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frequencies was processed by instantaneous ICA instead of dealing with the whole
convolutive problem [ 14 , 15 ]. The stability of the BSS solution was analyzed using
bootstrap resampling [ 16 ], obtaining a separability matrix to group the estimated
source signals in separable subspaces. The separable estimated source signals were
compared with the theoretical response of the material (calculated by transient
dynamic analysis through three-dimensional finite element models) for deter-
mining the reliability of the defect detection. The results showed that source
estimates fit well with the theoretical response of the material. In addition, was
found that the number of defects can be estimated by ICA in simulations and
experiments with various defective parallelepiped-shape materials of aluminium
alloy series 2,000.
This chapter presents the application of ICA mixture modelling to non-destruc-
tive testing based on the impact-echo technique. The application consists of dis-
criminating patterns for material quality control from homogeneous and defective
materials inspected by impact-echo testing. This problem is modelled as a mixture of
independent component analysis (ICA) models, representing a class of defective or
homogeneous material by an ICA model whose parameters are learned from the
impact-echo signal spectrum. These parameters define a kind of particular signature
for the different defects. The proposed procedure is intended to exploit to the
maximum the information obtained with the cost efficiency of only a single impact.
To illustrate this capability, four levels of classification detail (material condition,
kind of defect, defect orientation, and defect dimension) are defined, with the lowest
level of detail having up to 12 classes. The results from several 3D finite element
models and lab specimens of an aluminium alloy that contain defects of different
shapes and sizes in different locations are included. The performance of the clas-
sification by ICA mixtures is compared with linear discriminant analysis (LDA) and
with multi-layer perceptron (MLP) classification. We demonstrate that the mass
spectra from impact-echo testing fit ICAMM, and we also show the feasibility of
ICAMM to contribute in NDT applications in Sect. 5.3 .
The chapter also includes a section dedicated to describing the procedures both
for simulations and lab experiments employed to acquire the impact-echo signals
( Sect. 5.2 ). The final section includes the conclusions and future line of research of
this application ( Sect. 5.4 ).
5.2 Impact-Echo Measurements
5.2.1 Simulated Signals
The set of simulated signals came from the full transient dynamic analysis of 100
simulated models. Several studies have demonstrated a good approximation
between the theoretical material response calculated by using finite element
method (FEM) and the results obtained in impact-echo experiments [ 1 ]. The
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