Resonant ultrasound spectroscopy: Particular problems and solutions

In resonant ultrasound spectroscopy (RUS) one measures a set of resonance frequencies for a sample of material and then adjusts a set of parameters in a model to least squares fit those frequencies. Some problems may occur in the least squares fitting procedure. For example, there may be a parameter which has only a weak influence on the fit, and the fitting procedure may give this parameter an unphysical value; this may cause other parameters to take on reasonable but inaccurate values. Another problem is that the space spanned by the adjustable parameters may contain local minima in addition to the desired global minimum, so that a sufficiently fine mesh global search over the parameter space may be necessary. If there were six adjustable parameters (or more, e.g., for textured or piezoelectric samples), each with 10 possible initial values, then one would have to run a RUS computer program a million times (12 days per second of RUS program runtime), which is problematic. In this talk, solutions to these problems will be presented.