Optimal measurement point selection for resonant ultrasound spectroscopy of complex-shaped specimens using principal component analysis

Abstract

Traditional resonant ultrasound spectroscopy (RUS) uses the natural vibrations, or normal modes, of an object to determine the elastic properties of the object’s constituent material. When measuring the resonances of a sample, the measurement point is often selected based on user experience and intuition. This approach is often adequate when the sample has a simple geometry, but can be insufficient when testing complex-shaped samples. In such cases, multiple measurement points are used and the responses superimposed to obtain an overall resonance response. This approach can be effective but is time-intensive and can be still subject to error due to the possibility of missing modes. This paper introduces a method to automatically locate a minimal number of measurement points to extract sufficient modal information based on principal component analysis. The goal is to reduce the arbitrary nature of measurement point selection and measurement time while retaining the significant spectral information required for an accurate inversion. The efficacy of the method is demonstrated on a sample of relatively simple geometry as well as a part of greater complexity. The inversion results suggest that the modal information extracted from the few selected points is sufficient to yield accurate elastic constants.