Data Fusion Method and Probabilistic Pairing Approach in Elastic Constants Measurement by Resonance Ultrasound Spectroscopy

Resonant ultrasound spectroscopy (RUS) is a nondestructive technique for measuring the stiffness parameters of solid materials. Trying to achieve an improved automatic, elastic coefficients measurement via RUS, this work proposes a data fusion method based on Bayesian formulation and a probabilistic pairing approach. Several sets of RUS data have been acquired by measuring a novel piezoelectric crystal Ca
₃
NbAl
_0.5
Ga
_0.5
Si
₂
O
₁₄
(CNAGS) with a self-designed RUS measurement system. In order to suppress the influence of the phenomenon of frequency shifting, missing, and overlapping, a repeated measurement is executed to achieve the multiple measurement data fusion by using Bayesian formulation, and the posterior distribution of each parameter is estimated by reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm. Besides, an automatic probabilistic pairing method is proposed to solve the problem of frequency crossing so as to facilitate the frequency pairing process. The RUS measuring apparatus, the algorithm principle, and the calculation process are illustrated systematically in this paper. The algorithm is tested and analyzed based on the measured RUS data, and full sets of elastic coefficients of CNAGS specimen has been obtained in this work. Compared to the IEEE standard resonant method, the method proposed in this work can accomplish the characterization within a shorter time, and the relative error of the results is less than 2%.