|
Academic Open Internet Journal |
Volume 13, 2004 |
COMPARATIVE STUDY OF
MEMBERSHIP FUNCTIONS FOR DESIGN OF FUZZY LOGIC FAULT DIAGNOSIS SYSTEM FOR
SINGLE PHASE INDUCTION MOTOR
Abstract:
This paper describes the application of fuzzy logic to
detect incipient faults in single-phase induction motor. The insulation failure
is considered to illustrate a fuzzy logic fault detector (FLFD). The FLFD is
simulated using fuzzy logic toolbox in MATLAB. The performance of fuzzy logic
fault detector has been analyzed through simulation studies with triangular,
trapezoidal, Gaussian membership functions and results are compared.
Investigations have been carried out considering three and five membership
functions of triangular, trapezoidal and Gaussian membership shapes. The FLFD
designed considering three membership functions requires minimum computation
time. The performance of FLFD designed considering three membership functions
of triangular shape is better than trapezoidal and Gaussian membership
functions.
Keyword: Stator winding fault, induction motor, Fuzzy logic
fault detector, membership function.
I.
INTRODUCTION
The
electric motors are widely used in
industries. They are subjected to different ambient and working conditions.
These lead to occurrence of incipient faults in the motors. It is necessary to
detect incipient faults at an early stage to reduce the down time of the motor.
The manufacturers and users of electrical machines rely on protections such as
over current, over voltage and earth fault to ensure safe and reliable
operation. The manufacturers are also keen to include diagnostic features in
the software to decrease machine down time and improve operational stability.
The
stator winding fault and bearing fault are the faults frequently occurred in
electrical machines. These faults produce symptoms of unbalanced / increased
line current and excessive heating.
Different
types of diagnostic methods are used to identify incipient faults involving
several fields of science and technology. They are generally classified as
those based on mathematical models of machine [1], [2]. Fuzzy logic based technique is proposed in
this paper to detect the stator winding fault since, the fuzzy system based
fault detection is a straightforward approach, which requires to define
membership functions and rules by studying the human operation.
The
design fuzzy logic fault detector with trapezoidal, Gaussian, triangular and
hybrid membership functions for single-phase induction motor is explained in
[3]-[7]. This paper presents the simulation results of FLFD with triangular,
trapezoidal and Gaussian membership functions and also presents comparative
study on the choice of membership function for the given application.
II. FUZZY FAULT DIAGNOSIS SYSTEM
A schematic of fuzzy fault diagnosis system is shown in
figure.1.The fuzzy fault diagnosis system is designed to monitor the stator
current, rotor speed and temperature. The stator winding fault produce the
symptoms of increased line current, decreased in rotor speed and increased
temperature. The fault signature is extracted on measuring the above
parameters. The fuzzy model was simulated using commercially available
software. The fault detection is carried out analyzing the fault signature
through the fuzzy rules derived from expert’s knowledge and experimental data.
The simulation procedure is explained in the section III. The performance
indices such as accuracy and computational time of fuzzy fault diagnosis system
are presented in the section IV.
Fig. 1. Fuzzy fault
diagnosis system
III. SIMULATION
The Fuzzy logic fault detector is simulated using Fuzzy
toolbox in MATLAB. To tune the FLFD,
data were obtained by conducting experiment on the single phase, 230V, and 50Hz
specially wound laboratory induction motor .The stator winding fault is created
externally and motor current (I), speed (N) and temperature (T) are measured. The experimental data are given in table.1.
Table
1. Experimental data
|
Condition |
Current (I)
A |
Speed (N)
rpm |
Temperature
(T)(°C) |
|
1 |
7.1 |
1480 |
41 |
|
2 |
7.3 |
1465 |
51 |
|
3 |
7.5 |
1460 |
52 |
|
4 |
7.9 |
1455 |
54 |
|
5 |
8.2 |
1450 |
58 |
|
6 |
8.8 |
1440 |
62 |
|
7 |
9.6 |
1430 |
68 |
The fuzzy model is
constructed with two inputs and single output (TISO). The rotor speed (N) and
stator current (I) are considered as inputs and temperature (T) is chosen as
output for the fuzzy model. The input variables are classified into three
membership functions such as low, medium and high. The output variable is
classified into three membership functions such as low, medium and high. The
current range is chosen from 7 to 10A, speed range is taken from 1420 to 1500
rpm and temperature range from 40°C to 70°C The relationship between
input and output variables is established through fuzzy rules as shown in
table.2.
Table
.2. Fuzzy rules for FLFD with three membership functions
|
Rules |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Current
(I) |
L |
L |
L |
M |
M |
M |
H |
H |
H |
|
Speed
(N) |
L |
M |
H |
L |
M |
H |
L |
M |
H |
|
Temperature
(T) |
L |
L |
L |
M |
M |
M |
H |
H |
H |
L: Low; M: Medium; H: High
Table 3 Fuzzy rules for
FLFD with five membership functions
|
|
VL |
L |
M |
H |
VH |
|
VL |
VL |
L |
M |
H |
VH |
|
L |
VL |
L |
M |
H |
VH |
|
M |
VL |
L |
M |
H |
VH |
|
H |
VL |
L |
M |
H |
VH |
|
VH |
VL |
L |
M |
H |
VH |
L: Low; M: Medium; H: High; VL: Very Low: VH: Very High
The defuzzification is
carried out by largest of maximum (LOM) method. The triangular, trapezoidal and
Gaussian membership functions used for simulation are shown in figure 2 –
figure 4. The similar procedure is repeated for five membership functions
classifying input and output variables into five regions such as high, very
high, medium, low and very low. The
five-membership functions used for simulation are shown in figure 5 – figure 7. The fuzzy rules are given in table 3.
Temperature, T (°C) Speed, N in rpm
Fig.2.Gaussian three membership function Fig.3. Trapezoidal three membership function
Speed, N in rpm Current. I in Ampere
Fig.4. Triangular three membership
function Fig.5. Triangular five membership function
Current. I in Ampere Current. I in Ampere
Fig.6. Trapezoidal five membership function Fig.7. Gaussian five-membership function
With proper choice of
values, the fuzzy fault diagnosis system is trained with different input–output
pattern. The results obtained through computer simulation are compared with
experimental results. The deviation of output of FLFD from the experimental
value is calculated as error. The effectiveness of FLFD is analysed in terms of
percentage error and computational time.
IV.
RESULTS AND DISCUSSION
The simulation study is carried out
using MATLAB. The results obtained through computer simulation with thee and
five membership functions of triangular, trapezoidal and Gaussian shapes are
shown in table.4 and table.5 respectively.
The error for each input pattern is calculated and tabulated. The computational
time of FLFD with three and five membership functions are given in table.6.
From table 4 and table 6, it is found that the FLFD with three-membership
function of triangular shape gives minimum error and requires minimum
computation time.
Table.4 Simulation results of FLFD with three
membership functions
|
Experimental value (T) (°C) |
Triangle |
Trapezoidal |
Gaussian |
|||
|
Output of FLFD |
Error (%) |
Output of FLFD |
Error (%) |
Output of FLFD |
Error (%) |
|
|
41 |
40.9 |
0.24 |
40.9 |
0.24 |
40.9 |
0.24 |
|
51 |
51.1 |
0.19 |
51.1 |
0.19 |
51.1 |
0.19 |
|
52 |
52.0 |
0 |
52.0 |
0 |
52.0 |
0 |
|
54 |
54.1 |
0.18 |
54.1 |
0.18 |
54.1 |
0.18 |
|
58 |
58.0 |
0 |
58.0 |
0 |
58.3 |
0.51 |
|
62 |
61.9 |
0.16 |
61.9 |
0.16 |
60.7 |
2.09 |
|
68 |
67.9 |
0.14 |
67.9 |
0.14 |
67.9 |
0.14 |
|
Average error |
0.13 |
0.13 |
0.48 |
|||
Table. 5 Simulation results of FLFD with five membership
functions
|
Experimental value (T) (°C) |
Triangle |
Trapezoidal |
Gaussian |
|||
|
Output
of FLFD |
Error (%) |
Output of FLFD |
Error (%) |
Output of FLFD |
Error (%) |
|
|
41 |
40.9 |
0.24 |
40.9 |
0.24 |
46.9 |
14.39 |
|
51 |
51.1 |
0.19 |
51.1 |
0.19 |
54.4 |
6.66 |
|
52 |
52.0 |
0 |
52.0 |
0 |
52.0 |
0 |
|
54 |
54.1 |
0.18 |
54.1 |
0.18 |
53.5 |
0.92 |
|
58 |
58.0 |
0 |
58.0 |
0 |
58.0 |
0 |
|
62 |
61.9 |
0.16 |
61.9 |
0.16 |
61.6 |
0.64 |
|
68 |
67.9 |
0.14 |
67.9 |
0.14 |
67.0 |
1.47 |
|
Average error |
0.13 |
0.13 |
3.44 |
|||
Table. 6 Comparison of
computation time of FLFD
|
Membership function |
Triangle (Time
in seconds) |
Trapezoidal (Time
in seconds) |
Gaussian (Time
in seconds) |
|
Thee
membership functions |
11.32 |
13.90 |
14.06 |
|
Five
membership functions |
12.41 |
14.11 |
24.06 |
From table 5 and table 6, it is found
that FLFD with five membership functions of triangular shape gives minimum
error and requires minimum computation time. From the simulation results, it is
inferred that the performance of FLFD with triangular membership functions is
comparable with trapezoidal and Gaussian membership functions.
V. CONCLUSION
A fuzzy fault diagnosis system has
been designed with three and five membership functions of triangular,
trapezoidal and Gaussian shapes for a single-phase induction motor. The
performance of fuzzy fault diagnosis system is analyzed through computer
simulation and results were presented. From the simulation results, it is
inferred that the fuzzy fault diagnosis system with three triangular membership
functions well suited for this application since it gives minimum error and
requires minimum computation time. The accuracy of the fuzzy logic fault
detector can also be improved by choosing the appropriate defuzzification
scheme for a given problem. The simulation results are verified experimentally.
This method can also be extended to other type of electrical machines.
ACKNOWLEDGEMENT
The authors thank Dr.K.K.Padmanabhan
Principal, Kumaraguru College of Technology, and Coimbatore for his guidance
and support. The authors also thank Dr. S. Arumugam, Dean (Research), GCT
campus Anna University for providing research facilities.
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Technical College - Bourgas,