Data-driven time–frequency analysis of nonlinear Lamb waves for characterization of grain size distribution

Abstract

Nondestructive characterization of grain size distribution is significant for revealing the mechanical properties of metal materials. Traditional linear ultrasonic methods have been applied to estimate mean grain size but are less sensitive to small grain size. Nonlinear ultrasonic technology shows high sensitivity to microstructures, while it unfortunately encounters underdetermined problem in the characterization of microstructures across multiple scales. Combining linear and nonlinear ultrasonic responses would be a quite attractive way to achieve comprehensive observation of microstructural evolution. This work presents a data-driven approach for characterizing grain size distribution using nonlinear Lamb waves. The short-time Fourier transform (STFT) of detected ultrasonic signals were input into a convolutional neural network (CNN) to comprehensively learn the implicit linear and nonlinear dynamics involved with grain size distribution. Multiple convolution kernels slide across the STFT images with multiscale receptive fields to collectively model hierarchical representations and capture local correlation of interesting from time-frequency domain. The trained model achieved 94.7% accuracy in predicting mean grain size, and also achieved 95.4% and 86.3% accuracy in predicting the expectation and standard deviation of the lognormal distribution of grain size, respectively. The visual activation maps demonstrate that local interesting features are successfully captured. In particular, the prediction accuracy was demonstrated to reduce greatly after removing the fundamental frequency and second harmonic from the STFT images, confirming that incorporating linear and nonlinear ultrasonic information is indispensable for accurate characterization of grain size distribution.