Optimal Experiments with Acoustic-Seismic Sensors

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Optimal Experiments with Acoustic-Seismic Sensors

• James McClellan and Waymond R. Scott, Jr.
• School of Electrical and Computer Engineering
• Georgia Institute of Technology
• Atlanta, GA 30332-0250
• jim.mcclellan_at_ece.gatech.edu
• 404-894-8325

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Outline

• Introduction
• Seismic System
• Spectrum Analysis of Seismic Waves
• Location with Acoustic/Seismic Arrays
• Maneuvering Array (3x10)
• Cumulative Array strategy for imaging
• Optimal Experiments
• Examples

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Prototype Seismic Mine Detection System
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Data Movies

• All wave types
• Only the reflected wave
• After k-domain processing

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Typical Surface Sensor Arrays Used in
Experimental Model at Field Test Sites
Data is collected by 3-axis sensor - x,
Horizontal Channel - z, Vertical Channel
Elastic Wave Source
Linear Array of 16 Triaxial Accelerometers
Linear Array of 8 Triaxial Geophones
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Seismic SensorPseudo Color Graph y 20 cm
Bag of Dry Sand 5 cm Deep
Crushed Can 3 cm Deep
Mine TS-50 1.5 cm Deep
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Extract Reflected Waves

• Surface Waves Velocity vs. Frequency
• Parametric Model for surface waves
• IQML (Prony, Steiglitz-McBride)
• Multi-Channel Modeling
• Need robust method to work with field data
• Extract various types of waves
• Individual modes
• Exploit data collected from tri-axial sensors
• Polarization can be used to identify different
  wave types

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Frequency-Domain Model

• 2-D Fourier transform of sensor data s (x, t)
  represents signal as propagating plane waves
• Slowness k / ?
• Velocity ? / k
• k wave-number
• ? temporal frequency

Constant velocity is a ray from the origin
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Parametric Model for One Channel

• STEPS
• Take 1-D Fourier transform over time,
  s(x,t)-gtS(x,?)
• ARMA Modeling is done across x to obtain
• a space-frequency (k , ? ) model,
• Estimate a(?) and k(?) by IQML (aka St-McB/Prony)

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Results from Vector IQML

• k(?) vs. ? becomes velocity vs. O
• Extract individual modes from (k , ? ) and
  reconstruct them in time domain from the model
  parameters, i.e., Sum across frequency

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Spectrum Analysis via Prony
TS-50 at 1cm
VS1.6 at 5cm
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Home in on a Target

• Problem Statement
• Use a small number of source receiver positions
  to locate targets, i.e., landmines
• Minimize the number of measurements
• Three phases
• Probe phase use a small 2-D array (rectangle or
  cross)
• Find general target area by imaging with
  reflected waves
• Adaptive placement of additional sensors
• Maneuver receiver(s) to increase resolution
• Use Theory of Optimal Experiments
• On-top of the target
• End-game Verify the resonance

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Adaptive Sensor Placement
Target
Source
Probe Array
Probe Array finds general target area
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Ground Contacting Seismic Sensor Array Deployed
on a Small Robotic Platform
Source Platform
Sensor Platforms
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Experimental Setup of Seismic Landmine Detection
Measurements
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Choose Next Sensor Position

• Want to formulate an optimal maneuvering strategy
• Instead of adding One Sensor, move the Whole
  Array to the next optimal position
• Append the array data at the new position with
  previous data
• Estimate the target location
• Find the best next sensor position

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Steps in Optimal Maneuver

• Wave Separation by Prony
• Imaging algorithm
• - Data Model
• - ML solution for target position
  estimates
• - Performance bounds for position
  estimates
• Next optimal Array Position
• - D-optimal Design
• - Constrained Optimization

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Data Model
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Target Position Estimate

• The Cramer-Rao lower bound (CRLB) provides a
  lower bound for the variances of the unbiased
  estimators
• CRLB requires the inverse of the Fisher
  information matrix

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Fisher Information Matrix for Position Estimate
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Theory of Optimal Experiments

• The theory of optimal experiments uses various
  measures of the Fisher information matrix to
  produce decision rules
• Determinant
• Trace
• Maximum value along the diagonal
• D-optimal Design uses the determinant

X. Liao and L. Carin, Application of the
Theory of Optimal Experiments to Adaptive
Electromagnetic-Induction Sensing of Buried
Targets,'' IEEE Trans. on Pattern Analysis and
Machine Intelligence, vol. 26 , no.8, pp.
961-972, August 2004.
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Next Optimal Position
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Unique Problems for Seismic

• Target position is estimated from reflected
  seismic energy
• Source is nearby
• Need separation between forward and reverse waves
• Array position has to be between source and
  targets always
• Landmines reflections are not omni-directional
• Next array position has to be Constrained
• Between source and estimated target position
• Two ways to implement constrained optimization
• Circle constraint, or Penalty Function

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Constrained optimization for next array position
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Experimental Data Setup

• Single TS-50 landmine is buried at 1cm
• Reflected waves are separated at each position by
  using a line array of 15 sensors (3cm apart)
• Actual receiver is a single sensor (Synthetic
  Array)
• Measurements are grouped into line arrays
• From each line array, three sensors at equal
  distance positions are chosen
• With three line arrays, an array of nine sensors
  is available for 2-D imaging
• Inverse of the cost function is plotted for
  imaging algorithm

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First Iteration
ACTUAL TARGET (135,135) 5 ESTIMATE (102,120)
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Next array position values calculated on half
circle of radius30cm
Values calculated on half circle
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Second Iteration
ACTUAL TARGET (135,135) 5 ESTIMATE ALONE
(100,127), CUM(112,127)
ALONE
CUMULATIVE
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Next Array Position
Values calculated on half circle
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Third Iteration
ACTUAL TARGET (135,135) 5 ESTIMATE ALONE
(143,138), CUM(127,133)
ALONE
CUMULATIVE
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Fourth Iteration
ACTUAL TARGET (135,135) 5 ESTIMATE ALONE
(124,144), CUM(146,139)
CUMULATIVE
ALONE
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Four Iterations Cumulative Imaging
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Implementation

• 2D array (3 X 10)
• Three lines having 10 sensors each
• Sensors are ground contacting accelerometers
• LabView is used to control the movement of array
  and seismic source firing and interface with
  MATLAB
• Processing algorithms are implemented in MATLAB
• Target is a VS1.6 mine buried at 5cm

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Experimental Setup of Seismic Landmine Detection
Measurements
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Seismic Detection of VS-1.6 AT Landmine Buried
5cm Deep in Experimental Model
Landmine (22.2 cm diameter) buried 110 cm from
first measurement location in 171 cm linear
scan. 5 measurements with center line of sensor
array along a line over the burial
location. Compressional, Rayleigh Surface, and
Reflected Waves. Resonance of Landmine-Soil
System. Interactions of incident waves with
buried landmine evident in measured data.
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Wave Separation at each iteration along top-most
line array
2
1
3
4
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Demo in Sandbox
EXPERIMENTAL SETUP

• Target is localized in four iterations
• Each iteration takes 10 secs. for processing and
  30 secs. for data acquisition
• Total time for four iterations is 2 minutes
• Typical raster scan takes a few hours to locate
  the target with a large number of measurements

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Demo in Sandbox
EXPERIMENTAL SETUP

• Target is localized in four iterations
• Bracket start
• Each iteration takes 10 secs. for processing and
  30 secs. for data acquisition
• Total time for four iterations is 2 minutes
• Typical raster scan takes a few hours to locate
  the target with a large number of measurements

MOVIE of Experiment
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Four Iterations
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Four Iterations bracket start
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End-game Detection

• We can further scan in line with the last
  estimated target position
• Extract the reverse wave and try to locate the
  exact location of resonance
• Movies shown the extracted wave with the line
  array of 30 sensors, which is moved toward the
  target with 1cm increment
• Target center is (50,50) and the starting
  location and position of target is shown

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Movie VS-1.6 (5cm)
Extracted reverse wave as array moves near and
above the target
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Movie TS-50 (1cm)
Extracted reverse wave as array moves near and
above the target
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Constrained optimization for next array position
(2)
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Target Position Estimate
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Cramer-Rao Lower Bound

• The Cramer-Rao lower bound (CRLB) is an
  information theoretic inequality, which provides
  a lower bound for the variances of the unbiased
  estimators
• The Cramer-Rao lower bound is the inverse of
  Fisher information matrix

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Next Optimal Position
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Wideband RELAX algorithm
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Surface Plot for Displays
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Examples using Sandbox Data

• Single source is used
• Only the Reverse wave is used in processing
• Or, passive listening for Buried structures
• Remove the Forward wave
• Prony analysis, or spatial filter
• Frequency range
• obtained from Spectrum Analysis of measured data
• Future work
• use RELAX to separate Forward and Reverse waves
• Cylindrical wave model

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Steps in Optimal Maneuver

• Acquire data at the dense array
• Separate the forward and reflected waves
• Form a 2-D Imaging array at the new position
• Append new data to data from old positions
• Use 2-D Image to estimate the target position
• Find the next optimal array position
• Then move the array to the new position
• Repeat these steps until target is localized

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Wave Extraction via Prony
Position of upper line array 10 sensors, 3cm apart
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Extracted Reverse Wave (synthesized at one sensor)
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Wave Extraction via Prony
Position of middle line array 10 sensors, 3cm
apart
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Extracted Reverse Wave (synthesized at one sensor)
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Wave Extraction via Prony
Position of lower line array 10 sensors, 3cm apart
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Extracted Reverse Wave (synthesized at one sensor)
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Seismic Sensor
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Review from January

• Probe Phase
• Pick five sensors in a cross pattern
• Apply Imaging algorithm and plot the surface over
  a search grid
• Maneuver Phase
• Add one more sensor depending upon which
  direction to move
• Increase aperture of triangulation
• Spatial resolution increases which narrows down
  the area in which to search for target

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TS-50 (1cm)
Source at (-20,50)
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Next Measurement
1
2
3
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Steps in Optimal Maneuver
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Next Array Position
Circle constraint R30cm
Movement Penalty
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Four Iterations another run
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All Four Iterations Imaging with one array at a
time
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Data Model

• P-element array with position of every sensor is
  given in terms of array center
• Seismic wave penetration depth depends on
  frequency, hence a band of frequencies is used in
  processing
• K near-field wideband targets
• In the DFT, select L Frequency components
• Goal estimate location (z) of the targets from
  measured array data

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Movie of Experiment

• Demonstrate in real-time
• Extraction of reflected waves is crucial