Inverse Problem in Resonant Ultrasound Spectroscopy With Sampling and Optimization: A Comparative Study on Human Cortical Bone

The Bayesian inference with prior knowledge has been proposed recently to solve the inverse problem in resonant ultrasound spectroscopy. It allows inferring the elastic properties of high damping materials, such as cortical bone with less dependence on the initial guessed values. In this method, the estimation of the stiffness coefficients is expressed as a probabilistic solution to the inverse problem, which can be achieved by sampling or optimization methods. However, the detailed performance comparison of these two strategies applied to high damping materials has not been fully studied. In this work, the full stiffness tensor of 52 transversely isotropic cortical bone specimens was obtained using Markov chain Monte Carlo (MCMC) sampling and particle swarm optimization (PSO), respectively. Results showed that the local probability distributions of stiffness coefficients estimated by the two methods are consistent. Compared with MCMC, the average calculation speed of PSO is ten times faster [614 s ± 59 s (MCMC) versus 53 s ± 22 s (PSO)]. The mean standard error between theoretical and experimental resonant frequencies was slightly smaller for PSO compared with MCMC. In conclusion, PSO, a global optimization strategy, is suitable to solve the inverse problem for high damping materials.