Locating material defects via wavefield demixing with morphologically germane dictionaries

This article introduces a methodology for the detection and localization of structural defects in solid media using morphological demixing algorithms. The demixing algorithms are designed to separate spatiotemporal response data into two morphologically 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. Within the demixing paradigm, we explore two methods: in the first, we cast the demixing task in terms of a group Lasso regularization problem with simply structured orthonormal dictionaries; the second method makes use of a more morphologically germane dictionary whose additional structure allows for the localization of defects whose signature may be highly elusive, for example, buried in noise or masked by competing features. After the demixing is complete, an automatic visualization tool highlights the regions associated with potential anomalies and outputs their local coordinates. Since the method does 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.