Experimental validation of a fast non-iterative imaging algorithm for eddy current tomography Flavio Calvano 1 , Guglielmo Rubinacci 1 , Antonello Tamburrino 2 and Salvatore Ventre 2 1 Ass. EURATOM/ENEA/CREATE, DIEL, Università di Napoli Federico II, Italy 2 Ass. EURATOM/ENEA/CREATE, DAEIMI, Università di Cassino, Italy
17
Embed
Experimental validation of a fast non-iterative imaging algorithm for eddy current tomography
Experimental validation of a fast non-iterative imaging algorithm for eddy current tomography Flavio Calvano 1 , Guglielmo Rubinacci 1 , Antonello Tamburrino 2 and Salvatore Ventre 2 1 Ass. EURATOM/ENEA/CREATE, DIEL, Università di Napoli Federico II, Italy - PowerPoint PPT Presentation
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Experimental validation of a fast non-iterative imaging algorithm
for eddy current tomography
Flavio Calvano1, Guglielmo Rubinacci1, Antonello Tamburrino2 and Salvatore Ventre2
1 Ass. EURATOM/ENEA/CREATE, DIEL, Università di Napoli Federico II, Italy
2 Ass. EURATOM/ENEA/CREATE, DAEIMI, Università di Cassino, Italy
Eddy Current TomographyEddy Current Tomography
Probe
Conducting specimen
Anomaly
H0
Hr J
pick-up coil
excitation & pick-up
coil
a)
ImpedanceAnalizer
PC(InversionAlgorithm)
ECT coils
Vc
V
ImpedanceAnalyzer
(auto and mutualimpedances)
PersonalComputer
(imaging algorithm)
c
Anomaly (=i)
i1
i2
iM
Conductor (=b)
i>b
Problem DefinitionProblem Definition
Phase 1 Vc
coillI
coilkv
# l
# k
Phase 2
V
lj
Icoill
coilk
klcoilcoiljI
vZ
0
Eddy Current DataEddy Current Data
Key quantity for the inversion method
Low frequency expansionsLow frequency expansions
Matrix of the mutual impedances between coils
5)3(3
0
4)2(20
5)5(5)4(4)3(3)2(200
0with
O
O
Ojjj
coil
coil
coil
PLX
PRR
PPPPLRZ
Phase 1
Phase 2
Vc
D
Phase 1Phase 2 Vc
D
22 PP cVDD
MonotonicityMonotonicity
A. Tamburrino and G. Rubinacci, “Fast Methods for Quantitative Eddy-Current Tomography of Conductive Materials”, IEEE Trans. Magn., vol. 42, no. 8, pp. 2017-2028, 2006.
definite-semi positive is 2222 PPPP
DD false 22 PP
... for 22 PP VD
Phase 1Phase 2 Vc
V
Vkk false 22 PP
Phase 1
Phase 2Vc
k
22 and ... kkD PP
Inversion: underlying ideaInversion: underlying idea
Vkk false 22 PP
V
Inversion: underlying ideaInversion: underlying idea
Basic inversion algorithm:
Take as estimate of V the union ofthose k such that 0PP )2()2(
k
free error not 2P
corrupted areof seigenvalue The ~~ 2)2( PP k
The test for k is no longer valid !
The NoiseThe Noise
The Sign IndexThe Sign Index
1,1ˆ
1,
1,
M
jjk
M
jjk
ks
At each k we associate
jk , is the j-th eigenvalue of 22 ~~ PP k
Experimental setupExperimental setup
External CoilInternal diameter=5mm, external diameter=10.5mm, height=6.5mm, number of turns=700.
Internal Coilinternal diameter=1mm, external diameter=4mm, height=3mm, number of turns=180.
The excitation frequency is 20kHz
Benckmark: printed circuit board
ResultsResultsReconstructed Map
Region under test measurements
Test domain measurements 2kP 2P
ResultsResults
Reconstructed Map
ResultsResults
Reconstructed Map with top test domains Reconstructed Map with the bottom test domains
Top view Bottom view (scanned from the top view)
2.4252 0.2171-0.2098- 22.3422
kP
Top
Bottom
2.399 0.104-0.100- 21.5852
kP
Estimated Noise level : 50 m
ResultsResultsTop view Bottom view (scanned from the top view)
Reconstructed Map with top test domains Reconstructed Map with the bottom test domains
CONCLUSIONSCONCLUSIONS
•A fast inversion method for inverting eddy-current testing data has been applied to the identification of the shape of inclusions in a conductor by eddy current tomography.
•The eddy-current data consists of the variation of the impedance matrix using an a-priori designed with numerical simulation array of coils to scan the specimen under test.
•The second-order moment P(2) accounts for the resistive contribution to the changes of the impedance matrix occurring at relatively low frequencies.
•A direct imaging algorithm based on monotonicity principle is available that allows real-time imaging on directly measured experimental data.
REFERENCESREFERENCES
•A. Tamburrino and G. Rubinacci, “A new non-iterative inversion method for electrical impedance tomography”, Inverse Problems, pp. 1809–1829, 2002.
•A. Tamburrino and G. Rubinacci, “Fast Methods for Quantitative Eddy-Current Tomography of Conductive Materials”, IEEE Trans. Magn., vol. 42, no. 8, pp. 2017-2028, 2006.
•A. Tamburrino, S. Ventre, G. Rubinacci, “Recent developments of a Monotonicity Imaging Method for Magnetic Induction Tomography” accepted for publication on Inverse Problems.
•G. Rubinacci, A. Tamburrino, S. Ventre, “Eddy current imaging of surface breaking defects by using monotonicity based methods”, ACES Journal, vol.23, no. 1, pp. 46-52, 2008.