Fuzzy logic approach applied to the surge detection and isolation in centrifugal compressor

Abstract

The gas compressor plants are bodies sensitive to accidental defects, the consequences of these defects on good operation
of the gas pipeline can be critical. This paper presents an application of the fuzzy approach in fault detection and isolation
of surge in this compression system. This paper illustrates an alternative implementation to the compression systems supervision
task using the basic principles of model-based fault detection and isolation associated with fuzzy modelling approach. Application
results of a fault detection and isolation for a compression system are provided, which illustrate the relevance of the proposed
fuzzy fault detection and isolation method. This work is considered a first step in accessing the factors that affect the
success or limitations of surge detection and isolation in natural gas pipeline compressors.

Full text

ISSN 01464116, Automatic Control and Computer Sciences, 2010, Vol. 44, No. 1, pp. 53–59. © Allerton Press, Inc., 2010.
Original Russian Text © A. Hafaifa, F. Laaouad, K. Laroussi, 2010, published in Avtomatika i Vychislitel’naya Tekhnika, 2010, No. 1, pp. 74–83.
53
1
1. INTRODUCTION
Today the compression systems are subjected to highly hostile working conditions. The manufacturer
is greatly interested with any improvement in performance, life and weight reduction without loss of reli
ability. Therefore, it is worthwhile to carefully estimate the reliability of rotating systems in order to
improve the supervision and the control system or eventually modify the design. Reliability analyses of the
supervision structure require some information on the model of the compression system. We know it is dif
ficult to obtain the mathematical model for a complicated mechanical structure. The turbo compressor is
considered as a complex system where many modelling and controlling efforts have been made.
In the regard to the complexity and the strong non linearity of the turbo compressor dynamics, and the
attempt to find a simple model structure which can capture in some appropriate sense the key of the
dynamical properties of the physical plant, we propose to study the application possibilities of the recent
supervision approaches and evaluate their contribution in the practical and theoretical fields conse
quently. Facing to the studied industrial process complexity, we choose to make recourse to fuzzy logic for
analysis and treatment of its supervision problem owing to the fact that these technique constitute the only
framework in which the types of imperfect knowledge can jointly be treated (uncertainties, inaccuracies,
…) offering suitable tools to characterise them. In the particular case of the turbo compressor, these imper
fections are interpreted by modelling errors, the neglected dynamics and the parametric variations.
This work illustrates an alternative implementation to the compression systems supervision task using
the basic principles of modelbased fault detection and isolation associated with the selftuning of surge
measurements with subsequent appropriate corrective actions. Using a combination of fuzzy modelling
approach makes it possible to devise a faultisolation scheme based on the given incidence matrix.
The presented approach is based on the use of the fuzzy model. As was introduced in [10], by applying
a TakagiSugenotype fuzzy model with interval parameters, one is able to approximate the upper and
lower boundaries of the domain of functions that result from an uncertain system. The fuzzy model is
therefore intended for robust modelling purposes; on the other hand, studies show it can be used in fault
detection as well. The novelty lies in defining of confidence bands over finite sets of input and output mea
surements in which the effects of unknown process inputs are already included. Moreover, it will be shown
that by data preprocessing the fuzzy model parameteroptimization problem will be significantly
reduced. By calculating the normalized distance of the system output from the boundary model outputs,
1
The article is published in the original.
Fuzzy Logic Approach Applied to the Surge Detection
and Isolation in Centrifugal Compressor
1
A. Hafaifa
a
, F. Laaouad
a
, and K. Laroussi
b
a
Department of Industrial Process Automation, Faculty of Hydrocarbons and Chemistry
of BOUMERDES University, 35000, Algeria
b
Department of Electronic and Control Engineering, Faculty of Electronic and Control Engineering,
CUD University of DJELFA, 17000, Algeria
email: hafaifa@hotmail.com, ferhatlaaouad@yahoo.fr, kouiderlaro@hotmail.com
Abstract
—The gas compressor plants are bodies sensitive to accidental defects, the consequences of
these defects on good operation of the gas pipeline can be critical. This paper presents an application
of the fuzzy approach in fault detection and isolation of surge in this compression system. This paper
illustrates an alternative implementation to the compression systems supervision task using the basic
principles of modelbased fault detection and isolation associated with fuzzy modelling approach.
Application results of a fault detection and isolation for a compression system are provided, which
illustrate the relevance of the proposed fuzzy fault detection and isolation method. This work is con
sidered a first step in accessing the factors that affect the success or limitations of surge detection and
isolation in natural gas pipeline compressors.
DOI:
10.3103/S0146411610010074

54
AUTOMATIC CONTROL AND COMPUTER SCIENCES Vol. 44 No. 1 2010
HAFAIFA et al.
a numerical fault measure is obtained. The main idea of the proposed approach is to use the fuzzy model
in an FDI system as residual generators, and combine the fuzzy model outputs for the purpose of fault iso
lation. Due to data preprocessing, the decision stage is robust to the effects of system disturbances.
The paper presents an application of the fuzzy model in fault detection and isolation for the compres
sion system with interval type uncertain parameters. The FDI problem was split into two steps. In the
former step the fuzzy model along with data preprocessing and lowpass filtering were introduced into
the fault detection scheme. In the latter the combination of residuals was used in the faultisolation stage.
In its final part the paper gives some conclusions about this application.
2. SURGE SUPERVISORY SYSTEM
The transfer of gas along a pipeline is a common process in the oil, chemical and petrochemical indus
tries. For costeffectiveness, gas is usually transported at high pressure via a compressor before entering
the pipeline. The compressor efficiency is maximised when the flow rate through it is kept low and the
pressure high, with the minimum possible flow rate being restricted by the risk of compressor entering
surge condition.
The surge phenomena is an unstable and undesirable operating condition of the compressor, occurring
when the flow through it is reduced to the point where the compressor discharge pressure is less than the
line pressure. This causes a momentary flow reversal, reducing line pressure and causing erratic flow out
put. With the reduced line pressure, flow through the compressor is reestablished, causing line pressure
to increase and the cycle to begin again. If the factors leading to the surge condition are not correctly and
quickly rectified, the output will continue to oscillate resulting in damage to the compressor. The surge
supervisory system offers:
• Protection against compressor damage such as bent shafts, cracked or ruptured castings, damaged
impeller and bearings.
• Reduction in compressor downtime and productivity costs.
• Savings on maintenance costs.
Although all surge supervisory system techniques are based on a similar concept—to maintain a min
imal flow at extreme conditions  surge supervisory system with fuzzy fault detection and isolation
achieves this with a robust and efficient supervision module offering configuration and operator interface
flexibility. If and when required by the process, the supervision module takes into account the following:
(1) Location of the flow measurement,
(2) Type of compressor (axial, reciprocating or centrifugal),
(3) Type of operating speed (constant or variable),
(4) Value of discharge and suction pressures,
(5) Value of inlet temperature,
(6) Value of the compression ratio,
(7) Composition of the transported gas (density, specific heat, molecular weight),
(8) Characteristics of all valves used in the control process.
Fuzzy fault detection and isolation method defining the surge point over a wide range of changing con
ditions makes it possible to set the control line for optimum surge protection without unnecessary re
cycling. This method automatically compensates for changes in pressure rise, mass flow, temperature, and
compressor rotor speed. The system utilizes a characterization of compression ratio versus compensated
compressor inlet flow function as control parameters. This algorithm allows for use of the surge control
system in this paper, resulting in minimized recycle or blowoff flow. This method reduces the initial cost
and simplifies engineering, testing, operation, and maintenance associated with the system when com
pared to alternative methods. The input signals required to facilitate use of the surge control algorithm on
centrifugal compressors are the suction flow differential pressure, suction pressure and discharge pressure
as indicated in Fig. 1.
Using the fuzzy logic model it was possible to analyze the deficiencies of the original surge control algo
rithm by observing the “real” surge margin calculated from the compressor performance, the objective of
an antisurge controller should not be limited to basic independent machine protection. The antisurge
control performance as an integral part of the machine performance control must be considered. Storing
real surge points, applying fuzzy logic control of the recycle valve (variable gain depending on operating
region) and compensating for interaction between surges, overload and process control can significantly
expand the operating window. This allows operation very close to the actual surge lines (4–8%) under all
process conditions. Straight line surge control, even with variable slope, must make allowance for the poor
fit to actual surge points by using a wider margin (15–20%).

AUTOMATIC CONTROL AND COMPUTER SCIENCES Vol. 44 No. 1 2010
FUZZY LOGIC APPROACH APPLIED 55
Interim remedial actions to improve the surge control constants were carried out until an advanced
complex control system was installed. An identical steadystate model that was built separately helped to
design and test the revised compressor surge control algorithm prior to commissioning on the compressor
[1–3].
3. THE COMPRESSION SYSTEM MODEL
Over fifteen years ago, Moore and Greitzer developed a phenomenological model for rotating stall and
surge [6]. This pioneering work modeled the compression system with just three components:
• The first component is the inlet duct that allows infinitesimally small disturbances at the duct
entrance to grow until they reach an appreciable magnitude at the compressor face.
• The second component is the compressor itself, modeled as an actuator disk, which raises the pres
sure ratio by doing work on the fluid.
• The third component is the plenum chamber (or diffuser) downstream, which acts as a large reservoir
and responds to fluctuations in mass flow with fluctuations in pressure behind the actuator disk.
In this paper, we are considering a compression system consisting of a centrifugal compressor, close
coupled valve, compressor duct, plenum volume and a throttle. The throttle can be regarded as a simpli
fied model of a turbine [13]. The model to be used for controller design is in the form:
(1)
where
m
is the compressor mass flow,
p
p
is the pressure downstream of the compressor,
L
c
is the length of
compressor and duct,
A
1
is the area of the impeller eye (used as reference area),
N
is the spool moment of
inertia. The two first equations of (1) are equivalent to the model of [4, 17].
The MooreGreitzer model gives rise to three ordinary differential equations, the first for the non
dimensional totaltostatic pressure rise
Δ
p
across the compression system, the second for the amplitude
of mass flow rate fluctuations m, and the third for the nondimensional, spool moment of inertia. In the
above equations,
σ
and
β
are constants that are characteristics of the system. The quantity
φ
T
determines
P
·p
kP01
ρ01Vp
mk
tPpP01
––(),=
m
·A1
Lc
P01 1ηimN,()
Δhideal
CpT01
+
⎝⎠
⎛⎞
4k1–()
k

Pp
–,=
N
·1
2Jπ
 ηtmturCpt,ΔTtur
2πN
2r22σπNm–
⎝⎠
⎛⎞
,=
⎩
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎧
Engine Compressor
PT
FT TT
User
Surge supervisory system
Recirculate Gas
FT : Flow Transmitter
PT : Pressure Transmitter
TT : Temperature Transmitter
TTPT
Anti Surge Valve
Fig. 1.
Compression System.

56
AUTOMATIC CONTROL AND COMPUTER SCIENCES Vol. 44 No. 1 2010
HAFAIFA et al.
how much mass will be removed in a usercontrolled fashion through a bleed valve. It may be written
as [3]:
(2)
The functional form between
φ
and
ψ
is simply the performance map and is often approximated by [9]:
(3)
where
a
,
b
,
c
, and
d
are constants which must be determined by a curve fit of the experimental data. The
most important approximations underlying the MooreGreitzer model are that (i) it is valid under small
perturbations
m
, and, (ii) the time scale of the dynamics governing
m
is much faster than the time scale of
the dynamics governing
φ
.
The present work has analytically integrated the right hand side of Eq. (1). This integration does not
require a priori assumptions about the analytical form of the performance map [7, 8]. Note that the
MooreGreitzer model does not attempt to explain what physical mechanism triggers these instabilities.
Rather, it attempts to determine the favorable conditions under which the disturbances will grow, and what
can be done to suppress the instabilities. Its simplicity, mathematical elegance, and generality have led to
wide acceptance and use of this model by researchers in industry, government and academia. It is also used
in surge control research with the belief that rotating stall is a precursor to surge, and with the expectation
that elimination of rotating stall will also eliminate the development of surge.
The instabilities within compression systems can be studied using energy considerations. As shown by
Gysling and Greitzer [14] the rate of energy input by the compressor to the fluid (over and above the steady
state input) may be written as:
(4)
If this integral is positive, energy is added to the fluid by the compressor, and the disturbances will grow
in amplitude. In the performance map of the compression systems, the slope of the curve is negative to the
right side of the peak. In this region, a small increase in mass flow rate
δφ
will decrease pressure, so that
δ
(
Δ
p
) is negative.
4. FUZZY MODEL OF COMPRESSION SYSTEM
The fuzzy logic model is a rulebased system that receives information fed back from the plant’s oper
ating, in this case the normalized fluctuations of
Φ
and
Ψ
. These crisp values are fuzzified and processed
using the fuzzy knowledge base [16, 17]. The fuzzy output is defuzzified in throttle and CCV gains in order
to control the plants operating conditions.
A fuzzy system involves identifying fuzzy inputs and outputs, creating fuzzy membership functions for
each, constructing a rule base, and then deciding what action will be carried out. The response of the sys
tem is used to model the control system. Increasing either the throttle gain
γ
T
or CCV gain
γ
V
will stabilize
the system with a penalty of pressure lost across the plenum. The fluctuations of the mass flow coefficient
ΔΦ
and pressure coefficient
ΔΨ
are normalized before being sent to the fuzzy model as the crisp input by
the following [4, 12]:
(5)
(6)
Samples of the coefficients are taken at regular timestep intervals,
Δ
t
=
kh
where
k
is a constant and
h
is the RungeKutta time step size [2, 3, 13]. The crisp output from the fuzzy model adjusts both control
gains by the following:
(7)
Triangular membership functions are defined for each classified category of input and output of the
compression system. The base of each triangular membership function rests on the intervals of each cat
egory, and the apex of the triangle is located above the midpoint of the interval.
φTγΔP.=
ψabφcφ2dφ3,++ +=
δEδΔP()δφA.d
Annulus
∫
=
ΔΨi
ΨiΨiΔt+
–
Max ΨiΨiΔt+
,()
,=
ΔΦi
ΦiΦiΔt+
–
Max ΦiΦiΔt+
,()
 .=
γiΔt+γiγiΔγi.+=

AUTOMATIC CONTROL AND COMPUTER SCIENCES Vol. 44 No. 1 2010
FUZZY LOGIC APPROACH APPLIED 57
4.1. Constructing the Rule Base
For the case of two inputs and one output, the rule base is constructed by creating a matrix of options
and solutions. The matrix has the input variable along the top side. The entries in the matrix are the desired
response of the system, the changes in either throttle or CCV gain. The rule base of three rules can be cre
ated [5, 6]:
(1) If [
ΔΨ
is Low] or [
ΔΦ
is Low] Then [
Δγ
V
and
Δγ
T
is Low]
(2) If [
ΔΨ
is Medium] or [
ΔΦ
is Medium] Then [
Δγ
V
and
Δγ
T
is Medium]
(3) If [
ΔΨ
is High] or [
ΔΦ
is High] Then [
Δγ
V
and
Δγ
T
is High]
5. APPLICATION RESULTS
The results of tows simulations are presented in this section. The first is the results of simulations of the
compression system in surge, and the second simulation is the compression system with control of surge
using fuzzy fault detection and isolation method.
The response of the different types of surge can be seen in Figs. 2–5.
0100200300
Time, s
54.1
54.0
53.9
53.8
53.7
Mass flow aspiration
0100200300
0.25
0.20
0.15
0.10
0.05
Residual of Mass
flow aspiration
Residual
0100200300
56.5
56.4
56.3
56.2
0100200300
0.40
0.35
0.30
0.25
0.20
Residual of Mass
flow aspiration
Time, s
Fig. 2.
Gas flow at the input of the compression
system.
0100200300
Time, s
622
620
618
616
614
Mass flow downstream
0100200300
0.10
0.05
0
–0.05
–0.10
Residual of Mass
flow downstream
Residual
0100200300
605
600
595
0100200300
0.10
0.05
0
–0.05
–0.10
Residual of Mass
flow downstream
Time, s
Fig. 3.
Gas flow at the output of the compression
system.
0100200300
Time, s
40
38
36
34 0100200300
–0.1
–0.2
–0.3
–0.4
–0.5
Residual of
pressure aspiration
Residual
0100200300
80
40
0100200300
2
1
0
–1
Time, s
Pressure aspiration
60
20
Residual of
pressure aspiration
Fig. 4.
Input gas pressure of the compression
system.
0100200300
Time, s
100
95
90
85
80
0100200300
0.8
0.6
0.4
0.2
Residual of pressure
downstream
Residual
0100200300
77.05
0100200300
0.50
0.49
0.48
0.47
Time, s
Pressure downstream
Residual of pressure
downstream
77.00
76.95
76.90
76.85
Fig. 5.
Output gas pressure of the compression
system.

58
AUTOMATIC CONTROL AND COMPUTER SCIENCES Vol. 44 No. 1 2010
HAFAIFA et al.
The response of the compression system with control of surge using fuzzy fault detection and isolation
is shown in Figs. 6–9.
Fuzzy fault and detection of different complexities were studied; the larger the computational time but
also the better the results. A model FDI controller with a longer prediction horizon and a small control
weighting factor provides good performance in terms of surge detection and isolation and reduced error.
However, the observation on the variation of the controller output provided an interesting result. Imple
menting such a controller on a realtime system would probably be prohibitive due to the fact that there
are limitations on the incremental variation of the compression system.
CONCLUSIONS
According to the above study, we can notice that the obtained compressor model is still complex and
very difficult to manipulate, even it gives satisfactory results and even identical to reality. Consequently, it
will be necessary to write a much simpler model that we can easily manipulate for fault detection and iso
lation purposes. A fault modeling strategy is proposed that is able to model a large class of faults by a lim
ited number of fault models, which correspond to the extreme values of the considered faults. Identifica
Mass flow aspiration
Residual of Mass
flow aspiration
Residual
Time, s
480
460
440
4200 204060
0.2
0.1
0
–0.20 204060
–0.1
Residual of Mass
flow aspiration
480
460
440
4200204060
0.2
0.1
0
–0.20 204060
–0.1
Time, s
Fig. 6.
Gas flow at the input of the compres
sion system.
Residual
Time, s
1400
1300
1200
11000204060
0.2
0.1
0
–0.20 204060
–0.1
2500
2000
1500
10000 204060
0.2
0.1
0
–0.20 204060
–0.1
Time, s
Mass flow downstream
Residual of Mass
flow downstream
Residual of Mass
flow downstream
Fig. 7.
Gas flow at the output of the compres
sion system.
Residual
Time, s
45
40
35
300204060
0.2
0.1
0
–0.20 204060
–0.1
50
45
400 204060
0.2
0.1
0
–0.20204060
–0.1
Time, s
Residual of
pressure aspiration
Pressure aspiration
Residual of
pressure aspiration
Fig. 8.
Input gas pressure of the compression
system.
Residual
Time, s
95
90
85
800204060
0.2
0.1
0
–0.20204060
–0.1
95
90
850204060
0.2
0.1
0
–0.20 204060
–0.1
Time, s
Residual of pressure
downstream
Pressure downstream
Residual of pressure
downstream
Fig. 9.
Output gas pressure of the compres
sion system.

AUTOMATIC CONTROL AND COMPUTER SCIENCES Vol. 44 No. 1 2010
FUZZY LOGIC APPROACH APPLIED 59
tion of faults is performed by estimating the weights of the models in a model set designed with the pro
posed fault modeling method, in a multiple model framework. The advantage of this framework, the used
of fuzzy logic method, a recent method that satisfies the requirements sited above. In addition, due to its
simplicity, this method is very adequate and practical for the study of complex nonlinear systems. The
great benefit of this fuzzy logic approach is that the controller does not require the knowledge of the com
pressor map in order to find a desired equilibrium point. As well the same model can operate under active
and passive surge control without the knowledge of which method is being implemented. The decision
making is based solely on the compression system output, allowing the fuzzy model to be easily adapted
to any turbo compressor system.
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