Agnostic Anomaly Detection Methodologies with Robust Inference Capability in Solid Media

Abstract

This thesis introduces a collection of methodologies for the detection and localization of structural defects in solid media using morphological demixing algorithms. The demix- ing algorithms are designed to separate spatiotemporal response data into two morpho- logically antithetical components: one contribution captures the spatially sparse and temporally persistent features of the medium’s response, while the other provides a representation of the dominant, globally smooth component as it would be observed in a defect-free medium. In order to perform the demixing, we aim to decompose each of the components via a dictionary with befitting topological structure. Within the demixing paradigm, we explore two distinct categories of methods: in the first, we con- sider pre-defined dictionaries whose structure is inspired by the behavior of propagating wavefields, and secondly, a method which learns the dictionaries directly from the data itself. The former can be split into two sub-methods: the first casts the demixing task in terms of a group Lasso regularization problem with simply structured orthonormal dictionaries, while the second method uses a standard Lasso formulation, but makes use of more morphologically germane dictionaries. After the demixing is complete, an automatic visualization tool highlights the regions associated with potential anomalies and outputs their local coordinates. Since the methods do not invoke any knowledge of the material properties of the medium, or of its behavior in its pristine conditions, and is solely based on data processing of current wavefield information, it is endowed with significant model agnostic and baseline-free attributes. These properties are desirable in systems where there exists limited or unreliable a priori knowledge of the constitutive model, when the physical domain is highly heterogeneous or compromised by large damage zones, or when accurate baseline simulations are unavailable. The efficacy of the proposed method is evaluated against synthetically generated data and experimental data obtained using a scanning laser Doppler vibrometer.