2008 INTERNATIONAL CONFERENCE ON PROGNOSTICS AND HEALTH MANAGEMENT

New Features for Diagnosis and Prognosis ofSystems Based on Empirical Mode

Decomposition

Hiralal Khatri, Kenneth Ranney, Kwok Tom, Romeo del Rosario

Abstract- We present a new procedure to generate additionalfeatures for system diagnosis. The procedure is based onempirical mode decomposition of measured signals obtained bymonitoring the relevant state of a system. This procedure isdifferent from the conventional procedures for defining features,which are generally obtained using the statistics of the measuredsignal, the matched filter outputs, and the wavelet decompositionof measured signals. Features derived by this new procedurecomplement the existing features for diagnosis, and thereforethey should improve performance of the classifier used todiagnose systems. We illustrate the procedure by generating newfeatures for diagnosis of the AH64A helicopter transmissionassembly.

Index Terms- diagnosis, empirical mode decomposition,features, prognosis

I. INTRODUCTION

Cost and availability of complex engineering equipment canbe enhanced by incorporating condition-based, predictivemaintenance and repair. Equipment such as helicopters, tanks,trucks etc may be difficult to diagnose because their complexdynamical systems may be nonlinear, nonstationary, quasi­periodic and chaotic, especially if there is a fault. Certainparameters that can directly indicate the health of a systemmay not be readily observable, and so its condition must bediagnosed on the basis of the vibrations measured at selectedlocations. Sometimes, certain characteristics of the vibrationscan be related to faults in gears or bearings, but in general therelationship between the vibrations and the operationaldynamics of the underlying system are unknown or toodifficult to characterize. Consequently, empirical algorithmsare used to diagnose the condition of the equipment basedupon vibrations measured at selected locations. Tests areconducted under controlled operating conditions andsometimes with seeded faults to gather sufficient data fortraining and testing of the diagnostic algorithms.

Manuscript received May 19,2008.This work was carried out at the Army Research Laboratory.Authors' address: Army Research Laboratory, Sensors, 2800 Powder Mill

Rd., Adelphi, MD 20783-1138, e-mail: (hkhatri@arl.army.mil)

9778-1-4244-1936-4/08/$25.00 © 2008 IEEE

Since rolling element bearings and gears are widely used inmodem rotating machinery, a number of procedures [1-5]have been developed to generate features that help detectfaults in such components based on measured vibrations.Algorithms based on statistics of the measured vibration aresummarized in [1]. A number of diagnostic procedures havebeen developed by using wavelet decomposition [2-4]. Phase­space based features for fault detection are discussed in [5].The vibrations resulting from a fault in rotating machinery willhave cyclical behavior and analysis of the cyclostationarityphenomena is reviewed in [6]. Fusion of features fordiagnosis of electromechanical systems is discussed in [7]. Forsuccessful fusion, we need features that have low crosscorrelation. We show that new features can be developedbased on empirical mode decomposition of vibration data,which may complement existing features and thereby enhanceaccuracy of diagnosis by fusion of all the features.

II. EMPIRICAL MODE DECOMPOSITION

Analysis of time series (nonlinear and/or non-stationary) byempirical mode decomposition (EMD) is introduced in [8] togenerate "intrinsic mode functions" (IMFs) and to determine"instantaneous frequency" ofIMFs via Hilbert transforms.Our objective here is to determine the potential ofEMD forgenerating new and more sensitive features for diagnosis ofequipment. We find that the statistical parameters computedfrom the IMFs are more sensitive to changes in the time seriesthan those computed directly from the original data. This isbecause the power spectral densities of the lower order IMFsare concentrated at higher frequencies and are more sensitiveto changes in the time series than the power spectrum of theoriginal data.

We start with a brief description of the numerical proceduregiven in [8] to generate the IMF's. Local maxima and minimaof the data, x(t), are identified and the maxima are connectedby a smooth curve, usually generated by a cubic-spline, as theupper envelope. Similarly, a lower envelope is generated fromthe minima. The two envelopes should bracket all the data

between them. Let Eu (t) and E, (t) denote the values of

upper and lower envelopes as a function of discrete time t. Themean of the two envelopes is

M(t) = (Eu(t) + E[(t))/2.

The difference between the data and the mean envelope givesthe residue:

hI (t) = X(t) - M(t) ,where the subscript denotes level of iteration . This process is

iterated with ~ (t) representing a new time series whose

upper and lower envelopes and mean envelope, M I (t) , are

computed to obtain the value for next iteration:

hi+I(t) = hi(t) - Mi(t) , where i=I,2, ....

Ideally, this process is continued until the residue hi (t)satisfies the conditions specified for IMFs: (1) in the whole

data set hi (t) , the number of extrema and the number of zero

crossings must either equal or differ at most by 1; and (2)

M i (t) = 0 for all t. It is not always advisable or efficient to

test for these conditions. Instead, the authors [8] recommendthat the iteration process be terminated when the value of the

standard deviation, SD:

SD =t [[hi(t) ~ hi_I (t)]2 ] ,~ hi _I (t)

is below a selected value, generally in the range of (0.2-0.3).

Note that when h;(t) = hi-I(t) for all t, no further reduction

in residue is possible so hi (t) is considered to have

converged and SD =0 . The value of SD is used to gage thelevel of convergence.

This gives us the first IMF, denoted as c1(t) = hi(t). To

obtain subsequent decompositions, Cj (t) , where j=2, 3... treat

the residue rj (t) :

rj (t) = rj -1 (t) - Cj (t) , (with ro(t) = x(t)) ,

as the signal to be decomposed and repeat the aboveprocedure to obtain the IMF of the residue. Thisdecomposition process can be stopped based on predeterminedconditions. Note that if n IMFs are obtained then

n

x(t) =}: cj(t) + rn(t).j=I

III. DECOMPOSITION OF VIBRATION DATA

We illustrate the potential of EMD for generating new featuresfor diagnosis of machinery by analyzing the vibration datameasured by an accelerometer attached to the underside of thenon-rotating main rotor swashplate of an AH64A helicopter[9]. We had 6 sets of this vibration data, the first four setswere from rotors with no known faults ("normal data") and theremaining 2 sets were from rotors with faults ("faulted data").Each set consisted of 262, 144 samples with sampling periodof 0.0208 ms, thus, each set represented data collected over5.4613s. Fig. 1 shows the first 2000 samples of one of thenormal data sets and Fig. 2 shows similar samples for one of

the faulted data sets. Note that the amplitude of the faulteddata set is much larger than that of the normal data set. Bothdata sets exhibit some amplitude modulation and there aretimes when the peaks have negative values and the valleyshave positive values.

The ratio of the mean squared acceleration for the faulted datasets with respect to the lowest mean squared accelerationobtained from the four normal data sets is much higher thanthe corresponding ratios of the remaining three normal datasets, see Fig. 3. The power level of the faulted system is muchhigher than the normal system (ratio near 40) so we may notneed any special detector to classify the data set as faulted.However, we will use this data set to investigate the potentialof the IMFs for developing new features that may be moresensitive to the condition of the rotor swashplate. Generally, ina complex dynamical system like a helicopter, the statistics ofthe measured signals are time varying - depending upon thesystem load and environmental conditions. We do not wantthe features to be so sensitive that they will misdiagnose thesystem to be faulty just because it is operating under differentconditions. To reduce the probability of false diagnosis, wedivide a given data set into blocks and define features basedon the average values of selected parameters.

The transients introduced by the cubic-spline curve-fittingprocedure at the start and the end of the data can significantlydistort the values of IMFs near the corresponding start and endof the data range. To minimize the effects of these transients,

Cj (t) s U=1, ... ,12) of each of the six sets were generated by

using all the data points (262,144 samples) and then only

240,000 contiguous samples of cj(t) s near the middle of the

set were used for further processing. Each of the resultant

Cj (t) s were then separated into 12 consecutive blocks of

20,000 samples each (blocks ofO.416s each) to enable us to

investigate any long term variations in Cj(f) s. The twelve

cj(t) s generated from one of the normal data sets are shown

in Figs. (4-6). We have plotted only the first 2,000 samplesfrom the first block so that we can show some level of detail.

Fig. 4 shows the first four IMFs starting with cI (t) at the top

and ending with c4(t) at the bottom. Similarly, Fig. 5 shows

Cs(t) to cg(t) and Fig. 6 shows c9 (t) to C12 (t). Notice that

the lower ordered Cj (t) s show faster variations with time

(higher frequencies) and that all the IMFs are centered aboutzero and most of the peaks have positive values and most ofthe valleys have negative values. Figs. (7-9) show thecorresponding IMFs obtained from one of the faulted data.These IMFs look similar to those of the normal data set exceptfor their amplitudes and frequencies. The power (mean squarevalue of the IMF data) in each of the twelve blocks as afunction of mode number for one of the normal data sets isshown in Fig. 10. The power level varies slightly from blockto block (different line types) for any given mode number but

in general, the levels are consistent from one block to anotherindicating that the blocks have captured the essence of thewhole data set.

Next, we examine the Fourier transforms of the IMFs. Thetransforms of the IMFs were obtained for each blockseparately and the results were quite similar for all the blocks.Figs. (11-20) show the average amplitudes often IMFs for thesix data sets (two faulted and four normal). These amplitudeswere obtained by averaging over the 12 blocks and 10frequency samples (24Hz apart). Note that the data has beenshown for different frequency ranges (abscissa) where theamplitudes are significant so that finer details may be easilyseen. The transforms are shown only for the first 10 modesbecause the transform characteristics of the last two modes donot change significantly between the normal and faulted datasets. The dominant frequencies of the IMFs and themodulation rates decrease as the IMF number increases. Thereis a difference in frequency where the amplitudes peak and inthe frequency bands over which the amplitudes are relativelyhigh for the normal and the faulted data sets. We use thesedifferences to generate features for discriminating between thenormal and faulted data sets.

First, the power levels of some of the IMFs from normal andfaulted data sets can provide new features. We averaged thepower over the twelve blocks for each of the modes, andobtained the ratios of the average powers for the two faultedand the three normal data sets to the remaining fourth normalset and the results are shown in Fig. 21. The ratios areobtained relative to the IMFs of data set no. 3, which has thelowest power level, see Fig. 3. These ratios for the two faulteddata sets are much higher than the ratios for the three normaldata sets. The ratios for modes 1 thru 8 are greater than 20 forthe faulted data sets and less than 5 for the three normal datasets. Further, the ratios for mode 1and 6 of the faulted datasets are near 80 and 60, respectively. Thus, the power ratio ofthese two modes are higher than the power ratio of the originaltime series (near 40) and are therefore better features forclassifying faulted and normal data. For this data set, the ratiosfor mode 1 and 6 are good candidates for new features.

Second, the maximum power spectral densities, i.e. themaximum of the squares of the Fourier transforms amplitudes,of some of the IMFs can provide new features. The ratio of themaximum power spectral densities for each of the IMFs of thetwo faulted data sets and three normal data sets relative to themaximum of the corresponding IMF of the normal data set no.3 is shown in Fig. 22. The ratios for IMF no. 1,5 and 6 of thefaulted systems are much higher than for the three normalsystems and should be potential candidates for the second setof new features to help classify faulted and normal data sets.

Third, the shift in frequency where the maximum powerspectral density occurs when the system develops a fault canlead to new features. Here we exploit the frequency shift bytaking the ratio of the maximum power spectral density foreach IMF of the test data to the power density of the normaldata set no. 3 at the same frequency where the maximumdensity occurred for the test data. This feature takes advantage

of the fact that the peaks in the power spectrum of the faulteddata set are shifted from the corresponding peaks of thenormal data set. Note that the ratios for modes 1 and 6 arequite high and the reason is obvious from Figs. 11 and 16.This is our third set of new features. Alternately, one can usethe difference in frequencies at which the maximum poweroccurs for the normal and the faulted data.

Weare proposing these three sets of features for assisting indiagnoses of the gear box. A summary of the values of thesefeatures as compared to the ratio ofpower levels of faulteddata to normal data is given in Table 1. Since these featuresare obtained by using a new methodology, it is likely tocomplement the existing features and hence improve theclassifier which combines all the features to make a diagnosis.Clearly, further tests are needed to gage the advantages ofthese features, especially at the initiation and increasing levelsof faults.

TABLE 1. SUMMARY OF FEATURE VALUES-RATIOS OF FAULTED DATA TO

NORMAL DATA VALUES

Feature Description Feature valueMaximum power ratio of raw data 40Feature set 1 - power ratio ofIMF #1, #3 60,80Feature set 2 - ratio of max spectral 110,80,70density ofIMF #1,#5, #6Feature set 3 - ratio of density at same 400,300,500frequency ofIMF #1,#5,#6

IV. SUMMARY

Empirical mode decomposition of measured signals of therelevant state of a system can generate additional features forsystem diagnosis. We have shown that three sets ofnewfeatures for diagnosis of transmission box of AH64Ahelicopter can be generated based upon application of modedecomposition of measured vibration data. This procedure isdifferent from the existing procedures for defining features forthe transmission box and therefore these new features shouldcomplement the existing features for diagnosis and improveperformance of the classifier used to diagnose the system.

ACKNOWLEDGMENT

The authors wish to thank Mr. Jonathan Keller, U.S. ArmyAviation and Missile Research Development and EngineeringCommand (AMRDEC).

REFERENCES

[1] Decker, H.J., Lewicki, D.G. "Spiral Bevel Pinion Crack Detection in aHelicopter Gearbox", Technical Memorandum, U.S. Army ResearchLaboratory, 2003.

[2] Tse, P.W, Peng, Y.H, Yam, R. "Wavelet analysis and envelope detectionfor rolling element bearing fault diagnosis - their effectiveness andflexibilities", Journal of Vibration and Acoustics, ASME, July 2001.

[3] Staszewski, W.J. "Structural and mechanical damage detection usingwavelet", The Shock and Vibration Digest, Vol. 30 No. 6,Nov. 1998.

[4] Wang, C, Gao, R. "Wavelet transform with spectral post-processing forenhanced feature extraction", IEEE Transactions on Instrumentation andMeasurements, Vol. 52, No.4, August 2003.

[5] Hively, L.M., Protopopescu, V.A. "Machine failure forewarning viaphase-space dissimilarity measures" Chaos, American Institute ofPhysics, Vol. 14, No.2, June 2004.

[6] Gardner, W.A., Napolitano, A., Paura, L. "Cyclostationarity: half acentury of research", Signal Processing, Vol. 86, Issue 4, April 2006.

[7] Byington, C. Garga, Data Fusion for Developing Predictive Diagnosticsfor Electromechanical Systems, Chapter 23 of CRC Press Handbook ofMulti-sensor Data Fusion, edited by Hall and Linas, CRC Press, Spring2001.

[8] Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q.,Yen, N.C.,Tung, C.C., Liu, H.H., "The empirical mode decompositionand the Hilbert spectrum for nonlinear and non-stationary time seriesanalysis", Proc., R. Soc. Lond. Sere A 454, pp. 903-995, 1998.

[9] Keller, J.A. , Branhof, R., Dunaway, D., Grabill, P. "Examples ofcondition based maintenance with the vibration managementenhancement program", presented at the American Helicopter Society61 st Annual Forum, Grapevine, Texas, June 1-3,2005.

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Time

Fig. 1. Representative 2000 contiguous samples of measured acceleration data of the normal system

20

15

10

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-15

200 400

Time index

Fig. 2. Representative 2000 contiguous samples of measured acceleration data of the faulted system.

40

35

30

0 25+-'ro'-'- 20Q)

~ 150(l.

10

5

01 2 3 4 5 6

Data set index (1-4 normal, 5, 6 faulted)

Fig. 3. The power ratios of six data sets relative to the lowest power of the normal data

2

0

-20 200 400 600 800 1000 1200 1400 1600 1800 2000

2

0CD

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C 1C>CO 0~

-10 200 400 600 800 1000 1200 1400 1600 1800 2000

2

0

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Time index

Fig. 4. The first four (1-4) intrinsic mode functions of the first normal system data set. Subplots are ordered starting with the first mode at the top.

0.5

0

-0.50 200 400 600 800 1000 1200 1400 1600 1800 2000

0.2

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-10 200 400 600 800 1000 1200 1400 1600 1800 2000

0.5

0

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Time index

Fig. 5. The next four (5-8) intrinsic mode functions of the first nonnal system data set. Subplots are ordered starting with the fifth mode at the top.

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-0.50 200 400 600 800 1000 1200 1400 1600 1800 2000

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Time index

Fig. 6. The last four (9-12) intrinsic mode functions of the first nonnal system data set. Subplots are ordered starting with the ninth mode at the top.

10

0

-100 200 400 600 800 1000 1200 1400 1600 1800 2000

10

0-c::J -10+-'

C 0 200 400 600 800 1000 1200 1400 1600 1800 2000C) 10CO~ 0

-100 200 400 600 800 1000 1200 1400 1600 1800 2000

5

0

-50 200 400 600 800 1000 1200 1400 1600 1800 2000

Time index

Fig. 7. The first four (1-4) intrinsic mode functions of the first faulted system data set. Subplots are ordered starting with the first mode at the top

5

0

-50 200 400 600 800 1000 1200 1400 1600 1800 2000

10

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-50 200 400 600 800 1000 1200 1400 1600 1800 2000

2

0

-20 200 400 600 800 1000 1200 1400 1600 1800 2000

Time index

Fig. 8. The next four (5-8) intrinsic mode functions of the first faulted system data set. Subplots are ordered starting with the fifth mode at the top.

1

0

-10 200 400 600 800 1000 1200 1400 1600 1800 2000

0.5

0Q)-c::J -0.5~ 0 200 400 600 800 1000 1200 1400 1600 1800 2000c: 0.5OJCO

0~

-0.50 200 400 600 800 1000 1200 1400 1600 1800 2000

0.5

0

-0.50 200 400 600 800 1000 1200 1400 1600 1800 2000

Time index

Fig. 9. The last four (9-12) intrinsic mode functions of the first faulted system data set. Subplots are ordered starting with the ninth mode at the top.

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0.2

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0.15

0.05

Q)

~oc..

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Fig. 10. Power level for each of the twelve blocks (different line types) of the first normal data set plotted as a function of mode number.

X 104

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Faulted

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+-' .,L.-

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X 104

Fig. 11. Amplitude of the Fourier transform of the IMF number 1, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets.

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4000

X 104

5

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3EL.

~ 2.5CJ)C 2COL.

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02000 3000

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Fig. 12. Amplitude of the Fourier transform of the IMF number 2, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selected frequencyrange.

X 104

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Faulted

3

2.5

EL..

S(/)cOJ 1.5L..t... ,L.. I

Q) wi 1·C::Jo

LL. to.5

2000 3000 4000 5000 6000 7000 8000

Frequency

Fig. 13. Amplitude of the Fourier transform of the IMF number 3, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selected frequencyrange.

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+-'

C. 10000ECOE 8000L..

~~ 6000COL..

+-'

CD 4000·C::J

~ 2000

Faulted

1000 2000 3000 4000 5000 6000 7000

Frequency (Hz)

Fig. 14. Amplitude of the Fourier transform of the IMF number 4, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selected frequencyrange.

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0500 1000 1500 2000 2500 3000 3500 4000 4500

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Fig. 15. Amplitude of the Fourier transform of the IMF number 5, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selected frequencyrange.

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0500 1000 1500 2000 2500 3000 3500 4000

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Fig. 16. Amplitude of the Fourier transform of the IMF number 6, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selected frequencyrange.

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4

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co 2.5

EI.-

Q 2tJ)Cco 1.5l.-+-'I.-Q)

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0500 1000 1500 2000 2500 3000

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Fig. 17. Amplitude of the Fourier transform of the IMF number 7, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selected frequencyrange.

1200 1400 1600 1800 2000 2200200 400

2

X 104

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12000

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~ 6000enccoL-

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0500 1000 1500 2000 2500

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Fig. 19. Amplitude of the Fourier transform of the IMF number 9, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selected frequencyrange.

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5000

7000

3000

8000

6000C.EroEL-

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200 400 600 800 1000 1200 1400

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Fig. 20. Amplitude of the Fourier transform of the IMF number 10, averaged over 12 blocks and 24 Hz, plotted for each of the six data sets for selectedfrequency range.

121086

Faulted

42

90

80

70

60

50

L.. 40Q)

~0 30a..

20

10

00

Intrinsic mode function number

Fig. 21. Ratio of average power of 12 blocks of nonnal and faulted data set with respect to that of the nonnal data set number 3 plotted as a function of modenumber.

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120

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Fig. 23. Ratio of maximum power spectral density of faulted and normal data set to the power spectral density of normal data set number 3 at the same frequencywhere the maximum density occurred for the test data.