A method for identifying false positive frequencies extracted from resonant ultrasound spectra for highly dissipative materials

Abstract

Resonant ultrasound spectroscopy (RUS) is a nondestructive technique, and one of its applications is to determine the elastic constants of a solid by measuring its free-vibration resonant frequencies. For dissipative materials, the vibration spectrum peaks are broad and strongly overlapped, and in some cases, the resonant frequencies extracted by a linear prediction filter are considered to be false positive frequencies that cannot be paired with theoretical resonant frequencies. The inverse identification of elastic constants is also seriously influenced when these false positive frequencies are wrongly paired with theoretical resonant frequencies. In this paper, a new selection index and an extraction process for RUS resonant frequencies are studied to discard false positive frequencies. The change in the relative error between the theoretical and extracted frequencies was employed to update the traditional frequency selection index. An extraction process was proposed by combining a trial-and-error method and a Bayesian method. A bone-mimicking material (quality factor, Q ≈ 30) and the simulated resonant spectra were adopted to validate the proposed method. The performance of identifying false positive frequencies was effectively improved by using the new selection index. Moreover, the proposed process can be applied to enhance the pairing and estimation accuracy for RUS. Calculations of the elastic constants for distinct specimens presented good consistency. The new method proposed in this paper provides a better analysis of the elastic constants in highly dissipative materials and can help to extend the application range of RUS.