The correlation dimension: A robust chaotic feature for classifying acoustic emission signals generated in construction materials

In the field of acoustic emission (AE) source recognition, this paper presents a classification feature based on the paradigm of nonlinear dynamical systems, often referred to as chaos theory. The approach considers signals as time series expressing an underlying dynamical phenomenon and enclosing all the information regarding the dynamics. The scientific knowledge on nonlinear dynamical systems has considerably improved for the past 40 years. The dynamical behavior is analyzed in the phase space, which is the space generated by the state variables of the system. The time evolution of a system is expressed in the phase space by trajectories, and the asymptotic behavior of trajectories defines a space area which is referred to as a system attractor. Dynamical systems may be characterized by the topological properties of attractors, such as the correlation dimension, which is a fractal dimension. According to Takens theorem, even if the system is not clearly defined, it is possible to infer topological information about the attractor from experimental observations. Such a method, which is called phase space reconstruction, was successfully applied for the classification of acoustic emission waveforms propagating in more or less complex materials such as granite and concrete. Laboratory tests were carried out in order to collect numerous AE waveforms from various controlled acoustic sources. Then, each signal was processed to extract a reconstructed attractor from which the correlation dimension was computed. The first results of this research show that the correlation dimension assessed after phase space reconstruction is very relevant and robust for classifying AE signals. These promising results may be explained by the fact that the totality of the signal is used to achieve classifying information. Moreover, due to the self-similar nature of attractors, the correlation dimension, and thus a correlation dimension-based classification approach, is theoretically insensitive to signal absorption.