Particle Swarm Optimization-Based Identification of the Elastic Properties in Resonant Ultrasound Spectroscopy

Resonant ultrasound spectroscopy (RUS) is an experimental measurement method for obtaining elastic constants of an anisotropic material from the free resonant frequencies of a sample. One key step of the method is to adjust elastic constants to minimize the difference between calculated and experimental frequencies. The method has been widely used in the determination of elastic constants of solid materials with high Q value, such that the resonant frequencies can be easily extracted from the measured spectrum. However, for materials with high damping, the identification of the resonant modes becomes difficult due to the overlap of resonant peaks and the absence of some modes. Thus, the success of RUS depends largely on initial guessing of elastic constants. In this article, these limitations are addressed with a new RUS approach. First, the identification of resonant modes is transformed into a linear assignment problem solved by the Hungarian algorithm. Second, the inversion of the elastic tensor is achieved using the particle swarm optimization (PSO) algorithm. This method, having the ability of global optimization in the search space, is less sensitive to the initial guess of the elastic constants. The PSO algorithm was successfully applied for the first time to RUS data, providing estimates of elastic constants that were in good agreement with reference values. First, simulated data for a transversely isotropic sample of enamel of rectangular parallelepiped shape were used to validate the proposed RUS method. Second, the proposed RUS approach was validated using experimental data collected on a sample of transversally isotropic bone-mimicking material.