Fast direct and inverse EMI algorithms for ... - Semantic Scholar

Fast direct and inverse EMI algorithms for enhanced identification of buried UXO with real EMI data a

F. Shubitidze *a, K O’Neill b, I. Shamatava a, K. Sun a and K.D. Paulsen a Thayer School of Eng. Dartmouth College, Cummings Hall, HB 8000, Hanover NH, 03755, USA b USA ERDC Cold Regions Research and Eng. Lab.,72, Lyme Road, Hanover NH, 03755, USA

Abstract- Discrimination of buried unexploded ordinance (UXO) from innocuous buried items remains a challenging, top priority problem for the electromagnetic induction (EMI) sensing community. In general, classification is an inverse problem, requiring very fast and accurate representation of the target response. To address this critical issue, this paper presents a very fast, rigorous way to compute EMI scattering from a realistically complex, composite target. Full interaction between all parts of the object are included in the calculations. The method is based on a hybrid of the full method of auxiliary source (MAS) [1] and the MAS-thin skin depth approximation formulation (MAS-TSA) [2], together with new modal decomposition and reduced source set techniques [3]. For general excitation, a primary field is decomposed into the fundamental spheroidal modes on a fictitious spheroid surrounding a real target. Finally the total response from the target is reproduced using only a few auxiliary magnetic charges. A least square minimization is used for discrimination an unseen object’s orientation and position. Numerical results are given and compared with experimental data.

I. INTRODUCTION In the last several years, EMI sensors, operating from 10’s of Hz up to several hundred kHz, have shown the considerable progress in the detection and discrimination of buried UXO. Most if not all UXO are composite objects with distinct, relatively homogeneous sections, each consisting of different metal, e.g., head, body, tail and fins, copper banding, etc. A significant fraction of fired ordnance does not explode, and after impact remains unseen underground and dangerous for a long time. Further, in many highly contaminated sites, multiple UXO together with widespread clutter appear simultaneously within the field of view of the sensor. The false alarm rate produced by clutter is extremely high and typically causes the majority of remediation costs being spent on excavating innocuous items. Thus, at present the major problem is discrimination not detection. In the EMI sensing, a time varying electromagnetic field is used to illuminate a highly conducting and permeable metallic target. The primary field induces eddy currents inside the target which then produce a secondary EM field which is measured. Recent numerical and experimental studies have revealed that the characteristics of the secondary field are determined by the target geometry and its EM parameters. Magnetic fields radiated by both the sensor and the object decay very rapidly as a function of distance. Therefore, the sensor affects different materials and sections of the target

0-7803-7929-2/03/$17.00 (C) 2003 IEEE

differently. The transmitted near field produces much stronger excitation of the closest portion of the target. In turn, the parts of the target radiating closest to the receiver disproportionately influence the scattered signal. These proximity effects are particularly important for identification and discrimination of multiple and composite objects. Analytical techniques based on simple resonating magnetic and electric dipoles will break down when sensors pass close to the target, as is often the case in UXO surveying. In general, UXO discrimination based on EMI response is an inverse problem, demanding very fast and accurate calculation of the forward EMI scattering problem. In order to address this need, in this paper solution of the forward EMI problem is divided into three steps. In the first step, any input primary field is decomposed into fundamental spheroidal modes on a fictitious spheroid surrounding an arbitrary real target. The primary field varies greatly over the spatial scale of the target and cannot be approximated by a simple average field. In the next step, the full EMI induction problem is solved in 3-D for each spheroidal fundamental mode. Finally, in the third step the scattered field for each excitation mode is reproduced using only a small number of auxiliary sources, with amplitudes determinated by matching the secondary potential field over a fictitious spheroid. Thereafter, for a given prospective target and any hypothetical relation to the sensor, the EMI problem breaks down only to determining the coefficients of spheroidal fundamental modes for the primary field around the target. The full scattered field at any observation point can be obtained simply and quickly by superposing the saved modal solutions. The main goal of this paper is to investigate the accuracy of the proposed forward and inverse algorithms against experimental data. II. DIRECT AND INVERSE ALGORITHMS Most if not all UXO's are bodies of revolution (BOR). In EMI surveying the target is illuminated by an arbitrarily oriented, time varying primary magnetic field. To take advantage of the axial symmetry of the target, it can be surrounded by a fictitious spheroid having the same axis (the overall method does not depend on axial symmetry of

4160 0-7803-7930-6/$17.00 (C) 2003 IEEE

the target). On the fictitious spheroid the primary magnetic field can be expressed as:

& H pr =

∞

∞

1

¦ ¦¦b

pmn

& pr H pmn

&

determination of m is a crucial step. For estimation of these parameters we apply a simple least square minimization procedure:

& sc & & (m) − H meas |2

(1)

min | H

m =0 n = m p =0

& ­H d ½ H prpmn = − ∇ ® o Pnm (η)Pnm (ξ)Tpm (φ) ¾ ¯ 2 ¿ where

(η, ξ, ϕ)

& meas

is the measured secondary magnetic field at a where H given observation point for different frequencies and

(2)

& & H sc (m) is magnetic field obtained from the forward model

are the usual spheroidal coordinates,

using a reduced number of auxiliary sources.

d = 2 b − a is the inter focal distance, a and b are respectively minor and major semi-axis of the spheroid, the Pnm are Associate Legendre functions of first kind [3], and 2

2

Tpm (ϕ) are trigonometric functions. The bpmn are & pr coefficients of the primary field, H pmn is the pmn mode the

primary magnetic field. Using well established orthogonality properties of the Associated Legendre functions [3] and trigonometric functions, the b pmn coefficients can be determined from the primary field [3]. For each fundamental mode the primary magnetic field on the boundary of the real scatterer can be easily calculated once the b pmn are determinated. After that, using the hybrid full MAS /MASTSA method [1], [2], the target’s response for each input pmn & mode primary magnetic field b pmn H pr pmn can be obtained; Finally, using the MAS, the scattered field outside the fictitious spheroid can be expressed by a set of auxiliary magnetic charges placed on the auxiliary spheroid, once the

q ipmn is determined for each pmn mode and source location ri′ , the secondary magnetic amplitude of the reduced sources

field can be represented as:

& H sc =

∞

∞

1

N

¦ ¦ ¦b ¦q pmn

m =0 n = m p =0

pmn i

& & * G(r, ri′, ϕ)

(3)

i =1

Thus, the ultimate process of rapid forward calculation consists of 1) for any given sensor-target configuration, decomposing the primary field into fundamental spheroidal modes with equations (1)-(2); and 2) quickly calculating the scattered field by scaling the pre-determined source strengths

q pmn associated with the each pmn fundamental spheroidal k mode. For a given target and any hypothetical relation to the sensor, the EMI response can be represented as a function of position

(4)

and

orientation

& & H sc (m) ,

where

& m = {x o , yo , z o , φ, θ} , x o , yo , z o are target’s center location and φ, θ are polar and azimuthal angles. In order to

III. RESULTS For the validity of the proposed reduced sources algorithm for composite targets, we examine scattering from a machined object containing three distinct parts: aluminum, permeable steel, and brass cylinders illuminated by a concentric loop antenna about 40 cm in outer diameter. The cylinders are lined up along their axes of symmetry; the permeable cylinder is in the middle part. The cylinder parameters are: aluminum cylinder L1=6 inch, L1/2a1=4, σ=3. 107 S/m, µ1r=1; magnetic steel L2=3 inch, L2/2a2=2, σ=4 106 S/m, µ2r=60; and brass (non-magnetic) with L3=3 inch, L3/2a3=2, σ=1.2 107 S/m, µ1r=1. The distance between measurement plane and middle point of the target is z =29 cm. First, the hybrid MAS and MAS-TSA algorithms are used to obtain full solutions for each fundamental mode (m=0,..,10,, n=1,..,25) at 17 frequencies. Once the calculation is completed, the amplitudes of auxiliary magnetic charge rings are determined. Next, the scattered potentials on the auxiliary spheroid are calculated for each fundamental pmn mode. A new, much smaller set of auxiliary elementary magnetic charges is then located on an additional auxiliary spheroid, without regard for the details of the target geometry. The amplitudes of charges in the reduced set of sources are determined by having them produce the proper scattered potential on the first (exterior) auxiliary spheroid. In measurements, the antenna traveled parallel (Fig. 1 a-c) and perpendicular to (Fig. 1 d-f) to the object axis of symmetry, between positions 0 (center of the object) and 30 cm from its center, with data collected every 10 cm. All simulated and measured data agree very well, despite the proximity of the target, its heterogeneity, and the relative faintness of the signal beyond its ends. The results emphasize that the response from the UXO has quite different characteristics depending on the antenna position. Next the reduced set of sources together with least squares approximation were applied for inferring the target’s position and orientation. The target’s center was at xo= 0, yo=0, zo=35 cm in the global coordinate system, with orientation φ = 0, θ = 47.50 . Measurements were made over a 5x5 grid of points above target. For determination of & m = {x o , yo , z o , φ, θ} the least square minimization

carry out discrimination using both GPR and EMI sensing, the

0-7803-7929-2/03/$17.00 (C) 2003 IEEE

4161 0-7803-7930-6/$17.00 (C) 2003 IEEE

producing parameter values: x1 = 0.5cm, y1 = 1 cm, z1 = 33cm , and φ = 0 , θ = 43.50

algorithm for cases including noise and clutter, to discriminate an actual UXO from realistic EMI data.

IV. CONCLUSION

ACKNOWLEDGMENT

In this paper, for fast and accurate representation of EMI response from heterogeneous targets including all interactions between parts, a new algorithm is developed and tested against experimental data from a composite target. The algorithm is based on the decomposition of the primary potential into fundamental spheroidal excitation modes. Once the detailed EMI solution is obtained for each mode, the secondary field is represented with a small number of elementary magnetic charges. Thereafter, solutions for any sensor –target configuration can be obtained simply by determining a linear combination of the saved solutions, which can be done extremely quickly using the reduced set of sources. In a test against measurements on a very heterogeneous target, these pre-computed modal responses were used for inverting the object’s orientation and position. Results were very good in this noise-free EMI test. In future work we extend the new modal decomposition - reduced sources

This work was supported by the DoD Strategic Environmental Research and Development Program and US Army CoE ERDC BT25 program, with code development was supported by the USA CoE ERDC AF25 program.

algorithm

was

run,

REFERENCES: [1]. F. Shubitidze, K. O’Neill, S. A. Haider, K. Sun and K. D. Paulsen, ”Application of the method of auxiliary sources to the wideband electromagnetic induction problem,” IEEE Trans. Geosci. Rem. Sens., 40 (4) , 928-942, 2002. [2]. F. Shubitidze, K O’Neill, K. Sun, I. Shamatava and K.D. Paulsen, “A combined MAS-TSA algorithm for low frequency electromagnetic induction problems,” Proc. ACES2003, Monterey, CA, March 24-28, 2003. [3]. F. Shubitidze, K O’Neill, I. Shamatava, K. Sun, and K.D. Paulsen, “Analysis of EMI scattering to support UXO discrimination: Heterogeneous and multi objects ”. AeroSense Technologies and System for Defense & Security. Orlando Fl, April 21-25, 2003. 1 500

1 500

Q u a d r a tu re

500 0

In p h a s e

-50 0 -1 0 0 0

a)

-1 5 0 0

100

1000

10

500 0 In p h a s e

-50 0 -1 0 0 0

d)

-1 5 0 0

D a ta S im u la t io n

-2 0 0 0

Q u a d ra tu re

1 000

Re {Hz} & Im{Hz}

Re {Hz} & Im{Hz}

1 000

-2 0 0 0

4

D a ta S im u la t io n

100

1000

10

4

1500

1 000

Q u a d ra tu r e

1000

Q u a d ra tu re

Re {Hz} & Im{Hz}

Re {Hz} & Im{Hz}

500

0 In p h a s e

-50 0 b)

-1 0 0 0

-1 5 0 0

1000

10

0

In p h a s e

-5 0 0 -1 0 0 0

e)

-1 5 0 0

D a ta S im u la t io n 100

5 00

-2 0 0 0

4

D a ta S im u la t i o n

100

1 000

10

4

800

600 Q u a d ra tu re

400

600

200

400

Re {Hz} & Im{Hz}

Re {Hz} & Im{Hz}

Q u a d ra tu re

0

In p h a s e

-20 0 -40 0

c)

-60 0 -80 0 -1 0 0 0

1000

10

0 -20 0

In p h a s e

-40 0

f)

-60 0

D a ta S im u la t io n

100

200

-80 0

4

D a ta S im u la t io n 100

1000

Fig. 1 Scattered magnetic field versus frequency. 0-7803-7929-2/03/$17.00 (C) 2003 IEEE

4162

0-7803-7930-6/$17.00 (C) 2003 IEEE

10

4