FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

INVERSION PROBLEM
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The inversion is a mathematical process which yields the true
dimensions of the flaw based on the signals obtained with sensing
coils. A number of works address purely theoretical inversion
protocols and very little work is done on experimental data.
The modelling of lift-off as well as the response of practical
probes is well understood. A flaw response in both twodimensional
and three-dimensional geometries has also been
developed. Although great progress has been made in improving
mathematical modelling of eddy current responses, the theory has
not been adequately tested against experimental practice. A
flowchart of the inversion is shown in Figure 6.
We developed a novel image producing method based specifically on
array concepts. A hexagonal array (AB type) is suggested as
shown in Figure 7« Calculations by W.G. Simpson et.al. (9) have
shown that the change in impedance due to a point defect can be
approximated by a complicated relationship represented by the
equation below, where F (x)=signal response, x=distance from
centre of coil and r=effective coil radius. Simply put, the
coil is not sensitive under its centre.
F (x) = A M - cos
F (x) = 2A xlexp - [x - l\ | L< x < r
2A xlexp - /x - i\ 1
F (x) = A exp |-2fx-r
x ]
r)
~ I V 2 JJ
The parameter of interest (eg. crack depth) in matrix form is:
T =
t(i,l) t(i,m)
t(n,i) t(n,m)
where (i,k) is the location of the coil with (i,k) coordinates.
The response of the n X m coils is also described by the matrix
S =
s(n,i) s(n,m)
The measured S matrix should be transposed into a T matrix.
Let us assume that the response of the coil at location n,m is a
weighted sum of the crack depth values (t) at the nearest
neighbour positions.
s(m,m) = t(n-1,m-1) + t(n, m-1) + t(n-1,m) + t(n, m+1)
+ t(n+1, m-1) + t(n+1,m)