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.

REFERENCES

[1] A. J. Morris& E. B. Martin (1997), Process Performance

monitoring Fault Detection Through Multivariate Statistical

Process Control, IFAC Fault Detection, Supervision and

Safety for Technical Process, UK.

[2] A. Simoglou, E. B. Martin,A. J. Morris, M. Wood & G. C.

Jones (1997), Multivariate Statistical Process Control

System, IFAC Fault Detection, Supervision and Safety for

Technical Process, UK.

[3] J. F. MacGregor & T. Kouriti (1995), Statistical process

control of multivariate processes. Control Engineering

Practice, 3(3): 403-414.

[4] S. L. Jämsä-Jounela, M. Vermasvuori, P. Endén & S.

Haavisto (2003), A process monitoring system based on the

Kohonen self-organizing maps, Control Engineering

Practice, 11: 83-92.

[5] T. Komulainen, M. Sourander & S. L. Jämsä-Jounela

(2004), An online application of dynamic PLS to a

dearomatization process, Computers & Chemical

Engineering, 28(11): 2611-2619.

[6] R. J. Patton, P. M. Frank & R. N. Clark (1989), Fault

diagnosis in dynamic system: theory and applications,

Prentice Hall.

[7] R. Isermann & P. Ballé (1997), Trends in the Application of

Model-based Fault Detection and Diagnosis of Technical

Processes, Control Engineering Practise, 5: 709-719.

[8] J. Chen & R. J. Patton, “Robust Model Based Fault

Diagnosis for Dynamic Systems”, Kluwer Academic

Publishers ISBN 0-7923-841-3, 1999.

[9] J. M. F. Calado, J. Korbicz, K. Patan, R. J. Patton & J. M.

G. S da Costa, Soft Computing Approaches to Fault

Diagnosis for Dynamic Systems, Invited Special Issue

Paper, European Journal of Control, 7(2-3), July 2001.

[10] J. F. MacGregor, T. E. Marlin, J. V. Kresta & B.

Skagerberg (1991), Multivariate statistical methods in

process analysis and control, AIChE symposium

proceedings of the 4th international conference on chemical

process control, 67: 79-99, New York: AIChE Publ.

[11] I. T. Jolliffe (1986), Principal Component Analysis.

Springer-Verlag, New York.

[12] A. Hoskkuldon (1988), PLS Regression Methods, J.

Chemometric, 2: 211-228.

[13] B. Jönsson B, L. Klarnäs & M. Norberg (2003), Inteligent

Alarm Handing In the Steel Manufacturing Industry, Per-

Olof Norberg, Advanced Process Control Ltd. & O

Marjanovic and Keith Smith, Control Technology Centre

Ltd.

[14] X. Wang, U. Kruger & B. Lennox (2003), Recursive partial

least squares algorithms for monitoring complex industrial

processes. Control Engineering Practice, 11: 613-631.

[15] P. Geladi & B. R. Kowalski (1986), Partial least squares

regression: A tutorial. Analytica Chimica Acta, 187; 1-17.

[16] D. Sauter, T. Boukhobza & F. Hamelin (2005),

Decentralized and Autonomous Design for FDI/FTC of

Networked Control Systems, NeCST Workshop in Ajaccio.

[17] S. Sauter & C. Aubrun (2006), A heating system as a

benchmark for networked control systems tolerant to faults.

Internal Documentation of the EU Project IST-004303

NeCST, UHP, Nancy.

[18] C. Perkgoz, C. Kambhampati, R. J. Patton & V. Palacka

(2005), Integration of OPC Tools in Network Control

Systems Tolerant to Faults, Proceedings of the 1st NeCST

Workshop on Networked Control Systems, Corsica,

http://www.strep-necst.org.

[19] J. M. F. Calado, J. Korbicz, K. Patan & R. J. Patton (2001),

Soft Computing Approaches to Fault Diagnosis for

Dynamic Systems. European Journal of Control, 7, 248-

286

[20] B. Lennox (2005), Ed. Special issue on Recent Advances in

Process Fault Monitoring. International Journal of

Adaptive Control and Signal Processing, 19(4)

[21] R.J. Patton, C. Kambhampati, A. Casavola, P. Zhang, S.

Ding & D. Sauter (2007), A Generic Strategy for Fault-

Tolerance in Control Systems Distributed over a Network,

Invited Special Issue Paper, European Journal of Control,

13: 280-296.

[22] R. J. Patton & S. Klinkhieo (2009), A Two-Level Approach

to Fault-Tolerant Control of Large Scale Systems based on

the Sliding Mode, Safeprocess’09, 30th June-3rd July,

Barcelona.

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