Patton, Senior Member IEEE
D
Joint 48th IEEE Conference on Decision and Control and28th Chinese Control ConferenceShanghai, P.R. China, December 16-18, 2009
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,ˆˆ
ˆ~
,
~
11
11
nnnTnn
nTi
n
i
in
n
i
i
nnnTnn
nTi
n
i
in
n
i
i
EYEQU
EquEYY
FXFPT
FptFXX
+=+=
+=+=
+=+=
+=+=
∑∑
∑∑
==
==
(1)
where n is the number of rank one component matrices,
Tiii ptX =
~and T
iii quY ˆ~
= , retained in the decomposition.
The vectors it and iu are referred to as the t-score vector
and u-score vector, the vectors ip and iq are loading
vectors, nX and nY represent the sum of n the rank one
component matrices to reconstruct the input matrix and
predict the output matrix, respectively, nE and nF are
residual matrices. The u-score vectors, iu , can be
estimated from the t-score vectors as follows:
nnnni BTbtbtuuU === ],,[]ˆ,,ˆ[ˆ1111 LL (2)
where nB represents a diagonal matrix containing the
regression coefficients of the score model, ib , determined
by PLS algorithm. The loading vectors are identified using a technique known
as singular value decomposition (SVD), which calculates
the loadings such that the first score explains the greatest
variation in the data, the second score the next and so on.
Each of the scores is uncorrelated to one another.
However, it should be noted that the scores are often
referred to as latent variables, i.e. each score vector
represents an instance of a particular latent variable or LV
[14]. Another way of looking at PLS is that it creates a new set
of variables (latent variables) which are reflective of true
dimensionality of the system. This new set of variables, are
a set of strongly correlated variables and often only a few
t-score vectors are needed to describe the process variation
or process performance [12]. The number of retained t-
score vectors is typically determined by cross-validation or
the analysis of variance, etc as demonstrated for example
by [3] and [10]. Fig. 1 shows the example of PLS algorithms the system
which contains original input (I) and original output (O),
respectively. PLS provides the PLST -transformation
which can reduce the dimensionality of the original input
(I) and output (O) with the relationship )(OfI p= to the
new dimensionality of X and Y which can reserve the
relationship between input and output to the term of
).(XfY m=
Fig. 1. Generic setup of PLS
In this case, it should be noted that the PLST -
transformation is not invertible, the dimensionality of X is
less than the dimensionality of I (DIM X < DIM I) and the
dimensionality of Y is less than the dimensionality of O
(DIM Y < DIM O). Namely, this has two implications: (a)
the relationship between X & Y need not have the same
characteristics as that between I & O (b) there need not be
a direct one to one relationship between the variables in
the space X and those in the space I on one hand and the
space Y and the space O on the other. In addition,
numerical analysis carried out in the transformed space
cannot be translated back to the original space.
III. THE NECST THREE-TANK BENCHMARK SIMULATION The NECST 3-Tank Bench Mark Simulation [16] and [17]
has been selected for both testing and verifying the ideas
developed in this paper. The model represents a real 3-tank
system (Fig 2) from the Research Centre for Automatic
Control in CRAN-UHP, Nancy, FRANCE. The concepts
presented will be later tested on this bench mark system. It can be seen that Fig. 2 shows the subsystem-1 has 3
inputs ( 1201 , QandPQ w ) and 3 states ( ],,[ 12111 VTLx = )
with the following dynamics:
1212
1001111
10120111
)(
QV
c
PTTQTLS
QQQLS
w
=
+−=
−−=
&
&
&
ρ (3)
Subsystem-2 has 2 inputs ( 2002 QandQ ) and 3 states
( ],,[ 20222 VTLx = ) with the following dynamics;
2020
20323220022112222
2323220021222
))(()()(
)(
QV
TTQQTTQTTQTLS
QQQQQQLS leak
=
−′++−+−=
−′++−+=
&
&
&
(4)
Subsystem-3 has 2 inputs ( 3203 QandQ ) and 2 states
( ],[ 3233 VLx = ) with following dynamics:
3232
33032320333 )(
QV
QQQQQLS leak
=
−−′+−=
&
&
(5)
pf
mf
X
Y
I
O
PLSTPLST
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Fig. 2. Schematic diagram of NeCST Three-Tank
Benchmark System
where 3,2,1,0,,,,, =iQQVTLS leakiijijiii are the cross-
sectional areas of each tank, the level of liquid in tank-i,
the temperature of liquid at the centre of the tank-i, the
volume of liquid passing from tank-i to tank-j, the liquid
flow rates between tank-i to tank-j, and the leak from tank-
i, respectively. ij =0 means the buffer tank. wP is the
power input. ρ and c are the density and the specific
heat capacity of the liquid inside the tank. It should be noted that the flow-rates on the system are
controlled by either pumps or valves. The system working
as follows:
• Pump_1 is kept constant at 0.75 m3/sec.
• Tank-1 is fed by Valve01 (Q01).
• Tank-2 is fed by Valve02 (Q02) and Pump_2
(Q12).
• Tank-3 is fed by Pump_3 (Q03). The liquid inside the Tank-1 is heated by an electrical
heater. The Tank-2 is taking preheated liquid from the
Tank-1 (Q12) and mixes it with a solution coming from the
Tank-3 (Q32). Valve32’, Valve_leak_1, Valve_leak_2, and
Valve_leak_3 are totally closed (Q’32 = Q10 = Qleak2 = Qleak3
= 0) and Valve30 is totally opened during the simulation. The performance objectives for the system are as follows:
• Maintain the levels of each tank, L1 at 0.75 m, L2
at 0.3 m and L3 at 0.5 m.
• Maintain the temperature of 1st and 2nd tank, T1 at
30oC and T2 at 28
oC.
The system is simulated initially without any faults and
from Fig. 3 it can be seen that the outputs track the
reference signal. The desired values (reference) for each
control objective are shown in the dashed lines [18]. This example system constitutes a distributed control
problem under autonomous learning supervision with each
tank represented as one subsystem in the inter-connected
structure. This involves the use of two-level constrained
optimal control, fitting to the structure of a receding
horizon control problem with an added supervision layer to
compensate the inter-connection disturbance (states)
yielding good fault-tolerance properties. However, in this
study the fault information is not actually used for
improving the fault-tolerant control performance. Details
of this approach can be found in [21]. Further studies have
involved fault compensation within this distributed system
structure [22].
0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
L id
: (dashed lines) L i : (solid lines)
Level (
m)
time (s)
L 1
L 3
L 2
0 500 1000 1500 2000 2500 3000 3500 4000 4500 500020
22
24
26
28
30
32
T id
: (dashed lines) T i : (solid lines)
Tem
pera
ture
( o
C)
time (s)
T 1
T 2
Fig. 3. System outputs without fault
IV. FDI FOR EXPERIMENTAL PLATFORM
In order to study and develop FDI for the system when
subjected to different types of faults, the experiment
platform has been enhanced with the addition of 3 new
software modules, as shown in Fig. 4. This modification
allows for real-time /on-line FDI. It should be noted that
the simulation is running in real-time.
Fig. 4. On-line FDI scheme for Three-Tank System. First, the original input (I) and output (O) variables from
Three-Tank simulation are collected and sent to PLS
platform by the Data collection module. This module is
I
O Y
X
Information
of faults
Three-Tank
Simulation
PLS
algorithm
FDI
Fault
analyzer
Input
parameters
Data
Collection
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developed using LabVIEW© (National Instruments,
http://www.ni.com) running as a real-time parallel with the
three-tank simulation. Namely, the both input and output
variables from the Three-tank simulation (using
MATLAB) have been send to Data collection module
(using LabVIEW) every time interval (second) and such
data will be collected and saved into the buffer within this
module in term of the input and output matrices with the
matrix sizes KxN and KxM, respectively, and then transfer
these matrices to the next module. Second module is the PLS module, which takes the data,
collates them into the relevant matrices, and performs the
dimensionality reduction, and also determines the other
values required for the FDI. However, as discussed in
Section II, it should be noted that the dimensionality of
original inputs and outputs are less than the dimensionality
of the new ones and these new variables are linear
combinations of the original measured variables. In the simulation, 44 input variables (I) were measured
along with 22 output variables (O). The results from the
PLS module using these variables are presented in Tables
1, and 2. Fig.5 shows the results after processing the PLS
variables, shows the score and the corresponding
explanations for the variances. From the results, it can be seen that the first three scores of
the new dimensionality (X and Y) have captured the major
features in the data. In other words only three score/latent
variables (1st, 2nd and 3rd) are sufficient to describe the
process performance while the 4th
score contains very little
variation and it can be assumed that this value explains the
measurement noise in the system. Table 1 & 2 below list
the variance of each of these scores:
Score % Variance Cumulative Variance
1 68.26 68.26
2 20.272 88.532
3 11.118 99.65
4 0.35 100
Table 1: Variance information of the input variables
Score % Variance Cumulative Variance
1 75.331 75.331
2 15.3 90.631
3 7.569 98.2
4 1.8 100
Table 2: Variance information of the output variables Fig.5 also shows that the first three latent values of X and
Y can describe over 99.65% and 98.2% of the variation. However, as has been pointed out in [1] and [2], it is very
important that the lower scores are not to ignored since
they can provide additional information to aid process fault
detection.
0
20
40
60
80
1 2 3 4Score/Latent vector
Va
rian
ce
Exp
lain
ed
(%
)
Input variables (X) Output variables (Y)
Fig.5. Example of new input/output data sets produced by
PLS algorithm. The results of the PLS module are then analysed by the
fault analyzer module. This can provide information of: (a)
process performance, (b) changes in the underlying
operations of the process and (c) real- time implementation
of a process monitoring schemes. However, when a process is recognized to be out of
control or there are faults occurring, the fault analyzer
needs specific methods to identify which variables are
responsible for the change in the process. It may be
possible to identify the set of the original variables whose
contribution has increased over that defined in the nominal
model and which are responsible for non-conforming
behavior. One approach is through the implementation of a
process variable contribution plot which depicts the
change in the new observation variables relative to the
average value calculated from the nominal PLS model [1]
and [2]. Next section, fault analyzer, using (xi, yi) pairs which can
provide the certain cluster for the particular patterns of
faults will be discussed and the simulation results are also
presented.
V. FAULT ANALYSIS MODULE
As discussed in Section IV, the fault-detection abilities of
the FDI systems were evaluated using the simulation
datasets, for period of 5,000 seconds under fault condition.
Fig. 6 shows the FDI system for three-tank system in case
of fault free.
Definition 1: ttUtUdU ililil ∀−+= ),()1(
where ilU is output score/latent value-l of tank-i,
respectively.
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Fig. 6. FDI residuals for three-tank simulation for fault-
free case
The next sets of simulation results were carried out with
bias faults (20%, 40% and 60%) of the electrical heater
operating point after t = 2500 seconds. The results of these
simulations are shown in Figs. 7, 8 and 9.
0
5
10
15
20
-50 -30 -10 10 30 50
Output latent value #1
Ou
tpu
t la
ten
t valu
e #
4
Fig. 7. The example of the FDI system for three-tank
simulation: (a) the fault detection (Fault in tank-1 is
detected only) and (b) the relationship between the process
and /or quality variables between output latent variable #1
and #4 due to bias fault (20% of heater operating point).
Fig. 8. The example of the FDI system for three-tank
simulation: (a) the fault detection (Fault in tank-1 is
detected only) and (b) the relationship between the process
and /or quality variables between output latent variable #1
and #4 due to bias fault (40% of heater operating point).
Fig. 9. The example of the FDI system for three-tank
simulation: (a) the fault detection (Fault in tank-1 is
detected only) and (b) the relationship between the process
and /or quality variables between output latent variable #1
and #4 due to bias fault (60% of heater operating point). Fig. 7(a), 8(a) and 9(a) show the faults with 20%, 40% and
60% bias of heater operating point in tank-1 are detected
(only detected).
PLS for Tank-1
Fault detected
Relative to the
magnitude of fault
PLS for Tank-1
Fault detected
Relative to the
magnitude of fault
Relative to the
magnitude of fault
(a)
(b)
(a)
(b)
Fault detected
PLS for Tank-1
(a)
(b)
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Fig. 7(b), 8(b) and 9(b) present (xi, yi) pair with the
particular pattern of clusters (fault information) depending
upon; fault types, fault sizes, etc. It should be noted that in this study, the only the electrical
heater fault with the various magnitudes (e.g. the
magnitudes of bias faults; 20%, 40% and 60% of heater
operating point, respectively) are presented. Throughout the simulation results it can be seen that the
FDI units using PLS algorithm is able to detect faults and
also identify the subsystem where the fault is occurred.
ACKNOWLEDGMENT
S Klinkhieo acknowledges PhD scholarship funding from
the Synchrotron Light Research Institute (SLRI) under the
Royal Thailand Government and discussions with C
Kambhampati of the Computer Science Department at Hull
University. The authors are grateful for funding support
from the EC FP6 IST programme under contract No. IST-
004303NeCST (Project NeCST http://www.strep-
necst.org/ )
VI. CONCLUSION There have been numerous studies on the utility of MSPC
in general and PLS in particular. These results and studies
have shown that PLS is a useful tool for both modeling,
and controlling process plants as well as for an integrated
condition monitoring system. All of these studies indicate
that that MSPC based methods are able to handle the high
dimensionality of the data, which is a given in process
plants, and also extract relevant information from this data.
It is this property which is attractive, and has been used
here. This paper presented ideas for the development of an
FDI methods based on PLS and clustering. However, the
concepts though are generic; they require fine tuning and
are application dependent. The results obtained from the
test platform used, namely three-tank system using
“primary” process data indicates promising results.
Currently work is underway to make the FDI method more
efficient and less process specific.
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