For piezoelectric materials with high mechanical quality factors, resonant ultrasound spectroscopy (RUS) is a superior alternative to electric resonance methods for characterizing the elastic and piezoelectric constants. Resonant mode identification constitutes the primary challenge in RUS because mode omission and overlap cannot be avoided in the measurement of resonant ultrasound spectra, which conventionally requires the labor-intensive manual matching of experimental and simulated resonance frequencies. In this study, a combination of a deep neural network (DNN) and dynamic time warping (DTW) is proposed for automatic mode identification. The DNN efficiently maps the material constants of the piezoelectric rectangular parallelepipeds to the resonance frequencies. Although computing the resonance frequencies for training the DNN is time consuming, the trained DNN is significantly faster than the Rayleigh-Ritz method. For an experimentally measured resonance frequency sequence, the generated resonance frequency sequences using the DNN form a reference dataset. A novel DTW algorithm then performs optimal alignment between the measured and reference sequences, enabling robust mode identification through maximal similarity matching. The proposed method is validated using comprehensive simulations and experimental testing on a Fuji C-213 piezoelectric sample (Fuji Ceramics Co., Ltd., Fujinomiya, Shizuoka, Japan) at multiple temperatures. The results demonstrate comparable accuracy to manual identification methods while achieving substantial efficiency improvements.
Yang et al. (Sun,) studied this question.