Contents lists available at ScienceDirect

Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing 25 (2011) 1339–1352

0888-32

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jnlabr/ymssp

The combined use of vibration, acoustic emission and oil debrison-line monitoring towards a more effective condition monitoringof rotating machinery

T.H. Loutas a, D. Roulias a, E. Pauly b, V. Kostopoulos a,n

a Applied Mechanics Laboratory, Department of Mechanical Engineering and Aeronautics, University of Patras, Patras GR-26500, Greeceb Research & Development Directorate System, Architecture Department, Eurocopter, Marseille 13725, France

a r t i c l e i n f o

Article history:

Received 27 February 2010

Received in revised form

21 July 2010

Accepted 16 November 2010Available online 22 November 2010

Keywords:

Gearbox

Wear detection

Acoustic emission

Vibration monitoring

Condition monitoring

Signal processing

70/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ymssp.2010.11.007

esponding author. Tel.: +30 2610 929441; fa

ail address: kostopoulos@mech.upatras.gr (V.

a b s t r a c t

The monitoring of progressive wear in gears using various non-destructive technologies as

well as the use of advanced signal processing techniques upon the acquired recordings to

the direction of more effective diagnostic schemes, is the scope of the present work. For

this reason multi-hour tests were performed in healthy gears in a single-stage lab scale

gearbox until they were seriously damaged. Three on-line monitoring techniques are

implemented in the tests. Vibration and acoustic emission recordings in combination with

data coming from oil debris monitoring (ODM) of the lubricating oil are utilized in order to

assess the condition of the gears. A plethora of parameters/features were extracted from

the acquired waveforms via conventional (in time and frequency domain) and non-

conventional (wavelet-based) signal processing techniques. Data fusion was accom-

plished in the level of integration of the most representative among the extracted features

from all three measurement technologies in a single data matrix. Principal component

analysis (PCA) was utilized to reduce the dimensionality of the data matrix whereas

independent component analysis (ICA) was further applied to identify the independent

components among the data and correlate them to different damage modes of the gearbox.

Finally heuristic rules based on characteristic values of the resulted independent

components were set, realizing thus a health monitoring scheme for gearboxes.

The integration of vibration, AE and ODM data increases the diagnostic capacity and

reliability of the condition monitoring scheme concluding to very interesting results. The

present work summarizes the joint efforts of two research groups towards a more reliable

condition monitoring of rotating machinery and gearboxes specifically.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

In gearboxes and power drive trains in general, gear damage detection is very critical and its early diagnosis can lead toincreased safety in aviation and in various industrial applications. Thus the interest for their periodic non-destructiveinspection and/or on-line health monitoring is growing and effective diagnostic techniques and methodologies are theobjective of extensive research efforts over the last 50 years. To this direction, vibration monitoring has been widely used invarious industrial applications. In research level, much attention has been drawn towards the gear diagnostics field.

Few research teams have published experimental data coming from long-term testing to study the effect of natural gearpitting mostly upon vibration recordings. Dempsey et al. at GRC/NASA [1–5] have conducted some excellent experimental

ll rights reserved.

x: +30 2610 969 417.

Kostopoulos).

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–13521340

work and published interesting results from extensive gear testing at a special test rig utilizing vibration and oil debrismeasurements. With the clear goal to improve the performance of the current helicopter gearbox health monitoring systems,they have tested gears at high shaft speed for multi-hour periods (up to 250 h) and correlated special parameters-features(based on higher order statistical moments) extracted from the vibration recordings with the Fe debris mass accumulatedduring the tests. They have integrated their results in a fuzzy logic based health monitoring system with satisfactoryperformance for a series of tests.

Researchers in the field have also turned their efforts towards advanced signal processing techniques applied on vibrationrecordings coming mainly from artificial gear defects in short tests rather than monitoring gear pitting damage in multi-hourtesting. Wavelet transform and wavelet-based schemes are the state-of-the-art in this direction. The publications are quitemany in the field. Selecting a few, the works of Wang and McFadden [6,7] must be mentioned, that utilized time–frequencyanalysis techniques and showed that the spectrogram has advantages over Wigner–Ville distribution for the analysis ofvibration signals for the early detection of damage in gears. Wavelets have also been applied as a preprocessing for featureextraction. Works in the field of audio analysis [8] and biological signals, such as EEG [9] and electrocardiograph signals [10],have provided exceptional results proving that wavelet based feature extraction possess great potential for on-lineautomated monitoring and control. Recently the potential to rotating machine diagnostics was explored by Lou et al. [11].

The interest for applications of acoustic emission (AE) for condition monitoring in rotating machinery is relatively new andhas grown significantly over the last decade. AE in rotating machinery is defined as the elastic waves generated by theinteraction of two media in motion, i.e. a pair of gears. Sources of AE in rotating machinery include asperities contact,transient hydrodynamic oil pressure field developed on the gear during operation, friction, material loss, cavitations, leakage,etc. AE technique has drawn attention as it offers some advantages over classical vibration monitoring. Since AE is a non-directional technique, one AE sensor is sufficient in contrast to vibration monitoring, which may require information fromthree axes. Since AE is produced at microscopic level it is highly sensitive and offers opportunities for identifying defects atearlier stage of damage when compared to other condition monitoring techniques. As AE mainly detects high-frequencyelastic waves, it is not affected by structural resonances and typical mechanical background noise (under 20 kHz).

Eftekharnejad and Mba [12] studied the AE from helical gears based mainly in the root-mean-square of the recordedsignals. Tandon and Mata [13] applied AE to spur gears in a gearbox test-rig. They simulated pits of constant depth butvariable size and AE parameters such as energy, amplitude and counts were monitored during the test. AE was provedsuperior over vibration data on early detection of small defects in gears. Singh et al. [14] also applied AE technique incondition monitoring of test rig gearboxes, while vibration methods were also used for comparative purposes by placingaccelerometers on the gearbox casing. They also concluded that AE provided early damage detection over vibrationmonitoring. Toutountzakis et al. [15] investigated the influence of oil temperature and of the oil film thickness on AE activityand on AE signals captured during continuous running of a back-to-back gearbox test-rig. It was observed that the AE RMSvaried with time as the gearbox reached a stabilized temperature and the variation in AE activity RMS could be as much as 33%[16,17]. In [18] challenges and obstacles in the application of acoustic emission to process machinery are discussed whilst inHamzah and Mba [19] investigate the influence of operating conditions in recorded acoustic emission in helical gears as well.Recently, independent component analysis (ICA) has been applied to extract meaningful information from a collection of dataregarding rotating machinery health monitoring yielding promising results [20].

The present work consists of a comparative study of the combined application of vibration, AE and ODM monitoring onmulti-hour tests on healthy pairs of gears in order to monitor gear degradation and damage. Several statistical parametersderived from statistical analysis of various sensors. The most appropriate in reference to their diagnostic potential wereincorporated in a blind deconvolution signal processing scheme.

2. Experimental setup and test procedure

Fig. 1 shows the experimental setup used for the gears testing. The test rig consists of two gears made from 045M15 steelwith a module of 3 mm, pressure angle 201, which have 53 and 25 teeth with 10 mm face width. The axes of the gears aresupported by two ball bearings each. All the above are settled in an oil basin in order to ensure proper lubrication. The gearboxis powered by a motor and consumes its power on a generator. Their characteristics are as follows:

�

1 stage gearbox with two gears (25 and 53 teeth), � three-phase 5 hp motor (220 V, 9 A, 50 Hz, 1400 rpm) controlled by inverter, � single phase generator with continuous power consumption control (4.2 kV A, 3000 rpm, 50 Hz) with option for load

fluctuation,

� the oil pump is of wet type without oil recirculation, � the shafts are ball bearing supported.

This setup is an evolution of the setup used in a previous work [21]. The oil output at the bottom of the gearbox caseprovides more realistic ODM measurements as the debris circulation is ensured. Moreover, simpler and faster open-closeprocedure is accomplished.

Fig. 2. ODM sensor cross section (picture from Metalscan user’s manual).

Fig. 1. Experimental setup—lab scale single stage gearbox.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–1352 1341

As it is already mentioned, three non-destructive techniques monitor the gearbox during operation, vibration and acousticemission and oil debris monitoring. Three Bruel and Kjaer accelerometers were used for the vibration monitoring bothmounted upon the gearbox case, one in each side-axis. The sampling frequency used was 50 kHz and recordings of 1 sduration were obtained. One acoustic emission sensor by Physical Acoustics Corporation (USA) with a frequency range of100–800 kHz recorded continuous AE activity at a sampling rate of 2 MHz in friction contact with the rotating gear. The AErecordings duration is 100 ms. AE as well as vibration is recorded every 5 min. A special innovative device was designed inorder to mount the AE sensor in a rotating component avoiding thus the costly solution of the slip-ring that is typically used inliterature. Its effectiveness and operation is discussed elsewhere [22].

Oil debris data were collected using a commercially available oil debris monitoring (ODM) sensor (MetalSCAN byGASTOPS USA, Fig. 2). The sensor is in-line with the oil circuit. The oil circulation is assisted by a pump. Its operation is basedon the changes in the electromagnetic field caused by the metal particles passing through the sensor. The sensor measures thenumber of particles as well as their size from 225 to 1000 mm approximate diameter. A filter after the ODM sensor holds allparticles larger than 70 mm not allowing them to re-enter the oil circuit.

The recording of all the above data is realized by a National Instruments NI-6070 1MS/SEC FIREWIRE data acquisition cardand is assisted by special software in-house developed in Labview.

In the present study results from a representative test conducted at a healthy pair of gears shall be presented anddiscussed. The speed and load were kept constant throughout the test. Rotational speed was set at 1500 rpm and the load wasachieved through electric consumption at lamps of total power 3 kW. The test duration was 142 h. The end of the test is thecatastrophic failure of the gears with several teeth being cut-off.

3. Signal processing and feature extraction

3.1. Feature extraction

Significant effort was dedicated to the signal processing of the vibration and AE waveforms acquired during the tests.The goal set a priori was to calculate a number of parameters extracted by the signals and check their diagnostic capacity forthe actual condition monitoring of gears during the tests. In the literature, research groups involved in long term gear testing,have mainly used higher order moments and their combinations to form diagnostic parameters [1–5] with interestingbehavior during the tests. In this work, various features were extracted from each sensor (three accelerometers, one AE sensorand the ODM sensor). Those capable of diagnosing the evolving damage are identified and their behavior during the tests

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–13521342

is observed. Table 1 shows conventional features from the time and frequency domain that were calculated from the collectedvibration and AE waveforms. They are typical statistical moments and their combinations.

The wavelet transform was additionally utilized to develop more sophisticated diagnostic parameters and check theirbehavior during the tests. Wavelets are localized waves, which instead of oscillating forever like harmonic waves, drop to zerorather quickly. In contrast to the Fourier analysis which consists of breaking up a signal into sine waves of various frequencies,wavelet analysis breaks up the signal into shifted and scaled versions of the original (or mother) wavelet.

Wavelet transform can mainly be applied in two ways either via discrete wavelet transform (DWT) or via continuouswavelet transform (CWT). In discrete wavelet analysis, a signal is split into an approximation and a detail. Theapproximations are the low-frequency components of the signal and the details the high-frequency ones. The approximationis then itself split into a second-level approximation and detail and the process is repeated as many times as it is desirable.Mathematically this procedure is expressed as

DWðj,kÞ ¼ffiffiffiffiffi2j

p Z þ1�1

f ðtÞc�ð2jt�kÞdt ð1Þ

where DW(j, k) are the wavelet transform coefficients given by a two-dimensional matrix, j is the scale that represents thefrequency domain aspects of the signal and k represents the time shift of the mother wavelet.

f(t) is the signal that is analyzed and c the mother wavelet used for the analysis (c* is the complex conjugate of c).The inverse discrete wavelet transform can be expressed via:

f ðtÞ ¼ cX

j

Xk

DWðj,kÞcj,kðtÞ ð2Þ

where c is a constant depending only on c. Eq. (2) states that a given signal can be decomposed by the discrete wavelettransform into its wavelet levels, where the summation of these levels represent the original input signal. The decomposedwavelet levels are channeled in such a way that each level corresponds to a certain frequency range of the acquired signalwith minimal overlapping. Fig. 3 shows a 10-level decomposition of a typical AE waveform into its 10 approximations and onedetail.

The DWT-based methodology used in this work was introduced and described elsewhere [23] by the authors. Fig. 4schematically summarizes it. It comprises the discrete wavelet transform (DWT) of the time synchronous averaged acquiredvibration signals and AE signals in 10 levels of decomposition using the ‘db10’ wavelet. As far as the type of wavelet for thediscrete transform is concerned ‘db10’ is a good compromise of smooth function, without sharp edges as in the case of ‘db’wavelets of lower order.

The family of Daubechies wavelets was chosen because it consists of biorthogonal, compactly supported wavelets,satisfactorily regular though not symmetrical. Other wavelets having similar properties to the Daubechies family, such assymlets or coiflets were also tried with minor impact upon the results. The decomposed wavelet levels are split in a way thateach level corresponds to a certain frequency range. After the 10-level decomposition the energy of each level (10 details and1 approximation) is calculated as

Ei ¼XN

i ¼ 1

f 2i ðtÞ ð3Þ

Thus 11 parameters namely ED1–ED10 (for the 10 details) and EA10 (for the approximation).

Table 1Conventional parameters calculated from acquired waveforms.

Time domain parameters Frequency domain parameters

TD1 ¼

PN

n ¼ 1xðnÞ

N TD7 ¼

PN

n ¼ 1ðxðnÞ�TD1 Þ

4

ðN�1ÞTD42

FD1 ¼

PK

k ¼ 1sðkÞ

K FD8 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPK

k ¼ 1f 4k

sðkÞPK

k ¼ 1f 2k

sðkÞ

s

TD2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN

n ¼ 1ðxðnÞ�TD1 Þ

2

N�1

rTD8 ¼

TD5TD4 FD2 ¼

PK

k ¼ 1ðsðkÞ�FD1 Þ

2

ðK�1Þ FD9 ¼

PK

k ¼ 1f 2k

sðkÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPK

k ¼ 1sðkÞPK

k ¼ 1f 4k

sðkÞ

qTD3 ¼

PN

n ¼ 1

ffiffiffiffiffiffiffiffiffi9xðnÞ9p

N

� �2 TD9 ¼TD5TD3 FD3 ¼

PK

k ¼ 1ðsðkÞ�FD1 Þ

3

KffiffiffiffiffiffiFD2

p� �3

FD10 ¼FD6FD5

TD4 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN

n ¼ 1ðxðnÞÞ2

N

rTD10 ¼

TD4

1=Nð ÞPN

n ¼ 19xðnÞ9 FD4 ¼

PK

k ¼ 1ðsðkÞ�FD1 Þ

4

KFD22

FD11 ¼

PK

k ¼ 1ðfk�FD5 Þ

3 sðkÞ

KFD36

TD5 ¼max9xðnÞ9 TD11 ¼TD5

1=Nð ÞPN

n ¼ 19xðnÞ9 FD5 ¼

PK

k ¼ 1fksðkÞPK

k ¼ 1sðkÞ

FD12 ¼

PK

k ¼ 1ðfk�FD5 Þ

4 sðkÞ

KFD46

TD6 ¼

PN

n ¼ 1ðxðnÞ�TD1 Þ

3

ðN�1ÞTD32

FD6 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPK

k ¼ 1ðfk�FD5 Þ

2 sðkÞ

K

rFD13 ¼

PK

k ¼ 1ðfk�FD5 Þ

1=2 sðkÞ

KffiffiffiffiffiffiFD6

p

FD7 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPK

k ¼ 1f 2k

sðkÞPK

k ¼ 1sðkÞ

s

Where x(n) is a signal series for n=1,2, y ,N, N is the number of signal samples and s(k) is the windowed Fourier transform for k=1,2,y,K, K is the number of

spectrum lines, fk is the frequency value of the kth spectrum line.

Fig. 3. 10-level decomposition for a typical AE signal (amplitude vs. 105 samples).

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–1352 1343

3.2. Representative features from the ODM sensor

Fig. 5 depicts the ODM data during a typical gear test of approximately 150 h duration. The Fe mass and Fe mass rate aredrawn throughout the test and an expected monotonically rising behavior is observed. Stop-starts of the operation of thegearbox seriously affect the Fe mass and are highlighted in Fig. 5. The particle size distribution is also depicted in three distinctmoments of the test showing an increase of the larger size debris towards the end of the test.

Fe mass and Fe mass rate were measured at regular intervals during the test. They both show as expected a monotonicincrease throughout the test with the exception of ‘‘start’’/‘‘stop’’ events where a sudden jump in the measured features isnoted. Due to the latter effect, Fe mass and Fe mass rate features alone are prone to false alarms.

The particle size distribution was also measured and depicted in three distinct moments of the test showing an increase ofthe larger size debris towards the end of the test.

3.3. Representative features from the AE recordings

All the features extracted in Section 3.1 are normalized by division with their first value calculated at the very onset of thetest. Thus they all have a common onset from unity and this is a normalization that can be easily applied in an on-line health

Fig. 5. Fe mass, Fe mass rate evolution and particle size distribution during the test.

Discrete Wavelet transform – n levels of

decomposition

Energy content determination for each level

Plot of energy levels

Wavelet type

Number of levels

Time synchronous

averaging (only for

vibration signals)

Vibration and AE signals

Fig. 4. Flow chart of the DWT-based methodology.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–13521344

monitoring system rather than a normalization in the [0,1] range for example, which needs a priori knowledge of themaximum parameter value along the test.

The important information of each parameter under consideration is its trend during the test. Monotonic increase ordecrease of the parameter value would indicate a correlation to gear damage evaluation and would render the featurediagnostically potential.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–1352 1345

A visual inspection of the various features evolution during the test was enough to distinguish among the whole set ofcandidate parameters. From a plethora of features extracted from AE signals those which were relevant to the damageprogression (by showing a monotonic behavior during the tests) were kept as the most representative. This was a first,heuristic, dimensionality reduction. From this inspection, four parameters were kept and plotted in Fig. 6 versus test time.In the same graphs, features (Fe mass and Fe mass rate) from the ODM sensor are also depicted in order to correlate theparameters evolution with the actual gear damage progression as measured in real-time by the ODM sensor.

In Fig. 6 parameter TD4 from the time domain, parameters FD1 and FD6 from the frequency domain and the wavelet-basedparameter ED2 were selected as the most interesting (from a diagnostic point of view) and are presented in the same graphswith measurements from the ODM sensor in terms of Fe mass and Fe mass rate evolution during a typical multi-hour test inhealthy gears. The correlation between the parameters extracted from the AE recordings and the Fe mass rate evolution isobvious in the graphs. The stop–start at approximately 112 h gives an artificial peak in Fe mass rate but hardly affects AErecordings at all.

It is interesting to observe the behavior of parameter ED2. Apart from giving the highest percentage of increase during thetest, it also gives an earlier rise at approximately 100 h as compared to the other three parameters which seem to risealongside with Fe mass rate at about 130 h. This rise has a diagnostic potentiality and this behavior of ED2 parameter entailscharacteristics of advantageous diagnostic power.

3.4. Representative features from the vibration recordings

Figs. 7–9 entail the evolution of parameters FD1 and FD6 from the frequency domain and the wavelet-based ED1, ED2 asextracted from the vibration recordings. In all Figs. 6–9 for both monitoring techniques, very interesting correlations betweenthe parameters and the Fe mass rate are observed highlighting the diagnostic value of the proposed parameters. Againwavelet-based parameters seem to give earlier diagnostic warnings at about 100 h and along with the fact that they provide

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(c) FD6 and (d) ED2.

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ch1-accelerometer: (a) FD1, (b) FD10, (c) ED1 and (d) ED2.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–13521346

larger percentages of increase and thus they seem to excel in comparison with the conventional time or frequency domainparameters. The superiority of wavelet-based parameters is noteworthy.

3.5. Data fusion and independent component analysis (ICA)

Individual non-destructive techniques have strengths and weaknesses for detecting damage in different environments.Combining these strengths has the potential to improve the reliability of the condition monitoring system. When reliablesensor data are used, combining multiple sensors to make decisions produces improved detection capabilities, increases theprobability an event is detected and decreases the false or missed alarms [24,25].

There are several advantages of using sensor data fusion instead of relying on single sensor limits. Most notably, a morerobust operational performance and extended spatial/temporal coverage is possible since one sensor can contributeinformation while others are unavailable or lack coverage of a possible event. Another benefit is the increased confidenceresulted because more than a single sensor can confirm the same target or event thereby increasing assurance of its detection.

Since multi-sensor data were resulted after each test a scheme was necessary for data fusion and integration. Sensor datafusion in the field of health monitoring is realized in three levels: at the raw data level, feature level, or decision level [26]. Inthis work the second approach is followed. As described in the previous section, various features were extracted from theAE and vibration recordings. The ODM contributed two features: Fe mass and Fe mass rate. From the variety of featurescalculated only a few of them possess diagnostic value and exhibit interesting monotonic behavior during the tests(Figs. 6–9). These are integrated/fused in a data matrix containing vectors with the representative features from each sensor.In an approximately 142-h long test with 5-min periodic recordings about 1704 vectors are collected. Four features from eachaccelerometer, four from the AE sensor and two from the ODM sensor gives a dimension of 18 for the vectors of the datamatrix. Principal components analysis (PCA) is used to remove any correlation among the data and reduce the dimensionalityof the data matrix. Then independent components analysis (ICA) is applied in order to extract the independent componentsamong the reduced dimension data.

ICA is a statistical method that actually performs blind source separation. Extensive analysis is presented by Hyvarinenet al. [27]. Given a set of signals and assuming them to be a mixture of some original sources, the method tries to extract those

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accelerometer: (a) FD1, (b) FD10, (c) ED1 and (d) ED2.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–1352 1347

very sources. In matrix notation the problem is described as follows:

x¼As ð4Þ

where x is the matrix of the observed mixed signals, s is the unknown original source signals and A is the corresponding linearmixture matrix.

What we search for is an invertible matrix W such that

y¼Wx ð5Þ

where y is an estimation of the initial source matrix s and x is the mixed signal matrix. In order for ICA algorithm to performefficiently, the removal of any correlation among the data is needed. This procedure is called ‘‘whitening’’. After de-correlating thedata, the original sources can be acquired through a simple rotation. The rotation matrix, W, is calculated iteratively. The criterion ofthe iteration update will be the maximization of ‘‘non-normality’’ of the signals distribution. There are several measures of ‘‘non-normality’’. Statistical kurtosis is one. Maximizing kurtosis is a way to achieve statistical independence between signals. Anothercriterion is the minimization of mutual information. The calculation of mutual information is based on the signals cross entropyestimation. The cross entropy of two probability distributions p1 and p2, respectively, of a random variable y is defined as

HðyÞ ¼ �

Zp1ðyÞ logp2ðyÞdy ð6Þ

Since straightforward cross entropy calculation is difficult, especially when the underlining probability densities areunknown, several indirect estimations of cross entropy exist. ICA algorithm is applied in order to find an invertibletransformation W that minimizes this mutual information. Or, in other words, to find directions in which the cross entropy is

minimized. Analytically the whole procedure of data processing is depicted in the flow chart of Fig. 10 and is described below:

(A)

Preprocessing1. Formation of fused data matrix x from vectors containing features extracted from all sensors.2. Normalization of each row of x in the range [�1,1]

(B)

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Fig. 9. Parameters evolution and ODM measurements during a typical multi-hour test in healthy gears and recordings from the vibration ch3-

accelerometer: (a) FD1, (b) FD10, (c) ED1 and (d) ED2.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–13521348

3. ‘‘Whitening’’ of the data matrix. Let us assume EfxxTg to be the data covariance matrix. In order to transform the dataspace to one with unit covariance matrix, the eigen-value decomposition method can be applied on matrix EfxxT g.Applying the eigen-value decomposition method yields.

EfxxTg ¼ EDETð7Þ

where E is the orthogonal matrix of eigenvectors of xxT and D is the diagonal matrix of its eigen-values,D¼ diagðd1,. . .,dnÞ. Therefore, the new ‘‘whitened’’ data set ex can easily be estimated by the following expression:ex ¼ ED�1=2ET x ð8Þ

4. Reduction of feature space. After the application of step 3, a certain number of components of ~x are kept. thosecomponents hold more than 95% of the total variance of the initial x.

Core ICA algorithm1. An initial (random) weight vector w is chosen2. Let wnew ¼ EfxgðwT

old xÞg-EfguðwToldUxÞgwold. This is an approximate Newton iteration step

3. Let wnormnew ¼

wnew

:wnew:

4. If 99wnormnew �wold99

2oe then demixing matrix W=A�1 is obtained, or else return to step 2. e is a sufficiently small

number defined by the user as a stopping criterion.

E{} is the average operator whereas g is a non-linear estimator of entropy. In our case the hyperbolic tangent function is

chosen as a non-linear estimator.

4. Results

The number of independent components (ICs) was chosen equal to the two components held from the preprocessingstep 3 of Section 3.5 that contributed more than 95% of the total variance. Then ICA algorithm was applied. In particular, a fastimplementation of this algorithm that uses fixed point arithmetic, FastICA [28].

Featureextraction

Accelerometerch1

Time domain features TD1-TD11

Whitening of data – Principal Components Analysis

Dimension reduction

DWT-based features ED1-ED10, EA1

Frequency domain features FD1-FD13

ICA algorithm. Derivation of demixing matrix W

Extraction of features IC1 and IC2

IC 1>thrA

Yes

“Inspection”

No

“Normal condition”

No

IC2<thrBYes

Data matrix Formulation

Accelerometerch2

Accelerometerch3

AE sensor

ODM sensor

“Unexpected critical event- immediate

shut down”

“No need for immediateshut down”

Fe mass, Fe mass rate

Fig. 10. Condition monitoring scheme.

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-4

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Fig. 11. IC1 and IC2 evolution during the test.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–1352 1349

Fig. 11 depicts the evolution of the two resulted ICs from the fused data matrix during the test. IC_1 shows a monotonicevolution. Bearing in mind that the gears degrade increasingly with operational time due to natural wear, a correlationbetween IC_1 and normal gear degradation is established.

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–13521350

The question that rises is to what extend parameter IC_1 can be correlated to the actual gear deterioration. Visualinspection and evidence (photographs) is used for this reason by many researchers as a qualitative measure but it cannotdescribe the overall degradation of a gearbox. Moreover, in cases of very complex gear systems (planetary gearboxes,multistage gearboxes), the thorough visual inspection of the structure can be extremely difficult technically or unreliable. Inthe current work, the ODM recordings constitute a direct quantitative gear wear related measurement and thus represent atrustworthy deterioration criterion. An effort to correlate ODM recordings to IC_1 parameter is attempted.

In Fig. 12, IC_1 and Fe mass rate are plotted against operating time. Heuristic thresholds can be introduced in this pointthat distinguish between two or more different user defined damage or monitoring states. Decision rules of such type can besummarized in Table 2.

The second independent component, IC_2, seems to hold a different type of information. Although no significant change atthe trend of IC_2 is noted in the largest part of operational time, a steep decrease occurs at approximately 132 h. This decreaseat the value of IC_2 can be directly associated to the sudden increase at the value of iron particles production mass rate, asdepicted in Fig. 13. Consequently, this can be attributed to a sudden destructive event such as abnormal gear wear, single ormultiple gear tooth breakage or sudden rolling bearing failure. A heuristic threshold (or more) can also be introduced on IC_2in order to distinguish between two or more user defined areas as Table 3 suggests.

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ass

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area II

threshold A

area I

Fig. 12. IC_1 plotted along with Fe mass rate against operating time.

Table 2Condition monitoring criteria based on IC_1.

Figure area User defined label IC_1 constraint

Area I ‘‘Normal condition’’ IC_1othreshold A

Area II ‘‘Inspection’’ IC_14threshold A

0 20 40 60 80 100 120 140 160-5-4-3-2-1012345

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ass

rate

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IC_2

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area II

threshold B

area I

Fig. 13. IC_2 plotted along with Fe mass rate against operating time.

Table 3Condition monitoring criteria based on IC_2.

Figure area User defined label IC_2 constraint

Area I ‘‘No need for immediate shut down’’ IC_24threshold B

Area II ‘‘Unexpected critical event—immediate shut down’’ IC_2othreshold B

T.H. Loutas et al. / Mechanical Systems and Signal Processing 25 (2011) 1339–1352 1351

5. Conclusions

The combination and data fusion of three different measuring technologies for the condition monitoring of rotatingmachinery was studied in this work. Several conclusions can be deduced based on the results presented in the previoussections:

(i)

Various condition indicators/parameters were extracted from the recorded AE and vibration recordings. Conventionalparameters from the time or frequency domain as well as wavelet-based parameters were utilized. Their performancewas checked through a series of natural gear tests.

(ii)

A certain subset of parameters has shown an excellence in differentiating monotonically and thus diagnosing geardamage throughout the tests. More specifically: Parameters TD4, FD1, FD6, ED2 for Acoustic Emission recordings andParameters FD1, FD10, ED1, ED2 for vibration recordings.

(iii)

AE monitoring does not seem to offer any significant diagnostic advantages in the case of monitoring normal gear wear.On the contrary it was proven superior to vibration monitoring in the case of cracked tooth detection as a study of thesame group in [21] has revealed.

(iv)

Wavelet-based parameters possess a superiority presenting significantly larger percentage values and even earlierdiagnostically useful changes than the conventional parameters extracted from the time or frequency domain. Wavelettransform is conclusively more suitable to deal with such signals.

(v)

Independent component analysis applied on the fused data revealed independent components capable of monitoringthe basic damage modes of the gearbox.

Work in progress as well as future work also entails variable loading conditions to check the sensitivity and effectivity ofthe proposed methodology.

Acknowledgements

This research work was funded by European Commission in the framework of FP6-European project ADHER ‘AutomatedDiagnosis for Helicopter Engines and Rotating parts’. This support is gratefully acknowledged by the authors.

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