An accurate characterization of temperature-dependent material parameters of piezoceramics is crucial for the design and simulation of reliable sensors and actuators. This characterization is typically formulated as an ill-posed inverse problem, which is challenging to solve not only because of its ill-posedness, but also because of parameter sensitivities, which vary by several orders of magnitude and exhibit a strong coupling between parameters.
For this reason we propose a block coordinate descent (BCD) framework combined with a globalized regularized structure exploiting (GRSE) Quasi-Newton method. A systematic sensitivity-driven strategy for the optimal partitioning of material parameters into blocks is established. By analyzing first- and second-order sensitivity information, our method identifies blocks that minimize inter-block coupling and group parameters with similar sensitivity profiles. Subsequent to a finite element discretization, the derivatives required for both the sensitivity analysis and the optimization are computed accurately using algorithmic differentiation. The proposed BCD-GRSE method is validated through a numerical experiment with noisy synthetic data.
Finally, we present the reconstruction results for the piezoelectric material parameters of an annular sample based on physical measurement data.