2008_ieee transactions on industrial electronics_ phase sensitive detection of motor fault...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008 2539

Phase-Sensitive Detection of Motor FaultSignatures in the Presence of Noise

Bilal Akin, Member, IEEE, Umut Orguner, Member, IEEE, Hamid A. Toliyat, Fellow, IEEE, and Mark Rayner

AbstractIn this paper, a digital signal processor-based phase-sensitive motor fault signature detection technique is presented.The implemented method has a powerful line current noisesuppression capability while detecting the fault signatures. Be-cause the line current of inverter-driven motors involve low-orderharmonics, high-frequency switching disturbances, and the noisegenerated by harsh industrial environment, the real-time faultanalyses yield erroneous or fluctuating fault signatures. This sit-uation becomes a significant problem when the signal-to-noiseratio of the fault signature is quite low. It is theoretically andexperimentally shown that the proposed method can determinethe normalized magnitude and phase information of the faultsignatures even in the presence of noise, where the noise amplitudeis several times higher than the signal itself. Since it has lowcomputational burden, the developed algorithm is embedded tothe motor control program without degrading drive performance.Therefore, it is implemented without any additional cost usingreadily available drive processor and current sensors.

Index TermsBearing fault, broken bar fault, conditionmonitoring, current signature analysis, digital signal processor(DSP)-based fault diagnosis, eccentricity, fault diagnosis, lock-indetector, online monitoring, phase-sensitive detection.

I. INTRODUCTION

FAULT diagnosis of electric motors mainly becomes anessential concern in two cases: 1) the cost and refur-bishment of the machine is high; and 2) the motor cost andrepair expenses might not be substantial, but the cost associatedwith downtime is enormous. Condition monitoring providesadequate warning of incipient faults, diagnosing present main-tenance needs, scheduling future preventive maintenance, andminimum downtime [2]. Although a great number of studieshave been made on utility-driven motor fault analysis [1][6],inverter-fed motor fault diagnosis needs further research in or-der to overcome various challenges such as noise, dynamicallychanging excitation frequency and fault signature suppressioneffects of closed-loop regulator, etc. [7], [8]. Despite the factthat some expensive and complicated fault analyzers are com-mercially available, drive-embedded real-time fault analyzers

Manuscript received November 19, 2006; revised February 25, 2008.B. Akin and H. A. Toliyat are with the Department of Electrical and

Computer Engineering, Texas A&M University, College Station, TX 77843USA (e-mail: [email protected]).

U. Orguner was with the Department of Electrical and Electronics Engi-neering, Middle East Technical University, 06531 Ankara, Turkey. He is nowwith the Division of Automatic Control, Department of Electrical Engineering,Linkping University, 58337 Linkping, Sweden.

M. Rayner is with Toshiba Industrial Corporation, Houston, TX 77041 USA.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TIE.2008.921681

have not taken their place in the market. The main featuresexpected from such a product are as follows: low cost, lowvolume, noise immunity, and employing simple fault detectionalgorithms that can be executed in real time using industry-purpose microprocessors.

In the literature, several signal processing techniques arereported, focusing on the amplitude and frequency estimationof fault signatures that mostly utilize line current or vibrationdata [9][14]. Among these, the multiple signal classification(MUSIC) method estimates the frequency content of a signalor autocorrelation matrix using an eigenspace method [9]. Theability of this algorithm is enhanced for the nonstationarysignals to obtain better representations of the space vector ofvoltages induced in stator windings [10]. To solve the long com-putation time problem of numerous fault-related componentdetections, an algorithm that is based on zooming in a specificfrequency range is proposed with MUSIC [11]. Bellini et al.[12] present another procedure based on the statistical analysisof the current signal in the time domain, which is independentof the sampling frequency and the time acquisition period. Thismethod accurately detects the locations of the fault signatures;however, it does not provide amplitude information of differentfrequency components [12], which is one of the main issuessolved in this paper. Being a relatively different application, toanalyze the induction motor-driven multistage gearbox faults,discrete wavelet transform is applied to the demodulated currentsignal for denoising and removing the intervening neighboringfeatures [13].

In order to examine the practicability of the proposed meth-ods, some of the studies are implemented using industry-purpose microprocessors. Rajagopalan et al. [14] claim thatcontrary to common beliefs, the timefrequency distribution-based solutions are practical enough for commercial implemen-tations. In [14], after eliminating the fundamental componentand high-order frequencies using a switch capacitor filter, thestator current is processed in real time by a digital signalprocessor (DSP) that runs a fault diagnosis algorithm developedfor nonstationary signals based on Hilbert transformation andZhaoAtlasMarks distribution. In [8] and [15], the DSP is uti-lized for both motor control and reference-frame-theory-basedmotor fault diagnosis. In addition, a model-based rotor faultdiagnosis method employing electrical machine parameters isimplemented using the DSP [16].

Now that DSP technology is being applied to motor drivecontrol [17], the improved benefits of this processing unit arebeing realized in more applications than ever before, such asfault detection. The proposed fault detection method is imple-mented using the core processor of a motor drive; therefore,

0278-0046/$25.00 2008 IEEE

2540 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008

it does not produce any extra computing cost. Control-and-protection-purpose current sensors that are installed in the mo-tor drive provide line current information for real-time analysis.Therefore, no specialized hardware is required to realize phase-sensitive fault detection. Furthermore, the most complicatedmathematical tool used in the simple detection algorithm is thebasic trigonometric functions that can be handled with eitherlookup tables or numeric functions. The overall execution timeof the fault detection algorithm takes a few seconds to obtainhigh enough resolution. The measured fault signature ampli-tudes vary depending on the sensor and signal conditioningcircuit amplification, unless carefully calibrated. On the otherhand, depending on the operating point and machine geometry,the instantaneous amplitude of the fault signature will change.Therefore, fault analyses are mostly based on normalized valueswith respect to the fundamental component to have more gen-eralized results. In addition to the fault signature, the algorithmis run one more time to obtain the amplitude of the fundamentalcomponent for normalization.

A typical normalized fault signature is within the range of40 to 80 dB; hence, fault detection is quite prone to thenegative effects of the noise content in the current spectrum.Therefore, noise suppression is a critical requirement for smallfault signature detection, which is achieved by a phase-sensitivelock-in algorithm [18] in this paper. This method simply locksto and measures the particular frequency of interest, ignoringall other signals at the input. The eliminated signals mightbe either at the same frequency with different phase anglesor at some other frequencies. Fortunately, phase-sensitive faultdetection provides a technique for rejecting both ac and dc noisesources while the signal is measured. When the floor noise ishigh, the inspected small signatures will mostly be comparablewith the noise content, including the components at the samefrequency. A lock-in detector is capable of measuring small acsignals that are obscured by a large amount of noise. In fact,ac signals can be extracted even when dominated by far greaternoise.

In this paper, real-time amplitude measurement of fault sig-natures that might have been buried under noise is of directinterest. The lock-in detector is a phase-sensitive demodulatorthat examines how two entities are related based on autocorrela-tion. Its output is a function of the relative phase angle betweenthe input signal and the associated reference signal generated bythe processor. Therefore, the lock-in detector is used to measureboth the relative phase and the normalized magnitude of thefault signatures.

One of the most commonly used magnitude measurementtechniques is the fast Fourier transform (FFT) method [1][6].The main duty of the FFT radix algorithms is to reduce thecomplexity by decomposing the discrete Fourier transforms(DFTs) into smaller DFTs in a recursive manner [19][21].In order to compute the DFT of discretized signals, all signaldata should be stored and indexed. Moreover, to obtain highresolution and accurate results in inverter-driven systems, alarge number of data points should be buffered due to lowsignal frequency and high switching frequency constraints.Therefore, implementing FFT algorithms in real time usinglow-cost industrial processors is a challenge.

Wavelet-based fault diagnosis solutions are also proposed inthe literature [21], [22]. With this approach, the time resolutionbecomes arbitrarily good at high frequencies, whereas the fre-quency resolution becomes arbitrarily good at low frequencies.In wavelet-based solutions, a low-frequency content variationin time can easily be noticed; however, it is difficult to indicateany clear information about a specific fault. Even the changes intime due to supply unbalance, measurement error, etc., can beconsidered as machine faults. In [22], a very narrow frequencyinterval is successfully tracked. Nevertheless, the informationreporting the exact fault signature is obtained at the ninth level,which equates to enormous computational burden. Thus, real-time implementation of wavelets has still been a challengeas well.

II. PHASE-SENSITIVE DETECTION

Phase-sensitive detection is based on correlation of twosignals. In the correlation process, the input signal is comparedwith a reference signal, and the similarity between these signalsis determined [19][21]. Given two real-valued sequences x[n]and y[n] of finite power, the cross correlation of x[n] and y[n]is a sequence rxy[], which is defined by

rxy[] = limN

12N

Nn=N

x[n]y[n ] (1)

where is called the shift or lag parameter. The special case of(1) when x(n) = y(n) is called the autocorrelation. It providesa measure of self-similarity between different alignments of thesignals and is given by

rxx[] = limN

12N

Nn=N

x[n]x[n ]. (2)

Similarly, a lock-in detector takes a periodic reference signaland a noisy input signal and then extracts only that part of theoutput signal whose frequency and phase match the reference.To see how the phase-sensitive detector works, consider areference signal Iref , which is a pure sine wave with a frequencyof wref , i.e.,

Iref [n] = Iref cos(wrefn + ref) (3)and the noisy fault signal, i.e.,

Iin[n] = Ifault cos(wfaultn + fault)

+

Inoise cos(wnoisen + noise). (4)The multiplication of these two signals is given as

Iin[n]Iref [n]= Iref cos(wrefn + ref)Ifault cos(wfaultn + fault)+ Iref cos(wrefn + ref)

Inoise cos(wnoisen + noise)

= IrefIfault cos(wrefn wfaultn + ref fault)+ IrefIfault cos(wrefn + wfaultn + ref + fault)+

IrefInoise [cos(wrefn wnoisen + ref noise)+ cos(wrefn + wnoisen +ref + noise)] .

(5)

AKIN et al.: PHASE-SENSITIVE DETECTION OF MOTOR FAULT SIGNATURES IN PRESENCE OF NOISE 2541

The frequency of the generated reference signal is set to bethe same as the fault signal frequency; therefore, some of theterms in (5) are converted to dc, as given by

Iin[n]Iref [n]|wref=wfault= IrefIfault cos(ref fault)+ IrefIfault cos(2wrefn + ref + fault)

+

IrefInoise [cos(wrefn wnoisen + ref noise)+ cos(wrefn + wnoisen +ref + noise)] .

(6)

If this multiplication output is low-pass filtered by simplyaveraging, only two terms survive: 1) the dc term due tothe output of the system and 2) the noise component with afrequency near the reference signal. The rest of the noise andlow-order harmonics disappear, as shown in

III_ltered()K1cos(reffault)+K2

cos(refnoise).(7)

The interpretations of (5) and (6) in terms of the correlationfunctions and the proof of (7) for the case of sample averaginggiven in (1) are elaborated upon in Appendix A.

The phase of the noise signal randomly varies. In orderto minimize the effects of the noise content, the phase angledifference between the reference signal and the fault signalsshould be minimized for perfect matching. In other words, thecorrelation degree of the fault component is set to maximumin order to increase the signal-to-noise ratio (SNR), i.e., theratio of the correlation term coming from the fault componentto the sum of the terms coming from the noise components.There are some alternatives to maximize the low-pass-filteredportion of the autocorrelation function. One alternative is totrack the autocorrelation function and detect the peak pointwhere the phase angles of the reference signal and the faultsignal are the same. The second, and more efficient, method isto instantaneously examine the correlation of both cosinusoidaland sinusoidal reference signals to the same phase angle. Thearctangent of the correlation ratio results to the phase angledifference between the reference signal and the fault signal. Themaximum correlation degree and the minimum noise effect areobserved when the phase angles are equated to each other bysimply adjusting the phase angle of the reference signal. Thesimilar processes are repeated for the fundamental componentto calculate the correlation ratio between the fundamental andfault components to find the normalized magnitude of the faultsignature.

Overall, for each amplitude that is required, our methodmakes one addition and one multiplication for each measure-ment that is acquired. Therefore, its order of complexity is N ,where N is the number of data samples that are processed.The computational complexity of the angle-scan-based lock-in procedure is O(MN), where N is number of data samplesthat are processed for each angle, and M is the number ofangle values in the angle grid. On the other hand, the com-putational requirements of arctangent-based lock-in procedure

is O(N). The FFT method requires computations of the orderN log(N), which is a well-known fact. However, comparing itwith our method is, in a way, unfair because it calculates bothamplitude and phase information for N different frequencyvalues, whereas in our method, the number of frequenciesthat are involved is much less. The wavelet-based methodsrequire convolution with various kernel functions that can stillbe handled in the frequency domain in a numerically efficientway. Except for a couple of simple wavelets like Haar bases, itis expected that the computational cost of a wavelet transformis higher than that of an FFT, which can be considered as avery specialized wavelet transform and, therefore, is going tobe higher than our method. Nevertheless, it must be empha-sized that the obtained information about the signal in waveletmethods is much more than that obtained using our algorithm,which makes the comparison misleading and, hence, out of thescope.

III. SIMULATION RESULTS

In order to verify the effectiveness of the proposed method, atypical line current is modeled. A few low-order harmonics areadded to distort the fundamental component, as in the case ofinverter-driven motor line current. The total harmonic distortion(THD) is about 11% to 15%, including low-order harmonicssuch as third, fifth, seventh, etc., each utmost 25 dB. Apartfrom the low-order harmonics, relatively high amplitude whitenoise is added when compared to the fault signature, as shownin Fig. 1(a).

Initially, the phase angle detection is realized in order tofilter out the low-order harmonics, including the fundamentalcomponent, and to minimize the effect of the noise component.The phase angles of the fault component and the fundamentalare set to /6 and /2, respectively. The phase angle of thereference signal starts to increase from 0 to in order toexamine maximum correlation degree, as shown in Fig. 1(b).The correlation degrees between the fault component and thereference signal are given in Fig. 1(c). As shown in Fig. 1(c),the correlation degree increases when the phase angle of thereference signal comes close to the phase angle of the faultcomponent (/6). The phase angle of the reference signal isfixed at this point during the rest of the analysis to minimize theeffect of the noise where the examined correlation function ismaximum.

A number of tests were performed under the aforementionedconditions to examine the precision of the proposed method.The test parameters and the results of each simulation aregiven in Tables I and II. In the first simulation, a 40-dB faultsignature is injected to the modeled line current, in additionto low-order harmonics and white noise, the amount of whichare indicated in Table I. While defining the SNR in Table I,only the fault signal and white noise are considered. Althougha significant amount of noise and low-order harmonics areinjected to the line current, the 40-dB fault component issuccessfully filtered out with less than 1 dB error.

The impact of sampling time and number of data is tested,and the results are given in Table II. In the simulations, thesampling time is chosen to be close to the typical switching


Fig. 1. Simulation results. (a) Injected noise and inspected fault component.(b) Phase angle of the reference signal. (c) Correlation degree between thereference signal and the fault component with respect to the phase angle ofthe reference signal.

TABLE ISIMULATION RESULTS

TABLE IISIMULATION RESULTS

frequency interval of a motor drive. The number of samples ineach data window should carefully be determined to get rid ofinaccurate results. One should note that the undersampled orfewer data also provide sufficient precision down to a certainlimit, as shown in Table II. As the proposed method processeseach data in real time, the samples are buffered neither in the

simulations nor in the experiments. Therefore, one is free todetermine the upper limit of the sample number without takingthe memory limit into consideration. However, the duration ofthe test strictly depends on the number of samples that areprocessed. In Table II, four sampling time and number of datacombinations are given, where the test time varies from 0.1 to10 s. The test duration should be determined according to thesystem dynamics and how fast they change.

The ratio between the number of data and the switchingfrequency should be set to certain values depending on theduty cycle characteristics of the motor. This ratio should beequal or less than unity under dynamically changing duty cycleoperations to accurately track the dynamic changes. On theother hand, it can be set to a value larger than unity to increasethe resolution where the duty cycle profile is mainly constant. Inbrief, the tradeoff between precision, processing speed, and testduration plays a key role while determining the test conditions.

IV. EXPERIMENTAL RESULTS

A number of identical induction motors are modified to testthe bearing, broken rotor bar, and eccentricity faults. The faultsare obtained by simply drilling the bearing outer race and rotorcage bars and off-centering the bearing house, respectively.A conventional test bed is used in order to validate the proposedmethod to detect the stator current fault signature componentsof the three-phase induction machine. A 3-hp induction motoris loaded by a dc generator and is driven by a custom-designedSemikron inverter, as shown in Fig. 2(a) and (b), respectively.

The inverter control and the online fault diagnosis are per-formed by a 32-bit, 150-MHz fixed-point TMS320F2812 DSP.A signal conditioning board that includes the voltage and cur-rent sensors is designed and connected to the data acquisitionboard through the voltage amplifiers to scale the magnitudeand low-pass filters to set the frequency bandwidth to a correctrange. In order to obtain raw currentvoltage data, a 1.25-MS/s,16-bit resolution data acquisition card is used for offline tests.A 16-bit analog-to-digital converter (ADC) at a 256-kHz SR760FFT spectrum analyzer is used to monitor the real-time currentand voltage spectrums.

A. Ofine Experimental ResultsIn order to confirm the precision of the lock-in detector, a

motor with bearing outer raceway defects is tested. An artificialdefect is obtained by simply drilling the outer raceway using asmall bit made from a hard metal. In fact, the most challengingfault detection is reported to be in the case of a bearingfault due to the very low amplitude of fault signatures. Thechallenges that are encountered are not only the small bearingfault signatures but also the proximity between the floor noiselevel and the signature level. Therefore, computation of faultsignatures becomes quite prone to noise disturbance. A part ofthe healthy and faulty motor line current spectrums are recordedby the FFT analyzer to show a few bearing fault signatures at143.3, 167.5, 383.3, and 395.4 Hz, as shown in Fig. 3(a) and (b).At the same time, the line current data are recorded by thedata acquisition board for offline data analysis. These current


Fig. 2. Experimental setup. (a) DSP, signal conditioning system, and inverter.(b) Motorgenerator setup.

data are processed in Matlab by running the lock-in detectoralgorithm at the maximum correlation degree point in orderto minimize the noise effect. Each result is normalized withrespect to the fundamental component and then compared to thefault signatures measured by the FFT analyzer. The Hammingwindow is used to improve the accuracy of estimation. Thecomputed fault signature magnitudes using the lock-in detectorare quite satisfactory and close to the reference FFT signatureswith a very high proximity, as given in Table III. Four differentouter race fault frequencies and related signature amplitudes aregiven for both healthy and fault motor in Table III.

The fault decisions are made in a straightforward manner bysimply comparing the normalized fault signature amplitudeswith the predetermined thresholds obtained during the com-parative experiments for each fault. As another advantage ofthis method, normalized fault signature values are not relativefault indicators but are highly precise fault signature amplitudevalues, as experimentally verified in Table III. Therefore, adirect threshold comparison is employed to determine the statusof the fault and roughly classify it as follows: a signature lessthan 60 dB means good, between 60 and 40 dB meanstolerable eccentricity, and higher than 40 dB means severeeccentricity. The broken bar and bearing fault thresholds arealso determined in the same way according to the experimen-tal results obtained from identical healthy and faulty motors

Fig. 3. Experimental results. Normalized outer race bearing fault signaturesin the line current spectrum at (a) 143.3 and 167.5 Hz and (b) 383.3 and395.4 Hz.

TABLE IIINORMALIZED EXPERIMENTAL RESULTS

using the FFT analyzer. Depending on the application, a moregeneral and realistic threshold standard can be developed usingstatistical machinery failures and is used to give an indicationof overall health, as illustrated in [24]. In Section IV, it isexperimentally shown that the amplitude of the fault signa-tures dynamically changes depending on the operating point.Therefore, the shortcomings of a constant threshold can becompensated using an approximated adaptive threshold, whichis a function of the operating point, i.e., torque and speed.In [14], an adaptive threshold that varies as a fixed percentage ofthe fundamental frequency component (in this case, it is chosenas 2%) is proposed for automatic detection. In order to come upwith a complete dynamic behavior analysis of fault signatures,all the operating points should be taken into consideration,


TABLE IVNORMALIZED EXPERIMENTAL RESULTS

including low-speed region, saturation region, etc., which isconsidered as future work in this paper.

The noise immunity of the lock-in detector is tested byinjecting white noise to the experimentally obtained line currentat constant low-order THD in each step. The outer race faultsignature at 143.3 Hz is measured as 82.93 dB by the lock-indetector when the inherent experimental setup noise is on theline current. The effects of the noise on the lock-in detectorfindings are given in Table IV. In this analysis, graduallyincreasing white noise is added to the line current of the motorthat has an outer race bearing fault. In each level, the bearingfault signature is measured and recorded. It is shown in Table IVthat even if the amplitude of injected noise is several timeshigher than the inspected signature, the lock-in provides quitesuccessful results with acceptable errors.

B. Online Experimental Results

Similar tests are repeated online using the TMS320F2812DSP, which is employed for both inverter control and fault sig-nature detection. When using the DSP core for both purposes,the fault code is embedded into the main control algorithm asa subroutine that processes the measured current data in realtime. The number of data is chosen to be the same as thesampling frequency to synchronize the fault subroutine withthe motor control algorithm, which can typically be adjustedbetween 4000 and 20 000 depending on the applications. Onecan decrease the number of data to get a faster response inorder to track the fault signature updates during transients. Onthe other hand, resolution enhancement beyond 20 000 datahas negligible benefit for this application. Due to the lowcomputational burden of the proposed algorithm, a number offault signatures can be estimated in parallel and reported tothe user interface. After running the main control algorithm,the time period remaining until pulsewidth-modulation (PWM)counter underflow interrupt can be used for multisignatureprocessing in parallel and resolution enhancement purposes.In the arctangent mode, the data are processed in real timewithout buffering to get rid of the large-size memory require-ment. In the phase scanning mode, the highest correlationvalue is stored to compare it with the upcoming measuredline current data correlation in order to detect the maximumcorrelation. The fault signature frequencies are updated in eachswitching period using the fault models given in Appendix D.The stator frequency value used to update fault models is aknown parameter in both open- and closed-loop motor controlalgorithms. The rotor speed is either measured using the en-coder or estimated in most commercial ac drive applications.A 2048-pulse/revolution optical encoder is integrated to our

setup, as shown in Fig. 2. When the switching frequency is20 kHz, it takes 1 s to process 20 000 data and run arctan-gent method using the DSP. One should notice that this 1 scovers motor control algorithm execution, lock-in execution,and the free time periods until the PWM underflow interrupt.Instead of synchronizing the fault algorithm with the switchingfrequency, one can set the ADC for continuous conversion andutilize the whole free time in the switching period after theexecution of the motor control program for fault analysis toshorten the fault detection time. On the other hand, when thephase angle scanning method is run, it typically takes at most200 s to detect the fault using the DSP. Again, this time canbe shortened as previously mentioned. Because the embeddedADC in TMS320F2812 has 12 bits, the quantization errorsprevent sensing signals that are less than 65 dB. For furtherprecision, the system should be supported by an integrated or anembedded higher resolution ADC. The experiments are carriedout by testing broken rotor bar and eccentric motors.1) Lock-In for Systems With Slow Dynamics: In order to

realize online lock-in of the reference signal and fault signature,a few ways are possible. If the inspected motor is run atsteady state for periods or has slow dynamics, then phase anglescanning can be employed to find the phase angle of the faultsignature, as detailed in Appendix B. By simply incrementingthe phase angle of the reference signal generated in the DSP,one can find the minimum phase angle difference between theline current and the reference signal, where the correlationis maximized and the noise effects is minimized. Once thispoint is detected, the rest of the fault diagnosis process can becontinued at this point and is updated at each phase-differencezero crossing. By employing this method, the minimum phasedifference can be obtained at most in a couple of minutes withhigh precision. Shortening this time is possible, as mentioned inthe previous section. The correlation maximization and lock-inmechanism is depicted in Fig. 4 to visualize the algorithm runby the DSP.

Fig. 4(a) shows that the correlation degree of the faultcomponent is set to maximum at zero crossing of the phasedifference and fixed at the same point until the DSP detects thenext zero crossing for maximum noise suppression. A similarprocess is repeated for the fundamental component to normalizethe fault component, as shown in Fig. 4(b). Despite the de-crease in precision, phase angle scanning can be accelerated byincreasing the phase angle increments of the reference signalin each drive control cycle. Since the period of phase anglescanning is in the range of minutes, this method is mostlyappropriate for steady-state operations.

The results obtained in Fig. 5 using the DSP with 12-bitADCs are very close to the results obtained from the FFTspectrum analyzer that has two DSP cores and a 16-bit ADCwith a sampling rate of 256 kHz. The left sideband signatures ofan eccentric motor are measured to be 39.24 and 38.98 dBusing the FFT analyzer and the DSP, respectively. Fig. 5(a)shows the variation of the eccentricity sideband in the timedomain, and Fig. 5(d) shows the FFT analyzer result in the fre-quency domain. It is noticed that the fault signature magnitudeis not remarkably affected by the switching frequency of theinverter. Since this measurement is taken when the motor is


Fig. 4. Experimental results. (a) Phase difference between the reference signaland the fault component, as well as normalized left eccentricity sidebandcorrelation degree in real time. (b) Phase difference between the referencesignal and the fault component, as well as normalized fundamental componentcorrelation degree in real time.

running at steady state, the ratio of the number of data to theswitching frequency is mostly taken as unity, which providessufficient resolution. The correlations of the fault componentand the fundamental component with respect to the referencesignals generated by the DSP are given in Fig. 5(b) and (c). Itis possible to obtain smoother waveforms by simply processingmore data. These online experimental results confirm that theproposed method can successfully be adapted to real-timeapplications.2) Autotuning of Lock-In for Fast Dynamic Systems: In

order to examine the motors, the duty cycles of which arecontinuously fluctuating, an alternative autotuning algorithmis employed, as briefly mentioned in Section II as the secondmethod. In this method, the phase angle difference betweenthe reference signal and the fault signature can be calculatedusing the arctangent relation of the cross correlation and theautocorrelation at each fault signature detection cycle, as givenin Appendix C. Apart from the previous method, the phase an-gle of the reference signal is continuously updated each secondto obtain a zero phase difference between the reference signalgenerated by the DSP and the analyzed fault signature. Due tothis method, it is possible to track the fault signature not only

Fig. 5. Experimental results. (a) Left eccentricity sideband in real time.(b) Correlation degree between the reference signal and the fault component.(c) Correlation degree between the reference signal and the fundamentalcomponent. (d) FFT analyzer output.


Fig. 6. Experimental results. (a) Normalized fundamental and right eccentric-ity sideband correlation degree in real time. (b) FFT analyzer output.

at steady state but also during transients. Therefore, one canfollow the dynamic characteristics of fault signatures duringacceleration, deceleration, and loadings. If there are multiplemeasurements to be made, particularly during transients, thenumber of processed data should be optimized. Typically, a fewdrive control cycles data processing time is enough at steadystate, or one-half cycle will be sufficient during transients. Sincethe results are normalized, computation time will not affectthe relative amplitude of the fault signature or the correlationdegree. Note that less than half a control cycle significantlydegrades precision; therefore, one can utilize the whole freetime in the switching frequency period by setting the ADCfor continuous conversion and running this method independentfrom control-purpose software interrupts in the DSP program.

In Fig. 6, continuous tracking of the right eccentricity side-band is given. The phase lock-in is achieved in each drive con-trol cycle by the autotuning algorithm. Using phase-sensitivedetection, the right eccentricity sideband is measured as lessthan 1 dB error when compared to the FFT analyzer results.

In Fig. 7, the real-time fault signature tracking is shown.The purpose of this test is to demonstrate how fast and pre-cise the lock-in detector can adapt itself to a new operatingpoint. In the first test, an eccentric motor is loaded from noload to 0.33-p.u. load. Because the heavy loading might maskthe eccentricity fault signatures due to inertia damping effect,the motor is lightly loaded. In Fig. 7(a), the right eccentric-ity sideband variation in time is given. The test is startedwhen the motor is running at no load and then loaded from

Fig. 7. Experimental results. (a) Normalized right eccentricity sideband cor-relation degree in real time under no load and 0.33-p.u. load. (b) Normalizedbroken bar fault right sideband correlation degree in real time under 0.8- and1.1-p.u. load.

t = 80 s to t = 155 s. In general, the fundamental compo-nent is measured for normalization, but here, it is depicted torepresent the load torque. In Fig. 7(b), similar test results areshown for the broken bar fault right sideband variation. In thiscase, the test is started when the motor is running at 0.8-p.u.load and switched to 1.1-p.u. load for a while. These resultsprove that the proposed method has a powerful real-time faultsignature tracking capability. Because the excitation frequencyis available in the control algorithm and the rotor frequency ismeasured or estimated, these parameters are used to update thefault signature frequencies given in (D1) and (D2) in real timeat various operating points.

V. CONCLUSION

In this paper, a simple noise-immune real-time fault signaturedetection tool is presented. Since this method can easily beimplemented using the industrys general-purpose microcon-trollers without any additional hardware, personal computer,filters, and large-size memory, it can be adapted to single-and multiphase drive systems. The accuracy of the proposedmethod is experimentally tested, and the results are comparedto those of a commercial FFT analyzer. Furthermore, the noisesuppression capability of this method is verified by injecting


various amplitude white noises to the line current. All the testresults confirmed that the phase-sensitive lock-in detector is anexcellent and promising tool for drive-embedded real-time faultdetection systems.

APPENDIX AINTERPRETATIONS OF (5) AND (6) AND THE PROOF OF (7)

In this appendix, we first derive the general expressionfor the correlation function r[] between the noisy faultsignal, i.e.,

Iin[n] = Ifault cos(wfaultn + fault)

+

Inoise cos(wnoisen + noise) (A1)

and the reference signal, i.e.,

Iref [n] = Iref cos(wrefn + ref). (A2)

Then, what (5)(7) correspond to will be explained in thisframework. Using (1), we obtain (A3), shown at the bottom ofthe page.

The frequency of the generated reference signal is set to bethe same as the fault signal frequency. Thus, we obtain (A4),shown at the bottom of the page.

Interchanging the limit and sum operations with the mul-tiplications and other summation, we obtain (A5), shown atthe bottom of the page. We note here the following importantresult:

limN

12N

Nn=N

cos(w1n + w2 + )

={

cos(w2 + ), w1 = 00, otherwise (A6)

which basically stems from the fact that the summation overany sinusoidal function is finite no matter how big the sum-mation interval 2N is. Therefore, out of the noise terms in the

rtemp[] = limN

12N

Nn=N

[Iref cos(wrefn + ref)Ifault cos (wfault(n ) + fault)

+ Iref cos(wrefn + ref)

Inoise cos (wnoise(n ) + noise)]

= limN

12N

Nn=N

[IrefIfault cos(wrefn wfaultn + wfault + ref fault)

+ IrefIfault cos(wrefn + wfaultn wfault ref + fault)+

IrefInoise [cos(wrefn wnoisen + wfault + ref noise)

+ cos(wrefn + wnoisen wfault + ref + noise)]]

(A3)

r[] = rtemp[]|wref=wfault

= limN

12N

Nn=N

[IrefIfault cos(wfault + ref fault) + IrefIfault cos(2wfaultnx wfault ref + fault)

+

IrefInoise [cos ((wref wnoise)n + wfault + ref noise)

+ cos ((wref + wnoise)n wfault + ref + noise)]]

(A4)

r[]= IrefIfault limN

12N

Nn=N

cos(wfault+reffault)+IrefIfault limN

12N

Nn=N

cos(2wfaultnwfaultref+fault)

+

IrefInoise

[lim

N1

2N

Nn=N

cos ((wref wnoise)n+wfault+refnoise)

+ limN

12N

Nn=N

cos ((wref+wnoise)nwfault+ref+noise)]

(A5)


summation of (A5), only the ones that have wnoise wref =wfault are going to survive the limit process. As a result

r[] = IrefIfault cos(wfault + ref fault)+IrefInoise cos(wfault + ref noise). (A7)

Here, in order to maximize the fault component of the corre-lation function r[] by matching the phase fault, two differentapproaches can be followed.

1) Keep the phase ref fixed and evaluate r[] for different values. Then, the optimal phase value opt is given by

opt = ref + wfault argmax

r[].

2) Set = 0 and evaluate r[0] for different values of ref .Then, the optimal phase value opt is given by

opt = argmaxref

r[0].

In this case, it is also possible to use a second referencesignal, i.e.,

Isref [n] = Iref sin(wrefn + ref)

for which, with a similar analysis as above, the correlationfunction can be obtained as

rs[] = IrefIfault sin(wfault + ref fault)+IrefInoise sin(wfault + ref noise). (A8)

Then, the optimal phase value opt is given by

opt = ref arctan rs[0]r[0]

.

This paper uses the second approach and set = 0 in (5)and (6) and, finally, in (7). Equations (5) and (6) are specialcases of (A3) and (A4), respectively, with = 0 and withouta summation over n and a limit. Note that (7) is the same as(A7) with = 0. It is important to emphasize that averaging thesamples is just one way of getting rid of the ac terms in themultiplications of the cosines. A similar low-pass filtering witha filter whose coefficients sum up to unity would do about thesame, as already mentioned in Section II.

APPENDIX BPSEUDOCODE LOCK-IN: PHASE SCAN

Select wref : The reference frequencySelect Ng: The number of phase values in the phase grid0 < Select Ns: The number of data samples for making theevaluation of each phase value in the phase gridSet the phase value = 0

Set the data counter n = 1Set the phase counter p = 1Set the maximum correlation value rmax = Set the phase value that gives the maximum correlation =0Set the correlation value r = 0() For each piece of current data i[n] acquired

r = r +i[n] cos(wrefn + )

Ns

If n == NsIf r > rmax

rmax = r =

End of IfSet the data counter n = 1Set the correlation value r = 0If p == Ng

Stop: The optimal phase is given by .Else

Set = + (/Ng)p = p + 1Go to ()

End of IfElse

n = n + 1Go to ()

End of IfEnd of For.

APPENDIX CPSEUDOCODE LOCK-IN: ARCTANGENT

Select wref : The reference frequencySelect Ns: The number of data samples for obtaining theoptimal phase differenceSet the data counter n = 1Set the phase value that gives the maximum correlation = 0Set the correlation value rcos = 0Set the correlation value rsin = 0() For each piece of current data i[n] acquired

rcos = rcos +i[n] cos(wrefn)

Ns

rsin = rsin +i[n] sin(wrefn)

Ns

If n == NsStop: The optimal phase is given by =arctan(rsin/rcos)

Elsen = n + 1Go to ()

End of IfEnd of For.


APPENDIX DSOME FAULT-RELATED IDENTITIES

The frequency of the eccentricity fault sidebands is

feccentricity = f1

[1m

(1 sp/2

)], m = 1, 2, 3, . . .

= f1 m fr. (D1)

The frequency of the broken rotor bar fault sidebands is

fb = (1 2k s)f1, k = 1, 2, 3, . . . (D2)

where m and k are integers, s is the per-unit slip, f1 is thefundamental excitation frequency, fr is the mechanical rotationfrequency, and p is the number of poles.

REFERENCES[1] G. B. Kliman, R. A. Koegl, J. Stein, R. D. Endicott, and

M. W. Madden, Noninvasive detection of broken rotor bars in operatinginduction motors, IEEE Trans. Energy Convers., vol. 3, no. 4, pp. 873879, Dec. 1988.

[2] S. Nandi, H. A. Toliyat, and X. Li, Condition monitoring and fault diag-nosis of electrical machinesA review, IEEE Trans. Energy Convers.,vol. 20, no. 4, pp. 719729, Dec. 2005.

[3] M. E. H. Benbouzid and G. B. Kliman, What stator current processing-based technique to use for induction motor rotor faults diagnosis? IEEETrans. Energy Convers., vol. 18, no. 2, pp. 238244, Oct. 2003.

[4] M. J. Devaney and L. Eren, Detecting motor bearing faults, IEEEInstrum. Meas. Mag., vol. 7, no. 4, pp. 3036, Jun. 2004.

[5] J. H. Jung, J. J. Lee, and B. H. Kwon, Online diagnosis of induction mo-tors using MCSA, IEEE Trans. Ind. Electron., vol. 53, no. 6, pp. 18421852, Dec. 2006.

[6] J. F. Martins, V. F. Pires, and A. J. Pires, Unsupervised neural-network-based algorithm for an online diagnosis of three-phase induction motorstator fault, IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 259264,Feb. 2007.

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[8] B. Akin, U. Orguner, H. A. Toliyat, and M. Rayner, Low-cost motordrive-embedded fault diagnosisA simple harmonic analyzer, in Proc.IEEE APEC Conf., Anaheim, CA, Feb. 2007, pp. 243249.

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[10] F. Cupertino, E. Vanna, L. Salvatore, and S. Stasi, Analysis techniquesfor detection of IM broken rotor bars after supply disconnection, IEEETrans. Ind. Appl., vol. 40, no. 2, pp. 526533, Mar./Apr. 2004.

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[12] A. Bellini, G. Franceschini, and C. Tassoni, Monitoring of inductionmachines by maximum covariance method for frequency tracking, IEEETrans. Ind. Appl., vol. 42, no. 1, pp. 6978, Jan./Feb. 2006.

[13] A. R. Mohanty and C. Kar, Fault detection in a multistage gearbox bydemodulation of motor current waveform, IEEE Trans. Ind. Electron.,vol. 53, no. 4, pp. 12851297, Aug. 2006.

[14] S. Rajagopalan, T. G. Habetler, R. G. Harley, J. A. Restrepo, andJ. M. Alle, Non-stationary motor fault detection using recent quadratictimefrequency representations, in Conf. Rec. IEEE IAS Annu. Meeting,Tampa, FL, Oct. 2006, pp. 23332339.

[15] S. M. A. Cruz, H. A. Toliyat, and A. J. M. Cardoso, DSP implementationof the multiple reference frames theory for the diagnosis of stator faults ina DTC induction motor drive, in Proc. IEEE SDEMPED Conf., Atlanta,GA, Aug. 2003, pp. 223228.

[16] R. Wieser, C. Kral, F. Pirker, and M. Schagginger, On-line rotor cagemonitoring of inverter-fed induction machines by means of an improved

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[19] A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing.Englewood Cliffs, NJ: Prentice-Hall, 1989.

[20] S. S. Haykin and B. Van Veen, Signals and Systems. Hoboken, NJ:Wiley, 1998.

[21] V. Ingle and J. Proakis, Digital Signal Processing Using MATLAB.Pacific Grove, CA: Brooks/Cole, 2000.

[22] O. A. Mohammed, N. Y. Abed, and S. Ganu, Modeling and characteri-zation of induction motor internal faults using finite-element and discretewavelet transforms, IEEE Trans. Magn., vol. 42, no. 10, pp. 34343436,Oct. 2006.

[23] Z. Ye, B. Wu, and A. Sadeghian, Current signature analysis of inductionmotor mechanical faults by wavelet packet decomposition, IEEE Trans.Ind. Electron., vol. 50, no. 6, pp. 12171228, Dec. 2003.

[24] C. M. Riley, B. K. Lin, T. G. Habetler, and G. B. Kliman, Stator cur-rent harmonics and their causal vibrations: A preliminary investigationof sensorless vibration monitoring applications, IEEE Trans. Ind. Appl.,vol. 35, no. 1, pp. 9499, Jan./Feb. 1999.

Bilal Akin (S03M08) received the B.S. and M.S.degrees in electrical engineering from Middle EastTechnical University, Ankara, Turkey, in 2000 and2003, respectively, and the Ph.D. degree in electricalengineering from Texas A&M University, CollegeStation, in 2007.

He was an R&D Engineer from 1999 to 2000 withTubitak Bilten, Ankara, and from 2005 to 2007 withToshiba Industrial Division, Houston, TX. Since2007, he has been a Postdoctoral Research Associatewith Texas A&M University. His research interests

are advanced control methods in motor drives, fault diagnosis of electricmachinery, machine design, and DSP-based industrial applications.

Umut Orguner (S99M07) received the B.S.,M.S., and Ph.D. degrees from Middle East TechnicalUniversity, Ankara, Turkey, in 1999, 2002, and 2006,respectively, all in electrical engineering.

Between 1999 and 2007, he was with the De-partment of Electrical and Electronics Engineering,Middle East Technical University, as a Teachingand Research Assistant. Since January 2007, he hasbeen a Postdoctoral Associate with the Division ofAutomatic Control, Department of Electrical Engi-neering, Linkping University, Linkping, Sweden.

His research interests include estimation theory, multiple-model estimation,target tracking, and information fusion.


Hamid A. Toliyat (S87M91SM96F08) re-ceived the B.S. degree from Sharif University ofTechnology, Tehran, Iran, in 1982, the M.S. de-gree from West Virginia University, Morgantown,in 1986, and the Ph.D. degree from the Univer-sity of Wisconsin-Madison in 1991, all in electricalengineering.

In 1991, he joined the faculty of Ferdowsi Uni-versity of Mashhad, Mashhad, Iran, as an AssistantProfessor of electrical engineering. In March 1994,he joined the Department of Electrical and Computer

Engineering, Texas A&M University, College Station, where he is currentlythe Raytheon Endowed Professor. He has supervised more than 36 graduatestudents; published more than 310 technical papers, of which 92 papers arein IEEE TRANSACTIONS; and presented more than 50 invited lectures allover the world. He is the author of DSP-Based Electromechanical MotionControl (CRC, 2003) and the coeditor of Handbook of Electric Motors2nd Edition (Marcel Dekker, 2004). His main research interests and experienceinclude analysis and design of electrical machines, variable-speed drives fortraction and propulsion applications, fault diagnosis of electric machinery, andsensorless variable-speed drives. He is also an inventor and has ten issued andpending U.S. patents in these fields.

Dr. Toliyat is a member of Sigma Xi. He is an Editor of the IEEETRANSACTIONS ON ENERGY CONVERSION and was an Associate Editor ofthe IEEE TRANSACTIONS ON POWER ELECTRONICS. He is also the Chairof the Industrial Power Conversion Systems Department of the IEEE IndustryApplications Society (IAS). He was the General Chair of the 2005 IEEEInternational Electric Machines and Drives Conference, San Antonio, TX. Heis a Professional Engineer in the State of Texas. He was the recipient of thefollowing awards: the prestigious Cyrill Veinott Award in ElectromechanicalEnergy Conversion from the IEEE Power Engineering Society in 2004; theTexas Engineering Experiment Station Fellow Award in 2004 and 2006; theOutstanding Professor Award in 2005, the Distinguished Teaching Award in2003, the E.D. Brockett Professorship Award in 2002, the Eugene Webb FacultyFellow Award in 2000, and the Texas A&M Select Young Investigator Award in1999, all from Texas A&M University; the Space Act Award from the NationalAeronautics and Space Administration in 1999; the Schlumberger FoundationTechnical Award in 2001 and 2000; the Prize Paper Award from the IEEE PowerEngineering Society in 1996 and 2006; and Third Prize Paper Award from theIEEE IAS in 2006.

Mark Rayner, photograph and biography not available at the time ofpublication.

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