NONLINEAR INVERSION OF PIEZOELECTRICAL TRANSDUCER IMPEDANCE DATA

We describe a nonlinear least squares inversion algorithm for obtaining elastic and electromagnetic properties for piezoelectric materials from measured impedances. Richard Brent's PRAXIS, a general unconstrained minimization code is used for the nonlinear least squares fit. No explicit derivatives of the goal functional are required by this code. Bound constraints are imposed in order to limit the variability of the parameters to physically meaningful values. Since PRAXIS is an unconstrained optimization code, these constraints are introduced via a novel change of independent variables. The forward modeling is achieved by using a coupled finite element time domain code for the elastic and electro-magnetic parts of the problem. We also describe how a linearized sensitivity analysis can be used to suggest a priori which parameters can be calculated from impedances measured on a given sample. Numerical results are included.