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- 1. NC STATE UNIVERSITY Glenwood Garner SIAMES Research Group North Carolina State University Linear & Nonlinear Acoustic Modeling for Standoff Analysis Ph.D. Preliminary Examination May 20, 2010 10:00 am, MRC 463 ERL Anechoic Chamber Audio Spotlight Polytec PDV-100
- 2. NC STATE UNIVERSITY 2 Presentation Overview • Motivations, Objectives • Original Contributions • Third-Order Nonlinear Scattering • Fractional Calculus Spatial Power Law Model • Switched Tone Probing • Shear Wave Elasticity Imaging (SWEI) • Future Work
- 3. NC STATE UNIVERSITY 3 Linear & Nonlinear Acoustic Modeling for Standoff Analysis Table of Contents (abridged) I. Introduction 1. Overview 2. Original Contributions 3. Dissertation Outline 4. Published Works I. Literature Review 1. Linear Acoustic Theory 2. Nonlinear Acoustic Theory 3. Piston Radiators 4. Sound Scattering 5. Fractional Power Law Theory 6. Acoustic Fluid-Solid Interaction 7. Transient Effects 8. Shear Wave Elasticity Theory I. Third-Order Sound Scattering 1. Second Harmonic Characterization 2. Receiver Characterization 3. Numerical Techniques 4. Measurement 5. Results & Analysis IV. Fractional Diffusion Acoustic Piston Radiation 1. Finite Difference Method 2. Derivation of Spatial Power Law Dependence 3. Measurements 4. Results & Analysis IV. Switched Tone Transient Analysis 1. Long-Tail Transients 2. Log-Decrement Linear Metrology 3. Nonlinear Switched-Tone Model 4. Switched-Tone Measurement 5. Results & Analysis IV. Standoff Shear Wave Elasticity Imaging 1. Comparison Between Contacting & Non- contacting Methods 2. Application 3. Measurements 4. Image Processing 5. Results & Analysis IV. Conclusion & Future Work
- 4. NC STATE UNIVERSITY 4 Standoff Acoustic Analysis: Motivations 8 9 3 3 10 8.6 35 10 343 8.6 40 10 mm mm λ λ × = = × = = × 24,000 people killed or injured annually by over 100 million worldwide landmines, unexploded ordnance, and IEDs. • Human Prodders • Dogs • Metal Detectors • Infrared • Neutron Backscatter • Millimeter Wave Detection • Ground Penetrating Radar • Acoustics Lives endangered High false alarm rate Intolerant to soil moister/dielectric constant Better for detecting AT mines Mechanical effects, limited jamming, shielding, spoofing Gros (1998) Can we used acoustics to probe our environment for abnormalities? Mazzaro (2009)
- 5. NC STATE UNIVERSITY 5 Standoff Acoustic Analysis: Motivations Two-tone probing has been demonstrated in finding AP & AT mines. http://www.acoustics.org/press/154th/fillinger.html Current Technology Drawbacks • Requires ground shakers…or • Large amplitude loudspeakers • Not a standoff technique • Inherent nonlinearity of air • Acoustic beam spreading Research Objectives • Develop third-order nonlinear air model • Model thermal diffusion of piston sound beam • Explore nonlinear probing techniques • Adapt current techniques to standoff applications. Donskoy (2002), Korman (2004), Sabatier (2003)
- 6. NC STATE UNIVERSITY 6 Standoff Acoustic Analysis: Original Contributions • Developed third-order nonlinear air model, demonstrated use of cascaded second-order systems. • Demonstrated improved directivity of third-order nonlinear parametric array. • Fractional calculus spatial power law model for piston beams. • Evaluation of long-tail transients in geologic materials • Use of switched tones to generate third-order intermodulation. • Standoff application of shear wave elasticity imaging (SWEI) to locate inhomogeneities in targets.
- 7. NC STATE UNIVERSITY 7 Standoff Acoustic Analysis: Publications Glenwood Garner, Jonathan Wilkerson, Michael M. Skeen, Daniel F. Patrick, Ryan D. Hodges, Ryan D. Schimizzi, Saket R. Vora, Zhi-Peng Feng, Kevin G. Gard, and Michael. B. Steer “Acoustic-RF Anechoic Chamber Construction and Evaluation” Radio & Wireless Symposium, Orlando, FL, 2008. Glenwood Garner III, Jonathan Wilkerson, Michael M. Skeen, Daniel F. Patrick, Hamid Krim, Kevin G. Gard, and Michael B. Steer “Use of Acoustic Parametric Arrays for Standoff Analysis and Detection” Government Microcircuit Applications Conf., Las Vegas, NV, 2008. Glenwood Garner III, Marcus Wagnborg, and Michael B. Steer “Standoff Acoustical Analysis of Natural and Manmade Objects” Government Microcircuit Applications Conf., Orlando, FL, 2009. Glen Garner, Jonathan Wilkerson, and Michael B. Steer “Third-Order Distortion of Sound Fields” Government Microcircuit Applications Conf., Reno, NV, 2010 Glenwood Garner,and Michael Steer “Nonlinear Propagation of Sound in Air” IEEE Transactions on Geoscience and Remote Sensing (unpublished) Conference Journal
- 8. NC STATE UNIVERSITY 8 Third-Order Nonlinear Scattering: Overview *Taken from: http://spie.org/Images/Graphics/Newsroom/Imported/0569/0569_fig1.jpg When two sound beams (plane waves) interact at angle θ, phase interference produces Moiré bands*. Westervelt (1957) 22 2 2 02 ij i j T c t x x ρ ρ ∂∂ − ∇ = ∂ ∂ ∂ 2 2 02 2 0 1 , wheres s p q p c t t ρ ∂ ∂ ∇ − = − ∂ ∂ 0 2 20 2 4 2 2 0 0 0 1 1 cos 2 T P q p c c tρ ρ ρ θ ρ ρ = ∂ ∂ = + ÷ ∂ ∂ Lighthill (1952) c: sound speed p: pressure (total, scattered, incident) ρ: density a: transmitter radius q: simple source density Mixing Volume ( , )f a θ=
- 9. NC STATE UNIVERSITY 9 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 σ=βωr/c 0 2 HarmonicAmplitudeB(n) (σ) 1st Harmonic 2nd Harmonic 3rd Harmonic Third-Order Nonlinear Scattering: Overview Ingard & Pridmore-Brown (1956) 1 1 1 2 2 2 cos( ) cos( ) Tp p t k x p t k y ω ω = − + − 1 1 1 2 2 2 2 cos( ) cos( cos sin ) Tp p t k x p t k x k x ω ω θ θ = − + − − ( ) ( ) ( ) 2 0 1 1 sin cos 2 ( sin ) sin sin ir T i i i i i i i i r p D k a p e t k r r J k a D k a k a α θ ω θ θ θ − = = − = ∑ Muir & Willette (1972) Lauvstad &Tjotta (1962) Garner & Steer (2010) ( ) ( ) ( ) ( ) (1) (2)0 1 1 1 1 1 1 1 1 (1) (2) 2 2 2 2 2 2 2 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) T r p p B D p B D r p B D p B D σ θ σ θ σ θ σ θ = + + + r0/r=1 Lockwood, Muir, & Blackstock (1972) ( )0 0( ) lnD kr r rσ βε θ=
- 10. NC STATE UNIVERSITY 10 0 1 2 3 4 5 6 7 8 9 0 20 40 60 80 100 120 Intermodulation Power Sweep f1 = 55 kHz, f2 = 65 kHz Amplitude(dBSPL) Input Voltage (dB) f 1 55 kHz f 2 65 kHz IM3L 45 kHz IM3U 75 kHz f 1 attenuated f2 attenuated IM3L attenuated IM3U attenuated 4.5 5 5.5 6 6.5 7 7.5 x 10 4 0 2 4 6 8 10 Ultrasonic Attenuation Attenuation(dBSPL) Frequency (Hz) Single Tone Intermodulation Tones Third-Order Nonlinear Scattering: Distortion Transmitter and receiver nonlinearity must be characterized in all nonlinear measurements. p = 90 dB, r = 2m, f = 40kHz a = 0.22 m a = 0.016 m IM3 Power sweep for 55kHz & 65 kHz input frequencies, with & without acoustic attenuator (melamine foam) over microphone
- 11. NC STATE UNIVERSITY 11 Third-Order Nonlinear Scattering: Measurement ( ) ( ) 2 2 0 0 1 0 0 1 0 0 ' sin cos cos cos for 0 ' ' cos cos for 0 ' m m m m m m m m r r r r r r ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ − − = + + − + − − + < ÷ = + −− − > ÷ l l l l l l l • l = 2 meters • θ = 20º • f1 = 55 kHz, f2 = 65 kHz • p1 ≈ p2 ≈ 125 dB SPL • r0 = 7 meters • Independent signal generators and amplifiers to eliminate electrical intermodulation. • Conducted outside to prevent standing waves • Absorber used to mitigate side lobe interaction.
- 12. NC STATE UNIVERSITY 12 Third-Order Nonlinear Scattering: Measured Fields Very good agreement between measured and theoretical IM3. Scattered third-order 3 dB beam widths of 1.7 degrees. To be included in 1st journal paper (IEEE GRS), demonstrate directivity of third-order nonlinear air model.
- 13. NC STATE UNIVERSITY 13 Westervelt (1963), second-order scattering (red) • f1 = 64 kHz, f2 = 66 kHz • p1 = p2 = 111 dB SPL • a = 0.1 meters • ~18º beam width -1.5 -1 -0.5 0 0.5 1 1.5 0 5 10 15 20 25 30 Amplitude(dBSPL) φ (radians) Directivity Comparison IM3 Lower Theory Diff. Freq. Theory Third-Order Nonlinear Scattering: Directivity ( ) 2 2 2 4 0 0 04 2 cos si t s s s s p a e p r c ik ik ω β ω ρ α θ − = − + Third-order scattering (black) • f1 = 33 kHz, f2 = 64 kHz • p1 = p2 = 127 dB SPL • a = 0.1 meters • ~1.7º beam width At 2 kHz, you get a significant gain in directivity with third-order scattering compared to second-order scattering
- 14. NC STATE UNIVERSITY 14 Fractional Diffusion Model: Overview Used to model long-tail effects (stretched exponentials), power-law attenuation, and fractal geometries. 1( )( ) 0 2 2 1 ( ,0) j t krj t kr p r p e e r r a ωω −− = − = + 0 0.5 1 1.5 0 1 2 On-axis pressure, f = 80000, a = 0.016, r0 = 0.18758 distance (m) amplitude(Pa) 10 -4 10 -3 10 -2 10 -1 10 0 0 1 2 distance (m) amplitude(Pa) Blackstock (2000), Zemanek (1971)
- 15. NC STATE UNIVERSITY 15 Fractional Diffusion Model: Overview K Fractional order element, Schiessel (1995) ( ) 1 0 1 ( ) ( ) ( ) ( ) t m m d f f D f t d dt m t α α α α τ τ α τ + − = = Γ − −∫ • Fractional derivatives produce memory effects • Allow for smooth transistion between diffusive and wave phenomenon. • Good at capturing derivatives of varying scale. 2 2 2 u u b t x α α ∂ ∂ = ∂ ∂ • α = 1: Diffusion • α = 2: Wave Equation Caputo Fractional Derivative allows traditional initial & boundary conditions Agrawal (2002) (0, ) ( , ) 0, 0 ( ,0) ( ), 0 u t u L t t u x f x x L = = ≥ = < < (0, ) cos( ), 0 ( , ) 0 u t t t u t ω= ≥ ∞ = Typical boundary conditions Piston source boundary conditions (extend to 3D) Can we find an efficient, fractional order solution to model thermal diffusion of piston source? Mainardi (1994), Podlubny (1999)
- 16. NC STATE UNIVERSITY 16 Fractional Diffusion Model: Overview Current fractional models aim to capture fractional order power- law attenuation. ( ) 0 0 0 2 2 2 2 2 0 1 0 z z z u u u c t t τ ∂ ∂ ∇ − + ∇ = ∂ ∂ ( ) 0 2 2 2 0 1 1 z k c i k i ω ωτ β α = + = − Begin by adding a fractional viscous loss term to wave equation Apply Fourier time/space fractional derivatives to obtain the following dispersion relation where and using the Szabo smallness approximation cβ ω= 0 1 0 0 0 0 0 sin 2 2 z z z c α α ω τ π α + = = 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 500 550 600 650 700 750 ω/c = 732.733 propagationfactor(β) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -15 -10 -5 0 fractional derivative power (z 0 ) attenuation(αNp/m) 40 kHz No viscosity Classical viscosity Chen (2004), Holm (2010)
- 17. NC STATE UNIVERSITY 17 Can a spatial fractional inverse power law be derived (similar to computing a fractional dispersion relation) to model beam spreading from baffled vibrating piston source? 0 1 2 3 4 5 6 7 8 9 10 x 10 5 0 50 100 150 200 Frequency (Hz) Attenuation(dB/m) tem p. = 68, hum idity = 50 Analytic Attenuation Power Law Fit, α 0 = 6.0156e-012, z0 = 0.837 Fractional Diffusion Model: Method 0 y α α ω= 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0 0.5 1 1.5 2 2.5 f = 80000, theta = 0, p0 = 0.18758, y = 1 distance (meters) amplitude(Pa) Exact field pressure Fractional power law fit 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0 0.1 0.2 0.3 0.4 f = 80000, theta = 21.15, p 0 = 0.008, y = 1.3 distance (meters) amplitude(Pa) Exact field pressure Fractional power law fit 0 y p p r− =
- 18. NC STATE UNIVERSITY 18 Switched-Tone Probing: Overview Can the problems associated with standoff nonlinear analysis be avoided using switched tones? f1 f1f2 f2 • Inherent nonlinearity of air and non-perfect collimation cause intermodulation. • Due to lack of spatial (velocity) dispersion, switched tones remain separated in time and no intermodulation is generated. • If target has long-tail “ringing”, intermodulation is generated on the target’s surface. • Surface velocity is measured with laser doppler vibrometer (LDV).
- 19. NC STATE UNIVERSITY 19 Switched-Tone Probing: Physical Model Negative Stress -TJ Voltage V Particle Velocity vi Current I Body Force per unit volume Fi Source Voltage per unit length Vs Mass per unit volume ρ Inductance per unit length L Inverse stiffness coefficient cJJ -1 Capacitance per unit length C Inverse damping coefficient ηJJ -1 Conductance per unit length G 2 L zδ 2 L zδ C zδ z → V + − I → zδ¬ → ( )i JJ JJ J v c T t z t η ∂∂ ∂ + = − − ÷ ∂ ∂ ∂ Auld (1990) 0 0.2 0.4 0.6 0.8 1 -30 -20 -10 0 10 20 30 Time (sec) AcousticPressure(Pa) (a) Incident Mic Response 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 (b) LDV Response: Tau=0.17631, Q=1988.6441, fo =3590.2713 Time (sec) Velocity(mm/s) velocity peak detection exponential fit 1 2 2 2 ln 1 n d x T x πς δ ςω ς = = = − 1 2 Q ωτ = Log Decrement Walker (2007), RF continuous excitation Mazzaro (2009), RF switched tones Parker (2005), biological tissues
- 20. NC STATE UNIVERSITY 20 Switched-Tone Probing: Physical Model ADS Circuit Model Surface Velocity (Current) response to 25 Pa, 200 ms input signals 590 Hz 840 Hz Can you model physical resonance as an RF filter? • Probe a target using switched tones to characterize material type, density, composition. • Try using electrical diode model to capture physical nonlinearity. • Goal: Demonstrate on uniform samples shapes to verify this phenomenon is a material property • Goal: Demonstrate invariance to sample shape.
- 21. NC STATE UNIVERSITY 21 Switched-Tone Probing: Current Results • Third-order intermodulation generated by switched tones in metal, plywood, and fiberglass. • Did not see this response in microphone placed next to targets. • Need to employ windowed FFT and shorter duration tones to eliminate possibility of standing wave error & parametric effect. • Applied Physics Letters draft completed.
- 22. NC STATE UNIVERSITY 22 Shear Wave Elasticity Imaging: Overview SWIE is a linear metrology technique that relies on a localized change in stiffness to indicate an inhomogeneity. 2 2 2 2 0 1 0 c t ξ ξ ∂ ∇ − = ∂ ( ) 2 2 2 2 0 1 0 1 ( )c x t ξ ξ γ ∂ ∇ − = + ∂ r ( ) 2 2 1 E c ρ ν = + x r ( )0,0 Modify the general linear shear wave equation to have piecewise Young’s modulus of elasticty. Shear waves typically excited using low frequency shaker and measured using Doppler ultrasound (contacting method). Propose using low frequency speaker (sub- woofer) and LDV to measured surface velocity/displacement (standoff method). Gao (1995), Parker (1996) – Sonoelasticity Imaging 0E '( )E x
- 23. NC STATE UNIVERSITY 23 Shear Wave Elasticity Imaging: Application Can we use SWEI to model and measure the vibration pattern of materials at standoff ranges? Expanded polystyrene model (StyrofoamTM ) 3 10kg mρ = 0.03 0.07ν = − 0.830 GPaE = 1,1 690 Hzf = 0.225 m 0.19 m Predicted (1,1) mode (converted to velocity) and velocity measured with LDV To do: Verify predicated amplitudes are correct, measure higher modes, measure different materials.
- 24. NC STATE UNIVERSITY 24 Shear Wave Elasticity Imaging: Application Can we use SWEI to detect dense objects hidden within soft targets? 0.225 m 0.19 m 5 cm 7.5 cm inhomogeneity × 580 Hz excitation, 2.2 m standoff distance Medical Imaging 0 0 0 '( ) 8 ', ' , E x E ρ ν ρ ν ≈ × ≈ Standoff Detection 0 0 '( ) 241,000 ' 700 E x E ρ ρ ≈ × ≈ × To do: Implement inhomogeneous lossy model, determine maximum detection depths in various materials. Incredible difference in stiffness & density compensate for poor solid-air matching.
- 25. NC STATE UNIVERSITY 25 Standoff Acoustic Analysis: Remaining Tasks • Implement numerical integration for third-order scattering model? • 90% MATLAB code finished • Submit to IEEE Geosciences & Remote Sensing • Develop fractional diffusion model • Complete switched-tone probing measurements • Determine best time domain methods and signal processing • Use shorter pulses to mitigate parametric effect • Submit to Applied Physics Letters • Complete standoff SWEI measurements • Different materials/inhomogeneities • Geologic Materials/non-parallelepiped shapes • Submit to IEEE Geosciences & Remote Sensing Questions?

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