Automatic mode tracing of dispersion relations for guided waves in elastic waveguides via physics-driven affinity propagation (AP) clustering

Guided ultrasonic waves are attractive screening tools for elongated engineering structures due to their ability to propagate over long distances and flexibility in selecting mode-frequency combinations. Both computing dispersion solutions and accurately tracing them into dispersion curves are essential for guided waves’ non-destructive evaluation (NDE) and structural health monitoring (SHM) applications. Complex waveguide problems often require numerical methods to compute the eigen-solutions at discrete frequencies, and manual routines are usually adopted to trace different guided wave modes by directly comparing their mode shapes. However, challenges arise in intricate dispersion relations involving mode coupling, mode veering, and mode splitting. To address this, we propose an automated mode-tracing technique for guided waves via Affinity Propagation (AP) clustering. Upon solving the associated eigenvalue waveguide problem, physical field quantities are extracted to capture the alignment or dissimilarity features of different eigen-solutions. The physics-driven similarity matrix construction is performed by employing the weighted cosine distance and the similarity propagation in a high-dimensional feature space. High-quality set of exemplars and corresponding clusters (i.e. well traced guided wave modes) can be iteratively obtained using an optimized AP clustering algorithm. This paper presents the principles of the proposed technique, and then validates and illustrates its use through typical numerical examples. Accurate tracing of the dispersion curves has been achieved, independent of the eigenvalue computation procedures, and its robustness has also been manifested.