Nonlinear inversion of piezoelectrical transducer impedance data

We describe a nonlinear least squares inversion algorithm for obtaining ela stic and electromagnetic properties for piezoelectric materials from measur ed 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 imp osed in order to limit the variability of the parameters to physically mean ingful values. Since PRAXIS is an unconstrained optimization code, these co nstraints are introduced via a novel change of independent variables. The f orward modeling is achieved by using a coupled finite element time domain c ode for the elastic and electro-magnetic parts of the problem. We also desc ribe how a linearized sensitivity analysis can be used to suggest a priori which parameters can be calculated from impedances measured on a given samp le. Numerical results axe included.