optimal experiments with acoustic-seismic sensors james mcclellan and waymond r. scott, jr. school...
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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 TechnologyAtlanta, GA 30332-0250
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MURI Workshop 2-Aug-05 Scott/McClellan, Georgia Tech 2
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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All wave types
Only the reflected wave After k-domain processing
Data Movies
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Typical Surface Sensor Arrays Used in Experimental Model & at Field Test Sites
Linear Array of 16 Triaxial Accelerometers
Linear Array of8 Triaxial Geophones
Elastic WaveSource
Data is collected by 3-axis sensor
- x, Horizontal Channel
- z, Vertical Channel
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Seismic SensorPseudo Color Graph; y = 20 cm
Crushed Can3 cm Deep
Mine TS-501.5 cm Deep
Bag of Dry Sand5 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 / ω Velocity = ω / k k = wave-number ω = 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)->S(x,ω)
ARMA Modeling is done across x to obtain
a space-frequency (k , ω ) model,
Estimate a(ω) and k(ω) by IQML (aka St-McB/Prony)
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Results from Vector IQML
k(ω) vs. ω becomes velocity vs. Ω
Extract individual modes from (k , ω ) 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 phases1. Probe phase: use a small 2-D array (rectangle or cross)
Find general target area by imaging with reflected waves
2. Adaptive placement of additional sensors Maneuver receiver(s) to increase resolution Use “Theory of Optimal Experiments”
3. On-top of the target End-game: Verify the resonance
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Adaptive Sensor Placement
Probe ArrayProbe Array findsgeneral target area
1
2
3Additional sensors are added to the “cumulative array”
Target
Source
On-top forresonance
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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
3 by 10 Element Array of Ground-
Contacting Sensors
Seismic Source
VS-1.6 AT Landmine (5cm deep)
50 Tons of Damp, Compacted Sand
Scan Region of 2m by 2m
45 cm
174 cm
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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
Choose Next Sensor Position
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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
Steps in Optimal Maneuver
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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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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.
Theory of Optimal Experiments
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Next Optimal Position
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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
Unique Problems for Seismic
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Constrained optimization for next array position
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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
Experimental Data Setup
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ACTUAL TARGET : (135,135) ± 5ESTIMATE (102,120)
First Iteration
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Values calculated on half circle
Next array position values calculated on half circle of radius=30cm
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ALONE CUMULATIVE
ACTUAL TARGET : (135,135) ± 5ESTIMATE: ALONE (100,127), CUM(112,127)
Second Iteration
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Values calculated on half circle
Next Array Position
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Four Iterations: Cumulative Imaging
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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
Implementation
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Experimental Setup of Seismic Landmine Detection Measurements
3 by 10 Element Array of Ground-
Contacting Sensors
Seismic Source
VS-1.6 AT Landmine (5cm deep)
50 Tons of Damp, Compacted Sand
Scan Region of 2m by 2m
45 cm
174 cm
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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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12
34
Wave Separation at each iteration: along top-most line array
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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
EXPERIMENTAL SETUP
Demo in Sandbox
MOVIE of Experiment
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Four Iterations: bracket start
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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
End-game Detection
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Extracted reverse wave as array moves near and above the target
Movie: VS-1.6 (5cm)
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Extracted reverse wave as array moves near and above the target
Movie: TS-50 (1cm)