Application of ICAMM to Impact-Echo Testing - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 104

concrete reinforcement. A displacement of the fundamental frequency to a lower
value is the key to identifying the presence of a crack [ 1 ]. The physical phenomenon
of impact-echo corresponds to wave propagation in solids. When a disturbance is
applied suddenly at a point on the surface of a solid, the disturbance propagates
through the solid as three different types of waves: P-wave (normal stress), S-wave
(shear stress), and R-wave (surface or Rayleigh) [ 2 ]. After a transient period in
which the first waves arrive, wave propagation becomes stationary in resonant
modes that vary depending on the defects inside the material.
The applications of ICA and BSS are extensive in several areas such as bio-
medical signal processing, audio signal separation, and image processing [ 3 , 4 ].
Specifically, there are relatively few references of the use of ICA algorithms in NDT
[ 5 , 6 ]. The main difficulties of the application of BSS to vibration signals were
analyzed in [ 7 ]. They included the following: scaling and labelling indeterminacies
of the sources; the dynamic nature of the mechanical systems, which requires a
convolutive mixture of sources to be described; the physical relevance of the source
meaning; the determination of the exact number of sources a priori; the problem of
handling signals that are distributed in time and space; and the requirement of system
invertibility. In order to handle these difficulties, in [ 7 ], J. Antoni proposed focusing
the BSS problem on the separation of vibration signals into contributions of periodic,
random stationary and random nonstationary sources.
A method for acoustic emission characterization that is based on ICA and
higher-order statistics (HOS) applied to ring-type samples from steel pipes for the
oil industry was proposed in [ 8 ]. This method allowed low signal-to-noise ratio
(SNR) sources that were buried in mechanical non-gaussian noise to be separated
by taking advantage of the statistical independence basis of ICA. In addition, ICA
has been used to detect vibratory signals from termite activity in wood by sepa-
rating termite alarm signals generated in wood from known signals [ 9 ]. It has also
been used to identify embedded transient low-level events (combustion-related
noise sources such as combustion, fuel injection, piston lap, and valve operation)
in diesel engines [ 10 , 11 ]. These works show that the separation of sources with
small energy levels is possible by using ICA since it is based on the statistical
independence of the components and not on the energy associated to each fre-
quency component. Recently, the application of BSS to mechanical signals has
been adapted to extract only one signal of interest (or sequentially, more than just
one). This approach is referred to as blind signal extraction (BSE) or semi-blind
source separation (SBSS) since it exploits a priori knowledge about the signal of
interest. One example of BSE is the extraction of the mechanical signature of one
particular fault in the system for gearbox diagnostics [ 6 ].
We developed an application of ICA in the field of impact-echo testing in [ 12 ,
13 ]. In the first approach, the transfer functions between the impact point and the
defects in the material were modelled as ''sources'' for blind source separation. In
this work was considered that the sensors located on the material surface measured
a convolutive mixture of the contribution of each of the defects. From spectral
analysis, the dominant resonance frequencies that vary from homogeneous to
defective material were selected. The signal spectral content at the selected