| Description |
Guided waves are commonly used within the realms of nondestructive evaluation (NDE) and structural health monitoring (SHM). Their properties and characteristics are highly dependent on the medium in which they are propagating. In many practical applications, however, these properties are not known a priori and the amount of available data to estimate them can be very low. Consequently, it would be beneficial to several applications to be capable of retrieving guided wave properties from a limited set of experimental measurements for any structure of interest. It is specifically advantageous to identify and extract such information for complex media, such as anisotropic composite panels, that have found broad applications in modern structural engineering applications (such as aircrafts) but suffer from the unavailability of precise models of ultrasonic wave propagation. Therefore, this dissertation focuses on creating signal processing and machine learning strategies to analyze such complex structures without necessitating cumbersome, comprehensive data acquisition and processing, which can be costly and time-consuming. In the NDE and SHM literature, attempts at tackling this problem have resulted in several methodologies aimed at characterization, prediction, and reconstruction of guided waves from subsampled data. In particular, sparse wavenumber analysis (SWA) was proposed to recover dispersive properties of guided waves in an infinite, isotropic plate. Nevertheless, the restrictive assumptions in the SWA model render it ineffective when applied to more complex anisotropic structures. Moreover, its compressive capabilities can only be applied to the spatial dimension. In this dissertation, we introduce a number of extensions and modifications to the SWA model, intended to address the aforementioned shortcomings. More specifically, we modify the model such that it is capable of recovering information in the temporal dimension. We then extend the model into two dimensions to account for variations in wave velocities with respect to the direction of propagation. Finally, we combine these two notions to create a framework in which information retrieval is feasible in the presence of incomplete data in both time and space. In addition, attempts at characterization and reconstruction of guided waves with multipath reflections, as well as improving the two-dimensional model by incorporating information in the polar coordinates, are presented. iv |
