Application of ICAMM to Impact-Echo Testing - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 120

Fig. 5.8 Magnitude spectrum of the impact-echo signals for the simulated models. Abbrevia-
tions P passing through, HP half-passing through channel 2 channel 3
belonging to the four different classes difficult. In addition, not all the data for the
multiple-defect class are depicted in Fig. 5.9 , since they are very sparse in the
classification space. Homogeneous specimen data are concentrated in a small
spherical region which makes their classification easy. The crack and hole data are
in a wide area and describe straight-like trajectories; they are joined together with
some of the multiple-defect data. In spite of this, for this classification level (Level
ii- kind of defect), the Mixca algorithm was able to find a proper solution, which
reached an accuracy of 88.9%. Thus, the impact-echo signals of each model were
fitted to different ICA models whose parameters were estimated by Mixca.
Figure 5.10 shows a set of ICAMM parameters obtained during training for the
impact-echo experiments using 15 spectra features in the kind of defect level of
classification. The estimated mixing matrices (represented in grey scale) and the
sources with their distributions and kurtosis values for the four classes of materials
are shown. The ICA parameters estimated for each class showed different sources
with non-gaussian distributions. The differences in these parameters among the
classes clearly show the suitability of the ICAMM model for classifying different
kinds of defective materials inspected by impact-echo.
The estimated sources represent linear combinations of the spectrum elements
produced by the defects that activate different resonant modes of the material. In
this level of classification, the pattern of the defects was detected independently of
their orientation and dimension. These patterns are related to the number of point
flaws that build the defects and the spatial relationship between the flaws. In
defective materials, the propagated waves have to surround the defects; their
energy decreases and multiple reflections and diffraction with the defect borders
are produced. The patterns of the displacement waveforms are affected by the
shape of the defects [ 30 ] building a kind of signature of the defect. This signature
is distinguishable in the parameters estimated by Mixca since the mixing matrix is
different for every class and there are particular densities of the sources that are
recovered only for a specific class.
The results obtained have confirmed the theoretical development included in
Sect. 5.3.1 where it was demonstrated that an ICA model can be applied for every