Topological data analysis of coda waves to classify microstructural variability

Coda waves are multiply scattered waves appearing in the later portion of ultrasonic signals. They have been typically used for detecting local macrostructural variations in different media. Here we show the promising potential of coda waves for characterizing subtle microstructural variations in materials, and demonstrate that these variations are encoded in the shape of their waveforms. Specifically, we utilize sublevel persistent homology, a tool from Topological Data Analysis (TDA), to quantify the connected components of sublevel sets that are parameterized by coda waves’ function value. We use the resulting persistence diagrams to extract features for classifying different microstructures of Grade 91 steel. The persistence-based features that were explored are Carlsson Coordinates, Tent Functions, and Interpolating Polynomials. We use these features to train a classifier for identifying the underlying microstructure, and compare the resulting accuracy to its conventional Loss of Correlation (LOCOR) counterpart. The results suggest that TDA methods consistently outperformed LOCOR in both inter-class and intra-class classification, achieving overall accuracies above 80% for 3-class classification and over 90% for 2-class classification. This highlights the ability of coda waves to identify microstructures, and the effectiveness of TDA in capturing sub-wavelength features from the waveforms. We believe that combining coda waves with TDA-based analysis can provide an effective tool for non-destructive evaluation and microstructure characterization in various industrial applications.