Predictive Guided Wave Models Through Sparse Modal Representations

Ultrasonic guided waves are an attractive tool for structural health monitoring due to their capability to rapidly assess large regions of a structure. Yet, most guided wave based methods for detecting, locating, and classifying structural damage rely on our ability to accurately predict guided wave behavior. Characterizing and predicting guided wave behavior is difficult, particularly in mechanically complex materials such as fiber-reinforced composites. In this paper, we address this challenge through a sparse wavenumber analysis framework. Sparse wavenumber analysis integrates physics-based models, signal processing algorithms for compressive sensing, and a small number of local measurements to predict global wave behavior. We implement sparse wavenumber analysis for three wave systems: standing waves on a string, Lamb waves in an isotropic plate, and guided waves in a unidirectional, anisotropic plate. Through the use of simulation and experimental data, we show that sparse wavenumber analysis can accurately recover the sparse representations (i.e., the eigenmodes) of each system and then use these representations to predict global wave behavior. For the anisotropic plate, we accurately predict 149765 experimental time-domain measurements from only 36 local measurements.