A Fault Detection and Identification System for

Gearboxes using Neural Networks

M.H. Sadeghi, J. Raflee, F. Arvani, and A. Harifi

Center of Excellence for Mechatronics, University of Tabriz, Tabriz, IranCorresponding Author E-mail: j.rafiei@tabrizu.ac.ir

Abstract- This paper concentrates on a new procedurewhich experimentally recognizes gears and bearings faults of atypical gearbox system using a multi-layer perceptron neuralnetwork. Feature vector which is one of the most significantparameters to design an appropriate neural network wasinnovated by standard deviation of wavelet packet coefficients.The gear conditions were considered to be normal gearbox andslight- and medium-worn and broken-teeth gears faults and ageneral bearing fault which were five neurons of output layerwith the aim of fault detection and identification. A downscaled2-layer Multi-Layer Perceptron neural-network-based systemwith great accuracy was designed to carry out the task.Vibration signals were recognized as the most reliable source toextract the feature vector which were by piecewise cubichermite interpolation synchronized and pre-processed using thestandard deviation of wavelet packet coefficients in thisresearch.

Keywords- Fault Diagnosis, Non-destructive testing, NeuralNetwork, Wavelet, Gearbox

I. INTRODUCTION

The ever growing stringent requirements for conditionmonitoring of gearboxes which plays a significant role inindustrial applications using non-destructive tests makes thedesign and implementation of rapid, accurate assessmentsystems an undeniable obligation to prevent any downtime ofmachineries. Efficient incipient faults detection and accuratefaults diagnosis has been become a critical part ofmachineries to assure normal running. However due to thebackground noise some faults are not easy to recognize in themachine.Among the various methods for condition monitoring of

rotating machineries, Artificial Neural Networks (ANN)have become the outstanding method in the recent decadesexploiting their non-linear pattern classification properties,offering advantages for automatic detection andidentification of gearbox failure conditions, whereas they donot require an in-depth knowledge of the behaviour of thesystem.

Vibration signals which have been widely used in the

condition monitoring and fault diagnosis systems of rotatingmachinery [1-3] can be exploited as the detection medium inthis case due to straightforwardness of mensuration and therich contents of the signal incorporating system-criticalinformation. However for fault detection and identificationissues, the frequency ranges ofthe vibration signals are oftenwide; and according to the Shannon's sampling theorem, ahigh sampling rate is required, and consequently, large-sizedsamples are needed for the bearing fault detection purposes.Therefore due to existence ofsuperfluous data and their largedimensionality, there is a requirement to preprocessing toextract an appropriate and economized feature vector whichis used to train a well-educated ANN.

In the literature, there are many signal processing tools forvibration data, such as power spectrum, cepestrum, timedomain averaging, adaptive noise cancellation, demodulation,time-series analysis, time-frequency distribution, wavelet,high-order statistics, etc. among which techniques such astime-frequency distribution [4], wavelet [5] and higher-orderstatistics [6] deal with non-stationary signals as they can mapthe one-dimensional signal to a two-dimensionaltime-frequency plane.

In early 1990 Leduqe exploited wavelet to analyze thenoise mechanism of a centrifuge pump and this may be thefirst paper published in the field. Published papers haveinvestigated and confirmed the proficiency and efficiency ofwavelet transform in condition monitoring [7]. Momoh andDias [8] proved that the characteristics of wavelet transformoutweigh those of the Fourier transform in diagnostics of apower distribution system. Tse and Peng [9] showed that theeffectiveness of wavelet and Envelope Detection (ED)methods for rolling bearing elements fault diagnosis are ofthe same order, the former being computationally lesstine-consuming.ANN-based research to carry out the task can be

categorized into two distinct groups: fault identificationsystems with low efficiency which was presented by Kazlaset al [10] to recognize gears and bearings failures of ahelicopter gearbox and fault detection systems with high

0-7803-9422-4/05/$20.00 C2005 IEEE964

efficiency which is illustrated by Samanta et al. [11] to detectroller-bearing elements defects. Precisely speaking, faultidentification proves effective in the case of particular faultclassification systems, whereas this may be in conflict with asituation that there is a requirement to a comprehensive faultdetection system to provide accordingly precision andpromptness.

The objective of this research was to develop anANN-based system with high efficiency and the lowesterroneous outcome to identify faulty gears and detect faultybearing of a gearbox which has a lot of applications forpreventing from fatal breakdowns in rotary machineries.

I. PROCEDURE FOR DEVELOPMENT

In this research, the procedure consists of three stages,namely data acquisition for different faulty and faultless gearand bearing conditions, preprocessing using wavelet packetfor feature extraction, design of an appropriate neuralnetwork.

A. Data acquisitionThe experimental setup to collect dataset consists of a

four-speed motorcycle gearbox, an electrical motor with anominal rotation speed of 1420 (RPM), a load mechanism,multi-channel pulse analyzer system, a triaxial accelerometer,tachometer and four shock absorbers under the base of testbed, as depicted in Fig. 1.A. Test bed was designed to installgearbox, electrical motor and load mechanism with fourshock absorbers under bases to cancel out vibrations. Allvibration signals were collected from the experimentaltesting of gearbox using the accelerometer which wasmounted on the outer surface of the bearing case of inputshaft ofthe gearbox as shown in Fig.1.B, with three differentfault conditions that were slight-worn, medium-worn,broken-teeth of gear as shown in Fig. l.C and Fig. .D andfaulty bearing. The rotational speed of the system wasmeasured by tachometer which ran at a constant nominalspeed of 1420 (RPM). The signals were sampled at 16384(Hz) lasting 8 (S). Each gear was tested under the constantload.

GearboxLoad

Tachometer

Data _! ShockAcquisition AbsorberSystem

(A)

(B) (C) (D)Fig. l. (A) Experimental setup (B) Accelerometer location

(C) Broken teeth (D) Slight-worn teeth

B. Preprocessing ofvibration signalsThe preprocessing of vibration signals involves with

synchronization of the signal and computation of standarddeviation ofwavelet packet coefficients performed in thefollowing two steps to extract the feature vector.

1) Synchronization ofvibration signals:After obtaining a dataset, the first issue is to dimensionally

synchronize vibration signals from the revolution point ofview which were not equal following signals acquired bytachometer. To achieve this goal, interpolation was applied.Among interpolation techniques, Piecewise Cubic HermiteInterpolation [12] has the most efficiency as it tackles withhigh fluctuations and less smoothness of vibration signals.Assume "k to be the length of the kth subinterval,

hk = Xk+l - Xk

(1)Then the first difference, 6k is

6* = (Yk+1 - Yk) hk(2)Let dk designate the slope of the interpolant at Xkdk = P'(Xk)(3)For the piecewise linear interpolant, dk = dk-l orI

k

Suppose the following function on the intervalxk <xx <k+expressed in term of local variables s = x -xk andh = k,

3hs2 - 2s3 h3 -33hs2 + 2s3P(x) = h3 Yk+1 + h3 Yk+

s2(sh) d + h dkh2 k+1 h~~/2

(4)which is a cubic polynomial in s, and, hence in x, thatfulfilled four interpolation conditions, two on function valuesand two on the possibly unknown derivative values.P(Xk) = Yk , P(Xk+1 ) = Yk+IP'(xk) = dk, P'(xk+l ) = dk+l(5)To make P.C.H.I able to reproduce data, definition of theslopes dk is required as derivative values are not given.

After the synchronization of signals per each revolution,mining of feature vector was performed as extracting

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characteristic features from vibration signals is essential andforemost concern in fault detection and diagnosis systemsbecause firstly, it plays the most healing role in training aneural network even if it has an ill structure with improperparameters and secondly, due to complication and amount ofdata in the signals.

2) Feature extraction using waveletpacketAs mentioned previously, wavelet analysis has proved its

great capabilities in decomposing, denoising, and signalanalysis which made the analysis of nonstationary signalsachievable and detect transient feature components as othermethods were inept to perform since wavelet canconcurrently impart time and frequency structures. Waveletanalysis includes transforming a signal from the time domainto the time-frequency domain. Wavelet transform (WT)gives good time and poor frequency resolution at highfrequencies and good frequency and poor time resolution atlow frequencies. A wavelet is a waveform with very specificfeatures, such as a zero average and an effectively limitedduration. Analysis with wavelets involves with breaking up asignal into shifted and scaled versions of the original (ormother) wavelet.

Wavelets fall into two general categories i.e. continuousand discrete. Continuous Wavelet Transform (CWT) [13] is afunction of two parameters, explicitly time and frequencyand, therefore, bears a great information redundancy in signalor function being analyzed. By omitting several steps of theparameters rather than continuously varying the parameter,we can analyze the signal with a smaller set of scales withspecific amount of translation at each scale which is calledDiscrete Wavelet Transform (DWT) [14]. DWT analysis ismore efficient still with the identical accuracy. In the case ofDWT, the wavelet operates as a dyadic filter. In order to shiftalong a time axis, DWT analyzes the signal by applying awavelet filter with a specific frequency band which isdependent on the level of decomposition. To make localexamination of the signal feasible, it is required to shift it inthe time domain. Consequently, the signal can bedecomposed into a hierarchical structure with wavelet detailsand approximations at various levels as follows:

f(t) = jD,(t) + Aj(t)i=1

(6) where D, (t) denotes the wavelet detail and Aj (t) standsfor the wavelet approximation at the jth level.

Wavelet packet method [15] which is a generalization ofwavelet decomposition that offers a richer range ofpossibilities for signal analysis. The WT is made up of onehigh frequency term from each level and one low-frequencyresidual from the last level of decomposition. The waveletpackets, on the other hand, contain a complete set ofdecompositions and details at every level and hence

providing a higher resolution in the high frequency region i.e.the wavelet detail component at each level is furtherdecomposed to obtain its approximation and detailcomponents.

Wavelet packets consist ofa set oflinearly combined usualwavelet functions. Therefore wavelet packets inherit theattributes of their corresponding wavelet functions such asorthonormality and time-frequency localization. A waveletpacket is a function with three indices of integers i, j and kwhich are the modulation, scale and translation parameters,respectively [16],

KJO(t=2j/2 i(2i t-k), i=1,2,3,... (7)The wavelet functions y/f can be obtained from thefollowing recursive relations:

00

y 2j (t) = [2 , h(k);v (2t - k)-0

v 2j+l (t) = Vi2g(kiV'(2t-k)(8)The recursive relations between the jh and the (i + I)t

level components are,17(t) = fj - (t) +f2'1 (t)fj2i 1 (t) = Hfj(t),j+1 -

f,.2+ (t) = Gfj' (t),

(9)where H and G are the filtering-decimation operatorsassociated to the discrete filters h(k) and g(k) as follows,

H{.}= Lh(k-2t)k=-a

(10)

G{.}= ,g(k-2t)k=-

(11)which are the quadrature mirror filters associated with thescaling function and the mother wavelet function, Theoriginal signal f(t) afterj level of decomposition can bestated as,

2jf (t) = E fy(t)

i=l

(12)The wavelet packet component signal fji (t) can be stated bya linear combination of wavelet packet functions Y k (t) insuch a way:

00

fj(t) E Cc,k(t)yfJ,k(t)k=--oo

(13)

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where the wavelet packet coefficients c,k (t) can be obtained

from,

C,k (t) = Lf(t)Vj,k(t)dt (14)

providing that the wavelet packet functions are orthogonal:m,k (t)yjnk(t)=O if m.n

(15)There are two kinds of wavelet functions, orthogonal and

non-orthogonal. Among the widely used orthogonal waveletfunctions are Haar, Daubechies, Coiflets, Symlets and Meyer,etc, while the non-orthogonal ones include Morlet, Mexicanhat and DOG, etc. Since different types of wavelet functionshave different time-frequency structures, a function with atime-frequency structure matching superlatively that of thetransient component must be used to effectively detect thetransient component. In general, the smooth wavelets arebetter for regular, stationary, periodic data and the compactwavelets are better for non-stationary, transient data [17]. Asa result, Daubechies 4 (Db4) wavelet function has beenchosen for this case after several trials as it is often arbitrarilychosen for signal analysis and synthesis by experiments inmany papers in the field e.g. [18] there is no computationallogic behind the selection ofDaubechies order.The dilation equations may be used to generate orthogonal

wavelets. The scaling function q(t) is a dilated (horizontallyexpanded) version of p(2t). The dilation equation in generalhas the form [14]:q (t) = co0p(2t) + c,(p(2t - 1) + c2p(2t - 2) + c3ep(2t - 3)(16)The Daubechies D4 wavelet coefficients have values:

- (1+VF) c =(3+VF) c =(3-[3) -(V3 1)0

F0 ,C3= po 4X,/2 4X,0- 4>, 3_ 4,f

(17)Thus, a particular family of wavelets is specified by aparticular set of numbers, called the wavelet filtercoefficients. The above set of numbers c0,c1,c2,c3 is calledthe Db4 wavelet filter coefficients.It is not possible in general to solve directly for qP(t); theobvious approach is to solve for q(t) iteratively so thatfj (t) approachespfj_, (t) ,where,oj (t) = c0#j-l (2t) + cljql (2t - 1)

+ C20j_l1(2t - 2) + C30&j_l(2t - 3)(18)The scaling function for the Db4 wavelet that is obtainedfrom this iteration process, assuming the initial scalingfunction (po (t) equals 1 for 0 < t < 1 and 0 elsewhere.The D4 wavelet function w(t) for the four-coefficient scalingfunction defined in (1) can be computed asw(t) = -C33(2t) + C2 z(2t - 1) - cl b(2t - 2) + co q(2t - 3)(19)

In general, for an even number M of wavelet filtercoefficients Ck , k =1,2,...,M -1, the scaling function isdefined by

0(t) = ZCk O(2t - k)k=1

(20)and the corresponding wavelet is derived as

M-1

W(t) = E (-1) Ck O(2t + k -M + 1)k=-

(21)It is observed that the scaling function, viewed as a filter'simpulse response, has a low-pass form, whereas the waveletfunction has a high-pass form. Thus, the wavelet function isessentially responsible for extracting the detail(high-frequency components) of the original signal.As mentioned previously, the wavelet packet was applied

to all the signals up to the fourth level. In the end, thestandard deviation of wavelet packet coefficients ofpreprocessed signals were recognized to have the bestperformance and therefore chosen as feature vector of theneural network.

C. MLP neural network structure designArtificial neural networks which are also called

parallel-distributed-processing systems or connectionistsystems is made of simple processing units, called neurons[19] capable of storing experimental knowledge as a naturalpropensity, have a variety of architectures, remarkable ofwhich are the feed-forward and recurrent networks. The mostpopular neural network is the multi-layer perceptron, whichis a feedforward network and frequently exploited in faultdiagnosis systems, which has found an immense popularityin condition monitoring applications as it constitutes morethan 90% [20] of the current ANNs in the field, whereas therecurrent networks are predominantly utilized in nonlineardynamic feedback systems. Among all architectures, themulti-layer feed-forward networks trained using BackPropagation (BP) algorithm seem to be the most significantand widely used method in fault detection and diagnosissystems of rotating machinery. Fig. 2 depicts schematicallythe utilized ANN structure whose its specifications areshown in table I.

An important network design issue is the selection andimplementation of the network configuration. In general, atwo-layer MLP made up ofan input layer, a hidden layer, andan output layer which is the smallest achievable structure isapplied to reduce the developing expense ofthe fault detectorneural network, while maintaining the desired level ofaccuracy and robustness of the fault detector. Hyperbolictangent sigmoid transfer function was applied to all net layerswith Resilient Backpropagation training algorithm [21]. Theinitial weights were obtained randomly in a range of (-10, 10).

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Error function was chosen to be least mean square which wasengaged in a stopping criterion of 10. Training the networkto perform fault diagnosis was performed off-line andtherefore more training data are preferred over usinginadequate training data to accomplish greater networkaccuracy. A matrix with 525 processed elements comprising7x75 sampled data for every three faulty gear conditions asthree output neurons and three faulty bearing corditionsencapsulated in one output neuron for fault detectionpurposes and one faultless condition as a neuron was appliedto the network as the feature vector.

Faultless

SlightWorn

MediumWorn

BrokenI m+u

.00

0

Input OutHidden

Fig.2: Schematic diagram ofthe MLP network

4put

Im. CONCLUSION

An ANN-based procedure was presented for faultdetection and identification ofgearboxes using a new featurevector extracted from standard deviation of wavelet packetcoefficients of vibration signals of various faultless andfaulty conditions of a gearbox. Over and above the sturctureof ANN, an appropriate feature vector plays a vital role intraining a high performance ANN. Piecewise cubic hermiteinterpolation was used to synchrinize the vibration signals.Utilization of a time-frequency-based approach specificallywavelet transform which often reveals the faults the best ismandatory. Ultimately a MLP network with a 16:20:5structure has been used that not only is small in size but alsowith a 100% perfect accuracy and performance to identifygear failures and detect bearing defects. As a whole, Fig. 4depicts the total scheme of the fault identification system.

rl Gearbox

Accelerometer Tachometer

Gearbox Fault detection and Identification

Fig.4. Flowchart ofthe fault identification system

ieemt1 IV. AcKNowLEDGMENT

Faulty The authors would like to thank Prof. S. KhanmohammaiBearng and Dr. S. Dadvandipour, members of center of excellence for

mechatronics for their help throughout the research and Mr. M.Ettefagh and S. Chitsaz from the Vibration and Modal

TABLE I: vARIous NETWORK DESIGNS AND ITS RESULTS

Network Specifications Net 1 Net 2 Net 3 Net 4 Net 5

Nodes per Hidden layer 10 15 18 20 22Samples for training 7x75 7x75 7x75 7x75 7x75Samples for testing 7x75 7x75 7x75 7x75 7x75Correct detection of 76.3 73.5 80.0 100 100broken-teeth cases (%)Correct detection of 82.3 97.6 100 100 100slight-worn cases (%)Correct detection of 86.5 80.3 85.5 100 100medium-worn cases (%)Correct detection of faulty 99.9 99.7 100 100 100bearing cases (%)__Correct detection of 73.4 84.4 100 100 100undamaged cases (%) 7 8 1 1

Analysis Lab., Faculty of Mech. Eng., U. of Tabriz, fordevoting their time to do experimental aspects of thisresearch.

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M.Sc. student in the same major at the U. of Tabriz. His interests includecondition monitoring, application ofAI in Eng., machining processes, signalprocessing.

Farid Arvani was born in Tabriz, in 1981. He received his B.Sc. degree inManufacturing Eng. from the U. of Tabriz, Iran. He is currently consultantfor industrial projects. His current research fields include application ofAI in

manufacturing fields, condition monitoring, design andimplementation of mechatronic systems and industrialautomation and control.

Abbas Harifi was born in 1980. He received his B.Sc.and M.Sc. degrees in Control Eng. from the U. of Shiraz,

Iran, in 2002 and the U. of Tabriz, Iran, in 2005, respectively. He is nowPh.D. student in the U. of Tabriz. His research fields include AI, signal andimage processing, and nonlinear and adaptive control.

Morteza H. Sadeghi was born in Iran, in 1959, received B.Sc. degree inMechanical Eng. from the U. of Tabriz, Iran, in 1985, M.Sc. and Ph.D.degrees from the U. of Michigan, Ann Arbor, USA, in 1988 and 1993,respectively. He is currently assistant prof. in Dept. of Mech. Eng. andvice-chancellor of educational affairs in U. of Tabriz. His current researchinterests are dynamic system failure detection and identification, vibrationand modal analysis, application ofAl in mechanical systems.

Javad Rafiee was born in Iran in 1981. He received B.Sc. degree inManufacturing Eng. from the U. of Tabriz, Iran, in 2003 and, currently, is

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