COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
A Novel Fuzzyexpert Diagnosis System of Inner-faults for Three-phase
Squirrel Cage Induction Motors
Tak Son Cheang *, Si Leong Chan, Booma Devi Sekar, Ming Chui Dong
Faculty of Science and Technology, University of Macau, P.O. Box 3001, Macau, China
Email: [email protected], [email protected]
ABSTRACT
Three phase induction motors are widely used in industrial production all over the world. Due to high utilization rate,
frequent starting and changing load condition, the appearance of failures in induction motors is relatively high. A
sudden fault will cause large economic losses. Therefore, the early fault detection becomes very important. During
practical operation of three-phase induction motors in industry, the inner faults may occur in their rotor and stator
windings. These kinds of faults will make serious influence on the operation of the motor.
There is insufficient R&D in the diagnosis system of inner-faults of squirrel cage induction motor. Thus a new
research on the fuzzyexpert diagnosis system of inner-faults for three-phase induction motors is presented. The
purpose of fault diagnosis is to isolate the cause of a system malfunction in a timely manner.
This paper presents a new sequence performing diagnosis of the three-phase induction motors as: sample the fault
symptoms, carry the fuzzyexpert forward & backward inference, deduce the fault hypotheses and conclude the fault
discrimination. Among them, a novel technique of how to define the various membership functions and the relevant
fuzzy sets concerning the uncertainty issues based on the symptoms of motor faults (experimental data), and how to
construct the proper inference nets for producing the production rules are explained.
Finally, a series of experiments of diagnosing the stator and rotor faults are shown.
Key words: fault diagnosis, fault detection and isolation, model-based diagnosis, fuzzy sets, fuzzyexpert technology
INTRODUCTION
The overall view of various faults of induction machine and the traditional fault diagnosis methods can be observed
from Fig.1. According to the statistic data, the failures of the induction machine are mainly the rotor bar broken, and
the inter-turn faults of the stator windings, which are shown in Table 1 [1-2].
Table 1 Type and Occurrence of Various Faults of Induction Machine
Type of Faults
Occurrence (%)
Rotor bars broken
≈ 10.0
Inter-turn Faults of Stator Windings
≈ 15.0
Overheating Faults of Stator Windings
≈ 6.0
The most commonly used traditional diagnosis method is MCSA (Motor Current Signature Analysis), which relays
upon the FFT (Fast Fourier Transform) analysis and the demodulation of voltage and/or current. Although some
mathematical models had been developed in our previous papers [12, 13], however it is unrealistic to build up the exact
mathematical models for all possible faults of induction motor. As a result, it is natural to switch from the math⎯ 774 ⎯
model based diagnosis methods to math-model independent AI (Artificial Intelligent) based methods, such as ES
(Expert System), NN (Neural Networks), FL (Fuzzy Logic) etc.
Figure 1: Faults and fault diagnosis of induction machine
Some researchers conclude that following the current signature extraction the ES alone can be used for fault
identification [3] with clear causal explanation to the conclusion. But the disadvantages of rule-based system
become severe in handling the unpredictable strange fault cases. Instead, NN shows out comparatively his obvious
advantages in field of fault diagnosis of induction motor [4-9] due to having the tolerance and generalization
capabilities. However, his main drawbacks always make researchers feel headache, such as requiring input the
digitized data, big computational burden in network training, lack of perceptible casual explanation to the hypothesis,
etc. Moreover, both ES and NN can not handle the ambiguous events or symptoms, described by the linguistic terms
such as “getting bigger”, “almost”, “rather close to”, etc.
In these aspects, FL allows transforming the heuristic and linguistic terms into numerical values via defining the
fuzzy rules and membership functions. And also it can easily map the physical values, which are of the big different
scales, into the same scale scope. Unfortunately, very few researchers [10] had applied FL to fault diagnosis of
induction motor. Even fewer researchers had considered integrating the above methods actively for diagnosing the
faults of motors so far.
Concerning the uncertainty and ambiguity issues, deduced from analyzing the huge experimental data obtained by
measuring and simulating the various non-healthy induction motors, here in this paper, a novel fuzzyexpert diagnosis
system of inner-faults for three-phase induction motors is proposed, which inherits the main advantages of FL & ES,
and compensates their disadvantages in certain level.
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SYMPTOMS AND HYPOTHESES ANALYSIS
Deduced from our previous paper [11], besides the changes on line currents, voltages, active power, reactive power,
and power factor at the respective fault, the following additional symptoms for diagnosing the internal faults of
stator and rotor can be concluded:
1) Inter-turn Faults of Stator Windings – Symptoms Analysis
(1) There are 3rd harmonic component existed in the stator currents when the motor is healthy. When the inter-turn
fault of the stator windings occurs, the change of the 3rd harmonic component is obvious. Consequently the 3rd
harmonic component is considered as one of the main symptoms for diagnosing the inter-turn fault of the stator
windings.
(2) Due to the existence of the fluctuation of the negative phase component of the stator three-phase voltage, the
negative phase current will also fluctuates. This issue will mislead the diagnosis system to consider the existence of
the stator inter-turn fault. It is not practical only to consider the negative phase sequential current as the symptom of
the inter-turn fault. The effective negative-sequential admittance should also be considered.
(3) The zero sequential current and voltage are considered.
(4) When the internal stator fault develops, the temperature rise is another symptom to be considered.
2) Rotor Bars Broken – Symptoms Analysis
(1) Due to the fabrication problem of the induction motors, even the rotor is healthy, the stator currents may have the
sideband components of (1-2s) f1 and (1+2s) f1 and other higher harmonic components.
(2) The stator currents will contain the 3rd and 5th harmonic components or higher harmonic components in fault
status.
(3) The negative phase sequential admittance is considered as an indicator of the symptoms of faults.
(4)The zero sequence current and voltage is considered.
(5) When the internal rotor fault develops, the temperature rise is another symptom to be considered, although the
temperature rise is not obvious.
Concerning the above symptoms, the following parameters will be considered at this paper:
V (line Voltages),
I (line Currents),
AP (Active Power),
RP (Reactive Power),
PF (Power Factor),
VTHD (Total Harmonic Distortion of Voltage),
ITHD (Total Harmonic Distortion of Current).
TO DEFINE FUZZY SETS
The fuzzy sets are constructed based on the symptoms of the motor for diagnosing the type & location of the inner
faults. Concerning the symptoms summarized from the experimental data, the corresponding membership functions
should be well defined. Through which, the final fuzzy formula could reflect properly the mapping relationship
between the symptoms of motor and the correct type & location of fault inside the motor.
1. To Define Membership Function The model type Y90S-4 motors are used in experiment with 220V power supply.
Seven symptoms of motor under the status of Healthy, Stator Fault and Rotor Fault are tested. They are V, I, AP, RP, PF, VTHD
and ITHD, which are the common and key parameters to reflect or distinguish the type & location of fault. Table 2 shows only
the partial experimental data used for showing how to define the fuzzy sets.
Further analysis to the experimental data of Table 2 shows that the APVD (Absolute Phase Value Difference) of each
phase is balanced when the motor is in healthy status, and the APVD will increase when the fault occurs. The rest 5
symptoms: AP, RP, PF, VTHD and ITHD have the same phenomenon. Table 3 shows the APVD of voltage and
current for the healthy and fault motors corresponding to the Table 2.
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Table 2 Partial Experimental Data of Healthy and Fault Motors
Table 3 APVD of Healthy and Fault Motors
Based on these APVD data, a group of S-type membership function can be defined for the voltage, as shown on
Fig. 2, in which the grade represents the corresponding fault, while the grade 0 represents the healthy status.
Similarly, other 6 groups of S-type membership function can be defined.
It is worth to point out that the voltage APVD of stator fault falls in the range between 0.6V and 4V, while voltage
APVD of rotor fault falls in the range between 1.4V to 8V. Obviously, using APVD to construct voltage and other Stype membership functions can not only separate the healthy and fault status of motor, but also can distinguish the
specific fault type & its location clearly.
Figure 2: Voltage membership function of motor
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Figure 3: Hierarchical fuzzy sets of internal fault of motor
2. Architectural Design of Fuzzy Sets After defining 7 groups of S-type membership function, for better
categorizing and identifying the fault type & its location, the hierarchical fuzzy sets of internal fault of motor with 5
layers can be defined as shown on Fig. 3.
3. Fault Expressions and Their Calculations Based on the Defined Fuzzy Sets Based the above defined fuzzy
sets, using the gravity-average method to handle the experimental grades, the various fault equations F can be
expressed finally by:
7
F = ∑ ( Gi ⋅ X i )
(1)
i =1
where G is 100 times of the grade of membership function and X expresses 7 symptom vectors, each vector contains
the values obtained in A, B, C three phases.
Consequently, the Healthy state equation H can be written as:
→
→
→
→
→
→
→
H = 20 ⋅ V ( H ) + 20 ⋅ I ( H ) + 10 ⋅ AP ( H ) + 10 ⋅ RP ( H ) + 10 ⋅ PF ( H ) + 15 ⋅ VTHD ( H ) + 15 ⋅ ITHD ( H )
(2)
The equation of Stator Fault with 1 phase short FS1 is:
→
→
→
→
→
→
→
F = 20 ⋅ V ( S1) + 20 ⋅ I ( S1) + 10 ⋅ AP ( S1) + 10 ⋅ RP ( S1) + 10 ⋅ PF ( S1) + 15 ⋅ VTHD ( S1) + 15 ⋅ ITHD ( S1)
S1
(3)
The equation of Stator Fault with 2 phases short FS2 is:
→
→
→
→
→
→
→
F
= 20 ⋅ V ( S 2) + 20 ⋅ I ( S 2) + 10 ⋅ AP ( S 2) + 10 ⋅ RP ( S 2) + 10 ⋅ PF ( S 2) + 15 ⋅ VTHD ( S 2) + 15 ⋅ ITHD ( S 2)
S2
(4)
The equation of Stator Fault with 3 phases short FS3 is:
→
→
→
→
→
→
→
F
= 20 ⋅ V ( S 3) + 20 ⋅ I ( S 3) + 10 ⋅ AP ( S 3) + 10 ⋅ RP ( S 3) + 10 ⋅ PF ( S 3) + 15 ⋅ VTHD ( S 3) + 15 ⋅ ITHD ( S 3)
S3
⎯ 778 ⎯
(5)
The equation of Rotor Fault with 1 broken bar FR1 is:
→
→
→
→
→
→
→
F
= 20 ⋅ V ( R1) + 20 ⋅ I ( R1) + 10 ⋅ AP ( R1) + 10 ⋅ RP ( R1) + 10 ⋅ PF ( R1) + 15 ⋅ VTHD ( R1) + 15 ⋅ ITHD ( R1)
R1
(6)
The equation of Rotor Fault with 2 broken bars FR2 is:
→
→
→
→
→
→
→
F
= 20 ⋅ V ( R 2) + 20 ⋅ I ( R 2) + 10 ⋅ AP ( R 2) + 10 ⋅ RP ( R 2) + 10 ⋅ PF ( R 2) + 15 ⋅ VTHD ( R 2) + 15 ⋅ ITHD ( R 2)
R2
(7)
The equation of Rotor Fault with 3 broken bars FR3 is:
→
→
→
→
→
→
→
F
= 20 ⋅ V ( R 3) + 20 ⋅ I ( R 3) + 10 ⋅ AP ( R 3) + 10 ⋅ RP ( R 3) + 10 ⋅ PF ( R 3) + 15 ⋅ VTHD ( R 3) + 15 ⋅ ITHD ( R 3)
R3
(8)
The above equations can be expressed in a matrix-vector form as:
⎡ →
V (H )
⎡ H ⎤ ⎢ →
⎢ F ⎥ ⎢ V ( S1)
⎢ S1 ⎥ ⎢ →
S 2)
⎢ FS 2 ⎥ ⎢V (→
⎢
F
⎢ S 3 ⎥ = V ( S 3)
⎢F ⎥ ⎢ →
⎢ R1 ⎥ ⎢ V ( R1)
⎢ FR 2 ⎥ ⎢ →
⎢⎣ FR3 ⎥⎦ ⎢V ( R 2)
⎢ →
⎣⎢V ( R3)
→
I (H )
→
I ( S1)
→
I ( S 2)
→
I ( S 3)
→
I ( R1)
→
I ( R 2)
→
I ( R3)
→
→
→
AP ( H ) RP ( H ) PF ( H )
→
→
→
AP( S1) RP ( S1) PF ( S1)
→
→
→
AP ( S 2) RP ( S 2) PF ( S 2)
→
→
→
AP ( S 3) RP ( S 3) PF ( S 3)
→
→
→
AP ( R1) RP ( R1) PF ( R1)
→
→
→
AP ( R 2) RP ( R 2) PF ( R 2)
→
→
→
AP ( R3) RP ( R3) PF ( R3)
→
→
⎤
VTHD ( H ) ITHD( H )
⎥
→
→
⎡20⎤
VTHD ( S1) ITHD ( S1) ⎥ ⎢ ⎥
⎥ 20
→
→
VTHD ( S 2) ITHD ( S 2) ⎥ ⎢10 ⎥
→
→
⎥ ⎢10 ⎥
VTHD ( S 3) ITHD ( S 3) ⎥ ⎢ ⎥
→
→
⎥ ⎢10 ⎥
VTHD ( R1) ITHD ( R1) ⎢ ⎥
⎥ 15
→
→
⎢ ⎥
VTHD ( R 2) ITHD ( R 2) ⎥ ⎣15 ⎦
⎥
→
→
VTHD ( R3) ITHD( R3) ⎦⎥
(9)
The following example of Stator Fault with 1 Phase Short shows how to use the equation 9 in the fault diagnosis.
Once a real measurement is finished, the grades of 7 symptoms are obtained through the membership functions,
which are listed on Table 4.
Table 4 Grades of 7 Symptoms in Example of Stator Fault with 1 Phase Short
Substitute these grades into Eq. (9) and get the fault equations F as:
0
0
0
⎡H ⎤ ⎡ 0
⎢ F ⎥ ⎢ 0.95 0.58 0 0.52
⎢ S1 ⎥ ⎢
⎢ FS 2 ⎥ ⎢ 0.95 0.58 0 0.4
⎥ ⎢
⎢
⎢ FS 3 ⎥ = ⎢0 0.95 0.58 0 0.5
⎢ FR1 ⎥ ⎢ 0.16
0
0
0
⎥ ⎢
⎢
0
0 0.45
⎢ FR 2 ⎥ ⎢ 0.15
⎢ F ⎥ ⎢ 0.28
0 10 0.5
⎣ R3 ⎦ ⎣
0.4 0.19
0 ⎤ ⎡20⎤
0.2 0.02 0.1 ⎥⎥ ⎢⎢20⎥⎥
0.3
0
0 ⎥ ⎢10 ⎥
⎥⎢ ⎥
0.1
0
0.1 ⎥ ⎢10 ⎥
0.6
0
0.09⎥ ⎢10 ⎥
⎥⎢ ⎥
0.2 0.05 0.2 ⎥ ⎢15 ⎥
0.2 0.2 0.1 ⎥⎦ ⎢⎣15 ⎥⎦
After calculation, the following possibilities can be concluded:
Healthy is 6.85%;
Fault of Stator with 1 phase short is 39.60%;
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(10)
Fault of Stator with 2 phase short is 37.60%;
Fault of Stator with 3 phase short is 38.10%;
Fault of Rotor with 1 broken bar is 10.55%;
Fault of Rotor with 1 broken bar is 13.25%;
Fault of Rotor with 1 broken bar is 17.10%.
It indicates that the Stator Fault with 1 Phase Short has the highest possibility to occur, which exactly matches the
real situation.
INFERENCE NETS
Based on the above defined fuzzy sets and the fault calculation, the inference nets for obtaining the hypothesis and
the final conclusion step-by-step from the sampled symptoms can be constructed as shown on Fig. 4, where
(1) Inputs are the sampled values of 7 symptoms: V, I, AP, RP, PF, VTHD and ITHD
(2) Outputs are the fault type & its location
Based on this inference nets, it is easy to generate the production rules and build up the fuzzyexpert system.
Figure 4: Structure of Inference Nets
CONCLUSIONS
A novel technique of how to define the various membership functions and the relevant fuzzy sets concerning the
uncertainty issues based on the symptoms of motor faults (experimental data), and how to construct the proper
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inference nets for producing the production rules are proposed. After solving these key issues, the fuzzyexpert
system can be easily built up, which integrates the advantages of FL and ES in fault diagnosis of induction motor.
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