102
4 Application of the Set-Theoretic Algorithm to CFRP’s
-1.2x10
6
-1x10
6
-800000
-600000
-400000
-200000
0
200000
400000
600000
800000
1x10
6
-500 -400 -300 -200 -100
0
100 200 300 400
Jx
Ex
Anomalous Conductivity for (k,l,m) = (3,3,3)
Real
Imag
Jx = 81.51*Ex
-80000
-60000
-40000
-20000
0
20000
40000
60000
-10000 -5000
0
5000
10000
15000
20000
Jy
Ey
Anomalous Conductivity for (k,l,m) = (3,3,3)
Real
Imag
Jy = -3.783E-03*Ey
Fig. 4.14 Results for cell (k, l, m) = (3, 3, 3) after removing all pins and allowing all currents
to be nonzero. The lines are the set-theoretic estimates, in which all ‘experimental outcomes’ are
used. Top: σ xx . Bottom: σ yy
and it is explained in the discussion before Fig. 4.27. Figures 4.27, 4.28, 4.29, 4.30,
4.31, and 4.32 illustrate the result of applying the heuristic scheme, starting with the
zeroth iteration and ending with the fourth. The results are quite good, and give us
confidence in the method. Nevertheless, we believe that it can be sharpened, and no
longer be ’heuristic’, by applying formal statistical decision theory.
The development of the layer-stripping algorithm that was described in Sect. 4.5,
together with the inverse-quality metric and the heuristic classifier are three
extremely important results of our research, as they strengthen the set-theoretic,
voxel-based inversion algorithm.
4 Application of the Set-Theoretic Algorithm to CFRP’s
-1.2x10
6
-1x10
6
-800000
-600000
-400000
-200000
0
200000
400000
600000
800000
1x10
6
-500 -400 -300 -200 -100
0
100 200 300 400
Jx
Ex
Anomalous Conductivity for (k,l,m) = (3,3,3)
Real
Imag
Jx = 81.51*Ex
-80000
-60000
-40000
-20000
0
20000
40000
60000
-10000 -5000
0
5000
10000
15000
20000
Jy
Ey
Anomalous Conductivity for (k,l,m) = (3,3,3)
Real
Imag
Jy = -3.783E-03*Ey
Fig. 4.14 Results for cell (k, l, m) = (3, 3, 3) after removing all pins and allowing all currents
to be nonzero. The lines are the set-theoretic estimates, in which all ‘experimental outcomes’ are
used. Top: σ xx . Bottom: σ yy
and it is explained in the discussion before Fig. 4.27. Figures 4.27, 4.28, 4.29, 4.30,
4.31, and 4.32 illustrate the result of applying the heuristic scheme, starting with the
zeroth iteration and ending with the fourth. The results are quite good, and give us
confidence in the method. Nevertheless, we believe that it can be sharpened, and no
longer be ’heuristic’, by applying formal statistical decision theory.
The development of the layer-stripping algorithm that was described in Sect. 4.5,
together with the inverse-quality metric and the heuristic classifier are three
extremely important results of our research, as they strengthen the set-theoretic,
voxel-based inversion algorithm.