Introduction to Beamforming for Noise Source Localization

1. Introduction to Beamformingfor Noise Source Localization Bálint Kocsis PhD student kocsis@ara.bme.hu Csaba Horváth assistant professorhorvath@ara.bme.hu Budapest University of Technology and Economics Faculty of Mechanical Engineering Department of Fluid Mechanics

2. Outline • Basic acoustics • Microphones • Advanced acoustics • Microphone array • Time domain beamforming • Frequency domain beamforming • ROtating Source Identifier • Generalized InverseBeamforming

3. Basic acoustics – Sound wave Waves • An oscillation accompanied by a transfer of energy • According to direction of movement: Transverse / Longitudinal (Surface, etc.) • Requires / does not requirea medium: Mechanical / Electromagnetic waves Sound • A longitudinal mechanical wave transmitted through a physical medium • Distorts the medium by creating moving fronts of high and low particle compression • Compression wavespropagate as audiblewaves of pressure • http://clas.mq.edu.au/speech/acoustics/basic_acoustics/whatissound.html

4. Basic acoustics – Sound wave • https://www.docsity.com/en/news/physics/physics-sound-visual-representation-gifs/

5. Basic acoustics – Sound wave Acoustic wave • Flow properties • Unsteady • Requires a compressible medium • Small amplitudes → Linearized models • Wave properties • Interference, Reflection, Refraction, Transmission, Diffraction • Described using the acoustic wave equation • https://www.askiitians.com/iit-jee-wave-motion/velocity-of-wave/ • http://www.echocardiographer.org/Echo%20Physics/Sound%20Striking%20An%20Interface.html • http://www.gwoptics.org/ebook/interferometers.php

6. Basic acoustics – Sound wave Basic quantities (ambient or average value + perturbation value) • Pressure: • Velocity: • Density: • Temperature: • Sound pressure: • Root Mean Square of the sound pressure , [Pa] • Acoustic Intensity: • Acoustic Power:

7. Basic acoustics – Sound wave • Sound Pressure Level – SPL: [dB] • Standard Reference Sound Pressure Pa • Sound Intensity Level – SIL: [dB] • Sound Power Level – SWL: [dB] • Summation of levels • , • If,

8. Basic acoustics – noise & SPL • Human hearing threshold

9. Basic acoustics – noise & SPL • http://audiojudgement.com/how-to-calculate-decibels/

10. Basic acoustics –noise & SPL • Amplitude, Frequency,and phase • Amplitude is the magnitude of an acousticoscillation. It describeshow loud the sound is. • Frequency refers to how often the oscillation repeats, and it describes the pitch of the sound. • Phase describes the shift in time of asound wave. The phase shift between two sound signals can be expressed in degrees. • http://www.howmusicworks.org/103/Sound-and-Music/Amplitude-and-Frequency • https://en.wikipedia.org/wiki/Phase_(waves)

11. Basic acoustics –noise & SPL • Frequency bands • At times special frequency bands are used in processing data • Octave band: • The upper frequency limit () of the band is twice that of the lower frequency limit (): , and the mid-frequency of the band: • Third octave band: ,

12. Basic acoustics – noise & SPL • http://www.epd.gov.hk/epd/noise_education/web/ENG_EPD_HTML/m1/intro_5.html • https://www.cirrusresearch.co.uk/blog/2011/08/what-are-a-c-z-frequency-weightings/ • A-weighted Sound Pressure Level [dB(A)] • The perception of the human ear isfrequency dependent • Correction of measured SPL data

13. Basic acoustics – noise & SPL • Tonal noise sources – narrow frequency range • Whistle, Musical instruments, frequently repeating noise generating mechanisms • Broadband noise sources – wide frequency range • Noise of airfoils (leading edge, trailing edge), White noise, Pink noise, flow induced broadband noise

14. microphones • Measurement of noise • Very small amplitude values – Light and flexible • Unsteady, high frequencies – Low time constant • Microphones • Light diaphragm, which converts the sound waves into mechanical vibration • The motion is converted into an electrical signal • Main types • Condenser / capacitor microphone – changes the distance between the plates of a capacitor • Dynamic / moving coil microphone - electromagnetic induction • Piezoelectric / crystal microphone– pressure to voltage • Carbon microphone– electrical resistance changing • https://en.wikipedia.org/wiki/Microphone

15. microphones • Condenser / capacitor microphone • A thin, electrically conductive membrane close to a solid metal backplate • When sound waves hit the microphone, the diaphragm moves back and forth • The level of capacitance changes →small voltage changes are seen across the resistor • Low mass and inertia of the diaphragm →flat and extended freq. response • Requires a DC voltageto operate • High sensitivity • Less robust construction • Sensitive to humidity • https://www.electronics-notes.com

16. microphones • Dynamic / moving coil microphone • Consists of a magnet, and a diaphragm to which a coil is attached • The coil can move freely over the magnet • Sound waves hit the diaphragm→ the coil moves back and forth within the magnetic field → an electric current is induced • Do not require an internal preamplifier (as opposed to condenser mics.) • Frequency responseis not completely flat (response peakaround 2.5kHz) • The response peakcan increase the intelligibility of speech, and give a bright tone to the audio signal • Simple, sturdy design • Toleratesrough handling • Widely used • https://www.electronics-notes.com

17. microphones • Piezoelectric / crystal microphone • The operation is based on the piezoelectric effect • Certain materials generate an electric charge when a mechanical stress is applied • Sound waves hit the diaphragm→ mechanical stress → an electric charge is generated • Do not offer a particular wide frequency response • Offers a high output voltage into a high impedance • Bottom end of the market • Generally low cost units • Not widely used • http://electriciantraining.tpub.com/

18. microphones • Carbon microphone • When carbon granules are compressed their resistance decreases • Granules are contained within a small container that is covered with a thin metal diaphragm • Sound waves hit the diaphragm→ it vibrates → varying pressure → varying levels of resistance → the current passing through the microphone varies • Narrow range frequency response • Significant electrical noise • Older design • Were widely used in the early days of telephones • https://www.electronics-notes.com

19. microphones • Omnidirectional microphone • Frequency response is close to a perfect sphere in three dimensions • The body of the microphone is not infinitely small • Sound arriving from the rear → it gets in its own way ↓ • Slight flattening of the polar response for high frequencies ↓ • The smallest diameter microphone gives the best omnidirectional characteristics • Wavelength of sound at 10 kHz: 35mm • Usual microphonediameters: 5 to 25 mm • http://earthworksaudio.com/microphones/m-series/m30/

20. microphones • Frequency response of an omnidirectional Earthworks M30, 30kHz microphone • Flat free-field frequency response • Accurate in the time and frequency domain • Stable with respect to temperature and atmospheric conditions • http://earthworksaudio.com/microphones/m-series/m30/

21. Now we know the very basics about sound waves and how to measure them… LET’S TALK ABOUT SOUND PROPAGATION!

22. Advanced acoustics – WAVE equation • Conservation of mass (1D) • For acoustic quantities (mean velocity: ) • Second order terms can be neglected and the mean values do not change with time and position • 1D linear acoustic conservation of mass equation

23. Advanced acoustics – WAVE equation • Conservation of momentum • For acoustic quantities (mean velocity: ) • Second order terms can be neglected (for now: ) the static sound field is cancelled out (if and , then ) • 1D linear acoustic conservation of momentum equation

24. Advanced acoustics – WAVE equation • Using the 1D linear conservation equations of mass and momentum → ; → ; • Speed of sound (from the energy conservation and the constitutive equations) → • The homogenous linear wave equation for the acoustic pressure 1D 3D (similar form exists for various quantities)

25. Advanced acoustics – wave equation • The wave equation is homogenous → no source terms! (right hand side) • Only describes the propagation of the waves • No source or sink terms • Noise generation and attenuation cannot be accounted for in this form • In need of an inhomogeneous wave equation (source terms) ↓ • Introducing Lighthill’sanalogy

26. Advanced acoustics – LIGHTHILL’S analogy • Analogy: A complex fluid mechanical processthat acts as an acoustic source is to be represented as an acoustically equivalent source term • We consider the case of a limited source region embedded ina uniform stagnant fluid • The listener at a pointx at time t is surrounded by this uniform stagnant fluid characterized by the speed of sound • Theacoustic field at the listener is accurately described by the wave equation • S.W. Rienstra, A. Hirschberg, „An Introduction to Acoustics”, Eindhoven University of Technology, 2014

27. Advanced acoustics – LIGHTHILL’S analogy • For problems like the prediction of sound produced by turbulence, usingas the acoustic variable will be the most convenient • The equation of Lighthill (see the process of derivation in the source below) • : Lighthill stress tensor - contains three basic aeroacousticprocesses which result in sources of sound • : volume fraction pertaining to the injection into the source region • : the original density of the mass before mass injection • : external force • S.W. Rienstra, A. Hirschberg, „An Introduction to Acoustics”, Eindhoven University of Technology, 2014

28. Advanced acoustics – LIGHTHILL’S analogy • Lighthill stress tensor • : Reynolds stress tensor - non-linear convective forces • : viscous forces • : accounts for the deviation from a uniform sound velocityor the deviation from an isentropic behavior • S.W. Rienstra, A. Hirschberg, „An Introduction to Acoustics”, Eindhoven University of Technology, 2014

29. Advanced acoustics – Monopole NOISE source • Radiates sound equally well in all directions • Model: a pulsating sphere • Creates a sound wave by alternately introducing and removing mass into the surrounding area– volume source • Radiation efficiency is proportionate to: Examples • Boxed loudspeaker at low frequencies • Exhaust pipe radiation • Air compressors • Unsteady combustion • http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html

30. Advanced acoustics – Monopole NOISE source • Sound field of a monopole source: • : source intensity • : Dirac-delta function • : position of the sound source • position of the observer • The solution (using spherical coordinates): • :distance between the source and the observer • Gives the sound pressure at the observer • https://en.wikibooks.org/wiki/Aeroacoustics/Acoustic_Sources

31. Advanced acoustics – DIpole NOISE source • Two monopole sources • Equal strength, but opposite phase • Small distance compared to the wavelength of sound • Model: a sphere which oscillates back and forth • Does not radiate sound in all directions equally • Radiation efficiency isproportionateto: Examples • Guitar string • Whistling car antenna • Fan and airframe noise • http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html

32. Advanced acoustics – dipole NOISE source • Sound field of a dipole source: • :distributed force system • The solution of this equation: • : distance between the two counter-phased monopole sources • : wavelength • : angle between thesource axis and the observer • https://en.wikibooks.org/wiki/Aeroacoustics/Acoustic_Sources

33. Advanced acoustics – lateral quadrupole NOISE source • Four monopole sources (two opposite dipoles) • Alternating phase at the corners of a square • Directivity field:clover-leaf pattern • Model: a sphere which oscillates back and forth • Radiates well in front of each monopole source • Sound is canceled at points equidistant from adjacent opposite monopoles Radiation efficiency is proportionate to: Examples • Shear layers • Spinning vortices accelerating towards their center • http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html

34. Advanced acoustics – linear quadrupole NOISE source • Two opposite phase dipoles along the same line • Near field: four maxima and four minima the maxima along the axis is louder than the maxima perpendicular to the axis • Far field: two maxima along the axis two minima perpendicular to the axis • Radiation efficiency is proportionate to: Examples • Tuning fork (two dipoles) • http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html

35. Advanced acoustics – quadrupole NOISE source • Sound field of aquadrupolesource: • :Lighthill stress tensor • https://en.wikibooks.org/wiki/Aeroacoustics/Acoustic_Sources

36. Now we know how to describe basic acoustic phenomena… LET’S TALK ABOUT SOUND MEASUREMENT!

37. Microphone array – Single microphone measurements • Laboratory environment • Anechoic chamber • Absorbing walls (no reflection) • „Simulation” of free-field measurements • Microphone and noise source characteristics(frequency dependence and directivity measurements, acoustic impedance measurements • http://client2.springmedia.hu/index.php?tpl=page&cID=2 • https://en.wikibooks.org/wiki/Acoustics/Anechoic_and_Reverberation_Rooms

38. Microphone array– Single microphone measurements • Laboratory environment • Reverberation chamber • Concrete walls, noise reflecting paint • Diffuse acoustic field: homogenous and isotropic • Absorbing features of materials • http://client2.springmedia.hu/index.php?tpl=page&cID=2 • https://en.wikibooks.org/wiki/Acoustics/Anechoic_and_Reverberation_Rooms

39. Microphone array– Single microphone measurements • Sound level meter • Recording the noise using a microphone • Spectral results with the help of Fourier transformation • Noise pollution measurements • Industrial noise, aircraft noise, traffic noise • https://en.wikipedia.org/wiki/Sound_level_meter Mic1 SPL [dB] Frequency [kHz]

40. Microphone array – motivation • https://www.psa3.nl/nlr-highlights/ • Single microphone measurements provide spectral results • Characteristics, directivity, and amplitude can be defined • The location of the noise sources CANNOT be defined with single microphone measurements • During the investigation of complicated noise generating mechanisms, information regarding the location of the noise source is essential • PHASED ARRAY MICROPHONES combined with BEAMFORMING technology are able to localize noise sources.

41. Microphone array and BEAMFORMING basics • Microphone array • Phased array microphone system, acoustic telescope • Consists of numerous microphones positioned in a known pattern (along a line, in a plane, in a space) • Noise source localization • Short recording time, focus points are defined virtually • KOOP, L. (2007) Beam forming methods in microphone array measurements. Theory, practice and limitations. von Kármán Institute Lecture Series, RhodeSaint Genèse.

42. Microphonearray And Beamformingbasics • Measurement principle • The noise of an acoustic source propagates in the form of pressure fluctuation waves with the speed of sound • Microphones are located at different distances from the source • Due to the fact that the speed of sound is finite, different propagation times are needed to reach each microphone from the source • At a given time instant, the same sound waves are in different phase at the different microphones • KOOP, L. (2007) Beam forming methods in microphone array measurements. Theory, practice and limitations. von Kármán Institute Lecture Series, RhodeSaint Genèse.

43. Microphonearray And Beamformingbasics • The recorded signals • Thesignals have different amplitudes and phase shift • KOOP, L. (2007) Beam forming methods in microphone array measurements. Theory, practice and limitations. von Kármán Institute Lecture Series, RhodeSaint Genèse. amplitude phase shift

44. Microphone array and BEAMFORMING basics • The phase shift and amplitude difference can be corrected if the measurement geometry (r) is known • If the recorded noise component belongs to a real noise source (q1), then the phase and amplitude corrected signalswill have the same phase and amplitude.Therefore,it will be the same on every microphone (because it origins from the same source q) • Figureby Bence Tóth q1 q2 qm r12 r11 r22 rmm M1 M2 p1 p2 Mm pm

45. Microphone array and BEAMFORMING basics • The average of the recorded signals will agreewith that of the individual corrected signals • The RMS value of the average signal will be a large value • M1 is the recorded signal ofmicrophone No.1: p1 • M2: p2 • Average signal • RMS • Figureby Bence Tóth Amplitude [Pa] Time [ms] Amplitude [Pa] Time [ms]

46. Microphone array and BEAMFORMING basics • If there is no noise source in the investigated location (q2-qm), after carrying outthe amplitude and phase corrections on the recorded signals (pm), the individual corrected signalswill not be in phase and will not have the same amplitude. • Figureby Bence Tóth q1 q2 qm r12 r11 r22 rmm M1 M2 p1 p2 Mm pm

47. Microphone array and BEAMFORMING basics • The average of the recorded signals will not be equal with that of the individualcorrected signals and as a result of the destructive interference, the amplitude of the average signal will havea small value • The RMS value of the average signal will be a small value • M1: p1 • M2: p2 • Average signal • RMS • Figureby Bence Tóth Amplitude [Pa] Time [ms] Amplitude [Pa] Time [ms]

48. Microphone array and BEAMFORMING basics • Through the examination of a designated investigation plane using beamforming technology, each location is associated with a large or small amplitude • As a result, beamforming maps can be created, which show the dominant noise sources of the investigated domain

49. Time domain beamforming • Suppose a single monopole sound source in the measurement domain • The pressure fluctuation propagates in every direction in the form of spherical harmonic waves • Microphones are located in one plane at different distances from the source • Different propagation times needed to reach each microphone from the source • The sound waves reach the microphones with different phase • KOOP, L. (2007) Beam forming methods in microphone array measurements. Theory, practice and limitations. von Kármán Institute Lecture Series, RhodeSaint Genèse.

50. Time domain beamforming • The pressure signals at the microphones • Time delay:The time needed for the sound to get from the source to the observation point • Spherical pressure waves propagate, the amplitude of the waves decreases by the factor • The location of the source is unknown during the measurements • A grid is constructed in the plane where the sources are sought