Visser, Rene

English

Inverse source identification techniques are used to find the acoustic sources on the surface of a sound radiating object. One of the most general applicable methods is the inverse frequency response function method (IFRF). The standard IFRF technique uses acoustic pressure measurements performed on a measurement grid in the nearfield of an acoustic source to determine the corresponding normal velocities on the surface of the source. To relate the measured field pressures to the surface vibrations, a transfer matrix is calculated with a boundary element solver (BEMSYS). In the source localization process, this matrix needs to be inverted in order to predict the original surface normal velocities. Generally, the transfer matrix is ill-conditioned and can only be solved by applying regularization techniques. In this paper, apart from conventional pressure measurements, it is investigated whether the nearfield particle velocities, measured with a Microflown sensor, can be used to reconstruct the original source vibrations. By means of an experimental setup, a comparison is made between pressure based and velocity based IFRF

University of Twente Research Information

The 32nd International Congress and Exposition on Noise Control EngineeringJeju International Convention Center, Seogwipo, Korea,August 25-28, 2003[N382] Acoustic Source Localization based on Pressure and ParticleVelocity MeasurementsRené VisserUniversity of Twente, Mechanical EngineeringP.O. Box 217, 7500 AE Enschede, The NetherlandsEmail address: r.visser@utwente.nlABSTRACTInverse source identification techniques are used to find the acoustic sources on the surface ofa sound radiating object. One of the most general applicable methods is the inverse frequencyresponse function method (IFRF). The standard IFRF technique uses acoustic pressure mea-surements performed on a measurement grid in the nearfield of an acoustic source to determinethe corresponding normal velocities on the surface of the source. To relate the measured fieldpressures to the surface vibrations, a transfer matrix is calculated with a boundary elementsolver (BEMSYS). In the source localization process, this matrix needs to be inverted in orderto predict the original surface normal velocities. Generally, the transfer matrix is ill-conditionedand can only be solved by applying regularization techniques.In this paper, apart from conventional pressure measurements, it is investigated whether thenearfield particle velocities, measured with a Microflown sensor, can be used to reconstruct theoriginal source vibrations. By means of an experimental setup, a comparison is made betweenpressure based and velocity based IFRF.KEYWORDS: Acoustic source localization, BEM, IFRF, Inverse problems, MicroflownINTRODUCTIONExterior structural acoustics focuses on the relation between vibrations on the surface of astructure and the radiated sound field. In the IFRF source localization technique, the vibrationpatterns at the source surface are unknown and have to be determined from the sound fieldmeasured at several points near the source surface.Conventionally, these source localization methods are based on acoustic pressure measurements.However, due to recent developments in sensor technology it is possible to directly measureacoustic particle velocity with the so-called Microflown sensor (www.microflown.com). In anearlier study [8] it was shown by means of numerical simulations that the IFRF method basedon particle velocity measurements would, from a theoretical point of view, lead to improvedreconstructions of the surface vibrations. This paper deals with the experimental validation ofthis novel IFRF method in order to confirm these numerical findings.EXPERIMENTAL SETUPThe experimental setup, as shown in figure 1, consists of a hollow aluminum box with 30 mmthick walls. A flexible aluminum plate (1.1 mm thick) is clamped to the box by means ofreinforcement strips that are bolted to the box. The top of box is covered with a 30 mm thickplate. Inside the box a loudspeaker generates an interior sound field, in the frequency range200-1200 Hz, that causes the flexible plate to vibrate. Eventually, this plate vibration results ina sound field outside the box.170270220Figure 1: The experimental setup consists of an aluminum box with 30 mm thick walls. This studyfocuses on the configuration where a rigid and a flexible plate are attached to the top and front of the boxrespectively.In order to obtain the relation between the acoustic quantities surrounding the box and thestructural normal velocity of the box, a boundary element model is made as shown in figure 2.The source mesh of the model consists of 898 linear triangular elements with a total of 463 nodes.On a plane at a distance of 30 mm from the flexible plate an exterior field mesh consisting of256 nodes is defined.PSfrag replacements123PSfrag replacements123Figure 2: Source surface mesh of the box (left) and field mesh at a distance of 30 mm in front of the box(right). The field grid consists of 16x16 measurement points.To obtain a reference solution for the source localization methods, a laser vibrometer is used tomeasure the surface normal velocity of the flexible plate at 171 nodes of the BEM mesh (seedots in left side of figure 2). In the considered frequency range, it is allowed to assume that thethick walls of the box have a negligible surface velocity compared to the flexible front plate. Asa consequence, all the radiated sound originates from the front plate. Both the positioning anddata acquisition of the sensors is completely automated under the Matlab environment.BASIC RELATIONSConventional pressure based IFRFIn conventional IFRF methods [3, 4, 6] the task is to obtain the unknown surface velocities innormal direction (vn) from the acoustic pressures (pf ) measured at the field grid. This is doneby solving vn from the following system of equationspf = Hp · vn (1)where transfer matrix Hp represents the discretized equivalent of the Helmholtz integral equa-tion [1, 5, 7].Unfortunately, system (1) is a discrete ill-conditioned problem, which implies that arbitrarysmall perturbations in the measured pressure signal result in large errors in the solution ofthe surface velocities. Nevertheless, a meaningful solution can be found in both physical andmathematical terms with the help of regularization methods. It is known [3, 6] that standardregularization techniques like truncated singular value decomposition or Tikhonov regulariza-tion give adequate solutions in IFRF techniques. In this paper, a more efficient iterative leastsquares method (LSQR) was used to solve the system of equations [2].Novel particle velocity based IFRFIn contrast with the conventional pressure based IFRF method, the proposed novel sourceidentification method uses the acoustic particle velocities instead of pressures as measured fieldquantity. According to Euler’s equation of motion, the particle velocities can be calculated bytaking the gradient of the Helmholtz integral equation. The developed boundary element solverBEMSYS is then used to derive the transfer matrices from surface normal velocity to acousticparticle velocity in the field grid.Once the transfer matrices are known, the surface velocity can be reconstructed in several waysby separately solving each of the following systemsv1 = Hv1 · vn v2 = Hv2 · vn v3 = Hv3 · vn (2)where v1,v2 and v3 are the three mutually perpendicular field velocity components as indicatedin figure 2.Of course when multiple sensors are applied simultaneously, it is possible to solve combinationsof the (sub)systems (1) and (2), for example{pfv3}=[HpHv3]· vn (3)Like in the conventional IFRF method, the systems of equations based on particle velocity arealso ill-conditioned and require regularization [6].RESULTSFigure 3 shows the results of the laser vibrometer scan which forms the reference solution for thesource localization methods. The upper part of the figure gives the computed mass-normalizedkinetic energy (Ek =12∮SvHn vn dS) based on the measured surface velocities of the plate. It isclear that eight resonance frequencies can be observed in the considered frequency range. Thelower part of figure 3 illustrates the corresponding plate vibrations at the successive resonances.200 300 400 500 600 700 800 900 1000 1100 1200PSfrag replacementsFrequency [Hz]Kineticenergy[dB]310 514705729864 9011040 1109PSfrag replacementsFrequency [Hz]Kinetic energy [dB]31051470572986490110401109S(1,1) S(1,2) S(2,1) A(0,1,0) S(1,3) S(2,2) A(1,0,0) A(0,0,1)Figure 3: Results obtained by a laser Doppler scan of the plate: normalized kinetic energy (upper) andsurface normal velocity of the plate (lower) at the resonance frequencies. Capital S indicates a structurallydominated mode and A stands for acoustically dominated mode. Colors are scaled between +1 (white)and -1 (black).Note that only the surface velocities on the flexible front plate are shown. The vibration levelsof the remaining walls are much lower and hence they have a negligible contribution to theexterior acoustic field. Figure 4 illustrates the measured acoustic quantities in the field grid.These measured distributions are input for the different types of source localization methods.PSfrag replacementspf - S(1,1) pf - S(1,2) pf - S(2,1) pf - A(0,1,0) pf - S(1,3) pf - S(2,2) pf - A(1,0,0) pf - A(0,0,1)PSfrag replacementspf - S(1,1)pf - S(1,2)pf - S(2,1)pf - A(0,1,0)pf - S(1,3)pf - S(2,2)pf - A(1,0,0)pf - A(0,0,1)v2 - S(1,1) v2 - S(1,2) v2 - S(2,1) v2 - A(0,1,0) v2 - S(1,3) v2 - S(2,2) v2 - A(1,0,0) v2 - A(0,0,1)PSfrag replacementspf - S(1,1)pf - S(1,2)pf - S(2,1)pf - A(0,1,0)pf - S(1,3)pf - S(2,2)pf - A(1,0,0)pf - A(0,0,1)v2 - S(1,1)v2 - S(1,2)v2 - S(2,1)v2 - A(0,1,0)v2 - S(1,3)v2 - S(2,2)v2 - A(1,0,0)v2 - A(0,0,1)v3 - S(1,1) v3 - S(1,2) v3 - S(2,1) v3 - A(0,1,0) v3 - S(1,3) v3 - S(2,2) v3 - A(1,0,0) v3 - A(0,0,1)Figure 4: Acoustic quantities measured in field grid at a distance of 30 mm from the front plate. Thewhite rectangle indicates the outer contour of the box.PSfrag replacementsS(1,1) S(1,2) S(2,1) A(0,1,0) S(1,3) S(2,2) A(1,0,0) A(0,0,1)PSfrag replacementsS(1,1) S(1,2) S(2,1) A(0,1,0) S(1,3) S(2,2) A(1,0,0) A(0,0,1)Figure 5: Reconstructed plate vibrations by means of the IFRF method, (upper) the conventional pressurebased method and (lower) the novel method based on particle velocity measurement (v3). S indicates astructural mode and A stands for acoustic mode.Figure 5 shows the reconstructed surface normal velocities with the IFRF method based onpressure measurements (p) and based on particle velocity measurements in the direction per-pendicular to the field grid (v3). It is obvious that good agreement is found between thevibration patterns measured with the laser vibrometer and the results obtained with the sourcelocalization methods.To compare the quality of the reconstructed surface vibrations, the associated acoustic powerΠ = 12∮vHn p dS is evaluated. The acoustic power based on the laser scan method is consideredto be the most accurate and consequently it is used as reference for the results obtained withthe different types of IFRF methods. Figure 6 shows the reconstructed narrow band acousticpower predicted by the different methods.The differences between the total acoustic power based on the reconstructed surface normalvelocities and the power based on the directly measured surface normal velocities are collectedin table 1. From the table it becomes clear that a very acceptable deviation in total sound powerof about 1 dB is found for the various types of IFRF methods.200 400 600 800 1000 120030405060708090PSfrag replacementsFrequency [Hz]Π[dB](0dB=1E-12Wrms) laserIFRF pfIFRF v3200 400 600 800 1000 120030405060708090PSfrag replacementsFrequency [Hz]Π[dB](0dB=1E-12Wrms) laserIFRF pfIFRF v3reactiveactivereactiveactiveFigure 6: Comparison of acoustic power between direct laser measurement and IFRF method based onpressure (left side) and particle velocity (right side). The upper lines represent the reactive power (imag-inary part) whereas the lower lines represent the active power (real part).IFRF method Active power [dB rms] Reactive power [dB rms]pf 0.72 1.25v2 0.02 0.53v3 0.58 0.67Table 1: Difference in total sound power based on IFRF reconstructions versus laser vibrometer measure-ment.Furthermore it can be noticed that the results based on particle velocity measurements areslightly better than those based on pressure measurements.CONCLUSIONSIn this paper the practical application of different formulations of the IFRF source localizationmethod was investigated. By means of an experimental setup it was shown that very good agree-ment was found between the direct laser Doppler measurements of the source surface velocitiesand the reconstructed surface normal velocities with the IFRF methods. From a theoreticalpoint of view it was expected that the novel source localization method based on particle veloc-ity would result in slightly better reconstructed surface velocities compared to the conventionalpressure based IFRF method [8]. The validation experiments presented in this paper confirmedthese theoretical findings.ACKNOWLEDGEMENTSThis research is supported by the Dutch Technology Foundation (STW). The author would liketo thank his supervisor Henk Tijdeman and his other colleagues for their cooperation, valuablesuggestions and critical comments.REFERENCES[1] R.D. Ciskowski and C.A. Brebbia. Boundary Element Methods in Acoustics. Computational Mechan-ics publications, 1991.[2] P.C. Hansen. Regularization tools: A matlab package for analysis and solution of discrete ill-posedproblems. Numerical Algorithms, 6:1–35, 1994.[3] F. Márki and F. Augusztinovicz. Effects, interpretation and practical application of truncated SVD inthe numerical solution of inverse radiation problems. Proceedings ISMA25, pages 1405–1413, Leuven(Belgium), 2000.[4] J.D. Maynard. Nearfield Acoustic Holography: A Review. Proceedings Inter-Noise 2001, The Hague(Holland), 2001.[5] R. Visser. Direct Boundary Element Method - A Matlab Toolbox. Technical Report WB.01/TM-5031,University of Twente, Faculty of Mechanical Engineering, Enschede, The Netherlands, 2001.[6] R. Visser. Regularization in nearfield acoustic source identification. In Proceedings Eighth Interna-tional Congress on Sound and Vibration, pages 1637–1644, Hong Kong (China), 2001.[7] R. Visser. Computation of Near-Field Acoustic Quantities with an Adaptive Boundary ElementMethod. Technical Report CTW.02/TMK-5400, University of Twente, Faculty of Mechanical Engi-neering, Enschede, The Netherlands, 2002.[8] R. Visser. Inverse Source Identification based on Acoustic Particle Velocity Measurements. In Pro-ceedings Internoise, Dearborn - MI (USA), 2002.

[N382] Acoustic Source Localization based on Pressure and Particle Velocity Measurements

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[N382] Acoustic Source Localization based on Pressure and Particle Velocity Measurements

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