fault dialogis of spur gear box using artificial neural network

Fault diagnosis of spur bevel gear box using artificial neural network ANN, and proximal support vector machine PSVM Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Coim

Fault diagnosis of spur bevel gear box using artificial neural network (ANN), and proximal support vector machine (PSVM)

Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

1 Introduction

Malfunctions in machinery are often sources of reduced

productivity and increased maintenance costs in various industrial

applications For this reason, machine condition monitoring is

being pursued to recognize incipient faults As modern production

plants are expected to run continuously for extended hours,

unexpected downtime due to rotating machinery failures has

become more costly than ever before The faults arising in rotating

machines are often due to damages and failures in the components

of gear box assembly Fault diagnosis is an important process in

preventive maintenance of gear box, which avoids serious damage

if defects occur to one of the gears during operation condition

Early detection of the defects, therefore, is crucial to prevent the

system from malfunction that could cause damage or entire

system halt Diagnosing a gear system by examining vibration

signals is the most commonly used method for detecting gear

failures The conventional methods for processing measured data

contain the frequency domain technique, time-domain technique,

and time-frequency domain technique These methods have been

widely employed to detect gear failures The use of vibration

analysis for gear fault diagnosis and monitoring has been widely

investigated and its application in industry is well established[1–

3] This is particularly reflected in the aviation industry where the

helicopter engine, drive trains and rotor systems are fitted with vibration sensors for component health monitoring These methods have traditionally been applied, separately in time and frequency domains A time-domain analysis focuses principally on statistical characteristics of vibration signal such as peak level, standard deviation, skewness, kurtosis, and crest factor A frequency domain approach uses Fourier methods to transform the time-domain signal to the frequency domain, where further analysis is carried out, and conventionally using vibration amplitude and power spectra It should be noted that use of either domain implicitly excludes the direct use of information present in the other Time-frequency based energy distribution method was employed for early detection of gear failure[4] The frequency domain refers to a display or analysis of the vibration data as a function of frequency The time-domain vibration signal

is typically processed into the frequency domain by applying a Fourier transform, usually in the form of a fast Fourier transform (FFT) algorithm[5]

The works presented in [6–9] found that, the FFT-based methods are not suitable for non-stationary signal analysis and are not able to reveal the inherent information of non-stationary signals However, various kinds of factors, such as the change of the environment and the faults from the machine itself, often make the output signals of the running machine contain non-stationary components Usually, these non-stationary components contain abundant information about machine faults; therefore, it is important to analyze the non-stationary signals Most algorithms recently developed for mechanical fault detection are based on the

Applied Soft Computing 10 (2010) 344–360

A R T I C L E I N F O

Article history:

Received 8 July 2008

Received in revised form 6 April 2009

Accepted 2 August 2009

Available online 8 August 2009

Keywords:

Artificial neural network

Proximal support vector machine

Bevel gear box

Morlet wavelet

Statistical features

Fault detection

A B S T R A C T

Vibration signals extracted from rotating parts of machineries carries lot many information with in them about the condition of the operating machine Further processing of these raw vibration signatures measured at a convenient location of the machine unravels the condition of the component or assembly under study This paper deals with the effectiveness of wavelet-based features for fault diagnosis of a gear box using artificial neural network (ANN) and proximal support vector machines (PSVM) The statistical feature vectors from Morlet wavelet coefficients are classified using J48 algorithm and the predominant features were fed as input for training and testing ANN and PSVM and their relative efficiency in classifying the faults in the bevel gear box was compared

ß2009 Elsevier B.V All rights reserved

* Corresponding author at: Sohar University, Sohar, Oman.

E-mail address: nsaro_2000@yahoo.com (N Saravanan).

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assumption of stationarity of the vibration signals Some of these,

including cepstrum, time-domain averaging, adaptive noise

cancellation, demodulation analysis, etc.[10–12]are well

estab-lished and have proved to be very effective in machinery

diagnostics However, in many cases these methods are not

sufficient to reliably detect different types of faults There is a need

for new techniques which can cope with technological advances in

machinery, and which provide satisfactory fault detection

sensitivity A relatively small amount of applied research has

been done in the application of time-variant fault detection

methods It is known[13,14], that local faults in gear boxes cause

impacts As a result of this impact excitation, impulses and

discontinuities may be observed in the instantaneous

character-istics of the envelope and phase functions [14,15] Due to the

nature of these functions, vibration signals can be considered as

non-stationary[16]and strong non-stationary events can appear

in a local time period, e.g one revolution of gear in mesh The

analysis of non-stationary signals requires specific techniques

which go beyond the classical Fourier approach There exist a lot of

different time-variant methods, some are reviewed in[16–18]

In the recent past reports of fault diagnosis of critical

components using machine learning algorithms like SVM, PSVM

are reported[19] In ANN, the condition-monitoring problem is

treated as a generalization/classification problem based on

training pattern from the samples of faulty roller bearings[20]

However, the traditional ANN approaches have limitations on

generalization of results in models that can over-fit the data

Support vector machine (SVM) is used in many applications of

machine learning because of its high accuracy and good

generalization capabilities SVM is based on statistical learning

theory SVM classifies better than ANN because of the principle

of risk minimization In artificial neural network (ANN)

traditional Empirical Risk Minimization (ERM) is used on

training data set to minimize the error But in SVM, Structural

Risk Minimization (SRM) is used to minimize an upper bound on

the expected risk SVM is modeled as an optimization problem

and involves extensive computation, whereas, PSVM is modeled

as a system of linear equations which involves less computation

[21] PSVM gives results very close to SVM One of the more

recent mathematical tools adopted for transient signals is the

wavelet transform [22,23] Wavelet transform (WT) has

attracted many researchers’ attention recently The wavelet

transform was utilized to represent all possible types of

transients in vibration signals generated by faults in a gear

box[24] A neural network was used to diagnose a simple gear

system after the data have been pre-processed by the wavelet

transform [25] Wavelet transform was used to analyze the

vibration signal from the gear system with pitting on the gear

[26] Hence based on the literature review there exist a wide

scope to explore machine learning methods like ANN, SVM and

PSVM for fault diagnosis of gear box This paper is one such

attempt to apply machine learning methods like ANN and PSVM

to wavelet features of the vibration signal of the gear box under

investigation

This work deals with extraction of wavelet features from the

vibration data of a bevel gear box system and classification of Gear

faults using artificial neural network (ANN) and proximal support

vector machine (PSVM) The vibration signal from a piezoelectric

transducer is captured for the following conditions: Good Bevel

Gear, Bevel Gear with tooth breakage (GTB), Bevel Gear with crack

at root of the tooth (GTC), and Bevel Gear with face wear of the

teeth (TFW) for various loading and lubrication conditions of the

gear box

A group of statistical features like kurtosis, standard deviation,

maximum value, etc form a set of features, which are widely used

in fault diagnostics, are extracted from the wavelet coefficients of

the time-domain signals Selection of good features is an important phase in pattern recognition and requires detailed domain knowledge The Decision Tree using J48 algorithm was used for identifying the best features from a given set of samples The selected features were fed as input to ANN and PSVM for classification

1.1 Different phases of present work The signals obtained are processed further for machine condition diagnosis as explained in the flow chart inFig 1

2 Experimental studies The fault simulator with sensor is shown inFig 2and the inner view of bevel gear box is shown inFig 3 A variable speed DC motor (0.5 hp) with speed up to 3000 rpm is the basic drive A short shaft

of 30 mm diameter is attached to the shaft of the motor through a flexible coupling; this is to minimize effects of misalignment and transmission of vibration from motor

The shaft is supported at its ends through two roller bearings From this shaft the motion is transmitted to the bevel gear box by means of a belt drive The gear box is of dimension

Fig 1 Flow chart for bevel gear box condition diagnosis.

Fig 2 Fault simulator setup.

150 mm  170 mm  120 mm and the full lubrication level is

110 mm and half lubrication level is 60 mm SAE 40 oil was used as

a lubricant An electromagnetic spring loaded disc brake was used

to load the gear wheel A torque level of 8 N m was applied at the

full load condition The various defects are created in the pinion

wheels and the mating gear wheel is not disturbed With the sensor

mounted on top of the gear box vibrations signals are obtained for

various conditions The selected area is made flat and smooth to

ensure effective coupling A piezoelectric accelerometer (Dytran

model) is mounted on the flat surface using direct adhesive

mounting technique The accelerometer is connected to the

signal-conditioning unit (DACTRAN FFT analyzer), where the signal goes

through the charge amplifier and an Analogue-to-Digital Converter

(ADC) The vibration signal in digital form is fed to the computer

through a USB port The software RT Pro-series that accompanies

the signal conditioning unit is used for recording the signals

directly in the computer’s secondary memory The signal is then

read from the memory and replayed and processed to extract

different features

2.1 Experimental procedure

In the present study, four pinion wheels whose details are as

mentioned inTable 1were used One was a new wheel and was

assumed to be free from defects In the other three pinion wheels, defects were created using EDM in order to keep the size of the defect under control The details of the various defects are depicted

The size of the defects is a little bigger than one can encounter in the practical situation; however, it is in-line with work reported in literature[27] The vibration signal from the piezoelectric pickup mounted on the gear box was taken, after allowing initial running

of the gear box for some time

The sampling frequency was 12,000 Hz and sample length was

8192 for all conditions The sample length was chosen arbitrarily; however, the following points were considered Statistical measures are more meaningful, when the number of samples is more On the other hand, as the number of samples increases the computational time increases To strike a balance, sample length of around 10,000 was chosen In some feature extraction techniques, which will be used with the same data, as per the Nyquist criteria the number of samples is to be 2n The nearest 2nto 10,000 is 8192 and hence, it was taken as sample length Many trials were taken at the set speed and vibration signal was stored in the data The raw

Fig 3 Inner view of the bevel gear box.

Table 1 Details of faults under investigation.

G3 Gear with crack at root (GTC) 0.8  0.5  20

Table 2 Gear wheel and Pinion details.

Chordal tooth thickness 3.93 0.150

mm

N Saravanan et al / Applied Soft Computing 10 (2010) 344–360 346

vibration signals acquired for various experimental conditions

form the gear box using FFT are shown inFig 5(a)–(d)

3 Feature extraction

After acquiring the vibration signals in the time domain, it is

processed to obtain feature vectors The Continuous Wavelet

Transform (CWT) is used for obtaining the wavelet coefficients of

the signals The statistical parameters of the wavelet coefficients

are extracted, which constitute the feature vectors

The term wavelet means a small wave It is the representation of

a signal in terms of finite length or fast decaying waveform known

as mother wavelet This waveform is scaled and translated to

match the input signal

The Continuous Wavelet Transform[28]is defined as

WsðtÞ ¼

Z þ1

1

f ðtÞCs; jðtÞ dt where Cs; jðtÞ ¼ 1ffiffiffiffiffi

jsj

p C t t

s

 

is a window function called the mother wavelet, s is a scale andtis

a translation

The term translation is related to the location of the window, as the window is shifted through the signal This corresponds to the time information in the transform domain But instead of a frequency parameter, we have a scale Scaling, as a mathematical operation, either dilates or compresses a signal Smaller scale corresponds to high frequency of signals and large scale corresponds to low frequency signals

Fig 5 (a) Vibration Signal for Good Pinion wheel under different lubrication and loading conditions; (b) Vibration Signal for Pinion wheel with Teeth Breakage under different lubrication and loading conditions; (c) Vibration Signal for Pinion wheel with crack at root under different lubrication and loading conditions; (d) Vibration Signals for Pinion

Fig 5 (Continued ).

Fig 7 % Efficiency of Morlet wavelet coefficients.

N Saravanan et al / Applied Soft Computing 10 (2010) 344–360 348

The wavelet series is simply a sampled version of the CWT, and

the information it provides is highly redundant as far as the

reconstruction of the signal is concerned This redundancy, on the

other hand, requires a significant amount of computation time and

resources

3.1 Wavelet-based feature extraction

The multilevel 1D wavelet decomposition function, available in

Matlab is chosen with the Morlet wavelets specified It returns the

wavelet coefficients of signal X at scale N[29].Fig 6shows Morlet

wavelet

Sixty-four scales are initially chosen to extract the Morlet

wavelet coefficients of the signal data The efficiency of 64 scales of

Morlet wavelets was obtained using WEKA data mining software

and the coefficients of highest level are considered for

classifica-tion Since the eighth level gave maximum efficiency of 96.5%, the

statistical features corresponding to it were given as input for J48 algorithm to determine the predominant features to be given as an input for training and classification using SVM Fig 7 gives the efficiencies of all scales of Morlet wavelet

4 Using J 48 algorithm in the present work

A standard tree induced with c5.0 (or possibly ID3 or c4.5) consists of a number of branches, one root, a number of nodes and a number of leaves One branch is a chain of nodes from root to a leaf; and each node involves one attribute The occurrence of an attribute in a tree provides the information about the importance

of the associated attribute as explained in[31] A Decision Tree is a tree based knowledge representation methodology used to represent classification rules J48 algorithm (A WEKA implemen-tation of c4.5 Algorithm) is a widely used one to construct Decision Trees as explained in[19] The Decision Tree algorithm has been

Fig 8 (a) Good-Dry-No Load vs GTB, GTC, TFW-Dry-No Load (b) Good-Dry-Full Load vs GTB, GTC, TFW-Dry-Full Load (c) Good-Half No Load vs GTB, GTC, TFW-Half

Lub-No Load (d) Good-Half Lub-Full Load vs GTB, GTC, TFW-Half Lub-Full Load (e) Good-Full Lub-Lub-No Load vs GTB, GTC, TFW-Full Lub-Lub-No Load (f) Good-Full Lub-Full Load vs GTB,

applied to the problem under discussion Input to the algorithm is

set of statistical features of the eighth scale Morlet coefficients It is

clear that the top node is the best node for classification The other

features in the nodes of Decision Tree appear in descending order

of importance It is to be stressed here that only features that

contribute to the classification appear in the Decision Tree and

others do not Features, which have less discriminating capability,

can be consciously discarded by deciding on the threshold This

concept is made use for selecting good features The algorithm

identifies the good features for the purpose of classification from

the given training data set, and thus reduces the domain

knowledge required to select good features for pattern

classifica-tion problem The decision trees shown inFig 8(a)–(f) is for various

lubrication and loading conditions of different faults compared

with good conditions of the pinion gear wheel

Based on above trees its clear that of all the statistical features,

standard error, kurtosis, sample variance and minimum value play

a dominant role in feature classification using Morlet coefficients These four predominant features are fed as an input to SVM for training and further classification The scatter plot showing the variation of the statistical parameters of Morlet coefficients are shown in Fig 9(a)–(d) These features were given as input for training and testing of classifying features using SVM

5 Artificial neural network ANN is one of the approaches to forecast and validate using computer models with some of the architecture and processing capabilities of the human brain[22] The technology that attempts

to achieve such results is called neural computing or artificial neural networks ANN mimics biological neurons by simulating some of the workings of the human brain An ANN is made up of processing elements called neurons that are interconnected in a network The artificial neurons receive inputs that are analogous to

Fig 8 (Continued ).

N Saravanan et al / Applied Soft Computing 10 (2010) 344–360 350

the electro-chemical signals that natural neurons receive from

other neurons By changing the weights given to theses signals, the

network learns in a process that seems similar to that found in

nature i.e., neurons in ANN receive signals or information from

other neurons or external sources, perform transformations on the

signals, and then pass those signals on to other neurons The way

information is processed and intelligence is stored depends on the

architecture and algorithms of ANN.Fig 10shows the architecture

of ANN

A main advantage of ANN is its ability to learn patterns in very

complex systems Through learning or self-organizing process,

they translate the inputs into desired outputs by adjusting the

weights given to signals between neurodes

The proposed method diagnoses a gear box condition using ANN A multi layered feed forward neural network trained with error back propagation was used ANN’s are characterized by their topology, weight vector and activation functions They have three layers namely an input layer that receives signals from some external source, a hidden layer that does the processing of the signals and output layer that sends processed signals back to the external world

5.1 The back propagation algorithm of ANN The back propagation of an ANN assumes that there is a supervision of learning of the network The method of adjusting

Fig 9 (a) Vibration Signal for Good Pinion wheel under different lubrication and loading conditions; (b) Vibration Signal for Pinion wheel with Teeth Breakage under different lubrication and loading conditions; (c) Vibration Signal for Pinion wheel with Crack at root under different lubrication and loading conditions; (d) Vibration Signals for Pinion

weights is designed to minimize the sum of the squared errors for a

given training data set:

j – identifies a receiving node,

i – denotes the node that feeds a second node,

I – denotes input to a neuron,

O – denotes output of a neuron,

Wij– denotes the weights associated with the nodes

Each non-input node has an output level Ojwhere

Oj¼ 1

1 þ eI j; Ij¼X

where Ois each of the signals to node j (i.e., the output of node of i)

The derivation of the back propagation formula involves the use

of the chain rule of partial derivatives and equals:

di j¼@SSE

@Wi j

¼ @SSE

@Oj

  @O

j

@Ij

  @I

j

@Wi j

 

(2)

where by convention the left-hand side is denoted by dij, the change in the sum of squared errors (SSE) attributed to Wij Now error is given by

ei¼ ðDj OjÞ; SSE ¼X

ðDj OjÞ2 (3) Therefore,

@SSE

@O j

 

¼ 2X

Fig 9 (Continued ).

N Saravanan et al / Applied Soft Computing 10 (2010) 344–360 352

From the output of the output node, we obtain,

@Oj

@Ij

 

The input to an input node is Ij=P

WijOi

Therefore the change in the input to the output node resulting

from the previous hidden node, i, is

@Ij

@Wi j

 

Thus from above equations, the jth delta is

di j¼ 2ejOjð1  OjÞOi (7)

Now the old weight is updated by the following equation:

DWi jðnewÞ ¼hdi jOjþa DWi jðoldÞ (8)

For the hidden layers, the calculations are similar The only change

is how the ANN output error is back propagated to the hidden layer nodes The output error at the ith hidden node depends on the output errors of all nodes in the output layer This relationship is given by

ei¼X

After calculating the output error for the hidden layer, the update rules for the weights in that layer are the same as the previous update

5.2 Proximal support vector machine (PSVM)

PSVM is a modified version of support vector machine (SVM) The SVM is a new generation learning system based on statistical learning theory SVM belongs to the class of supervised learning algorithms in which the learning machine is given a set of features (or inputs) with the associated labels (or output values) Each of

Fig 10 ANN architecture.

Fig 11 Flowchart of PSVM.

Fig 12 Standard SVM classifier.