Characterization of Piezoelectric Material Parameters Through a Global Optimization Algorithm

Better understanding of the loss mechanisms and higher confidence in material data for piezoelectric materials are very important for transducer manufacturers. In this paper, a method is described to characterize these loss mechanisms using a global optimization algorithm, a 1-D equivalent circuit, and a simple experimental measurement. Two different cost functions were used in the optimization algorithm, one based on impedance and the other based on admittance. The sensitivities of these cost functions to the parameters being characterized are shown to be nonuniform. The results are compared to the results obtained from a local optimization method to show the advantage of using a global optimization algorithm. A way to quantify the uncertainty of the results is introduced by looking at the difference between the results obtained from the two different cost functions. It is shown here that the more ambient noise there is in the data, the wider the gap between the results found by the two cost functions. However, although the results from the individual cost functions diverge from the correct values with increasing noise, the average of the two cost function results remains within $5\%$ of the original value. Hence, even with noise in the measured data, the use of two cost functions can yield accurate material parameters.