Co-registered Vibrometry

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Co-registered Vibrometry Imaging A Combined
Synthetic-Aperture Radar Fractional-Fourier
Transform ApproachUniversity of New
MexicoFY2008University Project
May 2009NCMR Technology Review
PI Presenter Majeed Hayat
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Project Information

• Title of project Co-registered Vibrometry and
  Imaging A Combined Synthetic-Aperture Radar and
  Fractional-Fourier Transform Approach
• Lead organization University of New Mexico,
  Electrical Computer Engineering Department
• Project lead Professor Majeed M. Hayat
• Personnel
• UNM Faculty
• Prof. Majeed Hayat (ECE, 15)
• Prof. Balu Santhanam (ECE,15)
• Prof. Walter Gerstle (CIVIL Engr,15)
• Sandia collaborators Tom Atwood and Toby
  Townsend (10)

Graduate students Qi Wang (50) Srikanth
Narravula (50) Tong Xia (50) Tom Baltis
(25) Post Doc Matt Pepin (DOE funded)
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Program Details

• Date of award (190,959 for FY08) Aug. 1, 2008
• Date of receipt of funds Aug. 1, 2008
• Date work actually started May 15, 2008 (via
  Pre-award)
• Percent of FY-08 funds spent to date 80
• Percent of total work completed (over three year
  period) to date 33

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Project NarrativeObjectives

• To exploit a powerful signal-processing tool,
  called the fractional Fourier transform, which is
  suitable for representing non-stationary signals,
  to design a novel synthetic-aperture radar
  imaging strategy that yields simultaneous imaging
  and vibrometry.
• To test the new approach using both simulated and
  real SAR data the latter may be provided by our
  collaborators at Sandia National Laboratories.
• Tasks were revised in May 2008 to insure there is
  no duplication with newly awarded DoE award.

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Background 2-D SAR process

• The SAR signal is chirped in two dimensions
• in the u-dimension by the chirp pulse and
• in the v-dimension by the change in range to the
  scatterer.

Step 1 Deramp quadrature demodulation removes
the u-chirp
Step 2 Aperture compression and range
compensation remove v-chirp
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Previous Work Non-stationary case

• When the ground is vibrating the reflectance
  becomes time varying
• ?
• The return signal after steps 1 2 becomes
• Different processing is required to extract
  g(u,t)
• To proceed, we need to specialize g(u,t) to
  practical forms

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Analysis of Discrete Vibrating Points

• By using the existing quadratic demodulation
  process and low-pass filtering, the return signal
  of each sent pulse becomes a superposition of
  chirp signals
• Modulates the magnitude of each chirp
• Linear dependence between and the
  pair central frequency, chirp rate
• Need a method to measure the central frequency
  and chirp rate of each chirp signal
  simultaneously (FRFT)
• We use the Fractional Fourier Transform and its
  discretization

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Previous Work Discrete FRFT
The discrete fractional Fourier transform (DFRFT)
has the capability to concentrate linear chirps
in few coefficients
MA-CDFRFT

• Each peak relates to each target point
• Position of each peak is related to position
  velocity of point target

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DFRFT Estimates
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Previous Work Vibration Identification
Methodology
Return echo
quadratic demodulation low-pass filtering (A/D)
MA-CDFRFT
Read out the positions of peaks
Compute the central frequencies, and chirp rates
Compute positions, and velocities
Co-registration with traditional SAR imagery
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New Work 2-D Non-stationary case

• When the ground is vibrating the reflectance
  becomes time varying ?
• The return signal becomes
• Different processing is required to extract
  g(u,v,t)
• Practical forms
• Instantaneous velocity and sum of sinusoidal
  modes

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Model for Discrete Vibrating Points

• How can we estimate the motion of each
  discrete target?
• Piece-wise linear approximation
• Send successive pulses to estimate

• Pulse duration must be much shorter than
  vibrating period (at Nyquist rate)
• Low frequency vibration measurement limited by
  maximum collection time
• High frequency vibrations proportional to Doppler
  of single measurement instantaneous velocity

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Single Look Vibration Frequency and Direction
Cross-Range
Vibrating Target
?
Range
0
Changing aperture splits vibration into two sin
waves
Complex amplitudes estimate vibration direction ?
Fit of V(t) cos envelope also estimates direction
?
Multi-Look
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Single Look Approach Envelope Fit

• Fitting the phase change envelope uses the slight
  change in amplitude of the vibration over the
  synthetic aperture
• This method is least accurate around zero degrees
  when the vibration is directly aligned with the
  electromagnetic direction of propagation

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Multilook Approach Frequency and Direction
Estimates
How to calculate at multiple look angles
By taking two looks with different squint angles,
the average energy ratio these two looks is
The vibration direction can be resolved this way
using multiple look angles and fitting the
expected change in energy over the different
squint angles to resolve the vibration direction
Results
Actual T -60 -45 -30 0.0 30 45 60
Estimation -59.7 -45.2 -29.7 -0.05 30.02 45.4 59.95
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Animated Demonstration
The vibrating point target
T
The patch of ground
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Summary 2-D Methodology
Return echo
quadratic demodulation low-pass filtering (A/D)
MA-CDFRFT
Read out the positions of peaks
Compute the frequencies, chirp rates, positions,
and velocities
Estimate vibration frequencies and directions
Form SAR image and overlay vibration information
Multiple looks to measure and refine vibration
direction
Actual T -60 -45 -30 0.0 30 45 60
Estimation -59.7 -45.2 -29.7 -0.05 30.02 45.4 59.95
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Enhancing Resolution via Non-uniform Frequency
Sampling

• DFRFT DFT of the sequence zkp
• Non-uniform DFT
• Evaluates Z-transform at locations of interest in
  the set zk

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Nonuniform Sampling NDFT

• Provides better peak resolution for larger
  in-band/out-band ratios
• (¼ 0.8-1).
• Frequency domain samples can be concentrated
  around DFRFT peaks.
• Sharper peak locations translate to better
  center-frequency chirp-rate estimates.

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Subspace Approach

• DFRFT peak detection chirp parameter estimation
  akin to DFT -- based sinusoidal frequency
  estimation location of peak gives frequency
  estimate
• Periodogram approach is statistically
  inconsistent. Subspace approaches yield
  asymptotically consistent estimates.
• Covariance matrix of zkp is full-rank
  eigenvalue spectrum not separable into SN and N
  subspaces.
• Subspace approach ? rank reduction needed.

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Modeling Electromagnetic Wave Interactions with
Vibrating Structures
Monica Madrid (Ph.D. student) and Jamesina
Simpson (Assistant Professor) Electrical and
Computer Engineering Department, University of
New Mexico Leveraging DOE Funding

• Goals
• Construct full-Maxwells equations models of the
  interaction of specific synthetic aperture radar
  pulses with vibrating objects
• Produce simulated Doppler shift information for
  single / multi-mode vibrating buildings
  encompassing a variety of geometrical and
  material features.
• Methodology
• Employ the finite-difference time-domain (FDTD)
  method, a grid-based, wide-band computational
  technique of great robustness
• ( 2,000 FDTD-related publications/year as of
  2006, 27 commercial/proprietary FDTD software
  vendors)

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FDTD Modeling Details

• Model the structures using an advanced algorithm
  that accommodates both the surface
  perturbations1, as well as their internal density
  modulations2.
• Perform a near-to-far-field (NTFF) transformation
  to obtain the unique signatures of vibrating
  objects as would be recorded by a remote antenna
  system.
• Complete the model with the advanced
  convolutional perfectly matched layer (CPML) to
  terminate the grid and a total-field/scattered-fie
  ld formulation (TFSF) to generate the plane wave
  illumination of objects.

1 A. Buerkle, K. Sarabandi, Analysis of
acousto-electromagnetic wave interaction using
sheet boundary conditions and the
finite-difference time-domain method, IEEE TAP,
55(7), 2007. 2 A. Buerkle, K. Sarabandi,
Analysis of acousto-electromagnetic wave
interaction using the finite-difference
time-domain method, IEEE TAP, 56(8), 2008.
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Ongoing and Future FDTD Work

• Current status and ongoing work
• We have implemented a 2-D FDTD model
  incorporating the CPML boundary conditions, NTFF
  transformation, TFSF formulation and surface
  vibrating perturbations.
• Next steps will be to use the validated code to
  model a variety of structural geometries (rough
  surfaces, edges, corners) and materials
  (concrete, etc.), vibrating at specific modes as
  specified by the civil engineers on our team.
• Future Work
• Extend the 2-D model to a fully 3-D simulation of
  synthetic aperture radar signals interacting with
  vibrating structures.

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Modeling Vibrations and Physical Structures
- Tests simulate theoretical model - A speaker
simulates the vibrating mass m1 - An aluminum
disk and two steel beams simulate the spring-
mass system response - Matlab code controls the
vibration frequency generating a sinusoidal
excitation with well-controlled frequencies
Acceleration Amplitude (m/s2)
Forcing Frequencies (Hz)
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Structural Acoustics Experiment
Pressure transducer measures the pressure of a
sound excitation. A steel box will simulate a room
The speaker (inside the box) generates harmonic
forces causing the box to vibrate. The transducer
will measure the pressure of the sound, an
accelerometer attached to the box will measure
the acceleration of the walls
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SAR Vibrometry Laboratory Planning

• Simple laboratory for the experimental
  demonstration SAR-based vibrometry
• Initial equipment concept complete
• UNM Space allocated

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Summary of Effort Against Objectives
Original Objectives Work Completed
DSP strategy for multi-pulse SAR data acquisition (Q1-Q3) 1D and 2D analytical model for return signals FRFT-based deramp process Investigate practical multi-pulse implementations 1D and 2D practical model for vibrating objects Simulation tools for SAR signal generation Multi-pulse generalizations are in progress
Microwave pulse design and DFRFT processing (Q2-Q5) Tradeoff analysis between pulse width, chirp rate and detectable vibration frequency and speed 2D extensions in progress
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Summary of Effort against Objectives

• Side-by-side summary of the effort

Original Objectives Work Completed
Understanding and Modeling Physical Characteristics of Ground Vibrations (Q1-Q3) Analytical models of physical objects developed. Models validated via experiments
(Revised) Develop subspace-based estimation algorithms to increase robustness to noise (Q4-Q6) - In progress
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Summary of Effort against Objectives

• Side-by-side summary of the effort

Original Objectives Work Completed
(Revised) A simple laboratory platform to demonstrate the proposed sensing concept (Q7-Q8) - Microwave testing platform designed and equipment identified
(Revised) Solutions to inverse problem of identifying structures based upon signatures generated by the proposed approach (Q7-Q12) -
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Project Self-Assessment

• Several 1D and 2D vibration estimation
  algorithms have been developed
• A wide variety of vibrations may be estimated
  with range and cross-range methods
• Two methods for estimating multiple vibration
  frequencies and angles completed
• Signal processing method to improve vibration
  frequency resolution completed
• Subspace methods to improve robustness to noise
  underway
• Initial physical modeling of vibrating
  structures completed Extension to more complex
  structures underway
• Experimental testbed underway

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Patents, Publications, and Experiments Associated
with Project

• Q. Wang, M. M. Hayat, B. Santhanam, and T.
  Atwood, SAR Vibrometry using fractional-Fourier-t
  ransform processing, SPIE Defense Security
  Symposium Radar Sensor Technology XIII
  (Conference DS304), Orlando, FL, April 2009.
• B. Santhanam, S. L. Reddy, and M. M. Hayat,
  Co-channel FM Demodulation Via the Multi
  Angle-Centered Discrete Fractional Fourier
  Transform, 2009 IEEE Digital Signal Processing
  Workshop," Marcos Islands, Jan. 2009, FL, 2009.
• M. Madrid, J. J. Simpson, B. Santhanam, W.
  Gerstle, T. Atwood, and M. M. Hayat, "Modeling
  electromagnetic wave interactions with vibrating
  structures," IEEE AP-S International Symposium
  and USNC/URSI National Radio Science Meeting,
  Charleston, SC, June 2009, accepted.

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Summary

• Phase history information in SAR data can be
  exploited via DFRFT-based signal processing to
  estimate vibrations while performing usual
  imaging
• Vibration-axis ambiguities can resolved using a
  multiple-look approach combined with 2D analysis.
• We have developed an understanding of the
  capabilities and limitations of the DFRFT based
  approach for SAR vibrometry
• Additional validations are needed using
  simulations and experiments