Nondestructive evaluation of plates using Eddy current methods

David C. Dobson; Fadil Santosa

doi:10.1016/S0020-7225(97)00081-5

Nondestructive evaluation of plates using Eddy current methods

David C. Dobson
, Fadil Santosa

School of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The problem of determining defects in structures using eddy current methods is investigated. The goal of this work is to assess the extent to which accurate quantitative information about damage can be extracted from the data. For simplicity, we consider the problem of inspecting a plate in two dimensions. Damage is modeled as a change in the plate's conductivity. Electromagnetic field is generated by a pair of wires, which also serves as a measurement probe. The resulting mathematical model is analyzed by first deriving an integral identity, and second, by linearizing the relation between the conductivity anomaly and the data. We show that the problem of reconstructing a conductivity anomaly from eddy current data is quite unstable, and a method based on least-squares principle would fail to detect conductivity anomalies in some situation. An alternate method, one that obtains gross properties of the anomaly (in this case an average) is proposed, and is shown to be quite robust. Several numerical experiments which illustrate our main ideas are presented.

Original language	English (US)
Pages (from-to)	395-409
Number of pages	15
Journal	International Journal of Engineering Science
Volume	36
Issue number	4
DOIs	https://doi.org/10.1016/S0020-7225(97)00081-5
State	Published - Mar 1998

Bibliographical note

Funding Information:
Research partially supported by Air Force Office of Scientific Research, under Grant Nos F49620-93-1-0500, F49620-95-1-0305, and F49620-95-1-0497, National Science Foundation under Grant DMS-9503114, Department of Energy under Grant DE-FG02-94ER25225. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.

Publisher link

10.1016/S0020-7225(97)00081-5

Find It

Find It at U of M Libraries

Cite this

@article{c28a2f2262624c5a9a5c5731c49b8900,

title = "Nondestructive evaluation of plates using Eddy current methods",

abstract = "The problem of determining defects in structures using eddy current methods is investigated. The goal of this work is to assess the extent to which accurate quantitative information about damage can be extracted from the data. For simplicity, we consider the problem of inspecting a plate in two dimensions. Damage is modeled as a change in the plate's conductivity. Electromagnetic field is generated by a pair of wires, which also serves as a measurement probe. The resulting mathematical model is analyzed by first deriving an integral identity, and second, by linearizing the relation between the conductivity anomaly and the data. We show that the problem of reconstructing a conductivity anomaly from eddy current data is quite unstable, and a method based on least-squares principle would fail to detect conductivity anomalies in some situation. An alternate method, one that obtains gross properties of the anomaly (in this case an average) is proposed, and is shown to be quite robust. Several numerical experiments which illustrate our main ideas are presented.",

author = "Dobson, \{David C.\} and Fadil Santosa",

note = "Funding Information: Research partially supported by Air Force Office of Scientific Research, under Grant Nos F49620-93-1-0500, F49620-95-1-0305, and F49620-95-1-0497, National Science Foundation under Grant DMS-9503114, Department of Energy under Grant DE-FG02-94ER25225. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. ",

year = "1998",

month = mar,

doi = "10.1016/S0020-7225(97)00081-5",

language = "English (US)",

volume = "36",

pages = "395--409",

journal = "International Journal of Engineering Science",

issn = "0020-7225",

publisher = "Elsevier Ltd",

number = "4",

}

TY - JOUR

T1 - Nondestructive evaluation of plates using Eddy current methods

AU - Dobson, David C.

AU - Santosa, Fadil

N1 - Funding Information: Research partially supported by Air Force Office of Scientific Research, under Grant Nos F49620-93-1-0500, F49620-95-1-0305, and F49620-95-1-0497, National Science Foundation under Grant DMS-9503114, Department of Energy under Grant DE-FG02-94ER25225. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.

PY - 1998/3

Y1 - 1998/3

N2 - The problem of determining defects in structures using eddy current methods is investigated. The goal of this work is to assess the extent to which accurate quantitative information about damage can be extracted from the data. For simplicity, we consider the problem of inspecting a plate in two dimensions. Damage is modeled as a change in the plate's conductivity. Electromagnetic field is generated by a pair of wires, which also serves as a measurement probe. The resulting mathematical model is analyzed by first deriving an integral identity, and second, by linearizing the relation between the conductivity anomaly and the data. We show that the problem of reconstructing a conductivity anomaly from eddy current data is quite unstable, and a method based on least-squares principle would fail to detect conductivity anomalies in some situation. An alternate method, one that obtains gross properties of the anomaly (in this case an average) is proposed, and is shown to be quite robust. Several numerical experiments which illustrate our main ideas are presented.

AB - The problem of determining defects in structures using eddy current methods is investigated. The goal of this work is to assess the extent to which accurate quantitative information about damage can be extracted from the data. For simplicity, we consider the problem of inspecting a plate in two dimensions. Damage is modeled as a change in the plate's conductivity. Electromagnetic field is generated by a pair of wires, which also serves as a measurement probe. The resulting mathematical model is analyzed by first deriving an integral identity, and second, by linearizing the relation between the conductivity anomaly and the data. We show that the problem of reconstructing a conductivity anomaly from eddy current data is quite unstable, and a method based on least-squares principle would fail to detect conductivity anomalies in some situation. An alternate method, one that obtains gross properties of the anomaly (in this case an average) is proposed, and is shown to be quite robust. Several numerical experiments which illustrate our main ideas are presented.

UR - https://www.scopus.com/pages/publications/0032010535

UR - https://www.scopus.com/pages/publications/0032010535#tab=citedBy

U2 - 10.1016/S0020-7225(97)00081-5

DO - 10.1016/S0020-7225(97)00081-5

M3 - Article

AN - SCOPUS:0032010535

SN - 0020-7225

VL - 36

SP - 395

EP - 409

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

IS - 4

ER -

Nondestructive evaluation of plates using Eddy current methods

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this