Study on Location Algorithms of Beamforming based on MVDR · Study on Location Algorithms of...

Appl. Math. Inf. Sci.7, No. 6, 2455-2466 (2013) 2455

Applied Mathematics & Information SciencesAn International Journal

http://dx.doi.org/10.12785/amis/070639

Study on Location Algorithms of Beamforming based onMVDRAidong Deng1,∗, Hang Tong2, Jianeng Tang3, Hao Cao4, Kang Qin1 and Xi Yan1

1 National Engineering Research Center of Turbo-generator Vibration,Southeast University, Nanjing 210096, China2 Huadian Electric Power Science Research Institute, Hangzhou 310030,China3 College of Engineering, Huaqiao University, Quanzhou, Fujian 362021, China4 Hunan Electric Power Corporation Research Institute, Changsha 410007,China

Received: 3 Apr. 2013, Revised: 7 Aug. 2013, Accepted: 8 Aug. 2013Published online: 1 Nov. 2013

Abstract: Acoustic emission is an effective method of locating the rubbing fault. In order to solve the problem that satisfactory locationaccuracy is difficult to obtain because of the waveform distortion causedby signal propagation during the application of time delayestimation method in acoustic emission position estimation, beam-forming technique is applied to acoustic emission source location.Simulation studies have been made on the performance of near-field time-domain and frequency domain beam-forming in the locationof rubbing acoustic emission source. The paper adopts the wideband signal minimum variance distortionless response (MVDR) locationestimation method based on sub-band decomposition to avoid the problems of poor noise immunity and low resolution of traditionalbeam-forming. Decompose each group of array signals into a numberof sub-band of equal length, conduct Fourier transformation oneach sub-band to calculate the covariance matrix of each frequency component, get the two-dimensional joint distribution functionof the MVDR output power of each sub-band with respect to the distance and azimuth angle, then synthesize the MVDR power ofwideband signal, obtain the azimuth spectrum estimation of all frequency bands, and finally get the location of the acoustic source bythe peak point. The experimental results show that this algorithm can accurately identify the rubbing fault location.

Keywords: Acoustic emission, beamforming, MVDR, rubbing, location.

1 Introduction

Rotating machinery rubbing fault diagnosis techniquebased on acoustic emission (AE) has attracted more andmore attention from scholars in recent years. Acousticemission technique can not only determine the occurrenceof rotor rubbing fault, but also quickly find the rubbinglocation by AE source location technique which providesimportant information for the analysis of the fault causeand the troubleshooting. Sato [1] simulated thecontinuous rubbing state on a 350MW steam turbine unit,he pointed out that characteristic parameters got bydetecting AE envelope signal can be used as generationindicators of rubbing. Suzuki [2] used wavelettransformation to seek event counts or event count rate ofcharacteristic parameters of AE signal, he also used thismethod for rubbing fault detection of rotating machinery.Mba [3] studied the propagation of AE signal in largesteam turbine generator unit by choosing the low pressurerotor of a 550MW steam turbine as the detection object.

Experiment results showed that AE signal waveformgenerated at any point of the turbine shaft can be detectedat both ends of the shaft. Besides, through the rubbinglocation experiment, he pointed out that amplitudemodulation of AE signal provides important informationof interaction force of the rotor and the stator, whichprovides an effective method for rubbing location. Hall[4] presented a diagnosis of continuous rotor-statorrubbing based on the experiment on an operational500MW turbine unit via high frequency AEmeasurement, and calculated the rubbing location byusing the phase delay between adjacent AE modulations.Time delay estimation algorithm is generally adopted tocalculate the time difference of arrival (TDOA) inacoustic emission location, and determine the location ofsound emitting source according to the geometricstructure of the sensor. Omologo [5] proposed across-power spectrum phase delay estimation algorithm,achieving precise location of point acoustic sources in

∗ Corresponding author e-mail:[email protected]

c© 2013 NSPNatural Sciences Publishing Cor.

http://dx.doi.org/10.12785/amis/070639

2456 A. Deng et al: Study on Location Algorithms of Beamforming...

three-dimensional space under different conditions ofnoise and echoes; Yegnanarayana [6] extracted short-termspectral characteristics by dividing two time series ofhomologous sound signals into several segments of equallength, implemented time delay estimation on each set ofsegments based on this and he got better location effectthan that of generalized cross-correlation. Deng [7]proposed generalized cross correlation (GCC) time delayestimation of the best linear fraction Fouriertransformation domain filtering based on the samefractional order factor and different fractional orderfactor. Furthermore, to solve the problem that themaximum related point can not be obtained due towaveform variation caused by frequency dispersion effectin the propagation of acoustic emission signal, hepresented improved signal processing methods ofsegmented correlation multiplication processing andsegmented correlation exponential transformationprocessing. Ciampa [8] proposed an algorithm based onwavelet analysis and a Newton-based optimizationtechnique to identify the real-time acoustic emissionlocation, this method overcame the drawbacks of thetriangulation method in terms of estimating a priori groupvelocity and the need to find the best time-frequencytechnique for time-of-arrival determination. Dirk Aljets[9] used three sensors installed in a triangular array toestablish the direction from the sensor array to the AEsource by analyzing the arrival times of A0 component ofthe signal to the three sensors, the distance can also beevaluated by the separation of S0 and A0 mode at eachsensor respectively. To sum up, these algorithms based ontime delay estimation is to get the sample time delay bycalculating the time domain cross-correlation of differentsensor signals, and then calculate the spatial location ofacoustic source according to acoustic signal propagationtheory and array position. They require that the obtainedtime delay of sensors must be very accurate. However,these algorithms are largely restricted in rotor systemstructure. The reason is as follows: in rotor system, it isusually a length of non-continuous andnon-single-medium complex propagation path from therubbing source to the sensor, the rubbing motivatedmulti-modal AE wave has a serious signal distortion dueto the influence of many effects such as boundaryconditions, frequency dispersion and mode conversion,etc. in the propagation process. The map between the AEsource and the AE signals received by the sensor isnonlinear, the signal reaching the sensor is asuperposition of multimode waves with noise fromdifferent paths, and every channel sensor will collect poorcorrelation waveforms so that it is difficult to calculate theaccurate arrival time difference [10]. Beam-forming is asignal processing technology measuring space radiationacoustic field information by sensor array [11,12]. Thebasic idea is that do the weighted sum processing on eachelement output of the array, and according to differentoptimization criteria, make the array output producedifferent responses to signals from different spatial

directions so as to realize that the array beam points to theexpected signal and the null points to the interferingsignal. Beam-forming technology can not only estimatethe acoustic source direction of arrival (DOA), but alsoachieve the precise location of near-field acoustic source.Compared with the traditional time difference locationmethod, beam-forming method has many advantages suchas little impact of the channel attenuation, convenientsensor placement, less sensors, lower sampling rate andsimultaneous location of multiple acoustic sources. It hasbeen widely used in military technology fields such asradar, propagations, electronic warfare, sonar as well asaerospace technologies. AE location technology based onbeamforming also is also studied in recent years. For thedamage of large structures in civil engineering, McLaskey[13] implemented nondestructive testing researches basedon acoustic emission beamforming method, their studyresults showed that beamforming methos, compared withtraditional methods, is more economical and practicalbecause it is convenient for sensor placement, it canreduce the number of sensors to be used, it can reduce thesynchronization requirements of arrival time in allchannels and it can adopt a relatively lower sampling rate.He [14] conducted researches on acoustic emission signalpropagation characteristics which proved the feasibilityofbeamforming in acoustic emission signal processing bythe use of guided wave theory. Besides, he used near-fieldacoustic emission beamforming method to locaterotor-stator rubbing fault and successfully identified itslocation. For problems of poor noise immunity and lowresolution of traditional beam-forming method, this paperadopts the minimum variance distortionless response(MVDR) [15,16,17] beam-forming method to improvethe location accuracy and enhance the noise interferencesuppression performance of rubbing acoustic emissionsource location. At the same time, according to thewideband characteristics of rubbing acoustic emissionsignals, this paper adopts wideband near-field signalMVDR beam-forming algorithm based on sub-banddecomposition. This paper has analyzed the performanceof traditional beam-forming method and widebandnear-field signal MVDR algorithm based on sub-banddecomposition in rubbing acoustic emission sourcelocation through simulation and experiments.

2 Traditional near-field beam-forming

Beam-forming method can be classified into far-field andnear-field according to the distance between the acousticsource and the array. The far-field beam-forming methodbases on the fact that the signal source is located ininfinity, the incident signal can be considered a planewave, and there is no energy loss of the signal in thepropagation process. And the near-field beam-formingmethod bases on the fact that the acoustic source is apoint source which is the source point of divergentpropagation of the signal to the space around, there is an


Appl. Math. Inf. Sci.7, No. 6, 2455-2466 (2013) /www.naturalspublishing.com/Journals.asp 2457

acoustic energy attenuation in the propagation process,and the longer the distance is, the greater the attenuationwill be. Attenuation of acoustic emission is very obviousin the propagation process, so sensors shall be placed nearthe acoustic emission source as much as possible, allthese make it difficult to use the assumption of far-field,thus it must use near-field beam-forming method. In thefar-field case, it is usually used for the far-field acousticsource azimuths estimate. But it is different in near-fieldconditions because the angles and distances betweendifferent sensors on the same array and the point source(i.e. the focused acoustic source) are different, we need toestimate the angle and distance between the point sourceand a sensor. The beam-forming schematic diagram ofnear-field of linear array is indicated as Figure 1, and M isthe element number.

Fig. 1: Near-field beam-forming schematic diagram oflinear array

Select sensor 1 as the reference point in this modeland assume that the distance between the focusingacoustic source point and the reference point is r1, theazimuth is 1. Then the distance difference between thefocusing acoustic source point to the ith sensor and tosensor 1 is:

∆ r i = r1−√

r21+(ir )2−2irr 1cosθ1 i = 2,3, · · ·M (1)

Wherer1 in the above equation stands for the distancebetween the focused acoustic source point and sensor 1,and r stands for the distance between two adjacent arrayelements of linexar array. Set the propagation speed ofacoustic emission in the material as c, the time delays ofthe received signals of each sensor relative to thereference point are:

τi (θ1, r1) =r1−

√

r21+(ir )2−2irr 1cosθ1

ci = 2,3, · · ·M

(2)

Then, the beam-forming algorithm based on time-domainweighted summation is:

b(θ1, r1, t) =M

∑i=1

wiA(r i)xi (t − τi (θ1, r1)) (3)

The xi in the above equation stands for the signalmeasured by the ith array element,wi stands for the itharray element weighting coefficient,wi = e− j2π f τi(θ1,r1),in this equation,f stands for signal frequency.τi (θ1, r1)stands for the time delay of the ith sensor with respect tothe reference point when it is focused to some point. Forthe target source, we can adjust the signals to the samewavefront viaτi (θ1, r1) before the addition of signals i.e.there shall be a cophasal superposition of signals after thetime delay compensation, thus beam output in thisdirection is the largest and the beam output will becomescorrespondingly smaller when focused on other pointswhich plays a spatial filtering role.A(r i) stands for theenergy attenuation function of acoustic emission signalson the test rig guided-wave plate, this function is notapplied only to a specific frequency or a certain wavemode, but a wave group. Method of calculation is: set alinear sensor array of equidistance on the guided-waveplate, the first point of the array is the rubbing sourcewhich will be used to simulate the first rubbing acousticemission event, collect acoustic emission signals fromeach array element respectively and calculate the totalacoustic emission energy of all array elements in the sameperiod of time, we can get the energy attenuation ratio ofthe rubbing source and each point of different distance,then the energy attenuation function will be got by curvefitting. The significance of Eq. (3) lies in: the energyspectrum concentrated on some points can be obtained bytime delaying, weighting and summing operations on theoutput of each array element. If a focus point overlaps thetarget source, adjust the output signals of array elementsright to the same wave via time delay compensation oneach element i.e. the focus point signals reach the arraywith the same phase so that it will generate a maximumvalue of response in the energy spectrum forming a majorlobe, the direction of the major lobe is the direction of thetarget source. The above algorithm assumes that thesource signal is of a single frequency and ignores thenoise influence in the weighted summation process. Infact, rubbing acoustic emission source signals are thewave packet including large number of frequencycomponents mixed with noises during the propagation ofsignals. Under such circumstances, it means that there aremany source signals with different frequencies in thespace, the signal received by the sensor is thesuperposition of many source signals. Therefore, it isdifficult to achieve the separate location of source signalsonly in time domain. We can also implement frequencydomain processing on array signals to get thebeam-forming algorithm based on frequency domain. Forthe linear array with M array elements of equidistance,


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each element receives N data within the time ofT0, carryout Fourier transformation on these data of M groups toget the spectrum of received signals of each arrayelement:

Xi (ω) =N−1∑

n=0xi (n)Wnω

N =N−1∑

n=0xi (n)e− j 2π

N nω ,

i = 1· · ·M(4)

The weighted output of beam-forming algorithm infrequency domain is as follows:

B(r ,ω) =M

∑i=1

wiXi (ω)e− jωτi(r) (5)

Where r is a vector and its size equals the distance betweenthe focused point and the sensor; the direction of the vectoris the angle between the focal point and the reference arrayelement. Substitute Eq. (4) to (5) and simplify it then wecan get the normalized frequency domain beam-formingoutput:

B(r) =1M

M

∑i=1

wie− j2πω(i−1)τi (r)

N

(

N−1

∑n=0

xi (n)e− j2πkn

N

)

(6)

3 Simulation analysis of rubbing acousticemission source location based on near-fieldbeam-forming

Set the acoustic source signal frequency to 1,000Hz, thepropagation velocity of the acoustic source to 1,500m/sand the signal azimuth with respect to the reference pointto 40o. Besides, set a directional interference signal with afrequency of 5,000Hz, a propagation velocity of 3,000m/sand equal amplitude with the acoustic source signal in theplace of 10o direction angle with respect to referencepoint. The signal sampling frequency of this system is15kHz, add a white Gaussian noise with SNR of 10dBwhich is not directional and belongs to a kind ofbackground noises to the output of each array element.Set the array element spacing to 18cm, element number to32, its formation is linear array, and its azimuth angle canbe searched in the range from−90o to 90o evenly. Thecalculation results of time domain and frequency domainbeam forming are separately shown in Figure 2 andFigure 3.

As can be seen from Figure 2, for the directionalinterference, time-domain beam-forming cancommendably distinguish the azimuth angle between theinterference and the signal. In Figure 3(a), both signal andinterference produce a local peak in the frequency domainbeam-forming diagram which not only points out thedefinite azimuth angles of signal and interference, but alsogets the specific frequency band to which they are located.

Fig. 2: Formation diagram of time-domain beam with 32array elements

(a)Three-dimensional image of frequency-domain beam-forming

(b) Y-Z direction view of frequency-domain beam-forming

(c) X-Z direction view of frequency-domain beam-forming

Fig. 3: Formation diagram of frequency-domain beamwith 32 array elements

Simulation experiments show that both the time-domainand frequency-domain beam-forming algorithm areestimates of the distance and direction of the focal point,the time-domain algorithm shall identify the acousticsource point once according to the entire band, whenthere is interference in space which is different from thelocation of the source point, the beam pointing diagram



will form a peak in these two locations at the same time,and when the energy of the interfering signal is relativelystrong, the peak energy it produced will be greater thanthat of the acoustic source point which may lead to themisjudgment of the real source point. Comparativelyspeaking, frequency-domain algorithm can get a higherestimation accuracy, we can make use of the priorknowledge to get an approximate actual acoustic sourcesignal band, and when the background noise is strong,frequency domain beam-forming method can select localband of the signal frequency for energy weight toeffectively shield the impact of noise on other bands andultimately improves the accuracy of recognition location.Frequency-domain beam-forming method increases theamount of computation compared with time-domainmethod because the computation needs to be converted tothe frequency domain.

4 Forming of near-field MVDR beam

Traditional near-field beam forming method is establishedon the basis of accurate data, while in practicalapplications, many factors, including less beat numberdue to the fast speed, inaccurate estimate of signal arrivalangle, uneven signal propagation medium, concentrationof excessive signal energy on low frequency band and soon, would seriously affect the performance ofbeam-forming algorithm, especially the restriction of thesensor’s installation condition on rotating machinery.Moreover, the number of sensor arrangement is limitedwhich makes the number of array elements is small, and itwill result in a serious decline of the azimuth resolutionrate. MVDR is a direction estimation method with highresolution rate, and its basic idea is that the expecteddirection signal will pass through without distortion andwith a certain gain which minimizes the interference andnoise power. Since the given position spectrum by thealgorithm uses all the eigenvalues of data samplingcovariance matrix, among which the signal characteristicvalue which plays a leading role reflects the power of theacoustic source and the relative size of the sourcecontribution. Therefore, it reduces the contribution ofinterference signal and noise while retaining the usefulsignal, obtains the higher location resolution and noisesuppression performance, and it has more advantagesover the traditional beam-forming method in near-fieldacoustic source location.

4.1 Forming of near-field MVDR beam

Assume that the signal frequency isf0, array elementspacing isr, wave velocity isc, and it evenly distributesM array elements in the linear array, and under far-fieldcircumstance, the signal shoots on the linear array with anincidence angle ofθ0, the covariance matrixRx of X(t) is

as follows:

RX = E[

X (t)XH (t)]

= ARSAH +σ2I (7)

Here,XH(t) is the conjugate transpose ofX(t), RS equalsE[S(t)SH(t)] i.e. the correlation matrix of the sourcesignal among the received signals, andδ 2 stands for thenoise power, I stands for an M-order identity matrix.wi ischosen as the weighted value of the ith array elementsignal xi(t), then the output of the traditionalbeam-former is as follows:

YCBF (t) =WHX (t)√

2 (8)

where W= [w1,w2,...wM ]T in the above equation standsfor the weight vector matrix, andX(t) stands for the inputmatrix of array element. Then the array output power is asfollows:

PCBF (t) = E{

|y(t)|2}

=WHRXW (9)

The core idea of the MVDR algorithm is to keep thesignal energy of the incoming wave direction unchangedand minimum the signal energy on other directions, so itis essentially a constrained optimization problem. For thetraditional beam-forming algorithm, the weight vectormatrix WCBF is constant, but in the MVDR algorithm,WMVDR shall be adaptively given by the actual receivedsignal ambient noise and strength and distribution of thereal space target [16,18].

min{

WHMVDRRXWMVDR

}

sub jecttoWHa(θ) = 1 (10)

Here,a(θ) stands for the direction vector ofθ direction,anda(θ) equals[1e− j2π f dsinθ/c...e− j(M−1)2π f dsinθ/c]. Thepurpose of constraint thatWHa(θ) equals 1 is that theresponse of the fixed weight vector W in the viewingdirectionθ is the conventional coherent summation so thatthe contribution of noise and interference not in thedirection is the minimum. The optimal solution of Eq.(10) is as follows:

WMVDR=(R∗

X)−1a∗ (θ)

aH (θ)R−1X a(θ)

(11)

So the spatial spectrum of MVDR algorithm in far-fieldconditions is as follows:

PMVDR=1

aH (θ)R−1X a(θ)

(12)

Here, aH(θ) is the conjugate transpose operation ofmatrix a(θ), anda∗(θ) andR∗

X separately stands for theconjugate operation of matrixa(θ) and RX. In an idealsituation, the space spectrum ofMVDR algorithm isapproximately a function. It’s noticed that bothWVDR andPVDR in Eq. (11) and (12) are relevant to the correlationmatrix RX of the received signals, so the precision ofMVDR is influenced by the SNR. The above-mentioned




MVDR methods are deduced according to the far-fieldassumption which does not have the distance resolutioncapability i.e. it can not measure the distance ordistinguish the acoustic source of angles in the samedirection. Under near-field circumstance,MVDR algorithmbrings in the impact compensation of distance on the timedelay, so it can estimate the distance and azimuth anglesimultaneously. Assume that the distance between thescan point and the far left element (its number is 1) isr1and the azimuth angle at this point isθ1, so the distancebetween the scan point and the rest elements can beexpressed byr1 andθ1. The source point location can bedetermined if we can estimate the values ofr1 andθ1.

r i =

√

r21+(ri)2−2r1ri cosθ1 i = 2· · ·M (13)

Then the direction vector a is the joint two-dimensionalfunction ofr1 andθ1:

a(r,θ) =[

1,e− j2π f (r1−r2)/c · · ·e− j2π f (r1−rM)/c]

(14)

Accordingly, under the condition of near-field, the spatialspectrum ofMVDR algorithm is as follows:

PMVDR=1

aH (r,θ)R−1X a(r,θ)

(15)

Scan every point in the sound field and we can get thetwo-dimensional joint distribution function of arrayoutput power in respect to r andθ . When the arrayscanning point and the actual location of the acousticsource is coincident, the output power of cophasalsuperposition produced by the signal is the biggest oneand a peak will be formed in the acoustic diagram. Thespatial resolution ofMVDR algorithm is influenced bymany factors such as the signal frequency, the number ofarray elements, array element spacing and the distancebetween the actual acoustic source point and the array.The higher the frequency is, the greater the array size isand the closer the acoustic source apart from the array, thehigher the resolution will be.

4.2 The wideband signal MVDR locationestimation based on sub-band decomposition

The above algorithm is designed for narrow-band signals.For narrowband signals, the shifting phase method isusually used, while the incident signal is a wideband one,we can not use the traditional phase-shift method to formthe correct beam direction because different frequenciescorrespond to different phase shift values. As for suchwideband signals as rubbing acoustic emission signal, ifwe simply apply the above algorithm, it may lead to largeerrors and even incorrect results. Wideband signal can beseen as the summation of a number of narrowband signalsof adjacent frequency. There are two directions of

wideband signal processing, one is irrelevant signal-basedprocessing method i.e. decompose the wideband data intonarrowband data which is on non-overlapping frequencybands, then process and estimate the initial angle eachnarrow-band, and at last, we can get the final resultaccording to the combination of these initial estimates.The other one is coherent signal-based processing methodi.e. focus on the signal space of the non-overlappingfrequency points on the band to the reference frequencypoints, then focus on the wideband signals to thereference frequency points by the focusing matrix, andfinally estimate the direction by the narrowband signalprocessing method. Irrelevant signal processing methodneeds to perform a position estimate on every frequency,so there is a large amount of computation; and the key ofthe algorithm is to calculate the focusing matrix, thematrix dimension will be very large when the number ofsampling points is large, so it will be very difficult tofocus all the signals on a particular frequency by thefocusing matrix. Rubbing acoustic emission signal has avery large amount of data, for example, when therotational speed is 600r/min and the sampling frequencyis 500KHz, the number of sampling points of a rubbingcycle will be up to 50K bytes, and there will be a verylarge amount of computation if the focus transformationis performed on these data, and this algorithm will not besuitable for practical applications. In this paper, we willdivide the M group received wideband signals into Ssegments in the time domain, the length of each segmentis N0 points and do fast Fourier transform on eachsegment of data to form a band withf0/2 bandwidth, thusfrequency snapshots will be formed in each sub-band.

X (n, fk) = [X1 (n, fk) ,X2 (n, fk) · · ·XM (n, fk)] (16)

Xi(n, fk) stands for the frequency component of the nthfrequency snapshot of the ith group signal of the basedarray with the frequency offk , andXi(n, fk) stands forthe frequency component of all the n-th snapshots of thesignal with the frequency offk, so the covariance matrixunder this frequency is as follows:

R̃x ( fk) =1U

U

∑n=1

X (n, fk)XH (n, fk) (17)

The beam output power when the direction angle of thisfrequency component isθ is as follows:

PMVDR(r,θ , fk) =1

aH (r,θ , fk) R̃−1x ( fk)a(r,θ , fk)

(18)

The direction vectora(r,θ , fk) in the above equation

equals[

1,e− j2π fk(r−r2)/c · · ·e− j2π fk(r−rM)/c]

. Add up all

the narrow-band powers and normalize it, then we can getthe wideband output power:

PMVDR(r,θ) =1

Nf

Nf

∑k=1

PMVDR(r,θ , fk) (19)



Where Nf stands for the number of sub-banddecomposition, and after the FFT operation, we can getthe effective signal frequency range i.e. from 0 tof0/2.The frequency resolution of the frequency spectrum∆ fequals f0/N0, For example, whenN0 = f0/2, thefrequency resolution is 2Hz, then after the FFT operation,there are onlyN0/2 points in the arrange from 0 tof0/2,so Nf equalsN0/2 i.e. it will weights once every other2Hz. When the array scans to the acoustic source pointi.e. r → r1 andθ → θ1, PMVDR will form a peak. Sincethe MVDR algorithm weights on the entire frequencydomain and it combines the azimuth spectrum of allbands to get the wideband estimated result which makesits noise immunity stronger than that of the conventionalbeam-forming algorithm. This algorithm can alsoeffectively make the distinction in space domainespecially for directional noise or interference. At thesame time, the adoption of sub-band decompositionmethod makes it possible that MVDR algorithm can avoidthe harsh requirement that the signal must be narrowband,so it can be extended to the application in the widebandsignal. The flow chart of the algorithm is shown in Figure4. Calculation steps of the algorithm are as follows:

(1) Collect rubbing AE signals. If the number of arrayelements is M, M groups of data shall be collected.Rubbing AE signals belong to wideband signals.

(2) Sub-segment decomposition. Divided the receivedM groups of wideband acoustic emission signals intoseveral segments in time domain.

(3) Carry out FFT operations on each sub-band.(4) Calculate the covariance matrix and the direction

vector in each frequency.(5) Calculate the MVDR power output of each sub-

band.(6) Synthesize MVDR power of wideband signals.(7) Scan all points in the acoustic field, the

synthesized MVDR power will form a peak in the spatialspectrum when the array scans to the acoustic sourcepoint, space between the corresponding acoustic source ofthis peak value and the reference point and incidenceangle consist the location coordinates of rubbing acousticemission source point.

Add directional noise data to the data collected in thestep (1), thus it can be used to simulate rubbing AE signalscontaining noise.

5 Experiment analysis

Figure 5(a) shows the rotor rubbing test rig which is arotor system containing three bearings and two crosscomponents, these three bearings are sliding bearingswhich can simulate rotor imbalance shaft systemmisalignment, rubbing and other faults. Rubbing ofrotor-stator of the rotor system can be simulated throughrubbing bracket which is shown in Figure 5 (b). Install thebracket between bearing 2 and bearing 3, it can be movedand fixed on the rotor rig base, implement firm coupling

Fig. 4: Wideband signal MVDR algorithm flow diagrambased on sub-band decomposition

connection between the rubbing screw and theguided-wave plate, adjust the bracket to make the rubbingscrew located in the side of the rotor plate facing the shaftcenter along the shaft radial direction, then rubbing faultsof different degrees can be simulated by adjusting therubbing screw. AE signals generated by rubbing sourcecan be coupled to the guided-wave plate through rubbingscrew and then propagated to AE sensor array. Theposition of rubbing screw here is the focused pointacoustic source; its propagation diagram is shown inFigure 1. The experiment selects UT-1000 sensor with thefrequency response ranging from 60kHz to 1000kHz.Thegain of preamplifier is 40dB and the A/D resolution is 18bit. Most rotary mechanical rubbing faults are alwaysshown as local rubbing which periodically generates acluster of high-energy acoustic emission signals, and theenergy between the adjacent two clusters of rubbingacoustic emission signals is much smaller and it is mainlycaused by mechanical noise, environmental noise andelectromagnetic noise. A large number of experimentsshow that the energy of rubbing acoustic emission signalis concentrated on frequency segments below 100k.Figure 6 shows the time domain and frequency domaindiagrams of the continuous rubbing acoustic emissionsignal when the rotational speed is 350r/min and thesampling frequency is 500kHz; Figure 7 (a) is a wavecluster of Figure 6, and Figure 7 (b) shows the signaldetails of a shorter time period. It can be seen that all thegenerated rubbing acoustic emission frequency spectrumsare approximately the same whose energy are mainlyconcentrated on the frequency segment from 20kHz to50kHz. In order to reduce the computation, it only needsto weight the frequency segment from 20kHz to 100kHzafter the Fourier transform of each sub-segment, and thesignal energy of the rest frequency bands can beconsidered to be zero.




(a)Rotor rubbing test rig

(b) Rubbing bracket

Fig. 5: Rubbing test equipment diagram

Fig. 6: Time and frequency diagram of continuous rubbingacoustic emission signal

5.1 Location simulation of wideband signalMVDR based on sub-band decomposition underdifferent conditions

Set that the acoustic source signal frequency ranges from20kHz to 100kHz, the acoustic velocity is 1,500m/s, the

(a)Partial diagram of rubbing acoustic emission signals

(b) Signal commenced details with time length of 7ms

Fig. 7: Time and frequency diagram a cluster of rubbingacoustic emission signal

sampling frequency is 200kHz; the number of snapshotsis 20 and the formation is linear array. The azimuth anglebetween the acoustic source and sensor 1 is 60o, thedistance r is 4.50m; the array element spacing is 0.2m.stack white noise of different SNR to the collectedacoustic emission signals. Divide the target signalfrequency band into sub-bands every 100Hz, consideringthat the bandwidth of acoustic source signal is 80kHz,totally 801 frequency points will be just enough to coverthe entire frequency band. Calculate the beam energy ofeach frequency point and put them into Eq. (19) to besummed up, then we can get the MVDR spatial spectrumfunction about distance and azimuth angle. Figure 8shows the calculation result of wideband near-fieldsignals MVDR method based on sub-band decompositionof different SNRs and different array numbers. It can beseen that this method can correctly estimate the azimuthangle and the distance of the target signal under near-fieldwideband circumstance, the larger the number of arrayelements is and the higher the SNR is, the sharper the



(a)SNR is 10dB, the number of array elements is 5

(b)SNR is 5dB, the number of array elements is 5

(c)SNR is 10dB, the number of array elements is 15

(d)SNR is 5dB, the number of array elements is 15

Fig. 8: Wideband signal MVDR azimuth estimates basedon sub-band decomposition of different SNR and differentarray elements number

(a)emission signals without noise

(b)emission signals with noise

Fig. 9: The direction estimation diagrams of rubbingacoustic emission signal MVDR

main lobe will be and the lower side lobes’ energy willbecome. At the same time, it can also be seen from Figure8 that the algorithm will form a number of ”false peaks”in other positions which approximately is a hyperbola inthe polar diagram. This is because that there are numerouspoints of a constant distance difference to the two arrayelements in the plane, these points form a hyperbola, themore the passing hyperbola of a point there are, thegreater its output will be, and the intersection point of allhyperbola is the main lobe peak value. It will form amaximum peak value in all the hyperbola intersectionswhen the number of array elements is relatively small, butit will form a relatively large peak value in otherintersections which can not make the main lobe moreobvious from the side lobes. This is the reason why thepeak value in Figure 8 (d) is more obvious than that inFigure 8 (b) when the SNR are the same.

5.2 Actual rubbing acoustic emission sourcelocation

Take the actual rubbing acoustic emission signal in Figure6 as the source signal, assume that the distance betweenthe rubbing source (the position of rubbing screw on




guided-wave plate) and sensor 1 is 300mm, the azimuthangle is 30o, the array element spacing is 50mm, theelement number is 5, the array formation is linear arrayand sensor 1 is the reference point of the array. Assumethat there is a white Gaussian noise whose energy level isthe same as the source signal in the position with anazimuth angle of 60o and its distance to the sensor is500mm. After calculation, the rubbing acoustic emissionwave propagation velocity in the guided-wave plate isabout 3,000m/s, and the received signals of each elementcome after the time delay and stacking process of thesource signal and the noise signal. The received signals ofeach array element are divided into nine snapshots with alength of 50,000 points, so there are totally 5,000sub-bands in the frequency arrangement from 0Hz to100kHz with a band-width of 20Hz, the search anglerange is from 0o to 90o and the distance range is from0mm to 1000mm.

Figure 9 (a) shows the MVDR spatial spectrum ofrubbing acoustic emission signal after sub-banddecomposition, and we can see that MVDR space spectralestimation based on sub-band decomposition forms apeak value in the rubbing source, and the peak value pointis located on the position with a distance of 300mm and aazimuth angle of about 30o. Figure 9 (b) shows the spatialspectrum of rubbing acoustic emission signal MVDRwith noise, and we can see from the diagram that it formsa peak separately in the rubbing source and the noisesource which are very close to the actual location. It isdifferent from the frequency domain beam-formingmethod which distinguishes the signal from the noise interms of frequency; MVDR beam-forming method basedon sub-band decomposition distinguishes the signal fromthe noise in terms of space position. If we have someprior understanding of the acoustic source position beforethe calculation, we can also narrow the search area andreduce the search step size to further improve theaccuracy.

6 Conclusion

In this paper, the beam-forming method is applied to therotating machinery rubbing acoustic emission sourcelocation, and simulation study is performed on theperformance of traditional near-field beam-forming inrubbing acoustic emission source location and thewideband MVDR location estimation method based onsub-band decomposition is adopted. The conclusions areas follows:

(1) In case of large number of array elements, bothtime domain and frequency domain beam-forming caneffectively distinguish the location of the interference andthe signal. But when the interference signal is relativelystrong, the formed peak energy of it will be greater thanthat of the acoustic source, so the time-domain methodmight produce misjudgment on the real source position. Ifwe can get the approximate frequency band of the actual

acoustic source signal by the priori knowledge, we canselect the local frequency band where the signalfrequency locates and weight the energy of it by thefrequency domain wave method, and finally we caneffectively shield the influence of noise on otherfrequency bands and get a better positioning accuracy.

(2) When there are relatively few array elements, thewideband signal MVDR spatial spectral estimation basedon sub-band decomposition can efficiently distinguish thesignal and the noise in the aspect of space, and accuratelylocate the rubbing source.

(3) Beam-forming is able to effectively diagnose therubbing acoustic emission source location which providesa new way for rubbing fault source location.

Acknowledgement

This work was supported by the Natural ScienceFoundation of China under Grant No.51075068, No.60872073, No.60975017 and the Foundation of HuaqiaoUniversity (No.12BS228).

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Aidong Deng was bornin 1968. He received his B.E.degree in Industrial ElectricAutomation from HarbinShipbuilding EngineeringInstitute in 1991, theM.S. degree in 1994, and thePh.D. degree in 2008, bothfrom Southeast University.Currently, he is an associate

professor with the National Engineering Research Centerof Turbo-generator Vibration of School of Energy &Environment, Southeast University, Nanjing, China. Heworked in areas of measurement technology andinstruments, fault analyses and signal processing.Recently he has been working on acoustic emissiontechnology for rotating machinery fault diagnosisapplications.

Hang Tong was bornin 1987. He received his B.E.degree from China Universityof Mining and Technologyin 2009 and the M.S. degreefrom Southeast Universityin 2012. His research interestsinclude power engineeringand fault analyses.

Jianeng Tang wasborn in 1983. He receivedhis B.E. degree in ElectronicInformation Science andTechnology from XinjiangNormal University in2006, the M.S. degree in 2009from Ningxia University,and the Ph.D. degreein 2012 from SoutheastUniversity in Information and

Communication Engineering. Currently, he is withCollege of Engineering, Huaqiao University, Quanzhou,China. His main research interests include nonlinearsystems, chaos synchronization and control, complexnetworks, acoustic emission technology.




Hao Cao wasborn in 1982. He received hisdoctorate from the Departmentof Power Engineering,Southeast University,in 2012 and is currentlyworking at the Hunan ElectricPower Corporation ResearchInstitute in Changsha, China.His research areas are rotating

machinery fault monitoring and diagnosis, and rotordynamics and flow-induced vibration.

Kang Qin was bornin 1988. He received his B.E.degree from Nanjing Universityof Technology in 2011. Nowhe is a master degree candidatein Southeast University.His research interestsinclude fault analyses andacoustic emission technology.

Xin Yanwas born in 1989. He receivedhis B.E. degree from SuzhouUniversity in 2011. Nowhe is a master degree candidatein Southeast University.His research interestsinclude fault analyses andacoustic emission technology.


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