202

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 1, NO. 3, AUGUST 2005

Identification and Fault Diagnosis of a Simulated

Model of an Industrial Gas Turbine

Silvio Simani, Member, IEEE

Abstract—In this study, a model-based procedure exploiting an-

alytical redundancy for the detection and isolation of faults of a
gas turbine system is presented. The diagnosis scheme is based on
the generation of so-called “residuals” that are errors between es-
timated and measured variables of the process. The work is com-
pleted under both noise-free and noisy conditions. Residual anal-
ysis and statistical tests are used for fault detection and isolation,
respectively. The final section shows how the actual size of each
fault can be estimated using a multilayer perceptron neural net-
work used as a nonlinear function approximator. The proposed
fault detection and isolation tool has been tested on a single-shaft
industrial gas turbine model.

Index

Terms—Fault diagnosis, gas turbines, identification,

Kalman filtering, observers.

I. I

NTRODUCTION

T

HE control devices currently in use to improve the overall
performance of industrial processes involve both sophisti-

cated digital system design techniques and complex hardware
(sensors, actuators, processing units). The complexity means
that the probability of fault occurrence can be significant and an
automatic supervisory control system should be used to detect
and isolate anomalous working conditions as early as possible.

This study is motivated by the challenge of developing di-

agnostic tools for gas turbine systems to indicate the onset of
developing faults and provide a mechanism for predictive main-
tenance requirements. Although the gas turbine is a complex
dynamical system we show that the model-based approach to
fault detection and isolation (FDI) can work very well under
realistic fault conditions.

Two main aspects of the proposed methodology should be

underlined

. Firstly, the system complexity does not indicate a

requirement for a complex physical or thermodynamic model.
This is because for FDI input–output model identification
methods are used, thus obviating the requirement for phys-
ical models. A linear mathematical model (state-space or
input–output descriptions) of the input–output links are, in fact,
obtained by means of identification schemes. Auto Regressive
eXogenous (ARX) models can be used in connection with the
least square method. On the other hand, Errors-In-Variables
(EIV) models are used according to Kalman [1], [2]. In the latter
approach the identification technique is based on the rules of the
Frisch scheme, based on traditional application to the analysis
of economic systems [3]. This approach gives a reliable model
of the plant under investigation, as well as providing variances

Manuscript received September 20, 2004; revised January 18, 2005.
The author is with the Department of Engineering, University of Ferrara,

44100 Ferrara, Italy (e-mail: [e-mail]).

Digital Object Identifier 10.1109/TII.2005.844425

of the input-output noises [4]. Both of these approaches have
been used in this study. Secondly, in this study linear prototypes
for the design of linear output estimators [5]–[10] have been
developed instead of using complicated nonlinear models.
Non-linear modeling is far from a straightforward subject,
even if there is a steady increase in research in this subject.
Regardless of the surge in interest in nonlinear systems, the
linear approach to fault diagnosis is still advantageous in terms
of solution complexity and performance. This is especially true
if so-called robust solutions are sought, where the robustness is
used to minimize the effects of modeling errors.

The problem of fault detection and isolation (FDI) in dy-

namic processes has received great attention during the last two
decades and a wide variety of so-called model-based approaches
have been proposed [11]–[14]. Model-based methods all use
mathematical models of the plant being monitored. However,
the conceptual realization of these models can vary according to
the following approaches: the parity space [15], state estimation
[16]–[21], the fault detection filter [19], [22], [23] and param-
eter identification [11], [16], [18]. In each case, to guarantee that
faults can be detected and isolated (and distinguished one from
another), mathematical models of the process under investiga-
tion are required, either in state space or input-output or transfer
function form. State space descriptions generally provide math-
ematically rigorous tools for system modeling and residual gen-
eration that may be used in fault detection of industrial systems,
both for the noise-free case and the noisy environments. Resid-
uals should then be processed to detect an actual fault condition,
rejecting any false alarms caused by noise or spurious signals.

This work aims to define a comprehensive methodology for

fault diagnosis by using a state estimation approach, in con-
junction with residual processing schemes, including a simple
threshold detection. This work describes how this is achieved
in the noise-free case as well as the noisy case using statistical
analysis tools, when the data are affected by noise. The complete
procedures of model identification, residual generation and fault
identification and isolation have been tested on a single-shaft in-
dustrial gas turbine prototype. The study provides a description
of extensive simulation results.

II. P

LANT

M

ODEL

D

ESCRIPTION

In the following it is assumed that the monitored system, de-

picted in Fig. 1(a), can be described in fault-free condition, by a
linear, discrete-time, time-invariant, dynamic model of the type:

(1)

1551-3203/$20.00 © 2005 IEEE

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SIMANI: IDENTIFICATION AND FAULT DIAGNOSIS

203

where

is the state vector,

the process

output vector and

the control input vector.

,

, and

are constant matrices of appropriate dimensions obtained by

means of modeling techniques or identification procedures.

Under fault-free conditions, the input and the output link of

the sensors can be described by the following relation:

(2)

In real applications, variables

and

represent noises

which, due to technological reasons, affect sensor behavior.
They are generally described as white, zero-mean, uncorrelated
Gaussian noises. It is assumed that

and

are the only

available measurements from the real process.

The vectors

and

model input and output sensor faults, respectively. The scheme
shown in Fig. 1(a) describes the relations among the actual
sensor inputs

and

, the sensor faults

and

and the sensor outputs

and

.

According again to Fig. 1(a), when a component fault

occurs in the plant described by (1), the dynamic system will

be modeled as

(3)

A fault

may also occur on the regulator in the control

loop. In such a case, under the assumptions that

and

, the link among the output

of the regulator, its

input

and the controller fault

will be modeled as

(4)

where

represents the input–output behavior of the con-

troller.

Usually

,

,

, and

signals are described by

step and ramp functions representing abrupt and incipient faults
(bias or drift), respectively.

Under fault-free assumptions, representations of types (1) and

(2) are known as EIV models.

The design of state observers and Kalman filters requires the

knowledge of a state-space model of the system under investiga-
tion. When classical modeling techniques cannot be used since
the complete physical knowledge of the system is not available
or the model parameters are unknown, a black-box identifica-
tion approach has to be considered.

III. E

QUATION

E

RROR

M

ODELS

Equation Error (EE) models belong to an identification model

class that can be successfully exploited in this study and, in par-
ticular, different equation error models can be extracted from
the data. A specific discrete-time, time-invariant, linear dynamic
model, e.g. ARX or ARMAX (Auto Regressive eXogenous or
Auto Regressive Moving Average eXogenous) [24], [25], can
be selected only inside an assumed family of models.

On the other hand, the Frisch scheme [3] can be also applied

to perform the EIV dynamic system identification, in particular
when noise signals affecting the data have to be estimated [4].

Fig. 1.

(a) Monitored system and (b) the logic diagram of the fault detection

system.

Such a scheme allows to determine the linear discrete system
which has generated the noisy sequences as well as the variances
of the noises

and

corrupting the data [4]. In the ideal

Frisch scheme hypotheses, these signals are assumed zero-mean
white noises, mutually uncorrelated and uncorrelated with every
component of

and

.

In particular in this work, the input–output link will be

mathematically described by performing the identification of a
number of ARX Multiple-Input Single-Output (MISO) models
of the type

(5)

equal to the number

of the output variables has been per-

formed. The order

and the parameters

and

, with

, of the model have to be determined by the iden-

tification approach. The term

takes into account the mod-

eling error, which is due to process noises, parameter variations,
etc.

The next step is the transformation of input-output discrete-

time time-invariant linear models (5) into state-space represen-
tations. The state-space systems obtained by the equation errors
models are useful to design dynamic observers, whilst the ones
coming from the Frisch scheme can be used in order to build
Kalman filters.

It can be proved that a state-space formulation of the input-

output equation error model (5) in fault free conditions, for the

th output

becomes:

(6)

where the matrices

,

,

,

and

are functions of the order and the

and

parameters [26].

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204

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 1, NO. 3, AUGUST 2005

A. ARX Model Identification

Consider an assumed order for a SISO (Single-Input Single-

Output,

) ARX model (5) and the input-output sequences

observed in the time interval

. If the model

(5) is used to compute predicted output values

in the

times, for a given set of parameters:

(7)

the mean square prediction error

is given by

(8)

By introducing now the following Hankel matrices

and

:

..

.

. ..

..

.

(9)

and

..

.

. ..

..

.

(10)

it follows that

..

.

(11)

It can be proved that the parameter vector minimizing the cost
function (8) is given by

..

.

(12)

where

denotes the pseudo-inverse of the

matrix. The

algorithm gives an estimate

of , which converges asymptoti-

cally to the real parameter of the process that has generated the
data.

To estimate the order

of the ARX process, an integer

and the

matrix of input–output samples given

by

(13)

are considered.

If

in (5) the following properties hold:

for;
for;

(14)

It could be possible to consider the increasing sequence of
matrices:

(15)

where

and to evaluate their singularity. The first

singular matrix

would define the correct order for the model

. Unfortunately, the presence of

in (5) leads

to the nonsingularity of every matrix in (15).

It can be proved that if

is large enough, an estimate of the

standard deviation

of the process

in (5), is given by [27]

(16)

If the following, the quantity

is defined:

(17)

it can be shown that

for

,

for

and

for

. In other words, if

is large

enough, a sequence of decreasing values of

followed by a

stabilization once the correct order is reached, can be noted. The
criterion can be used to evaluate a suitable order or, at least, an
interval of admissible orders for the model before computing its
parameters. It is easy to show that

for an ARX

model with order

and parameters

given by (12).

If the value (17) is expressed as percentage of the standard

deviation of the measured output, the Predicted Per Cent Re-
construction Error criterion (PPCRE) is obtained [28]. The
PPCRE

gives the prediction error of an ARX model of order

without requiring any computation of its parameters and

predictions. The application of the PPCRE criterion consists
in computing an increasing sequence of PPCRE

(or

)

and in selecting the minimal order that, once increased, does
not lead to a significantly better performance. Relation (17) can
also be used in the application of the well-known FPE, AIC and
MDL order estimation criteria [26].

B. EIV Miso System Identification

In this section, the Frisch scheme procedure for the identifi-

cation of dynamic EIV MISO system from input-output

,

(with

) noisy (fault-free) sequences will

be summarized.

A finite sequence of the variables

observed with a constant sampling interval is considered. If dy-
namic linear relations exist among these variables, they can be
described by models of the type

(18)

which describe linear MISO (multiple-input, single output) dis-
crete-time systems whose order is

and whose parameters are

and

.

At first, the following problem is presented.
Problem 1 (Realization):

Given a noiseless input–output se-

quence

generated by a system of type

(18), determine the order

and the parameters

and

of

the system.

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SIMANI: IDENTIFICATION AND FAULT DIAGNOSIS

205

The following vectors and matrices can be defined:

(19)

(20)

(21)

(22)

(23)

(24)

(25)

where

is assumed large enough to solve the problem consid-

ered. Please note that the matrices

and

have the

same number of rows.

The matrix

is partitioned as follows:

..

.

..

.

. ..

..

.

(26)

To solve the realization problem it is possible to consider the
sequence of increasing-dimension matrices:

(27)

testing their singularity. As soon as a singular matrix

is

found then the order

and the parameters

,

describe the dependence relation-

ship of the th vector of

on the remaining ones.

In Problem 1 it has been assumed that

is large enough to

avoid unwanted linear dependence relationships due to limita-
tions in the dimension of the involved vector spaces; this means

. The minimal number of samples must be

therefore equal to

. If a lower number of samples is

available then only a partial realization problem can be solved.

In the noisy case the following identification problem can be

proposed.

Problem 2 (Identification):

Given a noisy input–output

sequence

unequivocally determine, if

possible, the order

and the parameters

and

of a model

(18) of the system which has generated the noiseless sequences

.

Note that in presence of noise the procedure described for the

solution of Problem 1 would obviously be useless since matrices

would always be nonsingular.

In the ideal Frisch scheme it is normally assumed that

(28)

where every noise term

and

is independent of every

other term

and

only and are known. Without loss

of generality, all the variables may be assumed as having null
mean value. Consequently the generic positive definite matrix

associated with the input-output noise-corrupted sequences

may always be expressed as the sum of two terms

(29)

where

(30)

since no correlation has been assumed among the noise samples
at different times. This condition is verified for additive white
noise with variance

and

on the input–output

sequences.

Problem 3:

Given a sequence of increasing-dimension

symmetric positive definite covariance

matrices:

(31)

find, for each , all diagonal nonnegative definite matrices

such that

(32)

It is worth observing now that, unlike the algebraic case, for
each

the noise space is always

, while the parameter

space is

. It can be noted that for each

the solu-

tion set of the previous relation describes, in the first orthant of
the

hyper-plane, a hyper-surface whose con-

cavity faces the origin [4].

Previous results hold for every value of . Since determina-

tion of the system order requires the increasing values of to be
tested, it is relevant to analyze the behavior of the associated
curves when varies. This corresponds to a comparison of the
admissible solution sets for different model orders. In this con-
text the following result can be proved [4].

Theorem 1:

The solution sets of condition

for dif-

ferent values of

are noncrossing curves [4].

It is also important to observe that, since we assume that a

system (18) has generated the noiseless data, for

all the

hyper-surfaces of type

have necessarily at least one

common point, i.e. the point

corresponding

to the true variances

and

of the noise affecting the in-

puts and the output of the system, respectively. The search for
a solution for the identification problem can thus start from the
determination in the noise space of this point.

The following considerations can now be stated. With refer-

ence to the diagonal nonnegative definite matrices:

(33)

the following properties hold.

•

If

the matrices

are positive definite.

•

If

the dimension of the null space of

and,

consequently, the multiplicity of its least eigenvalue, is
equal to

.

•

For

, the matrix

is characterized by a linear

dependence relation among its

vectors

and the coefficients which link the th vector of

to

the remaining ones are the parameters

and

, with

and

, of the system (18) which

has generated the noiseless sequences.

•

For

all linear dependence relations among the

vectors of the matrix

are characterized by the same

coefficients

and

.

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 1, NO. 3, AUGUST 2005

Fig. 2.

Monitored system.

If

models of the type (18) are used to describe the mathe-

matical behavior of a multivariable dynamic system with

in-

puts and

outputs

, the previous identification procedure

must be repeated

times. At every step the identification pro-

cedure must lead to the same values for the input noise variances

.

It is worth noting how this approach cannot be applied

immediately in the identification of real processes, since the
hypotheses on the linearity, finite dimensionality and time
independence of the system and on the additivity and whiteness
of the noise are not usually verified, so that the hyper-surfaces

have no common point for

. The definition

of a suitable criterion of model selection in such cases was
suggested in [29].

IV. R

ESIDUAL

G

ENERATION FOR

FDI

The problem treated in this work regards the detection and

isolation of the faults on the basis of the knowledge of the
measured sequences

and

. The structure of the fault

detection device is depicted in Fig. 1(b). The symptom (or
residual signal,

) generation is implemented by means of

dynamic observers or Kalman filters, driven by

and

,

in order to produce a set of signals,

, from which it will be

possible to isolate faults associated to actuators, components
and sensors. The symptom evaluation refers to a logic device
which processes the redundant signals generated by the first
block in order to estimate and unequivocally identify a fault
occurrence.

This work will present a FDI technique to elaborate a set of

symptoms from which it will be possible to unequivocally de-
tect faults. With reference to Fig. 1(b) the symptom signals are
differences between estimated signals (given by observers or
Kalman filters) and the actual ones supplied by the input and
output sensors.

Moreover, it is assumed that only a single fault may be present

in the actuators, components or input sensors of the plant at any
given time. On the other hand, multiple output sensor faults can
be handled.

V. N

OISE

-F

REE

F

AULT

D

IAGNOSIS

The aim of this study consists in finding a procedure in order

to detect and isolate faults on actuators, components and sen-
sors of single-shaft industrial gas turbine. The model of such
a turbine was developed in SIMULINK environment [30] and
it was supplied by the ALSTOM Power Technology Centre,
Whetstone, U.K. Fig. 2 shows the gas turbine layout as well as
its inputs and outputs.

The time series of data used to identify the models were

generated with a nonlinear dynamic model in SIMULINK
environment and they simulate measurements taken on the
machine with a sampling rate of 0.08 s and without noise
(

and

) due to measurement uncertainty

which, instead, is always present in the real measurement
systems. The nonlinear SIMULINK model of the gas turbine was
validated in steady state conditions against engine measurements
where available, and against the prediction of a more rigorous
steady state gas turbine model where measurements were not

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SIMANI: IDENTIFICATION AND FAULT DIAGNOSIS

207

TABLE I

T

URBINE

C

ONTROL

I

NPUTS

available. The SIMULINK model variables were found to be
within 5% of the measured and rigorous modeled values. For
the majority of variables the accuracy was within 1%. In the
dynamic case no model validation has been carried out as yet.

Orders and output reconstruction errors of each ARX model

are shown in Table II. The th model (with

and

monitored outputs) is driven by

and

and

gives the prediction of the th output

. The control inputs

are

and they are summarized in Table I.

Table I also reports measurement accuracy that depend on mea-
surement sensors exploited by the turbine prototype.

Even if, according to Fig. 2 the measurements of ambient and

pressure temperature (

and

) are inputs for the turbine, they

were not considered, since they are constant all the times.

The monitored outputs of the turbine prototype are

. Some of them (the most

meaningful that will be considered for the FDI task) are sum-
marized in Table II. Table II shows also the measurement
accuracy, due again to measurement sensors used by the turbine
prototype.

Each model was tested in different operating conditions and

it has always provided an output reconstruction mean square
error (MSE) lower than 0.5%. Moreover, two time series of data
generated by the gas turbine nonlinear model were exploited in
order to validate the ARX models. These models have always
provided in full simulation an output reconstruction error lower
than 1%.

A very effective way of evaluating the adequacy and flexi-

bility of identified models consists, in fact, in their use for per-
forming complete simulations (i.e. using only the initial samples
of the observed outputs) and in comparing the obtained predic-
tions with observed output samples. This procedure, that can
be applied when a single set of data is available, gives the best
results when applied to sequences different from those used to
identify the model. The mean square prediction error between
the observed outputs and the ones obtained by simulation can be
used to compare models with different orders. The reconstruc-
tion errors of each ARX model are summarized in Table III.

In the following, the FDI problem for the case of noise-free

measurements is solved firstly via the implementation of a bank
of output dynamic observers.

VI. S

IMULATED

F

AULT

C

ONDITIONS

Four gradually developing faults that may affect the turbine

prototype can be represented as follows.

1) Compressor contamination (core engine performance de-

terioration),

.

2) Thermocouple sensor fault (output sensor failure),

.

TABLE II

T

URBINE

O

UTPUTS AND

MISO ARX M

ODEL

C

HARACTERISTICS

TABLE III

D

YNAMIC

ARX M

ODEL

V

ALIDATION

3) High Pressure turbine seal damage (core engine perfor-

mance deterioration),

.

4) Fuel actuator friction wear (controller fault),

.

Note that in real industrial applications it is commonplace for
each of the above faults to develop slowly over a period of
months. For the purpose of this simulation—in order to avoid
excessively long duration simulations—the fault development
rate will be increased so that significant effects are present after
one hour. However this is still considerably longer than the du-
ration of the gas turbine dynamics which occur over periods of
seconds—a factor which must be taken account of in any FDI
algorithm design.

In the presence of a fault condition, the challenge for the de-

signer of an FDI algorithm may be summarized as follows.

1) Detect that a fault condition exists with minimum delay

from the initial occurrence of the fault.

2) Identify the nature, magnitude and location of the fault,

again with minimum delay from the initial occurrence of
the fault.

Note that it is desirable to avoid introducing perturbation signals
onto the model variables. In the first instance an FDI design
should be based upon data which is available from the normal
day to day operation of the plant, for example during transient
and over prolonged periods of steady state operations.

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 1, NO. 3, AUGUST 2005

The rate of development and magnitude of faults have been

set to nominal values in this case study. It will be of interest to
know how small the fault parameters can be made whilst still
maintaining good FDI performance.

A. Case 1: Compressor Contamination (Core Engine
Performance Deterioration)

Failure “case 1”, represents fouling of the surfaces of the

compressor blades, this reduces air flow, changes the blade aero-
dynamics and consequently changes the surface roughness. The
failure is modeled as a gradual decrease in mass flow rate for a
given pressure ratio. The fault signal

affects the monitored

system of Fig. 1(a) by means of the SIMULINK submodel rep-
resented in Fig. 3(a). The maximum decrease in mass flow rate
is set nominally at 5% while the fault development rate is set to
(5% decrease of normal flow rate)/hour.

In order to design the component

FDI scheme

(

,

and

), with respect to the

turbine SIMULINK model, the subsystem depicted in Fig. 3(b)
was considered.

The inputs for the subsystem are

,

,

, and

, while

,

, and

are the outputs directly affected by the fault

.

It was experimented with the turbine prototype model that the
most sensitive output signal to a ramp fault

is

output

measurement. It is worthy to note how the shape of

tran-

sient is determined by the input variation, not by the slowly de-
veloping compressor hauling fault

(which is also of very

small magnitude).

signal and

fault have, in fact, very

different magnitudes.

A second order

ARX MISO (

,

)

model was identified with an output reconstruction error

. The parameters of such a model, driven

by

and

signals, are represented by the vector

,

.

The diagnosis of the

signal (linked to the faulty turbine

component) requires the knowledge of the triple
with

and the identification of an ARX model with

two inputs which gives the prediction of the 13th output

.

Because of the noise-free case, in which

,

in

the system (6) the term

was neglected

.

In these noise-free conditions, the detection of a fault re-

garding the compressor was hence performed by using the
classical output observer configuration exploited for the FDI of
output sensor faults, as depicted in Fig. 4(a). The inputs

,

and the output

feed the observer to estimate the

signal

itself and to generate the residual

. The poles

of the output observer for the signal

were chosen near

0.5 according to the minimization of the function

. The

eigenvalues

, in fact, were chosen to maximize

the mean square error of the residual sensitivity

to

a fault and minimize the mean square error of the residual
in fault-free condition,

. The minimum

,

where

is the cost function

(34)

Fig. 3.

(a) Fault “case 1” SIMULINK submodel and (b) the monitored

subsystem.

Fig. 4.

(a) Observer scheme and (b) residual functions.

has to be found. The minimization of the cost function can
be performed by exploiting the Optimization Toolbox of
MATLAB, or even better, the Genetic Algorithm Optimization
Toolbox (GAOT) of MATLAB [31].

Finally, Fig. 4(b) shows the fault-free (solid line) and the

faulty residuals (dotted line).

B. Case 2: Fault Diagnosis of the Output Sensor

Failure “case 2” represents the malfunctioning of a ther-

mocouple in the gas path leading to a slowly increasing or
decreasing reading over time. The considered fault regards
the measurement of the

turbine output variable that mainly

affects the output sensor by means of the SIMULINK model

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SIMANI: IDENTIFICATION AND FAULT DIAGNOSIS

209

Fig. 5.

(a) SIMULINK fault model of the output sensor and (b) the residual

function

r(t).

depicted in Fig. 5(a). There is no limit placed on the error
magnitude while the fault development rate is set to (5% error
in measuring actual temperature)/hour.

In order to diagnose a single

fault on the th output

sensor (

,

,

and

) when the

measurement noises are negligible (

and,

),

with reference to system (6), the model of the th output observer

has the form:

(35)

where

is the th observer state vector,

represents a

fault on the th output sensor and the triple

is a

minimal state-space representation (completely observable) of
the link among the inputs of the process and its th output

.

In the absence of faults, it can be verified that, for the th

output, the residual
is equal to zero. In the presence of a fault on the th output sensor
the th output residual reaches a value different from zero and
this situation leads to a complete failure diagnosis.

In particular, the diagnosis of the

output sensor (thermo-

couple fault), represented in Fig. 5(a), requires the knowledge
of the triple

with

and therefore the

identification of an ARX model with two inputs which gives
the prediction of the 18th output

. A second order ARX

MISO model (

and

), driven by

and

input signals, was identified. Such a model gives an

output reconstruction error equal to

. The pa-

rameters of the ARX model are described by the vector

,

.

The poles of the output observer, whose scheme is similar to
the one depicted in Fig. 4(a), were chosen near 0.3 in order to
minimize the function

.

An incipient fault (drift) was generated in the output sensor of

the SIMULINK model by adding a ramp function with a slope
of

to the

output signals. Moreover, it was de-

cided to consider a fault during a transient since, in this case,
the residual error due to ARX model approximation is max-
imum and therefore it represents the most critical case. The fault
occurring on the single sensor causes alteration of the sensor
signal and of the residuals given by the output observer using
this signal as input. These residuals of Fig. 5(b) indicate a fault
occurrence when their values are lower or higher than the thresh-
olds fixed in fault-free conditions.

The fault detection logic scheme is obtained by comparing

the fault-free

and faulty

residual

obtained from the difference between the values computed by
the observer related to the output

and the ones given

by the sensor. Obviously, the non zero value of the residual in
Fig. 5(b) is due to the identified ARX model approximation.

The considered drift (ramp fault) starts at the instant

.

Since the observer gives the estimate

of

at the instant

by using measurements available from the instant

to

, a fault occurring at the instant

affects only

.

This change can produce an instantaneous peak in the monitored
residual function [5]. In such a case, the peaks are not due to in-
stantaneous changes in the input signals, e.g. fuel flow

or

butterfly valve position

. Thus, they may be used as incip-

ient detector of anomalous behavior of the output sensors.

C. Case 3: High Pressure Seal Damage (Core Engine
Performance Deterioration)

Failure “case” represents failure

of an HP turbine seal.

This results in a reduction in turbine efficiency. The fault is
modeled as a gradual reduction in turbine efficiency over time.
The maximum decrease in turbine efficiency is set nominally at
5% while the fault development rate is set to (5% reduction of
normal efficiency)/hour.

In order to detect such a fault, an output observer fed by

the inputs

,

and

is designed. Moreover,the

SIMULINK subsystem used to inject the component fault

into the monitored systems is depicted in Fig. 6(a).

Under noise-free conditions, with reference to system (6)
and neglecting

, the output observer was designed

for a third order MISO model which gives a mean square
reconstruction error equal to

and the eigen-

values were chosen near 0.3 to minimize the cost function

. The ARX parameter vector estimated is described

by

,

. The scheme used to generate the redundant

residual regarding the

output signal is equal to the one

designed for the previous fault cases. The fault free and the
faulty residual are also shown in the Fig. 6(b).

D. Case 4: Fuel Actuator Friction Wear

Failure “case 4”,

represents the loss of performance

due to wear of the fuel valve actuator. Again, the SIMULINK
model used to generate the fault signal

is depicted in

Fig. 7(a). As there are no specific actuator dynamics in the cur-
rent model, the wear effect of the valve actuator causing slower
response to demanded flow rates is modeled as a simple first
order lag on the resulting fuel flow. The time constant increases

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210

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 1, NO. 3, AUGUST 2005

Fig. 6.

(a) Fault SIMULINK subsystem and (b)

p (t) signal residuals.

linearly with the time to represent progressive wear damage to
the actuator.

In order to generate the residual for the diagnosis of the actu-

ator fault

, an output observer scheme was exploited again.

In particular, the inputs of the turbine, the fuel flow,

, the

valve angle,

and the outputs

,

,

,

and

were considered. The speed demand,

, one of the

inputs of the governor and

, the third output of the turbine

were also shown.

For each output, a third order

ARX model with

two inputs and one output (

,

) was identi-

fied. By means of the SIMULINK system (2), a single fault

was simulated and the most sensitive output to a fault

regarding the actuator was determined. The

residual

was the most sensitive, with a

.

The third order ARX parameter are collected in the param-
eter vector

,

.

The observer scheme exploited for generating the residuals

regarding the signal

is fed by the signals

,

,

and

. The signals are therefore used by the dynamic ob-

server to estimate the

signal itself. The effects of the fault

on the symptom signal

is shown in Fig. 7(b).

is the

residual concerning the

output measurement in fault-free

and faulty conditions. Because of the closed-loop configuration
of the subsystem considered in Fig. 7(a), the fault shape can not
be described by using a ramp function. The output observer fed
by inputs

and

was designed to estimate

. The

eigenvalues

were chosen near 0.4 to minimize the cost func-

tion

.

As an example, Fig. 7(b) shows how the fault occurring on

the single sensor causes alteration of the input and output sig-
nals and of the residuals given by the output observer using the

signal as input. These residuals indicate a fault occurrence

Fig. 7.

(a) Actuator fault SIMULINK model and (b) residuals in the presence

of

f (t) fault.

TABLE IV

F

AULT

S

IGNATURE

when their values are lower or higher than the thresholds fixed in
fault-free conditions. Fig. 7(b) shows the fault-free (solid line)
and faulty (dotted line) residual

obtained from the differ-

ence between the values computed by the observer related to
the output

and the ones given by the sensor.

VII. F

AULT

I

SOLABILITY

By performing residual sensitivity analysis, i.e. by selecting

the most sensitive residuals to the faults, the Table IV is ob-
tained, in order to isolate different fault occurring at the same
time.

In order to summarize the FDI capabilities of the presented

schemes, Table IV shows the “fault signatures” in case of a
single fault in each actuator, component and sensor. The resid-
uals which are affected by faults are marked with the presence of
“1“ in the correspondent table entry, while an entry “0“ means
that the fault does not affect the correspondent residual. The
bold face entries in the table represent the residuals affected by
the same faults. The italics “1“s are the distinguishable resid-
uals (they are bigger than a fixed threshold). Note how multiple
faults in actuator, components and sensor can be isolated since
a fault affects only the residual function of the observer driven
by the same output.

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SIMANI: IDENTIFICATION AND FAULT DIAGNOSIS

211

VIII. FDI

IN THE

N

OISY

E

NVIRONMENT

In this section, a FDI technique based on Kalman filters de-

signed in the case of noisy measurements is presented. Such a
design is enhanced by processing the noisy data according to the
Frisch scheme identification method [5], [8], [10]. Moreover,
fault size estimation can be performed by means of different
neural network architectures [8], [10]. In particular, neural net-
works can be used as function approximators to estimate single
sensor fault size. The proposed fault diagnosis tool when mea-
surements are affected by noise is tested on the power plant pre-
sented in the previous sections.

In recent years, neural networks have been exploited success-

fully in pattern recognition as well as function approximation
theory and they have been proposed as a possible technique for
fault diagnosis, too. Neural networks can handle nonlinear be-
havior and partially known process.

The aim of this paragraph is to suggest how artificial neural

networks can be exploited to approximate a large class of func-
tions, for fault diagnosis of an industrial plant. In particular,
the problem of the estimate of the slope of faults concerning
actuators, components and output sensors of an industrial
gas turbine can be solved. Faults modeled by ramp functions
create changes in several residuals obtained by using dynamic
observers (Kalman filters) of the process under examination.
A neural network can be used in order to find the connection
from a particular fault regarding input and output sensors to a
particular residual. Residuals are dependent only on sensors
faults. Therefore, the neural network evaluates patterns of
residuals, uniquely related to particular fault conditions [10].

A. Fault Estimation Device

The fault detection and diagnosis system produces and elabo-

rates a set of residuals from which it will be possible to estimate
the amplitudes of the faults regarding actuators, components and
input-output sensors.

With reference to Fig. 8 the symptom generator is designed

to produce a set of signals which are somehow redundant.
These signals are differences between estimated signals given
by Kalman filters and the actual ones supplied by the sensors.

In order to experiment with learning capabilities of artifi-

cial neural networks, on which the diagnosis device in Fig. 8
is based, a bank of classic Kalman filters are used. The number
of filters is equal to the number

of system outputs, and each

filter is driven by a single output measurement and all the in-
puts of the plant. Because of this configuration, the diagnosis
of faults is indeed very easy, since each output measurement is
directly connected to a single residual generator. The basic prin-
ciple of fault detection by using Kalman filtering is illustrated
in Fig. 9.

With reference to the time-invariant, discrete-time, linear dy-

namic system described by a minimal state-space realization

of the input-output MISO system (6) [26], the th

Kalman filter has the structure [32]:

(36)

Fig. 8.

Logic diagram of the fault detection system.

Fig. 9.

Bank of Kalman filters and NNs for residual generation and estimation.

TABLE V

F

RISCH

S

CHEME

M

ODEL

R

ECONSTRUCTION

E

RRORS

The variable

is the one step-ahead prediction of the

state

,

is the estimate of the th component

of the

output

given by the filter. A Riccati equation is used to com-

pute the time-variant gain

of the filter by means of the knowl-

edge of the covariance matrix of the input vector noise

and

the variance of the th component of the output noise

. It

can be proved that the innovation

is

a white process when all the assumptions regarding the system

and the statistical characteristics of the noises are

completely fulfilled. In particular, the innovation converges to a
steady state solution when the pair

is completely ob-

servable and the pair

is completely reachable.

B. Identification Procedure

The Frisch scheme can be applied to perform the dynamic

system identification of the plant [1]–[4], [33]. Such a scheme
allows to determine the linear discrete dynamic system which
has generated the noisy sequences as well as the variances of
the noises

and

corrupting the data. In the ideal as-

sumptions of the Frisch scheme, these signals are assumed white
noises, mutually uncorrelated and uncorrelated with every com-
ponent of

and

.

Table V summarizes the reconstruction errors concerning the

MISO models in the form (18) with two inputs (

and

)

and each monitored output variable, as output.

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212

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 1, NO. 3, AUGUST 2005

TABLE VI

F

RISCH

2-

ND

O

RDER

M

ODEL

P

ARAMETERS

TABLE VII

F

RISCH

N

OISE

V

ARIANCES

Tables VI and VII collect parameters of second order models

as well as the input and output noises.

On the basis of the data collected in Tables VI and VII, four

Kalman filters with two inputs

and one output

were designed. The detection strategy which is commonly

chosen in connection with Kalman filtering methods for failures
detection, consists in monitoring the innovations

. Because

of the linear property of system (1) and because of the effect of
faults on the system output measurements, any change in mea-
surements due to a fault is reflected in a change in the mean and
in the standard deviation of

.

In particular, since the Kalman filter produces zero-mean and

independent white residuals with the system in normal oper-
ation, a method for failure detection and isolation consists in
testing how much the sequence of innovations has deviated from
the white noise hypothesis. The tests which can be performed
on the innovations are the usual ones for zero-mean and vari-
ance, as cumulative sum algorithms as well as independence, as

-type. If a system abnormality occurs, the statistics of

change, so its comparison with a threshold fixed under no faults
conditions, becomes the detection rule.

In Figs. 10(a), 10(b), (11a), and (11b) the examples of the

turbine FDI performed by using the residual generated by the
Kalman filter with two inputs and one output are shown.

In particular, when the fault

affects the

residual

(“case 1”), Fig. 10(a) depicts fault-free and faulty residuals gen-
erated by the Kalman filter. It is driven by the input sensor signal

,

and the

signal itself. A ramped incipient com-

pressor fault (“case 1”), commencing at

causes a

change in the value of the

residual computed in fault-free

condition, as depicted in Fig. 10(a). It is important to note that,
in order to achieve the maximal fault detection capability, the
residual corresponding to the most sensitive filter to a failure on
the

measurement was selected, in accordance with Table V.

On the other hand, the

incipient ramp fault (“case 2”)

affects the output sensor for the measurement of the

signal

and commencing at the instant

s. Hence, in Fig. 10(b)

fault-free and faulty residuals regarding the

signal obtained

from the difference between the values

computed by the

Kalman filter in (36) with

and the ones measured by the

Fig. 10.

Kalman filter residuals

r(t) for the (a) “Case 1” and (b) “Case 2”.

sensor, are shown. Obviously, the nonzero value of the residual
in fault-free conditions is due to the ARX model approximation
and to the actual measurement noise.

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SIMANI: IDENTIFICATION AND FAULT DIAGNOSIS

213

Fig. 11.

Kalman filter residuals

r(t) for the (a) “case 3” and (b) “case 4”.

Fig. 11(a) shows the behavior of the residual when a ramped

incipient fault

(“case 3”) commences at the instant

. According to Table V, in this case,

is the moni-

tored signal for the FDI of a component of the turbine. Then,
Fig. 11(a) depicts the fault-free residual and its change due to
the fault occurrence, as the previous cases.

Finally, Fig. 11(b) shows the change in the fault-free residual

concerning the

measurement due to a ramped

incipient actuator fault (“case 4”). The

fault commences

at the instant

s. In Fig. 11(b), the fault-free and the faulty

residuals are shown.

Because the nature of the incipient ramp fault

affecting

the regulator into the feedback control loop, the output measure-
ments affected by the fault itself are different from ramp signals.

IX. M

INIMAL

D

ETECTABLE

F

AULTS

Tables VIII and IX summarize the performance of the fault

detection and isolation technique both in the noise-free and
noisy environments. The Table collect the minimal detectable

TABLE VIII

M

INIMUM

D

ETECTABLE

F

AULTS BY

M

ONITORING

R

ESIDUAL

AND

I

NNOVATION

V

ALUES

TABLE IX

M

INIMUM

D

ETECTABLE

F

AULTS BY

M

ONITORING

R

ESIDUAL

AND

I

NNOVATION

V

ALUES

Fig. 12.

Detection delay definition.

fault on the four measurements, in case the residual or inno-
vation value is monitored using a geometrical test and fixed
thresholds. The minimal detectable fault values in Tables VIII
and IX are expressed as percentage of the signal values and are
relative to the case in which the occurrence of a fault must be
detected as soon as possible.

It results that the values of the faults obtained by using geo-

metrical analysis on Kalman filter innovations, collected in Ta-
bles VIII and IX, are different than the ones reported in the same
Table and computed in the noise-free environment exploiting
classical observers. Tables VIII and IX show how faults mod-
eled by ramp functions may not be immediately detected, since
the delay in the corresponding alarm normally depends on fault
mode.

The minimal detectable fault can be found by fixing a detec-

tion delay, defined in Fig. 12. If a delay in detection is toler-
able the amplitude of the minimal detectable fault is lower. The
minimal detectable faults on the various sensors seem to be ad-
equate to the industrial diagnostic applications, by considering
also that the minimal detectable faults can be reduced if a delay
in detection promptness is tolerable.

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214

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 1, NO. 3, AUGUST 2005

X. S

OFTWARE

I

MPLEMENTATION

This section tries to describe shortly how the methods

described in the previous paragraphs could be implemented
in a real-world applications by means of the MATLAB and
SIMULINK software.

In particular, the System Identification Toolbox (of the

MATLAB or SIMULINK environments) provides the fol-
lowing tools.

•

It is possible to define arbitrary parameterizations of the
matrices in the input-output state-space form models used
in the previous sections. This MATLAB implementation
is able also to describe state-space or input-output models
with unknown parameters, i.e., the so-called idgrey
model on-line identification. The procedure, in connec-
tion with PEM (Prediction Error Methods, in MATLAB,
the function pem) techniques can be exploited for on-line
identifying a linear state-space model that is able to
describe the turbine model.

•

Once the parameterization of the state-space or input-
output forms (sspar) is defined, a basis for the cor-
responding realization is automatically selected to give
well-conditioned calculations. An alternative is to specify
an observer canonical form

'

' for the

system matrices. This is a grey-box model, since a struc-
ture of the uncertainty can be defined and canonical form
can be forced for estimating all models of a certain order.

•

The structure estimations can all be combined at the esti-
mation call pem(Data, m, ‘sspar’, ‘can’, ‘z’), which
is the same as set(m, ‘sspar’, ‘can’, ‘z’). A model m
is identified from the available data Data.

The overall procedure implemented in MATLAB and
SIMULINK used for describing the developed FDI method is
described the following.

•

On-line model estimation and identification in MATLAB:

'

'

, where mym-

file

contains the parameter model, in any form, par

the parameters of the state-space or input-output model,
aux

some auxiliary parameters); ‘d’ if the estimation

of the model ms is performed in the continuous-time
domain.

•

Again in MATLAB environment,

'

'

once

the ms state-space structure has been defined, the pem
function is the basic estimation command in the Identifi-
cation Toolbox and covers a variety of situations. data is
always an iddata object that contains the input-output
data. The function parameters Property and Value
can be used to select different estimation methods and
properties.

The design of observers and filters is performed in the
SIMULINK environment. On the other hand, the adaptive filter
functions in the Filter Design and Signal Processing Toolboxes
of MATLAB and SIMULINK implement the overall filter
design, replacing the adaptive algorithm with an appropriate
technique.

•

Least Mean Squares (LMS) algorithms represent the sim-
plest and most easily applied adaptive algorithms, the

Recursive Least Squares (RLS) algorithms represents in-
creased complexity, computational cost, and fidelity. In
performance, RLS approaches the Kalman filter (adap-
tkalman

) in adaptive filtering applications, at somewhat

reduced required throughput in the signal processor.

•

Compared to the LMS algorithm, the RLS approach
offers faster convergence and smaller error with respect
to the unknown system, at the expense of requiring
more computations. In contrast to the least mean squares
algorithm, from which it can be derived, the RLS adaptive
algorithm minimizes the total squared error between the
desired signal and the output from the unknown system.
Within limits, any of the adaptive filter algorithms can be
used to solve an adaptive filter problem by replacing the
adaptive portion of the application with a new algorithm.

•

As the signal into the filter continues, the adaptive filter
coefficients adjust themselves to achieve the desired re-
sult, such as identifying an unknown filter or cancelling
noise in the input signal. The adaptive filter in SIMULINK
can be considered as a box comprising the adaptive filter
and the adaptive RLS algorithm.

Hence, an online observer or filter realization for FDI applica-
tion is based on both the on-line identification of the process
models and of the design of the observer or filter itself. The
whole project is based on the characteristics of the input-output
signals to the observer or filter and a signal which represent the
desired behavior of the filter on its input. The design of the ob-
server or filter does not require any other frequency response
information or specification. To define the self learning process
the filter uses, the adaptive algorithm used to reduce the error
between the output signal and the desired signal has to be ex-
ploited. When the LMS performance criteria has achieved its
minimum value through the iterations of the adapting algorithm,
the adaptive filter is finished and its coefficients have converged
to a solution. When the input-output data change their character-
istics, sometimes called the filter environment, the filter adapts
to the new environment by generating a new set of coefficients
for the new data.

Moreover, once the adaptive observer or filter has been imple-

mented in connection with the on-line grey-box estimation algo-
rithm, the so-called residual signals can be generated. A residual
evaluation logic should be able to detect and isolate any fault oc-
currence in the presence of disturbance, modeling uncertainty
and measurement noise. Due to the particular FDI application,
the use of an adaptive threshold logic for robust FDI has to be
implemented. This task can be accomplished in SIMULINK by
using on-line and recursive estimators.

Finally, in many cases it may be necessary also to estimate

the fault-free thresholds on-line at the same time as the input-
output data is received. In this case, in particular, some deci-
sions on-line have to be made, as in adaptive control, adaptive
filtering, or adaptive prediction. For FDI applications, it is then
necessary to investigate possible time variation in the threshold
properties during the collection of data. Terms like recursive
identification, adaptive parameter estimation, sequential estima-
tion, and on-line algorithms are successfully used for such on-
line/adaptive threshold selection algorithms.

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SIMANI: IDENTIFICATION AND FAULT DIAGNOSIS

215

XI. C

ONCLUSION

This study has described a complete design procedure for FDI

in actuators, components and output sensors of a gas turbine
system. Although this is an application study based on a gas
turbine, the principles and methods used are applicable to al-
most any industrial system with dynamic behavior and with sets
of input-output measurements. The FDI tasks were performed
through the use of a bank of dynamic observers or, when the
measurement noises are not negligible, a bank of Kalman fil-
ters. In this study single faults on components of the system,
i.e., faults in actuators and output sensors, were considered.
This does not mean that multiple (simultaneous) faults are not
possible to isolate using model-based methods. Indeed, earlier
studies have shown that model-based methods for FDI are par-
ticularly suited to the detection and isolation of multiple faults,
when certain modeling and design conditions are satisfied. In a
later study we will consider this issue further.

The proposed method does not require physical knowledge

of the process under observation because the input-output links
are obtained by means of an identification scheme, based on
input-output models derived from the data. ARX models and
EIV models were used based on the least square method and the
scheme due to Frisch, respectively. The latter approach provides
estimates of the variances of the input-output noises, which are
required in the design of the Kalman filters. This identification
approach was applied to a SIMULINK model of a single-shaft
industrial gas turbine. In order to analyze the diagnostic ef-
fectiveness of the FDI system in the presence of changes or
drifts in measurements, faults were generated by means of ramp
functions.

The results obtained indicate that the minimal detectable

faults on the system actuator, component, and output sen-
sors are of interest for the industrial diagnostic applications.
However, since in real industrial applications incipient ramp
faults develop slowly over a long period and in order to avoid
excessively long duration simulations, the fault development
rate was increased so that significant effects were present after
shorter periods. This is a factor that must be taken into account
for FDI performance evaluation.

The main aspect of this work was the use of linear system

identification and modeling methods, although the system con-
sidered is nonlinear. This is considered important to avoid the
complexities that would otherwise be inevitable when nonlinear
models are used. As stated in the Introduction there is certainly
an increasing interest in the research literature in the use of non-
linear methods (nonlinear observers, extended Kalman filters,
fuzzy-logic methods, etc) and it is only a question of time before
these techniques find their way into full application projects.
However, as the feature of system supervision is to monitor the
operation and performance of the system with respect to an ex-
pected point of operation, linear system methods are still very
valid. Deviations from expected system behavior could be used
to monitor system performance changes as well as system com-
ponent malfunctions.

Finally, simulation results have shown that the minimal de-

tectable fault sizes, obtained by using geometrical analysis of
Kalman filter innovations, are smaller than the ones computed

in the noise-free environment, i.e. when compared with resid-
uals computed using dynamic observers. Moreover, if a detec-
tion delay is tolerable the amplitude of the minimal detectable
fault is lower. The minimal detectable faults on the various sen-
sors seem to be adequate for industrial diagnostic applications.
Furthermore, minimal detectable faults can be reduced if larger
detection delays are tolerable.

A

CKNOWLEDGMENT

The author wishes to acknowledge Dr. S. Daley and Dr. A.

Pike of the ALSTOM Power Technology Centre (Whetstone,
Leicester, U.K.) for the helpful discussions and for their valu-
able suggestions. He is also grateful to the management of the
ALSTOM Power Technology Centre for permission to publish
this work. He finally wishes to acknowledge Prof. R. J. Patton of
the University of Hull (U.K.) and Prof. C. Fantuzzi of the Uni-
versity of Modena and Reggio Emilia (Reggio Emilia, Italy) for
the helpful discussions and for their valuable suggestions.

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Silvio Simani

(M’99) was born in Ferrara, Italy, in

1971. He received the Laurea degree (cum laude) in
electrical engineering in 1996 from the Department
of Engineering, Università degli Studi di Ferrara, and
the Ph.D. degree in information science: automatic
control from the Department of Engineering, Univer-
sity of Ferrara and Modena, Italy.

He has been an Assistant Professor since 1992 and

a Research Associate since 1999, both in the Depart-
ment of Engineering, Università di Ferrara. He is also
a member of the Technical Committee SAFEPRO-

CESS since 2000. His research interests include fault diagnosis of dynamic pro-
cesses, system modeling and identification, and the interaction issues between
identification and fault diagnosis. In particular, his main research topics are in
the design and development of automatic fault detection and isolation proce-
dures regarding linear dynamic systems (industrial processes and power plants),
modeling and identification of linear and nonlinear dynamic models, fuzzy mod-
eling and control of linear and nonlinear algebraic and dynamic systems. He is
a reviewer for many international journals and is an author of several papers and
one book on these topics.

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