fault diagnosis of induction motors using signal processing based methods and optimal feature selection

Fault Diagnosis of Induction Motors using Signal Processing based Methods and Optimal Feature Selection... The signal processing methods for induction motor fault detection have recently

웬 옥 투

웬 옥 투

Fault Diagnosis of Induction Motors using Signal Processing based Methods and

Optimal Feature Selection

Abstract

Fault detection and diagnosis in rotating machines have been used widely in commercial systems over the past few decades Numerous works on machine conditions have been implemented with the aid of the MCSA (Motor Current Signature Analysis) method, the vibration-based methods, etc The purpose of these methods is to detect and diagnose faults in

an early stage and therefore allow contingency plans to be put into place before the problems worsen The dynamic and vibratory behaviours of the machine, such as vibration, sound, and temperature… are affected if the running condition is changed The behaviours can be useful indicators to detect problems within the machine as they vary abnormally from a standard when

a fault occurs Of the many signals which can be measured, the vibration signal has been the most useful to monitor the machine condition as in many cases the time domain vibration signals are sufficient to diagnose and can be easily measured with accelerometers

The signal processing methods for induction motor fault detection have recently received great attention because they do not need a typical mathematical model Many signal processing diagnostic procedures have been studied in this work to identify faults of the machines The decision tree, support vector machine (SVM), artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), and k-nearest neighbour (K-NN) have been applied to diagnose the condition of machines with rather high accuracy These methods have used vibration data as an indicator for monitoring the fault conditions In this work, the vibration data are measured in three dimensions to collect as much information as possible Then an optimal feature selection is proposed in this work for improving the classification performance

of the diagnostics system The classification results have proved the efficiency of the proposed optimal feature selection and the suitability of vibration data as an indicator for induction motor fault diagnosis

I would like to thank the examiners of this thesis, Professor Young-Soo Suh, Professor Jin Hur, Professor Myeong-Jae Yi, and Professor Heung-Geun Kim for their valuable comments and corrections

1.3 Objective and contribution

1.4 The structure of the thesis

1

1

3

6 7

2 Understanding the Basis of Induction Motor Faults

3 Methods for Fault Diagnosis of Induction Motor

3.1 FFT-based method

3.1.1 Case study 1 – Looseness case

3.1.2 Case study 2 – Stator winding fault

3.1.3 Case study 3 – Rub fault

3.1.4 Case study 4 – Unbalance Rotor

5.2.1 Genetic algorithm based feature selection

5.2.2 Principal Component Analysis

5.3 Some Experimental Results

6 Conclusions 74References 75Publications 79

List of Figures

Fig 1 Typical causes for machine failures

Fig 2 Bearing structural defects

Fig 3 Ball bearing geometry

Fig 4 Bearing time-domain vibration signals and FFT spectrum, (a) normal, and (b) defective

Fig 9 Frequency domain and time domain vibration signals of a misalignment case in three directions

Fig 10 Vibration spectrums (a) in radial direction (b) in axial direction

Fig 11 Vibration spectrums of case study 2

Fig 12 Vibration spectrums (a) in radial direction (b) in axial direction

Fig 13 Vibration spectrums in radial direction

Fig 14 General model based fault detection scheme

Fig 15 An adaptive network-based fuzzy inference system

Fig 16 An example of a k-NN classification The test pattern x can be classified either as positive or negative class

Fig 17 Typical structure of a decision tree

Fig 18 Hyperplanes for the SVM trained with two-class samples

Fig 19 Experimental setup

Fig 20 Accelerometer (a) is used in this work and induced faults (b) rotor unbalance, (c) bearing damage and (d) sensor measuring position

Fig 21 Time signal waveforms in 3 dimensions (Horizontal-Axial-Vertical): (a) Bearing damage (b) Bearing looseness (c) Rotor unbalance (d) Stator fault (e) Normal condition Fig 22 GA process

Fig 23 Weighted values of 18 features given by the genetic algorithm

Fig 24 (a) Normal bearing (horizontal, axial, and vertical); (b) Defective bearing time signals

Fig.25 Extracted features, (-, blue) normal and ( , red) defective bearing

Fig.26 The projection of the training data on the first three axes

Fig 27 Classification results of the conventional k-NN (-, square) and proposed k-NN ( , triangle) according to k; (a) evaluated with three, (b) four, (c) five, (d) six, and (e) seven features (vertical axis is the average accuracy, horizontal axis is k)

Fig 28 Decision tree without feature extraction

Fig 29 PCA-based decision tree with 9 new features

Fig 30 PCA-based decision tree with 4 new features

Fig 31 Decision tree with all features

Fig 32 Decision tree with 3 selected features

Fig 33 RF classification result of case 1 The test data classification error is 7.506%

Fig 34 RF classification result of case 2 The test data classification error is 7.748%

Fig 35 RF classification result of case 3 The test data classification error is 4.843%

Fig 36 RF classification result of case 4 The test data classification error is 4.358%

Fig 37 RF classification result of case 5 The test data classification error is 5.327%

Fig 38 Some bearing training patterns, defective (-) and normal ( )

Fig 39 Input membership functions (training with 150 epochs) (a) before training, (b) after training, and (c) targets and ANFIS system output

Fig 40 Input membership functions (training with 80 epochs), (a) before training, (b) after training, and (c) targets and ANFIS system output

List of Tables

Table 1: Time-domain features

Table 2: The 10 largest weight features

Table 3: The conventional k-NN classifier performance before and after feature selection Table 4: The weighted k-NN classifier performance before and after feature selection Table 5: Performance for the SVM classifier

Table 6: Compare the performance of normal decision tree and PCA based decision tree Table 7: k-NN classifier performance before and after feature selection

Table 8: Decision tree performance before and after feature selection

Table 9: SVM classifier performances before and after feature selections

Table 10: Decision tree (DT) performances before and after feature selections

Table 11: Performance comparison for SVM classifier (under the same condition) Table 12: Local optimum parameters are obtained from GA algorithm

Table 13: Performance comparison on multi faults diagnosis

Table 14: The main advantages and disadvantages of classifiers

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1 Introduction

1.1 Background and motivation

Major rotating machinery may have very high cost, once machinery is shut-down then not only affect the financial losses but also human lives Therefore, maintenance of rotating machine is an important factor to minimize the losses and keep the machine in good condition In recent years, diagnostic techniques have changed to increase the performance of rotating machine fault detection That because induction motors are becoming an increasingly important aspect of industrial processes The purpose of monitor condition or diagnosis of induction motor is to detect and diagnose faults in an early stage and therefore allow contingency plans to be put into place before the problems worsen It can be achieved either manually or on the basis of the expert system

The machines are designed to generate mechanical power from an energy source or convert mechanical power to electrical power, etc They therefore create forced vibration and dynamic stresses when are operated The dynamic and vibratory behaviours of the machine, such as vibration, sound, and temperature, are affected if the running condition is changed Then, these behaviors can be useful indicators to detect problems within the machine as they vary abnormally from a standard when a fault occurs For electrical machinery, the abnormal vibratory behaviors can be caused by either mechanical or electromagnetic defects The latter can be isolated by removing power then the vibration caused by electrical or magnetic defects will disappear Vibration caused by electrical problems can be analyzed to determine the nature of the defect For example, a defect such as stator winding fault produces two times line frequency component A broken rotor bar produces 1X component with two times slip frequency sidebands

The quality and effectiveness of a diagnosis procedure is most often limited by the availability of capable and skilled personnel With the equipments becoming more and more complex, maintenance personnel have to help setup and establish the maintenance program They may also assess the condition of the machine by comparing acquired data with healthy data Based on their knowledge of machinery and working experience, they will be able to determine whether an abnormal symptom is due to a defect, or to a change in operating condition However, this task is difficult even for experts because of a great amount of machinery knowledge and the influence of the environmental noises A major problem with rotating machinery is, they run smoothly for a

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long time and then suddenly develop a defect The defect may slowly increase and deteriorate the condition of the machine or suddenly develop into a shutdown condition It is difficult and also too expensive for the industry to employ maintenance personnel dealing with machinery problems and wait for an opportunity to diagnose an impending problem that may occur in the machine That is when intelligent classification systems have been developed to assist the machine fault diagnosis tasks by processing the fault data Up to now, there are many algorithms have been studied for this goal

With the knowledge of the machine behavior based on its design and operation that can be collected over time, it is possible to perform a diagnostic analysis of the machine under trouble Instead of using maintenance experts, an expert system using the knowledge-base of the machine can be used, so that the diagnostic decision can be quickly given whenever a fault occurs without employing the experts Most machine fault diagnosis systems utilize the expert system, which is mainly based on vibration symptoms or stator currents The principle of this method is the fact that the fault inside the machine structure can be visible as distinct frequency components in the spectrum The expert system can operate based on previously defined knowledge-base It basically consists of two parts, the data or knowledge-base and the inference engine, which is the diagnosis part The knowledge-base will be in general based on experience in carrying a particular task and

be gathered in a period of time An expert system can only be good if it possesses a good knowledge-base When a problem is sensed in the machine, the symptoms can be measured or observed and using the knowledge-base, the inference engine can applied to identify the possible defects

The condition monitoring techniques have changed over years as the machines became more sophisticated with increasing capacities and speeds Such techniques are initially done by recording the time domain signal and then using some procedures to extract the certain components, i.e frequency components or statistical characteristics Then the diagnostic processes are applied using that processed data In the past, these consume time and depend on the experience of operating experts In recent years with the development of microprocessors, personal computers and analog

to digital converters, diagnostic process through computer programs is becoming a standard practice The real time condition monitoring and diagnosis are becoming the realistic and effective techniques

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The work deals with some basics of understanding of induction motor faults, signal based processing methods for monitoring the condition of induction motor, the optimal feature selection using distance based criterion is considered to remove the irrelevant and redundant information in data set The thesis will be limited to vibration condition monitoring, through there could be some other useful indicators, for example, stator current

Since the most common faults of induction motors are rotor faults, stator faults, and bearing faults, four types of faults are simulated and classified in this work, namely, bearing looseness, bearing damage, rotor unbalance, and stator fault

1.2 Previous works

In recent years, rotating machine fault diagnostic technology continues to grow rapidly Many kind

of intelligent diagnostic methods have been developed, such as artificial neural network, fuzzy technology, decision tree, adaptive network-based fuzzy inference system, support vector machine, k-nearest neighbour, etc Those methods can use different machine condition indicator, such as current, voltage, speed, efficiency, temperature and vibrations Fault detection based on machine current or voltage relies on interpretation of the frequency components in the spectrum But it only can diagnose the electrical related and certain mechanical problems, such as broken rotor bar, broken rotor end ring, eccentricity, stator windings or power supply problems, bearing defects Nowadays, a principal tool for diagnosing machinery problems has been the vibration analysis That because the physical movement or motion of a rotating machine is normally referred to as vibration Almost common machine faults can be detected by analyzing the vibration data

The classification methods can be divided into three groups: signal processing based methods, model based methods, and FFT based methods

The FFT based methods are relied on the following principles:

- The machine problems have distinct frequency components that can be isolated and identified

- The FFT signature of a machine is compared over time, a problem can be detected if there are some changes in the FFT pattern, i.e the amplitude of each frequency component will remain constant until there is a change in the operation dynamics of the machine

However, an increase or decrease in amplitude may indicate degradation of the machine, but is not always caused by a problem Variation in load, operation, and other normal changes also generate

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a change in the amplitude of one or more frequency components within the FFT signature Therefore, it is important for FFT based method that the knowledge of machine faults be clearly understood Motor current signature analysis (MCSA) is a typical FFT based method which analyses the frequency components of stator current signals The fundamentals of MCSA are

illustrated via industrial case histories (W T Thomson et al 2003 [21]) But the FFT based

method is required operator persons with expert knowledge to make the final decision to either immediately repair the motor or let it run and prepare for a rectified plan

In order to replace the role of experts, the model and signal processing based methods have been developed to keep checking the data signatures continuously The signal processing based methods for fault detection have recently received great attention because it does not need a typical mathematical model Many signal processing diagnostic procedures have been introduced to identify faults of the machines The decision tree is proposed to diagnose the rotating machine and

bearing condition (V Sugumaran et al 2007 [1], W Sun et al 2007 [2], B S Yang et al 2000 [3],

D S Lim et al 2000 [4]) The support vector machine (Y Yang et al 2007 [5], A Widodo et al

2007 [6, 8], J Yang et al 2007 [7], A Rojas et al 2006 [9]), artificial neural network (B Samata

et al 2003, 2006 [10, 11], L B Jack et al 2002 [12], B Li et al 2000 [13], A Saxena et al 2007

[14]), adaptive neuron-fuzzy inference system (Y Lei et al 2007 [15], Z Ye et al 2006 [16]), and fuzzy logic (T Lindh et al 2004 [18]) have been applied to diagnose the condition of machines

with rather high accuracy Most of the methods have used vibration data as an indicator for monitoring the fault conditions In addition to these signal processing methods, which are based on characteristic analysis in the time or frequency domains, the model based methods are another way

to diagnose machine fault The model based fault detection for an induction motor is based on

analytical redundancy (C Combastel et al 2002 [23], K Kim et al 2002 [24]) Due to the

availability of the mathematical model, it is possible to model the electrical behaviour of an induction motor and is widely used to detect electrically related faults such as the rotor bar and stator winding faults However, this method requires an accurate mathematical model and is difficult to compensate for the uncertainties in practical applications Further, not all faults can be simulated by the model; however, for such cases, signal processing can be applied to design the

model The FFT based signal processing technique (H S Lim et al 2006 [25]) is used in

combination with a model-based method to estimate fault features, and while this is an effective method, it is applied only for two-condition situations

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Decision tree is concerned as a diagnostic tool in [1-4] B S Yang et al 2000 [3] and D S Lim et

al 2000 [4] have been developed decision trees for motor fault diagnosis based on Sohre’s

cause-result matrix [43] However, those systems can only be operated by experts and the input data can not imported without considering of maintenance personnel Those systems can give the high

reliability but need a great amount of machine knowledge W Sun et al 2007 [2] have recently

developed decision tree using PCA algorithm In that research, the authors use PCA to reduce features after data collection, preprocessing and feature extraction Then, C4.5 is trained by using the samples to generate a decision tree model But even PCA is an effective technique to reduce data dimension, but sometimes it can remove some useful information in the dataset Together with

a linear classification method as decision tree, k-nearest neighbour has also recently been applied

successfully for fault diagnosis of induction motor (R Casimir et al 2006 [29]) with stator current

and voltage features

The support vector machine (Y Yang et al 2007 [5], A Widodo et al 2007 [6, 8], J Yang et al

2007 [7], A Rojas et al 2006 [9]) is applied successfully to diagnose the motor and bearing

condition with many data processing techniques such as fractal dimension, IMF envelope spectrum, independent component analysis, nonlinear feature extraction Support vector machine in those researches has classification performance that outperforms many other methods In this work, support vector machine is also studied with the proposed optimal feature selection

Artificial neural network (B Samata et al 2003, 2006 [10, 11]) has been applied to fault bearing

detection using time-domain features Genetic algorithm is used to select the characteristic

parameters of the classifier and the input feature L B Jack et al 2002 [12], B Li et al 2000 [13],

A Saxena et al 2007 [14] have investigated neural network for applying to intelligent fault

diagnosis of rotating machine However, the neural network model basically has poor

generalization ability, so that it can not predict the novel samples well Fuzzy logic (T Lindh et al

2004 [18], G Goddu et al 1998 [19]) has been applied to bearing fault classification because it can

mimic human decisions But it is difficult to tune its parameters in order to maximize the reliability

of the system Combining the power of artificial neural network and fuzzy logic, adaptive

neuron-fuzzy inference system (Y Lei et al 2007 [15], Z Ye et al 2006 [16]) has been introduced for

machine fault diagnosis with good classification performance

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Although many classification algorithms are available for study, the research comparison (G Niu

et al 2007 [26]) shows no single algorithm has the best performance in all cases Taking this into

account, some special data processing can be considered to guarantee good classification results Many methods have been suggested for data preparation; two common ones are feature selection and feature extraction Further, principal component analysis (PCA) and independent component analysis (ICA) are two popular feature extraction techniques used to decrease data dimensions by extracting as much information as possible from a given data set In addition, decision tree using

the PCA technique for fault diagnosis have been shown to provide encouraging results (W Sun et

al 2007 [2]); however, for the purpose of feature selection, distance criterion has been effectively

used in many research studies, although it should be noted that some researchers have used GA to

choose the most appreciated features in a feature set (B Samanta et al 2003, 2006 [10, 11], Y Lei

et al 2007 [15]) Selection of the highest qualified features can help to improve system

performance as well as remove useless features that can spoil the performance of a diagnosis

1.3 Objective and contribution

The work focuses in signal processing based methods with optimal feature selection In this work, the data for signal processing based methods is obtained from time domain vibration signals To improve the classification performance, an optimal feature selection is required that reduces the data dimension and removes the irrelevant and redundant information in the data For these purposes, principal component analysis, and GA have been introduced For data preprocessing, there are two ways to apply: feature selection and feature extraction The feature extraction methods such as PCA (or ICA) can be used to extract useful information, although these approaches both require alteration of the original data Conversely, feature selection is a technique that selects a small subset within a dataset and does not change the original data If all the data are used as input of the classifier, they may make the classification processes become slower and reduce the system performance Therefore, the most difficult task for improving the system performance of the proposed methods is to select proper important features Here, we propose a simple selection method based on distance criterion and GA that provides high efficient method for classifying an induction motor fault Feature extraction using PCA methods is also tested and applied to bearing fault detection

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Vibration data measurements can be a useful motor fault indicator A tri-axial accelerometer is installed to collect the vibration signals in x, y, and z directions The efficiency of vibration measurements as a fault indicator has been verified in the thesis Tri axial vibration data can make extending the range of target without caring of direction of vibration amplitude due to motor installation

Another goal of this work is the evaluation of signal processing based methods with applying the proposed optimal features and vibration data, such as k-nearest neighbor, support vector machine, decision tree, random forest, etc The vibration data with optimal feature selection are applied to these methods and obtained promising results

1.4 The structure of the thesis

The first part shows some introduction of fault condition monitoring techniques The rapid development and importance of the machine fault diagnosis over years and the goal of this work are introduced briefly The second part describes some basis knowledge of machine failures such as bearing damage, stator unbalance and rotor unbalance As the availability of accurate sensors and fast computers, many techniques have been studied to analyze the machine condition The third part of this thesis introduces some methods for rotating machine fault diagnosis: decision tree, SVM, K-NN, random forest, etc The next part shows the experimental setup and diagnosed results

of signal processing based methods Finally are the conclusions and given future works

Chapter 1 is above briefly introduction

Chapter 2 presents the basic knowledge of induction motor faults, such as bearing faults, electrical induced faults and the other faults It also shows the time-domain signals and their FFT in three directions Some descriptions and characteristics of the faults are discussed

Chapter 3 introduces methods that are used for diagnosing induction motor faults FFT based method, model based methods, and signal processing based methods are discussed

Chapter 4 presents the measurement and experimental setup used in this work The data set are formed by 18 time-domain vibration signal features

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2 The Basic Knowledge of Induction Motor Faults

The design and operating characteristics of a machine determine both the type of defects and the vibration response to those defects Vibration analysis is difficult without a working knowledge of these characteristics The condition of the machine will affect the vibration response of the machine

on the shaft, bearings, housing, foundation, etc There are many causes that generate the failure as shown in Fig.1 and these causes should be removed as fast as possible to have the machine working

in a good condition

Bearing related faults 41%

Stator related faults 37%

Rotor related faults 10%

Others 12% Bearing related faults

Stator related faults Rotor related faults Others

Fig 1 Typical causes for machine failures

About 41% of failures are caused by bearing problems, 37% by stator, 10% by rotor, and 12% by other problems The symptoms of the machine and the causes are related to each other, the more

we know how to analyze the symptoms, the more we can find ways to identify the causes Therefore, understanding the basis knowledge of machine faults is necessary for the fault detection

of induction motor A good maintenance practice requires a good understanding of the causes in the machine

2.1 Bearing Damage

Rolling-elements bearings are the most common cause of machine failure The dynamic performance of motor bearing is highly influential on the performance of the entire motor system

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Therefore, an early detection of their damage is advantageous in keeping the downtime of a machine to a minimum Faulty bearing can cause the system to function incorrectly, and cause vibration increase at some specific frequencies that result from bearing defects depend on the defect, the bearing geometry, and speed of rotation These frequencies are fundamental cage frequency, ball pass outer raceway frequency, ball pass inner raceway frequency, and ball rotating frequency

Fig 2 Bearing structural defects

Ball pass outer raceway frequency f outer appears when the rolling elements are not on the best road

and can be calculated as:

1 cos2

r outer c

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2 2 2

2

r ball c

r cage c

Where θ is contact angle of bearing

f r is the rotating frequency

n is number of balls

PD is the pitch diameter of bearing

BD is the ball diameter

Fig 3 Ball bearing geometry

If bearing geometry is not available, the inner raceway and outer raceway frequencies can be approximated as 60% and 40% of the number of balls multiplied by the running speed, respectively This approximation is possible because the ratio of ball diameter to pitch diameter is relatively constant for the bearings

Time domain vibration signals and their FFTs are shown in Fig 4 for normal and faulty bearing (6206Z bearing type)

Pitch Diameter (PD)

Ball Diameter (PB)

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Fig 4 Bearing time-domain vibration signals and FFT spectrum, (a) normal, and (b) defective

bearing

2.2 Electrical Induced Faults

Electrical faults are rotor problems, stator related problems These faults produce vibration at 1X or

2 times of line frequency The common feature is the amplitude will disappear when turn off the power

When stator damage or phase unbalance appears, vibration will be produced at 2 times of line frequency When rotor problems such as broken rotor bar or broken end-ring occurs, the 2 times of slip frequency component and sidebands occur

Rotor Unbalance

0 2 4 6 8 10 12 14 16 18

Frequency (Hz)(a)

(b)

1 2 3 4 5 6 7 8

A axial (Hz)

0 50 100 150 200 0

1 2 3 4 5 6 7 8

-20 -10 0 10 20

30 A axial

t/20000 sec

0 500 1000 1500 2000 2500 -150

-100 -50 0 50 100

The motor parameters as follow: 5Hp, 220/380V, 4 poles, running frequency is 29.9 Hz

Fig 5 Frequency domain and time domain vibration signals of a rotor unbalance case in three

directions

Stator Unbalance

Stator faults are occurred in the stator core or in the stator windings Stator winding faults can be due to insulation damage, thermal damage caused by over current, or due to bad installation, etc Stator unbalance time domain signals and their frequency domain are shown in Fig 6 Motor parameters as follow: 3.7 kW, 4 poles, 220/380 V, voltage drop in 1 phase = 37 V, line frequency

is 60 Hz

1X

1X

1X

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

X: 120.2 Y: 0.9343

2 4 6 8 10

12

X: 29.91

120.2HzTime signal: Unbalance case

Time signal: Unbalance case

Normal Unbalance

Normal Unbalance

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

X: 120.2 Y: 0.8001

Partial Rub

Light rubs may clear themselves; however they have to be watched closely since continuous rubbing may lead to failures Rub may appear when:

- Surface-to-surface contact occurs

- The rotating unit hits another object

Time domain signals and their frequency domain of a rub case are shown in Fig 7 Motor parameters are 1HP, 2P, 220/380V, running frequency 58.65 Hz

10 20 30 40 50 60 70 80

10 20 30 40 50 60

5 10 15 20 25 30

The distortion could cause vibration problems in an indirect way

- By affecting the alignment condition of the machine,

- By causing rubs between stationary and moving parts

- By an uneven bearing contact

Usually the 1X component is present in the signal combined with other signature characteristics depending on the way the distortion affects the system The foundation distortion time domain signals and their frequency domain are shown in Fig 8 Motor running frequency is 29.9 Hz

4.5X

1/3X Time signal

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Horizontal

Radial

Vertical

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Fig 8 Frequency domain and time domain vibration signals of a distortion case in three directions

Misalignment

A misalignment at the coupling can cause friction and deflection forces in the coupling element

These forces are transmitted to the rotor bearing system Misalignment usually creates 1X

component and higher harmonics, particularly 2X component The misalignment time domain

signals and their frequency domain are shown in Fig 9 Motor parameters are 1.5 kW, 4 poles,

220/380 V, running frequency 29.9 Hz, line frequency 60 Hz

0 50 100 150 200 250 300 350 400 0

10 20 30 40 50 60 70 80 90 100

Hz

1X

2X 3X

4X 5X 6X

12X

11X 9X

0 50 100 150 200 250 300 350 400 0

10 20 30 40 50 60 70

Hz

1X

2X 3X

4X 5X 6X

12X 11X 9X

20 40 60 80 100 120 140

of these changes The frequency describes what is wrong with the machine, and the amplitude describes the relative severity of the problem

3.1.1 Case study 1 - Looseness case

The motor is driven at 29.3 Hz (1X) input frequency Predominant frequencies are 1X, 2X, 3X and 10X (multiple harmonic of running frequency) presented in the vibration spectrums in Fig 10

0 50 100 150 200 250 300 350 400 450 500 0

0.5 1 1.5 2 2.5

Hz

1X

2X 3X 4X

12X

0 50 100 150 200 250 300 350 400 450 500 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Hz

1X 2X 3X

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3.1.2 Case study 2 – Stator winding fault

In this case study, the component 120Hz is predominant (two times the power line frequency) from the vibration spectrums in Fig 11

0 100 200 300 400 500 600 700 800 900 1000 0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Hz

120Hz

1X

Fig 11 Vibration spectrums of case study 2

3.1.3 Case study 3 - Rub fault

In this case, induction motor is running at 53.7 Hz From the vibration spectrums at Fig 12, the predominant frequencies are multiples of 1/3X harmonic

0 50 100 150 200 250 300 350 400 450 500 0

1 2 3 4 5 6 7 8 9 10

Hz

1/3X

1X 5/3X 2X

2/3X 4/3X 7/3X

mV

(a)

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0 50 100 150 200 250 300 350 400 450 500 0

2 4 6 8 10 12

5X

Fig 12 Vibration spectrums (a) in radial direction (b) in axial direction

3.1.4 Case study 4 - Unbalanced rotor

The vibration spectrum in Fig 13 shows 1X as the predominant frequency

0 50 100 150 200 250 300 350 400 450 500 0

2 4 6 8 10 12 14 16

Hz 1X

Fig 13 Vibration spectrums in radial direction

3.2 Model-based methods

The model-based fault detection methods are based on the comparison between measurements and system model outputs This comparison results is called the residuals and used for parameter estimation

Reference Model

Measurements Healthy Output

(b)

- 26 -

Fig 14 General model based fault detection scheme

The general principle of model-based methods is shown in Fig 14 The quality of residual depends

on the model errors and disturbances The main advantage of this method is the fact that the existing redundancy can easily be evaluated by information processing without the need for

additional sensors (K Kim et al 2002 [24]) However, details of these methods are not concerned

in this work This thesis is going to concentrate in the signal processing based methods that are described in next parts

3.3 Signal processing-based methods

The signal-based fault detection methods are based on the statistical pattern recognition and decision making The thesis concentrates on these methods for fault detection of induction motor, such as ANFIS, K-NN, SVM, decision tree, etc These methods do not need any mathematical model for fault diagnosis

3.3.1 ANFIS

ANFIS is a neuro-fuzzy system whose structure is a multi-layer ANN It embeds fuzzy rules with the ANN and uses a backpropagation-like algorithm to fine-tune the parameters of the single-output, Sugeno-type fuzzy inference system The learning algorithm combines least-squares and back-propagation (BP) gradient descent methods Fig 15 illustrates a simple example of an ANFIS There are two rules for this example:

Rule 1: If X is A1 and Y is B1, then T1 = p1X + q1Y + r1

Rule 2: If X is A2 and Y is B2, then T2 = p2X + q2Y + r2

Layer 1, called fuzzification, is used to fuzzify the values of the input variables The parameters in this layer are generally referred to as premise parameters These premise parameters are fine-tuned

by the backpropagation-like algorithm Layer 2 is fuzzy AND performs a fuzzy AND operation at the nodes Layer 3 is normalization and layer 4 is fuzzy inference, which estimates the rule’s output Each rule’s output is a crisp value, and its parameters (pi, qi, and ri) are adjusted during the phase

of parameter identification These parameters are referred to as the consequent parameters Finally,

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layer 5, called defuzzification layer, calculates the sum of the outputs of all the rules and produces

a crisp output

Fig 15 An adaptive network-based fuzzy inference system

The learning operation of ANFIS includes 2 steps: in the first step, the premise parameters are assumed to be fixed and the optimal consequent parameters are estimated by an iterative least mean square procedure using training data The second step, the consequent parameters are assumed to

be fixed and the premise parameters are modified using back-propagation algorithm

By employing a hybrid learning procedure, ANFIS can refine fuzzy if-then rules obtained from experts to describe the input-output behavior of a complex system It can set up intuitively reasonable initial membership functions and start the learning process to generate a set of fuzzy if-then rules to approximate a desired dataset Due to the adaptive capacity of ANFIS, its applications

to learning control are immediate In this work, ANFIS is used to train a knowledge-based model for bearing fault detection

The details of ANFIS are introduced by J Shing et al (J Shing et al 1993 [37])

3.3.2 K-Nearest Neighbor

K-NN is an algorithm for pattern recognition that is based on calculation of the distances between a test pattern and all training patterns If the training set has n patterns {x1 xn}, then for each test pattern there are n distances to be calculated and k closest training patterns are identified as neighbours The test pattern classification is then assigned to the class of which most of the neighbours belong

A1 A2 B1 B2

The k-NN algorithm is carried out as follows:

Step 1: Determine the parameter k, which is the number of nearest neighbors

Step 2: Calculate the distance between each query-pattern of the target dataset and all of the training patterns

Step 3: Sort the distance and determine the nearest neighbors based on the kth minimum distance

Step 4: Examine k nearest neighbors and determine to which classification the majority of the neighbors belong; assign the classification to the pattern being examined

Step 5: Repeat the above procedure for every pattern in the target set

Fig 16 An example of a k-NN classification The test pattern x can be classified either as positive

+

+

-

-+ x

?