Chapter 4
Application of the Set-Theoretic
Algorithm to CFRP’s
4.1 Background
A major milestone that we have demonstrated is that the set-theoretic algorithm
works well with anisotropic media, such as CFRPs. Such problems require at
least two variables to be reconstructed at each voxel, such as the longitudinal
and transverse conductivities. The details are described in Sects. 4.3.1–4.3.2 in the
context of measuring FAWT (Fiber Areal-Weight), which is an important parameter
during the manufacture of CFRP prepregs. An interesting corollary is shown in
Sect. 4.3.2, in which a single transmitting coil is used with the same receiver array
as before, and very good results were achieved. This suggests that less extreme
T/R-arrays can be used in the algorithm, with the possibility of using sparse-grid
interpolation to fill in gaps in the measured data.
We begin our study of microstructure quantification problems in Sect. 4.4 with an
investigation of detecting and measuring delaminations using the model shown in
Fig. 4.7. The objective was to estimate the smallest delamination that is probably
detectable. The results shown in Table 4.2 suggest that it may be difficult to
distinguish a delamination 7 µm high from the background. There would appear
to be a better chance of detecting one that is 14 µm tall, and probably a pretty good
chance of detecting one that is 21 µm tall.
The problem suggested in Fig. 4.8 will be a major ’test-bed’ for applying settheoretic inversion to microstructure quantification. We have started the process
during this quarter by analyzing the model of Fig. 4.9, which represents the structure
of Fig. 4.8 without the voids. The host is as shown in Fig. 4.1, except that it is 0.4 mm
thick. The receive-array is 21×21, as before in the FAWT studies, so that N s = 441,
and there are 11 × 11 = 121 transmit positions in the transmitter array. The
excitation is at a frequency of 10GHz. Data for setting up the set-theoretic algorithm
are being generated, and the actual inversion process will be completed during
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_4
87
Application of the Set-Theoretic
Algorithm to CFRP’s
4.1 Background
A major milestone that we have demonstrated is that the set-theoretic algorithm
works well with anisotropic media, such as CFRPs. Such problems require at
least two variables to be reconstructed at each voxel, such as the longitudinal
and transverse conductivities. The details are described in Sects. 4.3.1–4.3.2 in the
context of measuring FAWT (Fiber Areal-Weight), which is an important parameter
during the manufacture of CFRP prepregs. An interesting corollary is shown in
Sect. 4.3.2, in which a single transmitting coil is used with the same receiver array
as before, and very good results were achieved. This suggests that less extreme
T/R-arrays can be used in the algorithm, with the possibility of using sparse-grid
interpolation to fill in gaps in the measured data.
We begin our study of microstructure quantification problems in Sect. 4.4 with an
investigation of detecting and measuring delaminations using the model shown in
Fig. 4.7. The objective was to estimate the smallest delamination that is probably
detectable. The results shown in Table 4.2 suggest that it may be difficult to
distinguish a delamination 7 µm high from the background. There would appear
to be a better chance of detecting one that is 14 µm tall, and probably a pretty good
chance of detecting one that is 21 µm tall.
The problem suggested in Fig. 4.8 will be a major ’test-bed’ for applying settheoretic inversion to microstructure quantification. We have started the process
during this quarter by analyzing the model of Fig. 4.9, which represents the structure
of Fig. 4.8 without the voids. The host is as shown in Fig. 4.1, except that it is 0.4 mm
thick. The receive-array is 21×21, as before in the FAWT studies, so that N s = 441,
and there are 11 × 11 = 121 transmit positions in the transmitter array. The
excitation is at a frequency of 10GHz. Data for setting up the set-theoretic algorithm
are being generated, and the actual inversion process will be completed during
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_4
87