Method of measuring by electrical impedance tomography
View Patent ↗An electrical impedance tomography method for the measurement of a body comprising a cylindrical part containing a fluid, the method comprising arranging a number of electrodes around a periphery of the cylindrical part of the body, simultaneously exciting each of the electrodes, each electrode being excited by a potential of a selected form, measuring the electrical properties of the body using electrodes, and processing the data from measuring step so as to obtain a signed data matrix representative of an image.
1 . An electrical-impedance-tomography measuring method of a body comprising a cylindrical portion containing a fluid, the method comprising:
arranging a number n e of electrodes around a periphery of the cylindrical portion of the body,
simultaneously exciting each of the n e electrodes, each electrode being excited by a potential V n exc having a form:
V
n
exc
(
t
)
=
A
∑
m
=
1
n
e
cos
(
2
π
f
m
t
)
[
δ
m
cos
𝕆
(
m
θ
n
)
+
δ
m
sin
𝔼
(
m
θ
n
2
)
]
where A is a signal amplitude, θ n is an angular position of electrode n, f m =m*f 0 is an oscillation frequency, f 0 is a fundamental frequency chosen such that f m is less than a Nyquist frequency of the system for all m, δ is the Kronecker delta, and
={2 k+ 1: k ∈ } is the set of odd integers
={2 k:k ∈ *} is the set of non-zero even integers,
measuring electrical properties V n meas of the body using the electrodes, and
processing data generated in the measuring step, by:
a) for each electrode E n , computing data points M n defined by:
M
n
(
k
)
=
1
RP
❘
"\[LeftBracketingBar]"
∑
p
=
0
P
-
1
V
n
meas
(
p
)
e
ik
β
p
❘
"\[RightBracketingBar]"
where R is a resistance of a resistor used to measure V n meas with V n meas =R I n across terminals of the resistor, P is a number of points in a discrete sequence of measurement of the current I n , p is a discrete time, k is a Fourier coefficient comprised between 1 and (n e −1) and β p =(2πp/P),
b) constructing a data matrix D from the data points M n (k) for all n and for all k, according to the equation:
D
=
(
{
M
n
(
1
)
}
{
M
n
(
2
)
}
{
M
n
(
3
)
}
⋮
{
M
n
(
n
e
-
1
)
}
)
[
[
.
]
]
,
and
c) constructing a signed data matrix, the elements of which are defined by the following equation when a phase shift Φ n,l (k) between an excitation potential at electrode 1 and a current measured at electrode n is less than π/2:
D
~
n
m
=
sin
(
Φ
n
,
l
(
k
)
)
❘
"\[LeftBracketingBar]"
sin
(
Φ
n
,
l
(
k
)
)
❘
"\[RightBracketingBar]"
D
n
m
[
[
.
]
]
and the elements of which are defined by the following equation when the phase shift Φ n,l (k) between the excitation potential at electrode 1 and the current measured at electrode n is greater than or equal to π/2:
{tilde over (D)} n m =Σ n m D n m
where Σ is a sign matrix defined such that an i-th element of a j-th row of Σ is the sign of cosine ([2π/([j 1]/2)]*(i−1)/n e ) for odd j and a sign of sine ([2π/(j/2)]*(i−1)/n e ) for even j.
2 . The method as claimed in claim 1 , wherein the set of potentials V n exc satisfy the condition:
∑
n
=
1
n
e
V
n
exc
(
t
)
=
0.
3 . The method as claimed in claim 2 , wherein an image is produced using a one-step iterative least-squares reconstruction algorithm applied to the signed data matrix.
4 . The method as claimed in claim 1 , wherein the electrodes are angularly distributed in a regular manner around a periphery of the body.
5 . The method as claimed in claim 1 , further comprising performing tomographic measurement of a two-phase flow, the body being a pipe of a nuclear installation.
6 . A computer program product comprising a non-transitory computer-readable medium storing instructions that are readable by a processor so that, when executed, the instructions cause an acquiring system to be controlled in order to implement the measuring method as claimed in claim 1 .
7 . A device for implementing the method as claimed in claim 1 , the device comprising:
an acquiring system comprising at least one programmable logic array, a module for generating analog signals, and a module for measuring analog signals;
a computer configured to control the acquiring system; and
a plurality of electrodes connected to the acquiring system.