On the optimality of harmonic excitation as input signals for the characterization of parameters in coupled piezoelectric and poroelastic problems

In this work we provide theoretical and numerical results regarding optimal designs of experiments with an emphasis on coupled problems like piezoelectrics and poroelastics. The work is motivated by the need of identifying parameters for complex problems from measured data, where it is a priori not clear which data are to choose. We assume a harmonic excitation of the systems and measurements related to different excitation frequencies. Results of optimal experimental designs under harmonic excitations are reviewed and adapted correspondingly, e.g., the D-optimality criterion is extended to the case of multiple fields. The manuscript at hand further reviews techniques to identify parameters and their statistical properties and discusses the previously derived theory for two examples, one coming from piezoelectricity, the other from poroelasticity. For these examples, it is analytically shown that they fit to the previously presented theory. Numerical results discussing the optimal choice of the fields to measure and finding the optimal excitation frequencies finalize this work.