Signal Modality Characterization: from Phase Space Reconstruction to Real Applications
Alicia Carrión García
The characterization of the modality of a signal is a new concept, which has been the subject of recent research. Its main purpose is to identify any changes in the nature of a real signal. The term "nature of a signal" refers to the underlying model that generates the signal from the point of view of two main characteristics: determinism and linearity. In this thesis, the modality of a signal is used for the advanced processing of acoustic signals, and in particular, in non-destructive tests of non-homogeneous materials, such as concrete.
The problem of the characterization of the modality begins with the correct reconstruction of the phase space (Chapter 2). This new domain allows identifying the different states of a signal, as to whether they are recurrent or not, depending on whether they are deterministic, respectively, random. In the field of non-destructive testing based on ultrasound, the material is excited with a purely deterministic signal. However, the nature of the received signal depends on the internal structure of the material. This working hypothesis allows us to propose measuring the degree of determinism as a complementary alternative to the usual ultrasound parameters such as attenuation and speed. The level of determinism has been found to be proportional to the level of porosity in cementitious materials (Chapter 3). It also allows characterizing the level of damage of mortar test pieces subjected to different kinds of damaging processes: external attack by sulphates, and loading processes (Chapter 4).
The study of the non-linearity or complexity of a time series is initially presented blindly (without having information about the input signal) through hypothesis tests: generating surrogate data and applying a statistical test. Significant progress has been made in adapting this approach to nonstationary data, a common feature of real non-linear signals. The main results in this regard have been achieved in the characterization of the
The concept of signal modality has also been used to perform a detailed study of the non-linear phenomenon of acoustic impact spectroscopy. This analysis has allowed understanding the variables involved, and thus, proposing a mathematical model that characterizes the phenomenon. The understanding of the phenomenon and the model have allowed proposing a new processing algorithm equivalent to the usual NIRAS technique, but optimal in its application. This processing alternative may mean significant advances, especially in industrial applications where time and effort are variables to be optimized (Chapter 6).
This thesis demonstrates that the characterization of the modality of a signal not only presents an alternative to the characterization of complicated real phenomena, but it also opens a new research perspective within the field of signal processing. The measure of determinism and the FANSIRAS algorithm have shown that the modality of a signal is an interesting tool for future research into the characterization of cementitious materials.