Autonomous characterization of grain size distribution using nonlinear Lamb waves based on deep learning.

Characterization of grain microstructures of metallic materials is crucial to materials science and engineering applications. Unfortunately, the universal electron microscopic methodologies can only capture two-dimensional local observations of the microstructures in a time-consuming destructive way. In this regard, the nonlinear ultrasonic technique shows the potential for efficient and nondestructive microstructure characterization due to its high sensitivity to microstructural features of materials, but is hindered by the ill-posed inverse problem for multiparameter estimation induced by the incomplete understanding of the complicated nonlinear mechanical interaction mechanism. We propose an explainable nonlinearity-aware multilevel wavelet decomposition-multichannel one-dimensional convolutional neural network to hierarchically extracts multilevel time-frequency features of the acoustic nonlinearity and automatically model latent nonlinear dynamics directly from the nonlinear ultrasonic responses. The results demonstrate that the proposed approach establishes the complex mapping between acoustic nonlinearity and microstructural features, thereby determining the lognormal distribution of grain size in metallic materials rather than only average grain size. In the meantime, the integration of the designed nonlinearity-aware network and the quantitative analysis of component importance provides an acceptable physical explainability of the deep learning approach for the nonlinear ultrasonic technique. Our study shows the promise of this technique for real-time in situ evaluation of microstructural evolution in various applications.