Research ArticleAir Ultrasonic Signal Localization with a BeamformingMicrophone Array

Ali Movahed 1 ThomasWaschkies2 and Ute Rabe 2

1University of Applied Sciences htw saar Saarbrucken Germany2Fraunhofer-Institut for Nondestructive Testing IZFP Campus E3 1 66123 Saarbrucken Germany

Correspondence should be addressed to Ute Rabe uterabeizfpfraunhoferde

Received 27 August 2018 Revised 16 January 2019 Accepted 24 January 2019 Published 11 February 2019

Academic Editor Jorge P Arenas

Copyright copy 2019 Ali Movahed et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Nondestructive testing methods are used to inspect and test materials and components for discontinuities or differences inmechanical characteristics Phased array signal processing techniques have been widely used in different applications but lessresearch has been conducted on contactless nondestructive testing with passive arrays This paper presents an application ofbeamforming techniques analysis using a passive synthetic microphone array to calculate the origin and intensity of soundwaves in the ultrasonic frequency range Acoustic cameras operating in the audible frequency range are well known In order toconduct measurements in higher frequencies the arrangement of microphones in an array has to be taken into considerationThisarrangement has a strong influence on the array properties such as its beam pattern its dynamics and its susceptibility to spatialaliasing Based on simulations optimized configurations with 16 32 and 48 microphones and 20 cm diameter were implementedin real experiments to investigate the array resolution and localize ultrasonic sources at 75 kHz signal frequency The results showthat development of an ultrasonic camera to localize ultrasonic sound sources is beneficial

1 Introduction

Ultrasonic arrays [1] for nondestructive testing (NDT) arewell known in industry to detect defects such as cracks orvoids in components flaws in welded joints or propertiessuch as thickness variations Inmost of theNDT applicationslinear and planar arrays are implemented in which the sameelements are active transmitters and passive receivers ofultrasonic signals Such phased arrays are deployed to createtwo-dimensional cross-sectional images and the sensorshave to be in contact with the component surface to performthe measurement or the component has to be immersed in acoupling medium such as water

In the field of air acoustics on the other hand acousticcamera systems are increasingly popular for detection visu-alization and analysis of sound sources These systems arebased on beamforming where an array of passive receiversis used to enhance identification of air acoustic emissionsby summing the received signals of all microphones withindividual delays [2 3]The received signals can bemultipliedby a weighting factor to suppress the interfering signals at

unwanted directions and steer the response of the arrayDelay and sum beamforming is a simple broadband methodwhich is advantageous to detect short pulses and transientsignals with high computational efficiency [4] Advanceddeconvolution [5 6] and super resolution [7] methods havebeen introduced to improve the dynamic range and spa-tial resolution in the beamforming map Although recentdeconvolution techniques try to extract the strongest sourceby neglecting the influence of element configuration on thebeamforming results and removing some of the artifactsproduced by this configuration in practice the quality of theresults will be still impacted by the array [8] Therefore itis significant that the array has good performance for theintended beamforming application

While beamforming with passive acoustic arrays is oftenused in sonar [9] and seismology [10] there are fewer appli-cations in ultrasonic nondestructive testing It was shownthat beamforming techniques can be used to improve theperformance of sensor arrays for acoustic emission monitor-ing of large concrete structures [11] Furthermore the timereversal MUSIC (multiple signal classification) algorithm

HindawiAdvances in Acoustics and VibrationVolume 2019 Article ID 7691645 12 pageshttpsdoiorg10115520197691645

2 Advances in Acoustics and Vibration

which produces high resolution images below the diffractionlimit was compared to the total focusing method (TFM)in processing of ultrasonic array data to resolve closelyspaced scatterers [12] The total focusing method requiresfull matrix capture each element of the array subsequentlysends a pulse into the examined volume while all elementsare simultaneous receivers The time signals of all channelsare individually digitized and stored After all N elementsemitted their pulses a matrix with N2 time signals (so-called ldquofull matrixrdquo) is availableThese data are reconstructedwith the synthetic aperture focusing technique (SAFT) whichis presently the dominating reconstruction technique forultrasonic array data in NDT SAFT is a delay-and-sumbased method which considers the acoustic time-of-flightbetween the emitter the receiver and each pixelvoxel in thereconstruction planevolume This reconstruction is calledtotal focusing because it delivers similar or even betterresults than a classical phased array which is actively focusedon all points of the reconstruction volume Examples forapplication of passive air coupled acoustic cameras in NDTare the detection of Lamb waves interacting with impactdamage in composite plates [13] and detection of impact echosignals taken of a concrete slab with artificial defects [14]Furthermore noise source localization of trains [15] cars [16]airplanes [17] and wind turbines is typical applications ofbeamformingmicrophone arrays However the conventionalair-coupled beamforming systems cannot be applied to themajority of ultrasonic NDT problems due to their frequencylimitation Detectors digitizers and element arrangementsof commercial acoustic cameras are optimized for signalfrequency below 20 kHz For navigation of robotic systems[18] or as an orientation aid for visually impaired people[19] systems in the ultrasonic frequency range around 40kHz were developed It was already pointed out [20] thatthe higher ultrasonic frequency provides the advantage ofbetter local resolution and less reverberation artifacts For anapplication in air-coupled ultrasonic testing an even higheroperating frequency of up to 500 kHzwill be neededThe aimof this work is to design and build an air-coupled receivingmicrophone array for ultrasonic range applications and toexamine its performance with real measurements

2 Array Shape and Design

The arrangement of the microphones is one of the mostimportant factors to enhance the results of beamformingKnowing the principles of microphone arrays the optimiza-tion of array design parameters makes it possible to investi-gate configurations that need fewermicrophones for a desiredapplication In this chapter the theoretical background forarray shape selection is explained

21 Array Pattern and Beam Pattern The response patternof a passive microphone array with M microphones dependson its individual sensors and on their arrangement in spaceThe array pattern describes the response of the array to planewaves with wave vector

997888rarr119896 and is defined as follows [2]

119882(997888rarr119896) = 119872sum119898=1

119908lowast119898119890119894997888rarr119896 ∙997888rarr119909119898 (1)

0

minus20

minus40

minus60

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mal

ized

Pow

er (d

B)

Angle of propagation (degrees)minus30 minus20 minus10 0 10 20 30

Figure 1 Beam pattern calculated for ring (dashed line) and linear(solid line) arrays at 75 kHz In order to have good separationbetween the lobes small beam width is desired

where k = 2120587120582 is the acoustic wave number 120582 is theacoustic wavelength 119908lowast119898 is a complex weight and 997888rarr119909119898 is thevector position of the 119898119905ℎ element with respect to the arrayorigin and 119898 is the number of the mth microphone m =1 2 3 119872 The beam pattern 119861(120579 120593) is the array responseas a function of direction evaluated for a fixed wave numberk = 2120587120582

119861 (120579 120593) = 119872sum119898=1

119908lowast119898119890119894119896997888rarr119906∙997888rarr119909119898 (2)

Here the vector 997888rarr119906 is the unit vector from the array origin tothe field point The angles 120579 and 120593 indicate the direction ofthe phase fronts of the incoming radiation ie the directionof997888rarr119896 = 119896997888rarr119906 in a spherical coordinate system To increase the

response of the receiving array in a specific direction 997888rarr119906 = 997888rarr119906 0of arrival the complex weights 119908lowast119898 can be defined as follows

119908lowast119898 = 10038161003816100381610038161199081198981003816100381610038161003816 119890minus119894119896997888rarr119906 0∙997888rarr119909119898 (3)

The main array parameters to be taken into account in thearray design are explained on a sample beam pattern simula-tion using a target angle of 0∘ in Figure 1This sample was cal-culated according to (2) by using MATLAB (TheMathWorksInc) The angular behavior in a plane perpendicular to thearray plane of a ring with 32 omnidirectional microphonesand 20 cm diameter was simulated For comparison thebeam pattern of a linear array with 20 cm length and 16omnidirectional microphones is shown The frequency wasset to 75 kHz which yields a wave length 120582 = 46 mm in air(sound velocity 343ms)The weights and array element fieldpattern were set to one The lobe centered on the target angleof 0∘ is called the main beamThe difference between the twominima on either side of the main beam defines the null-to-null beam width The width of the main lobe at -3dB iscalled the half power beam width and the difference betweenthe main lobe and maximum power of the first side lobe iscalled maximum side lobe level (MSL) The beams of equalmagnitude appearing at the angles of 20∘ and -20∘ in the beam

Advances in Acoustics and Vibration 3

010050minus005minus01

01

005

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minus005

minus01

y [m

]

x [m]

(a)

010050minus005minus01

01

005

0

minus005

minus01

y [m

]

x [m]

(b)

Figure 2 (a) Ring array with 32 elements and (b) spiral V = 82 array with 32 elements and 20 cm diameter

pattern of the line array and the beams at the angles of 15∘and -15∘ in the beam pattern of the ring array are gratinglobes Grating lobes appear eg in the linear array when thedistance between the microphones is larger than 1205822 [21]Figure 1 shows that the linear array has a lower MSL than thering array but strong grating lobes

The width of the main lobe defines the array resolutionwhich is a significant parameter that affects the sound sourcelocalization results and is influenced by the array geometryThe Rayleigh criterion is a well-known definition of resolu-tion at the diffraction limit which was first defined in optics[22] According to this criterion two waves are consideredjust resolved when the maximum of the diffraction patternof the first source is detected at the first minimum of thesecond source The respective equation for linear arrays (119897)and circular apertures (119888) (and microphone arrays) is givenby the following [3]

120579119877119897 = 120582L (4)

120579119877119888 = 122 120582D (5)

where 120579119877 is the resolved angle at the Rayleigh limit 120582 isthe wavelength of the source L is the length of the lineararray and 119863 (5) is the diameter of the circular array Asthe Rayleigh angle is small the approximation 120579119877 asymp 120576119877119889 canbe used where 120576119877 is the distance between the two sourcesand 119889 is the distance between the source and the arrayEquation (5) shows that the resolution improves with largerarray diameters but becomes worse when the measurementdistance or the wavelength is increased

In order to optimize the application of the microphonearrays it is important to have good source separation andas low as possible levels of the side lobes which means thatlarge diameters would be preferred On the other hand itis important to have small microphone spacing to achievea wide angle between the side lobes or to avoid side lobeswhen analyzing high frequencies To overcome this a varietyof microphone configurations (linear cross-shape periodic

grid circle and spiral) have been investigated in the literature[23] to report that circular and spiral arrangements havemorebenefits than the other geometries Taking this into accountand a moderate amount of receiving channels we considereda ring and a sunflower spiral [24] with M = 32 microphonesfor our measurements

22 Spiral Array Selection Higher frequency means lowerwavelength and it therefore increases local resolution On theother hand the attenuation of airborne sound increases withincreasing frequency For a first demonstration we thereforechose a center frequency of 75 kHz which is clearly inthe ultrasonic range but still low enough such that specialwide-band microphones are available In order to attain aresolution 120576119877 in the mm range at source array distance d ofseveral 10 cm we chose a diameter D of 20 cmThe sunflowerspiral formula describes different spiral configurations with afixed number of elements depending on a parameter V Thisformula in polar coordinates is given by the following [25 26]

119865 (119898) = (119903119898 (119898) 120579119898 (119898)) = (radic119898 2120587119898radic119881 minus 12 ) (6)

where rm and 120579m are the polar coordinates of the mth elementwith respect to the array origin and 119881 is the correspondingparameter to each unique configuration Different values ofV lead to different possible arrangements such as multi-armed spirals and linear configurations The configurationsare all different if V varies in steps of 01 in a range between1 and 9 We analyzed beam patterns of the arrangementswith V from 1 to 9 (step size 01) at 75 kHz and calculatedthe MSL of each V Among all the configurations V = 32and V = 82 showed the best MSL -1039 and -1015 dBrespectively [27] The single-armed spiral with parameterV = 82 was selected here for further evaluation becausethe spacing between all microphone positions is differentAn arrangement with high symmetry and equal microphonespacing a ring configuration serves for comparison Thetwo arrays chosen for further investigations in the ultrasonicfrequency range are shown in Figure 2

4 Advances in Acoustics and Vibration

005

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Figure 3 Simulated reconstruction result with sum and delay beamforming for a ring array with 32 elements (Figure 2(a)) at a distance of18 cm from two point sources which are separated by 5 mm (a) The sources are two spherical waves at 75 kHz (c) The sources are sphericalwaves at 74 and 76 kHz respectively (b) (d) Cross section of (a) and (c) at y = 0 Red dots show the position of the sources

3 Simulation and Beamforming

According to the Rayleigh criterion in (5) two sources at 75kHz frequency with a separation of 120576119877 = 5 mm (center-to-center) can be resolved with a ring array of 20 cm diameterwhich is 18 cm far from the source plane Generally theRayleigh resolution limit is only applicable when the signalsare not in phase [28] Furthermore simple formulas are onlyavailable for selected microphone configurations like ringsand lines Therefore we simulated the signals of two pointsources with a separation 120576119877 = of 5 mm with equal frequency(75 kHz) and with slightly different frequencies (74 kHz and76 kHz) We defined spherical waves as our sources whichhave the following form

119860(997888rarr119889 119905) = 1198600 119890119894(997888rarr119896997888rarr119889minus120596119905)

119889 (7)

where A0 is an amplitude and is the vector distance from thesource location to the microphone 119889 = |997888rarr119889| and 120596 = 2120587120582 isthe angular frequency of the spherical wave The amplitudesas a function of time 119891119898(119905) for the M microphones withpositions according to Figures 2(a) and 2(b) were producedby summation over the signals of the sources at differentchosen positionsThemicrophones and the sound sources arearranged in plane configurations parallel to each other Thedistance between the source plane and the microphone plane

is 18 cmThe simulated datawere reconstructedwith the delayand summethodThe basis of sum and delay beamforming isto calculate the relative delays from the points on the surfaceof a sound emitting object to each microphone in the arrayThe reconstruction function in time domain for the points inthe image plane is given by the following [4]

119891(997888rarr119883 119905) = 1119872119872sum119898=1

119891119898 (119905 minus 119898) (8)

where 997888rarr119883 is the vector position of the point in the recon-struction plane 119891119898 is the recorded time signal of the mth

microphone and 119898 is the relative delay The relative delaysare calculated from the absolute delays (120591119898) according to119898 = 120591119898 minus min(120591119898) The absolute delays have the form120591119898 = 119889119898c where c is the sound velocity

997888rarr119889119898 is the vectordistance between eachmicrophone in the array and the pointsin the image plane and |997888rarr119889119898| = 119889119898 The aforementionedconventional beamforming algorithm is the oldest and mostpopular signal processing algorithm As it is well suited forpulsed signals it was employed here to localize ultrasonic andacoustic sources in simulations and real experiments

Figures 3(a) and 4(a) show the absolute field of thereconstruction results of the two point sources with equalfrequency and with slightly different frequencies (Figures3(c) and 4(c)) using the ring and the spiral array with 32

Advances in Acoustics and Vibration 5

005

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y [m

]

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x [m]

(a)

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]

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x [m]

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er (d

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005

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x [m]

(d)

Figure 4 Simulated reconstruction result by sum and delay beamforming for a V = 82 spiral array with 32 elements (Figure 2(b))The spiralis located at a distance of 18 cm from two point sources which are separated by 5 mm (a) Point sources are two spherical waves at 75 kHz(c) Point sources are spherical waves at 74 and 76 kHz respectively (b) (d) Cross section of (a) and (c) at y = 0 Red dots show the positionof the sources

microphones as shown in Figures 2(a) and 2(b) respectivelyThe results are displayed with a -15 dB dynamic range forall cases and the size of the reconstruction plane is 60 mmtimes 60 mm (height times width) As it can be seen from Figure 1the grating lobes of the ring array appear at the angle of 15∘which is equal to 4712 mm when the source is 18 cm farfrom the array Therefore our chosen reconstruction planecovers the whole area of interest The distance between eachpixel in x- and y-directions is 03 mm This is even morethan 10 times smaller than the wavelength of the source(457 mm) The distance between the microphones and thereconstruction plane is 18 cm The graphs below the imagesshow a cross section of the data at y = 0 As can be seen inFigures 3(c) and 4(c) the sources which are out of phase areresolved by the ring array and by the spiral array As expectedthe spiral array exhibits a slightly lower local resolution Onthe other hand the ring array produces strong artefacts andside-lobes especially in case of in-phase sources (Figure 3(a))while the spiral array still locates the in-phase sources thoughbeing merged to one point (Figure 4(a)) In addition thespiral has a much lower side lobe level than the ring Theseparate localization of coherent sources is of relevance forNDT testing applications because in the typical NDT testingsituation the objects are actively excited to vibration with afixed frequency and phase As both array types have their

advantages and disadvantages ring and spiral were both usedin the experiments

4 Experimental Results

In order to evaluate the performance of the array designexperimental tests were conducted in the ultrasonic fre-quency range at 75 kHz and for comparison also in the acous-tic frequency range at 10 kHz and 20 kHz In both cases thesound source was placed behind a screen with two aperturesof 1 cm diameter and a center-to-center separation of 15 mmA commercial acoustic camera with 48 microphones wasavailable for the experiment in the acoustic frequency rangeFor the experiment in the ultrasonic frequency range a singlemicrophone in combination with a mechanical positioningdevice was used to collect the data at the 32 microphonepositions as depicted in Figure 2

41 Measurement with the Acoustic Camera In order toexamine the resolution in the acoustic frequency range weconductedmeasurements with a commercial acoustic camera(Gfai tech GmbH Berlin Germany) A Bluetooth speakerwas placed in a wooden box with two holes of 1 cm diameterand 15 cm center-to-center separation The speaker wasexcitedwith 10 kHz and 20 kHz continuouswave sinus signals

6 Advances in Acoustics and Vibration

Speaker Apertures

Woodenbox Microphone

array

Acousticcamerasystem

Signal generator

(a)

05

0

minus05

050minus05

y [m

]

x [m]

(b)

Figure 5 (a) Schematic set-up of the measurement (b) the spiral configuration of the commercial microphone array

60

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(b)

Figure 6 Source localization with the acoustic camera (spiral configuration) (a) at 10 kHz (b) at 20 kHz

from a signal generator A commercial 48-channel planar spi-ral configuration (83 cm diameter) and a ring configuration(75 cm diameter) with data acquisition and evaluation unitwere used to detect and localize the signals coming from twoholes (Figure 5) The camera was placed at a distance of 40cm from the holes The signals of the 48 microphones in thefrequency band from20Hz to 20 kHz (plusmn 3dB)were stored andprocessedwith the commercial software in frequency domainbeamforming The measurement was done with a 192 kHzsampling rate and the acquired time interval was 1 secondFigures 5 and 6 depict the localized acoustic signal with theavailable ring and spiral configurations in a color code imagesuperimposed to an optical photo taken with a digital camerain the center of the array According to the Rayleigh criteriondiscussed in Section 2 the minimum distance between two

sources which will be resolved by a circular aperture of 83cm diameter is 100 cm and 201 cm respectively at 20 kHzand 10 kHz frequency Although the holes are 15 cm farfrom each other the spiral does not resolve them as twosources as can be clearly seen in Figure 6 In comparisonthe ring configuration is able to localize two separate sourcesat 20 kHz which is in agreement with the simulations thata ring has a slightly better resolution than a spiral As theRayleigh limit cannot be calculated with simple analyticalformulas for spirals or other nonperiodic configurations itis more convenient to use amplitude thresholds to evaluateresolution Well-known limits are the 3-dB (half power) orthe 6-dB levels [2 12] Due to this we displayed the result ofthe acoustic camerawith a 6 dBdynamic rangewhich outlinesthe sources not resolvedThe results presented in Figures 5ndash7

Advances in Acoustics and Vibration 7

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Figure 7 Source localization with the acoustic camera (ring configuration) (a) at 10 kHz (b) at 20 kHz

were obtained by frequency domain beamforming Further-more we analyzed the data in time domain beamformingwhich delivered a lower local resolution and a high noise levelfrom background signals

Theoretically the angular resolutionwould improvewhenthe acoustic array would be positioned closer to the sourcebut because of the diameter of the arrays of 83 cm and 75 cma distance to the object below 40 cm would not improve thereconstruction result but leads to source localization insta-bility Experimentally it is not recommended to perform themeasurement closer than the diameter but the localizationmay even work to a certain distance

The appearance of the side lobes around the main lobeespecially in Figure 7(a) is due to the big interelement spacingin the array The resolution can be improved by increasingthe frequency of the sound source or by increasing the sizeof the array Increasing the size of the array will lead toa bigger element distance which produces more artefactsIncreasing the number of microphones while increasingthe diameter of the array will lead to more costs for theacquisition system Therefore it is more practical to havea dense microphone array even with fewer microphonesto be able to localize higher frequencies and decrease thecosts

42 Measurement with the Passive Synthetic Ultrasonic Micro-phone Array For the experiment in the ultrasonic frequencyrange an ultrasonic transducer with 6 cm aperture and acenter frequency of 75 kHz (15 bandwidth) was used tosend the signals A schematic set up is shown in Figure 8Thetransducerwas placed 65 cmbehind a 3mm thick corrugatedcardboard screenwith two holes of the same size and distanceas those in the wooden box for the acoustic experiment (1 cmdiameter 15 cm center-to center-separation)The transducerwas exited with a 75 kHz sinus burst signal with 3 cyclesand 220 V sending voltage Sinus burst signals are the typicaltype of excitation for air ultrasonic transducers They area compromise between a single frequency and a pulsed

Air ultrasonicsenderreciever

Burst 75 kHzCompu

Motor controllerter

US TransducerApertures

M

Screen

icrophonePositioncontrol

z

x

y

Figure 8 Schematic set-up of the measurement in the ultrasonicfrequency range

excitation A continuous wave measurement would damagethe transducers due to the high average power

To detect the direction of the sources defined by the holesan ultrasonic receiving array is needed For the experimentswhich will be presented here we employed a broadbandmicrophone with a constant sensitivity up to 100 kHz fre-quency and a diameter of 3 mm (Type 40 DP 18rdquo PressureMicrophone GRAS Sound amp Vibration Denmark) Themicrophone was mounted to a motorized 3-axis mechanicalpositioning device which was located in front of the screenWhile the distance to the screen (z-coordinate) was keptconstant the microphone was moved in x and y directionswith amanipulator to 32 specific positions to build the passivesynthetic spiral and ring arrays

One of the obstacles when designing high frequencymicrophone arrays is the small interelement spacing Forthe choice of the array configurations (see Section 22)we considered the microphone dimensions such that theminimum interelement spacing was always larger than the

8 Advances in Acoustics and Vibration

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0 02 04 06 08 1

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Time [s] times10-3

(a)

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Frequency [kHz]

Am

plitu

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]

(b)

Figure 9 (a) Recorded time signal of the first microphone at the spiral positions (V = 82) at 09 D distance from the source and (b) averagedspectra of the time signals calculated by fast Fourier transformation

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Figure 10 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

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Figure 11 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 32 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

diameter of the microphone The diameter of the arrays with32microphoneswas 20 cm and the smallest distance betweentwo microphone positions was 098 cm (214120582) in the spiralconfiguration and 196 cm (428120582) in the ring configuration

The ultrasonic time signal of each position was captureddigitized and stored in a computer A sampling frequency of20 MSs was chosen the length of the time interval was 1 msFor each microphone configuration the measurement wasperformed at three different screenndashmicrophone distances05D 065D and 09D respectively to investigate ultrasoundlocalization at distances less than the diameter of the array (D= 20 cm) The shorter distances were chosen for comparisonbecause ultrasonic sources have short wavelength whichincreases the attenuation as a function of distance As anexample for a typical shape of the received signals the time

signal captured with the first microphone of the spiral V =82 from the origin at 09 D measurement distance and theaveraged frequency spectra of the signals of all microphonescalculated by fast Fourier transformation are depicted inFigure 9 The first microphone is the microphone with thesmallest x and y coordinates in the center of the spiral inFigure 2(b)

With a program written in MATLAB the experimentaldata were delayed and summed to perform the time domainlocalization as explained in Section 3 (8) The results calcu-lated with the 32 signals obtained with the ring and spiralconfigurations are demonstrated in Figures 10 and 11 for thethree different measurement distances It can be seen that thearrays have the expected performance in agreement with thesimulations in Section 3 The ring with 32 elements delivers

Advances in Acoustics and Vibration 9

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Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

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Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

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Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

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Advances in Acoustics and Vibration 3

010050minus005minus01

01

005

0

minus005

minus01

y [m

]

x [m]

(a)

010050minus005minus01

01

005

0

minus005

minus01

y [m

]

x [m]

(b)

Figure 2 (a) Ring array with 32 elements and (b) spiral V = 82 array with 32 elements and 20 cm diameter

pattern of the line array and the beams at the angles of 15∘and -15∘ in the beam pattern of the ring array are gratinglobes Grating lobes appear eg in the linear array when thedistance between the microphones is larger than 1205822 [21]Figure 1 shows that the linear array has a lower MSL than thering array but strong grating lobes

The width of the main lobe defines the array resolutionwhich is a significant parameter that affects the sound sourcelocalization results and is influenced by the array geometryThe Rayleigh criterion is a well-known definition of resolu-tion at the diffraction limit which was first defined in optics[22] According to this criterion two waves are consideredjust resolved when the maximum of the diffraction patternof the first source is detected at the first minimum of thesecond source The respective equation for linear arrays (119897)and circular apertures (119888) (and microphone arrays) is givenby the following [3]

120579119877119897 = 120582L (4)

120579119877119888 = 122 120582D (5)

where 120579119877 is the resolved angle at the Rayleigh limit 120582 isthe wavelength of the source L is the length of the lineararray and 119863 (5) is the diameter of the circular array Asthe Rayleigh angle is small the approximation 120579119877 asymp 120576119877119889 canbe used where 120576119877 is the distance between the two sourcesand 119889 is the distance between the source and the arrayEquation (5) shows that the resolution improves with largerarray diameters but becomes worse when the measurementdistance or the wavelength is increased

In order to optimize the application of the microphonearrays it is important to have good source separation andas low as possible levels of the side lobes which means thatlarge diameters would be preferred On the other hand itis important to have small microphone spacing to achievea wide angle between the side lobes or to avoid side lobeswhen analyzing high frequencies To overcome this a varietyof microphone configurations (linear cross-shape periodic

grid circle and spiral) have been investigated in the literature[23] to report that circular and spiral arrangements havemorebenefits than the other geometries Taking this into accountand a moderate amount of receiving channels we considereda ring and a sunflower spiral [24] with M = 32 microphonesfor our measurements

22 Spiral Array Selection Higher frequency means lowerwavelength and it therefore increases local resolution On theother hand the attenuation of airborne sound increases withincreasing frequency For a first demonstration we thereforechose a center frequency of 75 kHz which is clearly inthe ultrasonic range but still low enough such that specialwide-band microphones are available In order to attain aresolution 120576119877 in the mm range at source array distance d ofseveral 10 cm we chose a diameter D of 20 cmThe sunflowerspiral formula describes different spiral configurations with afixed number of elements depending on a parameter V Thisformula in polar coordinates is given by the following [25 26]

119865 (119898) = (119903119898 (119898) 120579119898 (119898)) = (radic119898 2120587119898radic119881 minus 12 ) (6)

where rm and 120579m are the polar coordinates of the mth elementwith respect to the array origin and 119881 is the correspondingparameter to each unique configuration Different values ofV lead to different possible arrangements such as multi-armed spirals and linear configurations The configurationsare all different if V varies in steps of 01 in a range between1 and 9 We analyzed beam patterns of the arrangementswith V from 1 to 9 (step size 01) at 75 kHz and calculatedthe MSL of each V Among all the configurations V = 32and V = 82 showed the best MSL -1039 and -1015 dBrespectively [27] The single-armed spiral with parameterV = 82 was selected here for further evaluation becausethe spacing between all microphone positions is differentAn arrangement with high symmetry and equal microphonespacing a ring configuration serves for comparison Thetwo arrays chosen for further investigations in the ultrasonicfrequency range are shown in Figure 2

4 Advances in Acoustics and Vibration

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(b)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(c)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(d)

Figure 3 Simulated reconstruction result with sum and delay beamforming for a ring array with 32 elements (Figure 2(a)) at a distance of18 cm from two point sources which are separated by 5 mm (a) The sources are two spherical waves at 75 kHz (c) The sources are sphericalwaves at 74 and 76 kHz respectively (b) (d) Cross section of (a) and (c) at y = 0 Red dots show the position of the sources

3 Simulation and Beamforming

According to the Rayleigh criterion in (5) two sources at 75kHz frequency with a separation of 120576119877 = 5 mm (center-to-center) can be resolved with a ring array of 20 cm diameterwhich is 18 cm far from the source plane Generally theRayleigh resolution limit is only applicable when the signalsare not in phase [28] Furthermore simple formulas are onlyavailable for selected microphone configurations like ringsand lines Therefore we simulated the signals of two pointsources with a separation 120576119877 = of 5 mm with equal frequency(75 kHz) and with slightly different frequencies (74 kHz and76 kHz) We defined spherical waves as our sources whichhave the following form

119860(997888rarr119889 119905) = 1198600 119890119894(997888rarr119896997888rarr119889minus120596119905)

119889 (7)

where A0 is an amplitude and is the vector distance from thesource location to the microphone 119889 = |997888rarr119889| and 120596 = 2120587120582 isthe angular frequency of the spherical wave The amplitudesas a function of time 119891119898(119905) for the M microphones withpositions according to Figures 2(a) and 2(b) were producedby summation over the signals of the sources at differentchosen positionsThemicrophones and the sound sources arearranged in plane configurations parallel to each other Thedistance between the source plane and the microphone plane

is 18 cmThe simulated datawere reconstructedwith the delayand summethodThe basis of sum and delay beamforming isto calculate the relative delays from the points on the surfaceof a sound emitting object to each microphone in the arrayThe reconstruction function in time domain for the points inthe image plane is given by the following [4]

119891(997888rarr119883 119905) = 1119872119872sum119898=1

119891119898 (119905 minus 119898) (8)

where 997888rarr119883 is the vector position of the point in the recon-struction plane 119891119898 is the recorded time signal of the mth

microphone and 119898 is the relative delay The relative delaysare calculated from the absolute delays (120591119898) according to119898 = 120591119898 minus min(120591119898) The absolute delays have the form120591119898 = 119889119898c where c is the sound velocity

997888rarr119889119898 is the vectordistance between eachmicrophone in the array and the pointsin the image plane and |997888rarr119889119898| = 119889119898 The aforementionedconventional beamforming algorithm is the oldest and mostpopular signal processing algorithm As it is well suited forpulsed signals it was employed here to localize ultrasonic andacoustic sources in simulations and real experiments

Figures 3(a) and 4(a) show the absolute field of thereconstruction results of the two point sources with equalfrequency and with slightly different frequencies (Figures3(c) and 4(c)) using the ring and the spiral array with 32

Advances in Acoustics and Vibration 5

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(b)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(c)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(d)

Figure 4 Simulated reconstruction result by sum and delay beamforming for a V = 82 spiral array with 32 elements (Figure 2(b))The spiralis located at a distance of 18 cm from two point sources which are separated by 5 mm (a) Point sources are two spherical waves at 75 kHz(c) Point sources are spherical waves at 74 and 76 kHz respectively (b) (d) Cross section of (a) and (c) at y = 0 Red dots show the positionof the sources

microphones as shown in Figures 2(a) and 2(b) respectivelyThe results are displayed with a -15 dB dynamic range forall cases and the size of the reconstruction plane is 60 mmtimes 60 mm (height times width) As it can be seen from Figure 1the grating lobes of the ring array appear at the angle of 15∘which is equal to 4712 mm when the source is 18 cm farfrom the array Therefore our chosen reconstruction planecovers the whole area of interest The distance between eachpixel in x- and y-directions is 03 mm This is even morethan 10 times smaller than the wavelength of the source(457 mm) The distance between the microphones and thereconstruction plane is 18 cm The graphs below the imagesshow a cross section of the data at y = 0 As can be seen inFigures 3(c) and 4(c) the sources which are out of phase areresolved by the ring array and by the spiral array As expectedthe spiral array exhibits a slightly lower local resolution Onthe other hand the ring array produces strong artefacts andside-lobes especially in case of in-phase sources (Figure 3(a))while the spiral array still locates the in-phase sources thoughbeing merged to one point (Figure 4(a)) In addition thespiral has a much lower side lobe level than the ring Theseparate localization of coherent sources is of relevance forNDT testing applications because in the typical NDT testingsituation the objects are actively excited to vibration with afixed frequency and phase As both array types have their

advantages and disadvantages ring and spiral were both usedin the experiments

4 Experimental Results

In order to evaluate the performance of the array designexperimental tests were conducted in the ultrasonic fre-quency range at 75 kHz and for comparison also in the acous-tic frequency range at 10 kHz and 20 kHz In both cases thesound source was placed behind a screen with two aperturesof 1 cm diameter and a center-to-center separation of 15 mmA commercial acoustic camera with 48 microphones wasavailable for the experiment in the acoustic frequency rangeFor the experiment in the ultrasonic frequency range a singlemicrophone in combination with a mechanical positioningdevice was used to collect the data at the 32 microphonepositions as depicted in Figure 2

41 Measurement with the Acoustic Camera In order toexamine the resolution in the acoustic frequency range weconductedmeasurements with a commercial acoustic camera(Gfai tech GmbH Berlin Germany) A Bluetooth speakerwas placed in a wooden box with two holes of 1 cm diameterand 15 cm center-to-center separation The speaker wasexcitedwith 10 kHz and 20 kHz continuouswave sinus signals

6 Advances in Acoustics and Vibration

Speaker Apertures

Woodenbox Microphone

array

Acousticcamerasystem

Signal generator

(a)

05

0

minus05

050minus05

y [m

]

x [m]

(b)

Figure 5 (a) Schematic set-up of the measurement (b) the spiral configuration of the commercial microphone array

60

60

0

0

minus60

minus60

mm

mm

Press dB6452

640

630

620

610

600

590

5852

(a)

60

60

0

0

minus60

minus60

mm

mm

Press dB5617

550

540

530

520

510

5017

(b)

Figure 6 Source localization with the acoustic camera (spiral configuration) (a) at 10 kHz (b) at 20 kHz

from a signal generator A commercial 48-channel planar spi-ral configuration (83 cm diameter) and a ring configuration(75 cm diameter) with data acquisition and evaluation unitwere used to detect and localize the signals coming from twoholes (Figure 5) The camera was placed at a distance of 40cm from the holes The signals of the 48 microphones in thefrequency band from20Hz to 20 kHz (plusmn 3dB)were stored andprocessedwith the commercial software in frequency domainbeamforming The measurement was done with a 192 kHzsampling rate and the acquired time interval was 1 secondFigures 5 and 6 depict the localized acoustic signal with theavailable ring and spiral configurations in a color code imagesuperimposed to an optical photo taken with a digital camerain the center of the array According to the Rayleigh criteriondiscussed in Section 2 the minimum distance between two

sources which will be resolved by a circular aperture of 83cm diameter is 100 cm and 201 cm respectively at 20 kHzand 10 kHz frequency Although the holes are 15 cm farfrom each other the spiral does not resolve them as twosources as can be clearly seen in Figure 6 In comparisonthe ring configuration is able to localize two separate sourcesat 20 kHz which is in agreement with the simulations thata ring has a slightly better resolution than a spiral As theRayleigh limit cannot be calculated with simple analyticalformulas for spirals or other nonperiodic configurations itis more convenient to use amplitude thresholds to evaluateresolution Well-known limits are the 3-dB (half power) orthe 6-dB levels [2 12] Due to this we displayed the result ofthe acoustic camerawith a 6 dBdynamic rangewhich outlinesthe sources not resolvedThe results presented in Figures 5ndash7

Advances in Acoustics and Vibration 7

4065

400

390

380

370

360

3465

60

60

0

0

minus60

minus60

mm

mm

Press dB

(a)

3674

360

350

340

330

320

3074

60

60

0

0

minus60

minus60

mm

mm

Press dB

(b)

Figure 7 Source localization with the acoustic camera (ring configuration) (a) at 10 kHz (b) at 20 kHz

were obtained by frequency domain beamforming Further-more we analyzed the data in time domain beamformingwhich delivered a lower local resolution and a high noise levelfrom background signals

Theoretically the angular resolutionwould improvewhenthe acoustic array would be positioned closer to the sourcebut because of the diameter of the arrays of 83 cm and 75 cma distance to the object below 40 cm would not improve thereconstruction result but leads to source localization insta-bility Experimentally it is not recommended to perform themeasurement closer than the diameter but the localizationmay even work to a certain distance

The appearance of the side lobes around the main lobeespecially in Figure 7(a) is due to the big interelement spacingin the array The resolution can be improved by increasingthe frequency of the sound source or by increasing the sizeof the array Increasing the size of the array will lead toa bigger element distance which produces more artefactsIncreasing the number of microphones while increasingthe diameter of the array will lead to more costs for theacquisition system Therefore it is more practical to havea dense microphone array even with fewer microphonesto be able to localize higher frequencies and decrease thecosts

42 Measurement with the Passive Synthetic Ultrasonic Micro-phone Array For the experiment in the ultrasonic frequencyrange an ultrasonic transducer with 6 cm aperture and acenter frequency of 75 kHz (15 bandwidth) was used tosend the signals A schematic set up is shown in Figure 8Thetransducerwas placed 65 cmbehind a 3mm thick corrugatedcardboard screenwith two holes of the same size and distanceas those in the wooden box for the acoustic experiment (1 cmdiameter 15 cm center-to center-separation)The transducerwas exited with a 75 kHz sinus burst signal with 3 cyclesand 220 V sending voltage Sinus burst signals are the typicaltype of excitation for air ultrasonic transducers They area compromise between a single frequency and a pulsed

Air ultrasonicsenderreciever

Burst 75 kHzCompu

Motor controllerter

US TransducerApertures

M

Screen

icrophonePositioncontrol

z

x

y

Figure 8 Schematic set-up of the measurement in the ultrasonicfrequency range

excitation A continuous wave measurement would damagethe transducers due to the high average power

To detect the direction of the sources defined by the holesan ultrasonic receiving array is needed For the experimentswhich will be presented here we employed a broadbandmicrophone with a constant sensitivity up to 100 kHz fre-quency and a diameter of 3 mm (Type 40 DP 18rdquo PressureMicrophone GRAS Sound amp Vibration Denmark) Themicrophone was mounted to a motorized 3-axis mechanicalpositioning device which was located in front of the screenWhile the distance to the screen (z-coordinate) was keptconstant the microphone was moved in x and y directionswith amanipulator to 32 specific positions to build the passivesynthetic spiral and ring arrays

One of the obstacles when designing high frequencymicrophone arrays is the small interelement spacing Forthe choice of the array configurations (see Section 22)we considered the microphone dimensions such that theminimum interelement spacing was always larger than the

8 Advances in Acoustics and Vibration

40

20

0

minus20

minus40

0 02 04 06 08 1

Am

plitu

de [a

u]

Time [s] times10-3

(a)

100

50

00 20 40 60 80 100 120 140 160 180 200

Frequency [kHz]

Am

plitu

de [

]

(b)

Figure 9 (a) Recorded time signal of the first microphone at the spiral positions (V = 82) at 09 D distance from the source and (b) averagedspectra of the time signals calculated by fast Fourier transformation

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(a)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(b)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(c)

Figure 10 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 11 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 32 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

diameter of the microphone The diameter of the arrays with32microphoneswas 20 cm and the smallest distance betweentwo microphone positions was 098 cm (214120582) in the spiralconfiguration and 196 cm (428120582) in the ring configuration

The ultrasonic time signal of each position was captureddigitized and stored in a computer A sampling frequency of20 MSs was chosen the length of the time interval was 1 msFor each microphone configuration the measurement wasperformed at three different screenndashmicrophone distances05D 065D and 09D respectively to investigate ultrasoundlocalization at distances less than the diameter of the array (D= 20 cm) The shorter distances were chosen for comparisonbecause ultrasonic sources have short wavelength whichincreases the attenuation as a function of distance As anexample for a typical shape of the received signals the time

signal captured with the first microphone of the spiral V =82 from the origin at 09 D measurement distance and theaveraged frequency spectra of the signals of all microphonescalculated by fast Fourier transformation are depicted inFigure 9 The first microphone is the microphone with thesmallest x and y coordinates in the center of the spiral inFigure 2(b)

With a program written in MATLAB the experimentaldata were delayed and summed to perform the time domainlocalization as explained in Section 3 (8) The results calcu-lated with the 32 signals obtained with the ring and spiralconfigurations are demonstrated in Figures 10 and 11 for thethree different measurement distances It can be seen that thearrays have the expected performance in agreement with thesimulations in Section 3 The ring with 32 elements delivers

Advances in Acoustics and Vibration 9

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

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4 Advances in Acoustics and Vibration

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(b)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(c)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(d)

Figure 3 Simulated reconstruction result with sum and delay beamforming for a ring array with 32 elements (Figure 2(a)) at a distance of18 cm from two point sources which are separated by 5 mm (a) The sources are two spherical waves at 75 kHz (c) The sources are sphericalwaves at 74 and 76 kHz respectively (b) (d) Cross section of (a) and (c) at y = 0 Red dots show the position of the sources

3 Simulation and Beamforming

According to the Rayleigh criterion in (5) two sources at 75kHz frequency with a separation of 120576119877 = 5 mm (center-to-center) can be resolved with a ring array of 20 cm diameterwhich is 18 cm far from the source plane Generally theRayleigh resolution limit is only applicable when the signalsare not in phase [28] Furthermore simple formulas are onlyavailable for selected microphone configurations like ringsand lines Therefore we simulated the signals of two pointsources with a separation 120576119877 = of 5 mm with equal frequency(75 kHz) and with slightly different frequencies (74 kHz and76 kHz) We defined spherical waves as our sources whichhave the following form

119860(997888rarr119889 119905) = 1198600 119890119894(997888rarr119896997888rarr119889minus120596119905)

119889 (7)

where A0 is an amplitude and is the vector distance from thesource location to the microphone 119889 = |997888rarr119889| and 120596 = 2120587120582 isthe angular frequency of the spherical wave The amplitudesas a function of time 119891119898(119905) for the M microphones withpositions according to Figures 2(a) and 2(b) were producedby summation over the signals of the sources at differentchosen positionsThemicrophones and the sound sources arearranged in plane configurations parallel to each other Thedistance between the source plane and the microphone plane

is 18 cmThe simulated datawere reconstructedwith the delayand summethodThe basis of sum and delay beamforming isto calculate the relative delays from the points on the surfaceof a sound emitting object to each microphone in the arrayThe reconstruction function in time domain for the points inthe image plane is given by the following [4]

119891(997888rarr119883 119905) = 1119872119872sum119898=1

119891119898 (119905 minus 119898) (8)

where 997888rarr119883 is the vector position of the point in the recon-struction plane 119891119898 is the recorded time signal of the mth

microphone and 119898 is the relative delay The relative delaysare calculated from the absolute delays (120591119898) according to119898 = 120591119898 minus min(120591119898) The absolute delays have the form120591119898 = 119889119898c where c is the sound velocity

997888rarr119889119898 is the vectordistance between eachmicrophone in the array and the pointsin the image plane and |997888rarr119889119898| = 119889119898 The aforementionedconventional beamforming algorithm is the oldest and mostpopular signal processing algorithm As it is well suited forpulsed signals it was employed here to localize ultrasonic andacoustic sources in simulations and real experiments

Figures 3(a) and 4(a) show the absolute field of thereconstruction results of the two point sources with equalfrequency and with slightly different frequencies (Figures3(c) and 4(c)) using the ring and the spiral array with 32

Advances in Acoustics and Vibration 5

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(b)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(c)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(d)

Figure 4 Simulated reconstruction result by sum and delay beamforming for a V = 82 spiral array with 32 elements (Figure 2(b))The spiralis located at a distance of 18 cm from two point sources which are separated by 5 mm (a) Point sources are two spherical waves at 75 kHz(c) Point sources are spherical waves at 74 and 76 kHz respectively (b) (d) Cross section of (a) and (c) at y = 0 Red dots show the positionof the sources

microphones as shown in Figures 2(a) and 2(b) respectivelyThe results are displayed with a -15 dB dynamic range forall cases and the size of the reconstruction plane is 60 mmtimes 60 mm (height times width) As it can be seen from Figure 1the grating lobes of the ring array appear at the angle of 15∘which is equal to 4712 mm when the source is 18 cm farfrom the array Therefore our chosen reconstruction planecovers the whole area of interest The distance between eachpixel in x- and y-directions is 03 mm This is even morethan 10 times smaller than the wavelength of the source(457 mm) The distance between the microphones and thereconstruction plane is 18 cm The graphs below the imagesshow a cross section of the data at y = 0 As can be seen inFigures 3(c) and 4(c) the sources which are out of phase areresolved by the ring array and by the spiral array As expectedthe spiral array exhibits a slightly lower local resolution Onthe other hand the ring array produces strong artefacts andside-lobes especially in case of in-phase sources (Figure 3(a))while the spiral array still locates the in-phase sources thoughbeing merged to one point (Figure 4(a)) In addition thespiral has a much lower side lobe level than the ring Theseparate localization of coherent sources is of relevance forNDT testing applications because in the typical NDT testingsituation the objects are actively excited to vibration with afixed frequency and phase As both array types have their

advantages and disadvantages ring and spiral were both usedin the experiments

4 Experimental Results

In order to evaluate the performance of the array designexperimental tests were conducted in the ultrasonic fre-quency range at 75 kHz and for comparison also in the acous-tic frequency range at 10 kHz and 20 kHz In both cases thesound source was placed behind a screen with two aperturesof 1 cm diameter and a center-to-center separation of 15 mmA commercial acoustic camera with 48 microphones wasavailable for the experiment in the acoustic frequency rangeFor the experiment in the ultrasonic frequency range a singlemicrophone in combination with a mechanical positioningdevice was used to collect the data at the 32 microphonepositions as depicted in Figure 2

41 Measurement with the Acoustic Camera In order toexamine the resolution in the acoustic frequency range weconductedmeasurements with a commercial acoustic camera(Gfai tech GmbH Berlin Germany) A Bluetooth speakerwas placed in a wooden box with two holes of 1 cm diameterand 15 cm center-to-center separation The speaker wasexcitedwith 10 kHz and 20 kHz continuouswave sinus signals

6 Advances in Acoustics and Vibration

Speaker Apertures

Woodenbox Microphone

array

Acousticcamerasystem

Signal generator

(a)

05

0

minus05

050minus05

y [m

]

x [m]

(b)

Figure 5 (a) Schematic set-up of the measurement (b) the spiral configuration of the commercial microphone array

60

60

0

0

minus60

minus60

mm

mm

Press dB6452

640

630

620

610

600

590

5852

(a)

60

60

0

0

minus60

minus60

mm

mm

Press dB5617

550

540

530

520

510

5017

(b)

Figure 6 Source localization with the acoustic camera (spiral configuration) (a) at 10 kHz (b) at 20 kHz

from a signal generator A commercial 48-channel planar spi-ral configuration (83 cm diameter) and a ring configuration(75 cm diameter) with data acquisition and evaluation unitwere used to detect and localize the signals coming from twoholes (Figure 5) The camera was placed at a distance of 40cm from the holes The signals of the 48 microphones in thefrequency band from20Hz to 20 kHz (plusmn 3dB)were stored andprocessedwith the commercial software in frequency domainbeamforming The measurement was done with a 192 kHzsampling rate and the acquired time interval was 1 secondFigures 5 and 6 depict the localized acoustic signal with theavailable ring and spiral configurations in a color code imagesuperimposed to an optical photo taken with a digital camerain the center of the array According to the Rayleigh criteriondiscussed in Section 2 the minimum distance between two

sources which will be resolved by a circular aperture of 83cm diameter is 100 cm and 201 cm respectively at 20 kHzand 10 kHz frequency Although the holes are 15 cm farfrom each other the spiral does not resolve them as twosources as can be clearly seen in Figure 6 In comparisonthe ring configuration is able to localize two separate sourcesat 20 kHz which is in agreement with the simulations thata ring has a slightly better resolution than a spiral As theRayleigh limit cannot be calculated with simple analyticalformulas for spirals or other nonperiodic configurations itis more convenient to use amplitude thresholds to evaluateresolution Well-known limits are the 3-dB (half power) orthe 6-dB levels [2 12] Due to this we displayed the result ofthe acoustic camerawith a 6 dBdynamic rangewhich outlinesthe sources not resolvedThe results presented in Figures 5ndash7

Advances in Acoustics and Vibration 7

4065

400

390

380

370

360

3465

60

60

0

0

minus60

minus60

mm

mm

Press dB

(a)

3674

360

350

340

330

320

3074

60

60

0

0

minus60

minus60

mm

mm

Press dB

(b)

Figure 7 Source localization with the acoustic camera (ring configuration) (a) at 10 kHz (b) at 20 kHz

were obtained by frequency domain beamforming Further-more we analyzed the data in time domain beamformingwhich delivered a lower local resolution and a high noise levelfrom background signals

Theoretically the angular resolutionwould improvewhenthe acoustic array would be positioned closer to the sourcebut because of the diameter of the arrays of 83 cm and 75 cma distance to the object below 40 cm would not improve thereconstruction result but leads to source localization insta-bility Experimentally it is not recommended to perform themeasurement closer than the diameter but the localizationmay even work to a certain distance

The appearance of the side lobes around the main lobeespecially in Figure 7(a) is due to the big interelement spacingin the array The resolution can be improved by increasingthe frequency of the sound source or by increasing the sizeof the array Increasing the size of the array will lead toa bigger element distance which produces more artefactsIncreasing the number of microphones while increasingthe diameter of the array will lead to more costs for theacquisition system Therefore it is more practical to havea dense microphone array even with fewer microphonesto be able to localize higher frequencies and decrease thecosts

42 Measurement with the Passive Synthetic Ultrasonic Micro-phone Array For the experiment in the ultrasonic frequencyrange an ultrasonic transducer with 6 cm aperture and acenter frequency of 75 kHz (15 bandwidth) was used tosend the signals A schematic set up is shown in Figure 8Thetransducerwas placed 65 cmbehind a 3mm thick corrugatedcardboard screenwith two holes of the same size and distanceas those in the wooden box for the acoustic experiment (1 cmdiameter 15 cm center-to center-separation)The transducerwas exited with a 75 kHz sinus burst signal with 3 cyclesand 220 V sending voltage Sinus burst signals are the typicaltype of excitation for air ultrasonic transducers They area compromise between a single frequency and a pulsed

Air ultrasonicsenderreciever

Burst 75 kHzCompu

Motor controllerter

US TransducerApertures

M

Screen

icrophonePositioncontrol

z

x

y

Figure 8 Schematic set-up of the measurement in the ultrasonicfrequency range

excitation A continuous wave measurement would damagethe transducers due to the high average power

To detect the direction of the sources defined by the holesan ultrasonic receiving array is needed For the experimentswhich will be presented here we employed a broadbandmicrophone with a constant sensitivity up to 100 kHz fre-quency and a diameter of 3 mm (Type 40 DP 18rdquo PressureMicrophone GRAS Sound amp Vibration Denmark) Themicrophone was mounted to a motorized 3-axis mechanicalpositioning device which was located in front of the screenWhile the distance to the screen (z-coordinate) was keptconstant the microphone was moved in x and y directionswith amanipulator to 32 specific positions to build the passivesynthetic spiral and ring arrays

One of the obstacles when designing high frequencymicrophone arrays is the small interelement spacing Forthe choice of the array configurations (see Section 22)we considered the microphone dimensions such that theminimum interelement spacing was always larger than the

8 Advances in Acoustics and Vibration

40

20

0

minus20

minus40

0 02 04 06 08 1

Am

plitu

de [a

u]

Time [s] times10-3

(a)

100

50

00 20 40 60 80 100 120 140 160 180 200

Frequency [kHz]

Am

plitu

de [

]

(b)

Figure 9 (a) Recorded time signal of the first microphone at the spiral positions (V = 82) at 09 D distance from the source and (b) averagedspectra of the time signals calculated by fast Fourier transformation

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(a)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(b)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(c)

Figure 10 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 11 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 32 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

diameter of the microphone The diameter of the arrays with32microphoneswas 20 cm and the smallest distance betweentwo microphone positions was 098 cm (214120582) in the spiralconfiguration and 196 cm (428120582) in the ring configuration

The ultrasonic time signal of each position was captureddigitized and stored in a computer A sampling frequency of20 MSs was chosen the length of the time interval was 1 msFor each microphone configuration the measurement wasperformed at three different screenndashmicrophone distances05D 065D and 09D respectively to investigate ultrasoundlocalization at distances less than the diameter of the array (D= 20 cm) The shorter distances were chosen for comparisonbecause ultrasonic sources have short wavelength whichincreases the attenuation as a function of distance As anexample for a typical shape of the received signals the time

signal captured with the first microphone of the spiral V =82 from the origin at 09 D measurement distance and theaveraged frequency spectra of the signals of all microphonescalculated by fast Fourier transformation are depicted inFigure 9 The first microphone is the microphone with thesmallest x and y coordinates in the center of the spiral inFigure 2(b)

With a program written in MATLAB the experimentaldata were delayed and summed to perform the time domainlocalization as explained in Section 3 (8) The results calcu-lated with the 32 signals obtained with the ring and spiralconfigurations are demonstrated in Figures 10 and 11 for thethree different measurement distances It can be seen that thearrays have the expected performance in agreement with thesimulations in Section 3 The ring with 32 elements delivers

Advances in Acoustics and Vibration 9

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

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Advances in Acoustics and Vibration 5

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-5

-10

x [m]

(b)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(c)

Nor

mal

ized

Pow

er (d

B)

005

0

0minus005

minus5

minus10

x [m]

(d)

Figure 4 Simulated reconstruction result by sum and delay beamforming for a V = 82 spiral array with 32 elements (Figure 2(b))The spiralis located at a distance of 18 cm from two point sources which are separated by 5 mm (a) Point sources are two spherical waves at 75 kHz(c) Point sources are spherical waves at 74 and 76 kHz respectively (b) (d) Cross section of (a) and (c) at y = 0 Red dots show the positionof the sources

microphones as shown in Figures 2(a) and 2(b) respectivelyThe results are displayed with a -15 dB dynamic range forall cases and the size of the reconstruction plane is 60 mmtimes 60 mm (height times width) As it can be seen from Figure 1the grating lobes of the ring array appear at the angle of 15∘which is equal to 4712 mm when the source is 18 cm farfrom the array Therefore our chosen reconstruction planecovers the whole area of interest The distance between eachpixel in x- and y-directions is 03 mm This is even morethan 10 times smaller than the wavelength of the source(457 mm) The distance between the microphones and thereconstruction plane is 18 cm The graphs below the imagesshow a cross section of the data at y = 0 As can be seen inFigures 3(c) and 4(c) the sources which are out of phase areresolved by the ring array and by the spiral array As expectedthe spiral array exhibits a slightly lower local resolution Onthe other hand the ring array produces strong artefacts andside-lobes especially in case of in-phase sources (Figure 3(a))while the spiral array still locates the in-phase sources thoughbeing merged to one point (Figure 4(a)) In addition thespiral has a much lower side lobe level than the ring Theseparate localization of coherent sources is of relevance forNDT testing applications because in the typical NDT testingsituation the objects are actively excited to vibration with afixed frequency and phase As both array types have their

advantages and disadvantages ring and spiral were both usedin the experiments

4 Experimental Results

In order to evaluate the performance of the array designexperimental tests were conducted in the ultrasonic fre-quency range at 75 kHz and for comparison also in the acous-tic frequency range at 10 kHz and 20 kHz In both cases thesound source was placed behind a screen with two aperturesof 1 cm diameter and a center-to-center separation of 15 mmA commercial acoustic camera with 48 microphones wasavailable for the experiment in the acoustic frequency rangeFor the experiment in the ultrasonic frequency range a singlemicrophone in combination with a mechanical positioningdevice was used to collect the data at the 32 microphonepositions as depicted in Figure 2

41 Measurement with the Acoustic Camera In order toexamine the resolution in the acoustic frequency range weconductedmeasurements with a commercial acoustic camera(Gfai tech GmbH Berlin Germany) A Bluetooth speakerwas placed in a wooden box with two holes of 1 cm diameterand 15 cm center-to-center separation The speaker wasexcitedwith 10 kHz and 20 kHz continuouswave sinus signals

6 Advances in Acoustics and Vibration

Speaker Apertures

Woodenbox Microphone

array

Acousticcamerasystem

Signal generator

(a)

05

0

minus05

050minus05

y [m

]

x [m]

(b)

Figure 5 (a) Schematic set-up of the measurement (b) the spiral configuration of the commercial microphone array

60

60

0

0

minus60

minus60

mm

mm

Press dB6452

640

630

620

610

600

590

5852

(a)

60

60

0

0

minus60

minus60

mm

mm

Press dB5617

550

540

530

520

510

5017

(b)

Figure 6 Source localization with the acoustic camera (spiral configuration) (a) at 10 kHz (b) at 20 kHz

from a signal generator A commercial 48-channel planar spi-ral configuration (83 cm diameter) and a ring configuration(75 cm diameter) with data acquisition and evaluation unitwere used to detect and localize the signals coming from twoholes (Figure 5) The camera was placed at a distance of 40cm from the holes The signals of the 48 microphones in thefrequency band from20Hz to 20 kHz (plusmn 3dB)were stored andprocessedwith the commercial software in frequency domainbeamforming The measurement was done with a 192 kHzsampling rate and the acquired time interval was 1 secondFigures 5 and 6 depict the localized acoustic signal with theavailable ring and spiral configurations in a color code imagesuperimposed to an optical photo taken with a digital camerain the center of the array According to the Rayleigh criteriondiscussed in Section 2 the minimum distance between two

sources which will be resolved by a circular aperture of 83cm diameter is 100 cm and 201 cm respectively at 20 kHzand 10 kHz frequency Although the holes are 15 cm farfrom each other the spiral does not resolve them as twosources as can be clearly seen in Figure 6 In comparisonthe ring configuration is able to localize two separate sourcesat 20 kHz which is in agreement with the simulations thata ring has a slightly better resolution than a spiral As theRayleigh limit cannot be calculated with simple analyticalformulas for spirals or other nonperiodic configurations itis more convenient to use amplitude thresholds to evaluateresolution Well-known limits are the 3-dB (half power) orthe 6-dB levels [2 12] Due to this we displayed the result ofthe acoustic camerawith a 6 dBdynamic rangewhich outlinesthe sources not resolvedThe results presented in Figures 5ndash7

Advances in Acoustics and Vibration 7

4065

400

390

380

370

360

3465

60

60

0

0

minus60

minus60

mm

mm

Press dB

(a)

3674

360

350

340

330

320

3074

60

60

0

0

minus60

minus60

mm

mm

Press dB

(b)

Figure 7 Source localization with the acoustic camera (ring configuration) (a) at 10 kHz (b) at 20 kHz

were obtained by frequency domain beamforming Further-more we analyzed the data in time domain beamformingwhich delivered a lower local resolution and a high noise levelfrom background signals

Theoretically the angular resolutionwould improvewhenthe acoustic array would be positioned closer to the sourcebut because of the diameter of the arrays of 83 cm and 75 cma distance to the object below 40 cm would not improve thereconstruction result but leads to source localization insta-bility Experimentally it is not recommended to perform themeasurement closer than the diameter but the localizationmay even work to a certain distance

The appearance of the side lobes around the main lobeespecially in Figure 7(a) is due to the big interelement spacingin the array The resolution can be improved by increasingthe frequency of the sound source or by increasing the sizeof the array Increasing the size of the array will lead toa bigger element distance which produces more artefactsIncreasing the number of microphones while increasingthe diameter of the array will lead to more costs for theacquisition system Therefore it is more practical to havea dense microphone array even with fewer microphonesto be able to localize higher frequencies and decrease thecosts

42 Measurement with the Passive Synthetic Ultrasonic Micro-phone Array For the experiment in the ultrasonic frequencyrange an ultrasonic transducer with 6 cm aperture and acenter frequency of 75 kHz (15 bandwidth) was used tosend the signals A schematic set up is shown in Figure 8Thetransducerwas placed 65 cmbehind a 3mm thick corrugatedcardboard screenwith two holes of the same size and distanceas those in the wooden box for the acoustic experiment (1 cmdiameter 15 cm center-to center-separation)The transducerwas exited with a 75 kHz sinus burst signal with 3 cyclesand 220 V sending voltage Sinus burst signals are the typicaltype of excitation for air ultrasonic transducers They area compromise between a single frequency and a pulsed

Air ultrasonicsenderreciever

Burst 75 kHzCompu

Motor controllerter

US TransducerApertures

M

Screen

icrophonePositioncontrol

z

x

y

Figure 8 Schematic set-up of the measurement in the ultrasonicfrequency range

excitation A continuous wave measurement would damagethe transducers due to the high average power

To detect the direction of the sources defined by the holesan ultrasonic receiving array is needed For the experimentswhich will be presented here we employed a broadbandmicrophone with a constant sensitivity up to 100 kHz fre-quency and a diameter of 3 mm (Type 40 DP 18rdquo PressureMicrophone GRAS Sound amp Vibration Denmark) Themicrophone was mounted to a motorized 3-axis mechanicalpositioning device which was located in front of the screenWhile the distance to the screen (z-coordinate) was keptconstant the microphone was moved in x and y directionswith amanipulator to 32 specific positions to build the passivesynthetic spiral and ring arrays

One of the obstacles when designing high frequencymicrophone arrays is the small interelement spacing Forthe choice of the array configurations (see Section 22)we considered the microphone dimensions such that theminimum interelement spacing was always larger than the

8 Advances in Acoustics and Vibration

40

20

0

minus20

minus40

0 02 04 06 08 1

Am

plitu

de [a

u]

Time [s] times10-3

(a)

100

50

00 20 40 60 80 100 120 140 160 180 200

Frequency [kHz]

Am

plitu

de [

]

(b)

Figure 9 (a) Recorded time signal of the first microphone at the spiral positions (V = 82) at 09 D distance from the source and (b) averagedspectra of the time signals calculated by fast Fourier transformation

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(a)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(b)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(c)

Figure 10 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 11 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 32 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

diameter of the microphone The diameter of the arrays with32microphoneswas 20 cm and the smallest distance betweentwo microphone positions was 098 cm (214120582) in the spiralconfiguration and 196 cm (428120582) in the ring configuration

The ultrasonic time signal of each position was captureddigitized and stored in a computer A sampling frequency of20 MSs was chosen the length of the time interval was 1 msFor each microphone configuration the measurement wasperformed at three different screenndashmicrophone distances05D 065D and 09D respectively to investigate ultrasoundlocalization at distances less than the diameter of the array (D= 20 cm) The shorter distances were chosen for comparisonbecause ultrasonic sources have short wavelength whichincreases the attenuation as a function of distance As anexample for a typical shape of the received signals the time

signal captured with the first microphone of the spiral V =82 from the origin at 09 D measurement distance and theaveraged frequency spectra of the signals of all microphonescalculated by fast Fourier transformation are depicted inFigure 9 The first microphone is the microphone with thesmallest x and y coordinates in the center of the spiral inFigure 2(b)

With a program written in MATLAB the experimentaldata were delayed and summed to perform the time domainlocalization as explained in Section 3 (8) The results calcu-lated with the 32 signals obtained with the ring and spiralconfigurations are demonstrated in Figures 10 and 11 for thethree different measurement distances It can be seen that thearrays have the expected performance in agreement with thesimulations in Section 3 The ring with 32 elements delivers

Advances in Acoustics and Vibration 9

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

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Submit your manuscripts atwwwhindawicom

6 Advances in Acoustics and Vibration

Speaker Apertures

Woodenbox Microphone

array

Acousticcamerasystem

Signal generator

(a)

05

0

minus05

050minus05

y [m

]

x [m]

(b)

Figure 5 (a) Schematic set-up of the measurement (b) the spiral configuration of the commercial microphone array

60

60

0

0

minus60

minus60

mm

mm

Press dB6452

640

630

620

610

600

590

5852

(a)

60

60

0

0

minus60

minus60

mm

mm

Press dB5617

550

540

530

520

510

5017

(b)

Figure 6 Source localization with the acoustic camera (spiral configuration) (a) at 10 kHz (b) at 20 kHz

from a signal generator A commercial 48-channel planar spi-ral configuration (83 cm diameter) and a ring configuration(75 cm diameter) with data acquisition and evaluation unitwere used to detect and localize the signals coming from twoholes (Figure 5) The camera was placed at a distance of 40cm from the holes The signals of the 48 microphones in thefrequency band from20Hz to 20 kHz (plusmn 3dB)were stored andprocessedwith the commercial software in frequency domainbeamforming The measurement was done with a 192 kHzsampling rate and the acquired time interval was 1 secondFigures 5 and 6 depict the localized acoustic signal with theavailable ring and spiral configurations in a color code imagesuperimposed to an optical photo taken with a digital camerain the center of the array According to the Rayleigh criteriondiscussed in Section 2 the minimum distance between two

sources which will be resolved by a circular aperture of 83cm diameter is 100 cm and 201 cm respectively at 20 kHzand 10 kHz frequency Although the holes are 15 cm farfrom each other the spiral does not resolve them as twosources as can be clearly seen in Figure 6 In comparisonthe ring configuration is able to localize two separate sourcesat 20 kHz which is in agreement with the simulations thata ring has a slightly better resolution than a spiral As theRayleigh limit cannot be calculated with simple analyticalformulas for spirals or other nonperiodic configurations itis more convenient to use amplitude thresholds to evaluateresolution Well-known limits are the 3-dB (half power) orthe 6-dB levels [2 12] Due to this we displayed the result ofthe acoustic camerawith a 6 dBdynamic rangewhich outlinesthe sources not resolvedThe results presented in Figures 5ndash7

Advances in Acoustics and Vibration 7

4065

400

390

380

370

360

3465

60

60

0

0

minus60

minus60

mm

mm

Press dB

(a)

3674

360

350

340

330

320

3074

60

60

0

0

minus60

minus60

mm

mm

Press dB

(b)

Figure 7 Source localization with the acoustic camera (ring configuration) (a) at 10 kHz (b) at 20 kHz

were obtained by frequency domain beamforming Further-more we analyzed the data in time domain beamformingwhich delivered a lower local resolution and a high noise levelfrom background signals

Theoretically the angular resolutionwould improvewhenthe acoustic array would be positioned closer to the sourcebut because of the diameter of the arrays of 83 cm and 75 cma distance to the object below 40 cm would not improve thereconstruction result but leads to source localization insta-bility Experimentally it is not recommended to perform themeasurement closer than the diameter but the localizationmay even work to a certain distance

The appearance of the side lobes around the main lobeespecially in Figure 7(a) is due to the big interelement spacingin the array The resolution can be improved by increasingthe frequency of the sound source or by increasing the sizeof the array Increasing the size of the array will lead toa bigger element distance which produces more artefactsIncreasing the number of microphones while increasingthe diameter of the array will lead to more costs for theacquisition system Therefore it is more practical to havea dense microphone array even with fewer microphonesto be able to localize higher frequencies and decrease thecosts

42 Measurement with the Passive Synthetic Ultrasonic Micro-phone Array For the experiment in the ultrasonic frequencyrange an ultrasonic transducer with 6 cm aperture and acenter frequency of 75 kHz (15 bandwidth) was used tosend the signals A schematic set up is shown in Figure 8Thetransducerwas placed 65 cmbehind a 3mm thick corrugatedcardboard screenwith two holes of the same size and distanceas those in the wooden box for the acoustic experiment (1 cmdiameter 15 cm center-to center-separation)The transducerwas exited with a 75 kHz sinus burst signal with 3 cyclesand 220 V sending voltage Sinus burst signals are the typicaltype of excitation for air ultrasonic transducers They area compromise between a single frequency and a pulsed

Air ultrasonicsenderreciever

Burst 75 kHzCompu

Motor controllerter

US TransducerApertures

M

Screen

icrophonePositioncontrol

z

x

y

Figure 8 Schematic set-up of the measurement in the ultrasonicfrequency range

excitation A continuous wave measurement would damagethe transducers due to the high average power

To detect the direction of the sources defined by the holesan ultrasonic receiving array is needed For the experimentswhich will be presented here we employed a broadbandmicrophone with a constant sensitivity up to 100 kHz fre-quency and a diameter of 3 mm (Type 40 DP 18rdquo PressureMicrophone GRAS Sound amp Vibration Denmark) Themicrophone was mounted to a motorized 3-axis mechanicalpositioning device which was located in front of the screenWhile the distance to the screen (z-coordinate) was keptconstant the microphone was moved in x and y directionswith amanipulator to 32 specific positions to build the passivesynthetic spiral and ring arrays

One of the obstacles when designing high frequencymicrophone arrays is the small interelement spacing Forthe choice of the array configurations (see Section 22)we considered the microphone dimensions such that theminimum interelement spacing was always larger than the

8 Advances in Acoustics and Vibration

40

20

0

minus20

minus40

0 02 04 06 08 1

Am

plitu

de [a

u]

Time [s] times10-3

(a)

100

50

00 20 40 60 80 100 120 140 160 180 200

Frequency [kHz]

Am

plitu

de [

]

(b)

Figure 9 (a) Recorded time signal of the first microphone at the spiral positions (V = 82) at 09 D distance from the source and (b) averagedspectra of the time signals calculated by fast Fourier transformation

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(a)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(b)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(c)

Figure 10 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 11 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 32 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

diameter of the microphone The diameter of the arrays with32microphoneswas 20 cm and the smallest distance betweentwo microphone positions was 098 cm (214120582) in the spiralconfiguration and 196 cm (428120582) in the ring configuration

The ultrasonic time signal of each position was captureddigitized and stored in a computer A sampling frequency of20 MSs was chosen the length of the time interval was 1 msFor each microphone configuration the measurement wasperformed at three different screenndashmicrophone distances05D 065D and 09D respectively to investigate ultrasoundlocalization at distances less than the diameter of the array (D= 20 cm) The shorter distances were chosen for comparisonbecause ultrasonic sources have short wavelength whichincreases the attenuation as a function of distance As anexample for a typical shape of the received signals the time

signal captured with the first microphone of the spiral V =82 from the origin at 09 D measurement distance and theaveraged frequency spectra of the signals of all microphonescalculated by fast Fourier transformation are depicted inFigure 9 The first microphone is the microphone with thesmallest x and y coordinates in the center of the spiral inFigure 2(b)

With a program written in MATLAB the experimentaldata were delayed and summed to perform the time domainlocalization as explained in Section 3 (8) The results calcu-lated with the 32 signals obtained with the ring and spiralconfigurations are demonstrated in Figures 10 and 11 for thethree different measurement distances It can be seen that thearrays have the expected performance in agreement with thesimulations in Section 3 The ring with 32 elements delivers

Advances in Acoustics and Vibration 9

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

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Advances in Acoustics and Vibration 7

4065

400

390

380

370

360

3465

60

60

0

0

minus60

minus60

mm

mm

Press dB

(a)

3674

360

350

340

330

320

3074

60

60

0

0

minus60

minus60

mm

mm

Press dB

(b)

Figure 7 Source localization with the acoustic camera (ring configuration) (a) at 10 kHz (b) at 20 kHz

were obtained by frequency domain beamforming Further-more we analyzed the data in time domain beamformingwhich delivered a lower local resolution and a high noise levelfrom background signals

Theoretically the angular resolutionwould improvewhenthe acoustic array would be positioned closer to the sourcebut because of the diameter of the arrays of 83 cm and 75 cma distance to the object below 40 cm would not improve thereconstruction result but leads to source localization insta-bility Experimentally it is not recommended to perform themeasurement closer than the diameter but the localizationmay even work to a certain distance

The appearance of the side lobes around the main lobeespecially in Figure 7(a) is due to the big interelement spacingin the array The resolution can be improved by increasingthe frequency of the sound source or by increasing the sizeof the array Increasing the size of the array will lead toa bigger element distance which produces more artefactsIncreasing the number of microphones while increasingthe diameter of the array will lead to more costs for theacquisition system Therefore it is more practical to havea dense microphone array even with fewer microphonesto be able to localize higher frequencies and decrease thecosts

42 Measurement with the Passive Synthetic Ultrasonic Micro-phone Array For the experiment in the ultrasonic frequencyrange an ultrasonic transducer with 6 cm aperture and acenter frequency of 75 kHz (15 bandwidth) was used tosend the signals A schematic set up is shown in Figure 8Thetransducerwas placed 65 cmbehind a 3mm thick corrugatedcardboard screenwith two holes of the same size and distanceas those in the wooden box for the acoustic experiment (1 cmdiameter 15 cm center-to center-separation)The transducerwas exited with a 75 kHz sinus burst signal with 3 cyclesand 220 V sending voltage Sinus burst signals are the typicaltype of excitation for air ultrasonic transducers They area compromise between a single frequency and a pulsed

Air ultrasonicsenderreciever

Burst 75 kHzCompu

Motor controllerter

US TransducerApertures

M

Screen

icrophonePositioncontrol

z

x

y

Figure 8 Schematic set-up of the measurement in the ultrasonicfrequency range

excitation A continuous wave measurement would damagethe transducers due to the high average power

To detect the direction of the sources defined by the holesan ultrasonic receiving array is needed For the experimentswhich will be presented here we employed a broadbandmicrophone with a constant sensitivity up to 100 kHz fre-quency and a diameter of 3 mm (Type 40 DP 18rdquo PressureMicrophone GRAS Sound amp Vibration Denmark) Themicrophone was mounted to a motorized 3-axis mechanicalpositioning device which was located in front of the screenWhile the distance to the screen (z-coordinate) was keptconstant the microphone was moved in x and y directionswith amanipulator to 32 specific positions to build the passivesynthetic spiral and ring arrays

One of the obstacles when designing high frequencymicrophone arrays is the small interelement spacing Forthe choice of the array configurations (see Section 22)we considered the microphone dimensions such that theminimum interelement spacing was always larger than the

8 Advances in Acoustics and Vibration

40

20

0

minus20

minus40

0 02 04 06 08 1

Am

plitu

de [a

u]

Time [s] times10-3

(a)

100

50

00 20 40 60 80 100 120 140 160 180 200

Frequency [kHz]

Am

plitu

de [

]

(b)

Figure 9 (a) Recorded time signal of the first microphone at the spiral positions (V = 82) at 09 D distance from the source and (b) averagedspectra of the time signals calculated by fast Fourier transformation

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(a)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(b)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(c)

Figure 10 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 11 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 32 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

diameter of the microphone The diameter of the arrays with32microphoneswas 20 cm and the smallest distance betweentwo microphone positions was 098 cm (214120582) in the spiralconfiguration and 196 cm (428120582) in the ring configuration

The ultrasonic time signal of each position was captureddigitized and stored in a computer A sampling frequency of20 MSs was chosen the length of the time interval was 1 msFor each microphone configuration the measurement wasperformed at three different screenndashmicrophone distances05D 065D and 09D respectively to investigate ultrasoundlocalization at distances less than the diameter of the array (D= 20 cm) The shorter distances were chosen for comparisonbecause ultrasonic sources have short wavelength whichincreases the attenuation as a function of distance As anexample for a typical shape of the received signals the time

signal captured with the first microphone of the spiral V =82 from the origin at 09 D measurement distance and theaveraged frequency spectra of the signals of all microphonescalculated by fast Fourier transformation are depicted inFigure 9 The first microphone is the microphone with thesmallest x and y coordinates in the center of the spiral inFigure 2(b)

With a program written in MATLAB the experimentaldata were delayed and summed to perform the time domainlocalization as explained in Section 3 (8) The results calcu-lated with the 32 signals obtained with the ring and spiralconfigurations are demonstrated in Figures 10 and 11 for thethree different measurement distances It can be seen that thearrays have the expected performance in agreement with thesimulations in Section 3 The ring with 32 elements delivers

Advances in Acoustics and Vibration 9

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

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Submit your manuscripts atwwwhindawicom

8 Advances in Acoustics and Vibration

40

20

0

minus20

minus40

0 02 04 06 08 1

Am

plitu

de [a

u]

Time [s] times10-3

(a)

100

50

00 20 40 60 80 100 120 140 160 180 200

Frequency [kHz]

Am

plitu

de [

]

(b)

Figure 9 (a) Recorded time signal of the first microphone at the spiral positions (V = 82) at 09 D distance from the source and (b) averagedspectra of the time signals calculated by fast Fourier transformation

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(a)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(b)

005

0

minus005

0050minus005

y [m

]

x [m]

0

-2

-4

-6

-8

-10

(c)

Figure 10 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 11 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 32 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

diameter of the microphone The diameter of the arrays with32microphoneswas 20 cm and the smallest distance betweentwo microphone positions was 098 cm (214120582) in the spiralconfiguration and 196 cm (428120582) in the ring configuration

The ultrasonic time signal of each position was captureddigitized and stored in a computer A sampling frequency of20 MSs was chosen the length of the time interval was 1 msFor each microphone configuration the measurement wasperformed at three different screenndashmicrophone distances05D 065D and 09D respectively to investigate ultrasoundlocalization at distances less than the diameter of the array (D= 20 cm) The shorter distances were chosen for comparisonbecause ultrasonic sources have short wavelength whichincreases the attenuation as a function of distance As anexample for a typical shape of the received signals the time

signal captured with the first microphone of the spiral V =82 from the origin at 09 D measurement distance and theaveraged frequency spectra of the signals of all microphonescalculated by fast Fourier transformation are depicted inFigure 9 The first microphone is the microphone with thesmallest x and y coordinates in the center of the spiral inFigure 2(b)

With a program written in MATLAB the experimentaldata were delayed and summed to perform the time domainlocalization as explained in Section 3 (8) The results calcu-lated with the 32 signals obtained with the ring and spiralconfigurations are demonstrated in Figures 10 and 11 for thethree different measurement distances It can be seen that thearrays have the expected performance in agreement with thesimulations in Section 3 The ring with 32 elements delivers

Advances in Acoustics and Vibration 9

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Advances in Acoustics and Vibration 9

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 12 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 13 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 16 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 14 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

better resolution but more side lobes There is an extremeappearance of artefacts in the reconstruction plane when thearray is placed very close (05 D) to the source which makesit difficult to find the exact position of the holes To examinethe influence of the distance of the array to the source thedistance of the microphone from the screen was increased to065 D and 09 D The best results were achieved when themeasurement distance was 09 D a bit less than the diameterof the arrays

To get a better overview we repeated the measurementswith 16 and 48 microphone positions and kept the diameterof the arrays constant to 20 cm Figures 12ndash15 depicts thereconstruction results The reconstruction images with 16microphones especially at smaller measurement distancesare not reliable which make it difficult to find the exact

position of the sources On the other hand arrays with48 microphones demonstrate precise localization The cal-culation with 48 microphones demands more computationtime and memory capacity which is unfavorable for mostof the applications To analyze these results quantitativelywe measured MSL and API (array performance indicator)from Figures 10ndash15 The results of this analysis are shown inthe Table 1 API is a dimensionless measure of the resolutionof the microphone arrays which is defined as the area of asource calculated at -6 dB from its peak divided by the squareof the wavelength [12]The beamwidth in the field of acousticsource localization is defined as the width of the main beamat -3 dB Therefore we calculated the area of each source at-3 dB from its maximum value and added these values to findAPI for each case in Table 1 It can be seen from the table that

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

10 Advances in Acoustics and Vibration

Table 1 Results of post processing experimental data

Ring 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -020 065 -025 066065 D - - -200 074 -150 07509 D -089 108 -410 110 -410 112Spiral 82 16 Microphones 32 Microphones 48 Microphonesd MSL (dB) API MSL (dB) API MSL (dB) API05 D - - -145 154 -410 167065 D - - -440 165 -600 16809 D -224 200 -565 189 -620 194

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(a)

005

0

minus005

0050minus005

y [m

]0

-2

-4

-6

-8

x [m]

(b)

005

0

minus005

0050minus005

y [m

]

0

-2

-4

-6

-8

x [m]

(c)

Figure 15 Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 82)with 48 elements Z-distance of the microphone to the screen (a) 05 D (b) 065 D (c) 09 D

API increases with an increase in the number ofmicrophonesexcept the case with 16-microphone spiral arrangement at 09D which delivers a high value After a closer look at thisreconstruction it was seen that the area of right source at -3dB is extended and seems bigger This could happen becauseof a calculation with a smaller number of microphonesMoreover the reconstruction with 16 microphones at shortmeasurement distances is not trustworthy and the images failto deliver reasonable values for MSL and API The MSL ofthe ring array does not improve even with large number ofmicrophones however spiral array gains better MSL with48 microphones mostly at long measurement distances Ingeneral the MSL difference between 32 and 48 microphonesis not abundant and a smaller number of microphones leadto better resolution

In order to make sure that the two maxima obtained bybeamforming in Figures 10ndash15 are not caused by aliasing orby side lobes but can be attributed to the two real sources werepeated the measurements with single sources by coveringone of the holes Figure 16 shows the result when the left andthe right hole were covered respectively In this case justone of the sources is visible in each measurement As themeasurement set-up was moved a small amount to one sideboth sources are shifted to the left compared to the resultsin Figures 10ndash15 We measured the x-position correspondingto the center of each peak in Figure 16 The center-to-centerdistance between the peaks is 13 mm which is close butnot exactly equal to the expected 15 mm The reason forthe deviation could be in the experimental set-up as wellas in the properties and position of the spiral and will

005

0

minus005

y [m

]

005

0

minus005

y [m

]

0050

0013

minus005

x [m]

(b)

(a)0

-2

-4

-6

-8

-10

0

-2

-4

-6

-8

-10

Figure 16 Beamforming result at 75 kHz frequency calculated withexperimental data from the spiral configuration at 18 cm distancefrom the screen (a) Left hole covered (b) right hole covered

have to be examined in future The experiments presentedin Figures 10ndash15 clearly show that the source localizationat 75 kHz frequency was successful and sources with the

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Advances in Acoustics and Vibration 11

separation distance less than 15 mm can be resolved Inaddition to the delay and sum beamforming in the timedomain we also tested frequency domain beamforming withthe experimental data The frequency domain beamformingshowed stronger side lobe levels For this reason these resultsare not shown

5 Conclusion and Future Work

This research work presents first steps towards an ultrasonicmicrophone array for NDT applications Ring and spiralconfigurations with 32 elements and 20 cm diameter weredesigned and simulated to examine the array resolution andlocalize ultrasonic sources at 75 kHzThe simulations demon-strated that the ring array outperforms the spiral array withrespect to the resolution but deliversmore artefacts especiallyin case of two coherent sources A set of experiments inthe ultrasonic frequency range at 75 kHz was performed tocorroborate the simulations As ultrasonic multichannel dataacquisition systems would be expensive we performed theultrasonic experiments in this studywith a singlemicrophoneand a single data acquisition system This microphone wasmoved to the required positions with the help of a motordriven mechanical positioning system A screen with twoholes with 15 mm center-to-center separation distance placedin front of an ultrasonic transducer was used as the testsource Delay and sum beamforming in time domain servedas a simple method for the simulations and for the processingof the ultrasonic experimental data The measurement at09 D distance between array and screen showed very goodresults without extreme appearance of side lobesThenumberof microphones is very important as it defines the necessarynumber of channels of the electronics and therefore theoverall costs of the system A comparison to the performanceof ring or spiral systems with 16 and 48 microphones showedthat 32 microphones are a good compromise at the chosengeometrical conditions

In order to demonstrate the influence of the operatingfrequency a source with the same geometry (a screen withtwo holes with a center-to-center separation distance of15 mm) but with lower frequency (10 kHz and 20 kHz)was examined with a commercial acoustic camera equippedwith 48 microphones The best result was obtained withfrequency domain beamforming in this case Neverthelessit was clearly demonstrated that higher frequency provideshigher local resolution as even sophisticated post-processingcannot compensate for all artefacts and broadening effects

The results of this study have shown that source localiza-tion by beamforming is possible in the ultrasonic frequencyrange above 40 kHz and that it is possible to improve the localresolution by using ultrasonic frequency In future studies theinfluence of parameters such as measurement distance arrayconfiguration pulse length and frequency ranges will haveto be investigated and optimized in more detail Localizationof ultrasonic sources with arrays could be very promising inthe context of NDT as for example in leakage detection inautomotive or aerospace industry Industrial processes suchas welding processes for example do not only emit acousticsignals but also signals in the ultrasonic frequency range

Process monitoring at increased frequency could benefitfrom a higher signal to noise ratio due to a lower level ofreverberation and environmental noise signals as well as ahigher local resolutionThis could be exploited by applicationof passive contactless ultrasonic arrays

Data Availability

Themeasured MATLAB data used to support the findings ofthis study are available from the corresponding author uponrequest

Disclosure

Some parts of theworkwere presented as an oral presentationat DAGA Conference 2018 in Munich and Fraunhofer VisionTechnologietag 2018 in Jena

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

A part of this work has been funded by the GermanMinistryof Economics and Technology in the frame of the pro-gram ZIM (Zentrales Innovationsprogramm Mittelstand)contact ZF4234102LT6 cooperative project BeamUS500 andIZFP project part BeamUS500-Sensor The authors grate-fully acknowledge Nico Brosta and Katharina Bonaventurafor helping with ultrasonic data acquisition and MATLABprogramming

References

[1] B W Drinkwater and P D Wilcox ldquoUltrasonic arrays for non-destructive evaluation a reviewrdquo NDT amp E International vol39 no 7 pp 525ndash541 2006

[2] H L Van Trees ldquoOptimum array processingrdquo in Part IVof Detection Estimation and Modulation Theory Wiley NewDehli India 2002

[3] D H Johnson and D E Dudgeon Array Signal ProcessingConcepts and Techniques Prentice Hall Upper Saddle River1993

[4] O Jaeckel ldquoStrengths and weaknesses of calculating beam-forming in the time domainrdquo in Proceedings of the BerlinBeamforming Conference (BeBeC) 2006

[5] P Sijtsma ldquoCLEAN based on spatial source coherencerdquo inProceedings of the 13th AIAACEAS Aeroacoustics Conference(28th AIAA Aeroacoustics Conference) Italy May 2007

[6] T Brooks and W Humphreys ldquoA deconvolution approachfor the mapping of acoustic sources (DAMAS) determinedfrom phased microphone arraysrdquo in Proceedings of the 10thAIAACEAS Aeroacoustics Conference Manchester GreatBritain 2004

[7] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo IEEE Transactions on Antennas and Propagationvol 34 no 3 pp 276ndash280 1986

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

12 Advances in Acoustics and Vibration

[8] Z Prime and C Doolan ldquoA comparison of popular beam-forming arraysrdquo in Proceedings of the Annual Conference ofthe Australian Acoustical Society Victor Harbor Australia RedHook NY USA 2013

[9] S D Somasundaram N R Butt A Jakobsson and L HartldquoLow-complexity uncertainty-set-based robust adaptive beam-forming for passive sonarrdquo IEEE Journal of Oceanic Engineeringpp 1ndash17 2015

[10] E Ruigrok S Gibbons and K Wapenaar ldquoCross-correlationbeamformingrdquo Journal of Seismology vol 21 no 3 pp 495ndash5082017

[11] G C McLaskey S D Glaser and C U Grosse ldquoBeamformingarray techniques for acoustic emission monitoring of largeconcrete structuresrdquo Journal of Sound and Vibration vol 329no 12 pp 2384ndash2394 2010

[12] C Fan M Caleap M Pan and B W Drinkwater ldquoA com-parison between ultrasonic array beamforming and superresolution imaging algorithms for non-destructive evaluationrdquoUltrasonics vol 54 no 7 pp 1842ndash1850 2014

[13] H Pfeiffer M Bock I Pitropakis et al ldquoIdentification ofimpact damage in sandwich composites by acoustic cameradetection of leaky lamb wave mode conversionsrdquo e-Journal ofNondestructive Testing (NDT) pp 1435ndash4934 2013

[14] R Groschup and C U Grosse ldquoEnhancing air-coupled impact-echo with microphone arraysrdquo in Proceedings of the Interna-tional Symposium Non-Destructive Testing in Civil EngineeringBerlin Germany 2015

[15] B Barsikow W F King III and E Pfizenmaier ldquoWheelrailnoise generated by a high-speed train investigated with a linearray of microphonesrdquo Journal of Sound and Vibration vol 118no 1 pp 99ndash122 1987

[16] U Michel and B Barsikow ldquoLocalisation of sound sources onmoving vehicles with microphone arraysrdquo in Proceedings ofEuroNoise Naples Italy 2003

[17] U Michel B Barsikow B Haverich et al ldquoInvestigation ofairframe and jet noise in high-speed flight with a microphonearrayrdquo in Proceedings of the 3rd AIAACEAS AeroacousticsConference Atlanta GA USA 1997

[18] M Yang S Hill and J Gray ldquoLocalization of plane reflectorsusing a wide-beamwidth ultrasound transducer arrangementrdquoIEEE Transactions on Instrumentation and Measurement vol46 no 3 pp 711ndash716

[19] S Harput and A Bozkurt ldquoUltrasonic phased array device foracoustic imaging in airrdquo IEEE Sensors Journal vol 8 no 11 pp1755ndash1762 2008

[20] V Kunin M Turqueti J Saniie and E Oruklu ldquoDirection ofarrival estimation and localization using acoustic sensor arraysrdquoJournal of Sensor Technology vol 01 no 03 pp 71ndash80 2011

[21] F J Pompei and S Wooh ldquoPhased array element shapes forsuppressing grating lobesrdquoThe Journal of the Acoustical Societyof America vol 111 no 5 p 2040 2002

[22] L Rayleigh ldquoXXXI Investigations in optics with special refer-ence to the spectroscoperdquo Philosophical Magazine vol 8 no 49pp 261ndash274 1879

[23] A Nordborg J Wedemann and L Willenbrink ldquoOptimumarray microphone configurationrdquo in Proceedings of the 29thInternational Congress and Exhibition on Noise Control Engi-neering Nice France 2000

[24] H Vogel ldquoA better way to construct the sunflower headrdquoMathematical Biosciences vol 44 no 3-4 pp 179ndash189 1979

[25] H Segerman ldquoThe sunflower spiral and the fibonacci metricrdquoin Proceedings of the Bridges Mathematics Music Art Architec-ture Culture pp 483ndash486 University of Texas at Austin 2010

[26] E Sarradj ldquoA generic approach to synthesize optimal arraymicrophone arrangementsrdquo in Proceedings of the Berlin Beam-forming Conference (BeBeC) 2016

[27] A Movahed T Waschkies and U Rabe ldquoComparison of dif-ferent microphone arrays for signal processing of air-ultrasonicsignals in nondestructive testingrdquo in Proceedings of the SHMNDT Conference Saarbrucken Germany 2018

[28] R Lerch G Sessler and D Wolf Technische Akustik Grundla-gen und Anwendungen Springer Berlin Germany 2009

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom