Title: Piezoelectric Inverse Problems with Resonance Data: A Sequential Monte Carlo Analysis
Speaker: Edrissa Gassama (Case Western Reserve University)
Abstract: Piezoelectricity is a property of certain materials that allows the conversion of mechanic deformation into electric voltage potential, and vice versa. The wide use of piezoelectric materials, e.g., in transducer technology and energy harvesting makes the design problem of optimizing the material parameters and geometry an important target in scientific computing. In energy harvesting in particular, the design of devices with impedance resonances in a predetermined range is of particular interest: Matching the resonances with the ambient vibration frequencies lead potentially to higher efficiency of the device. In this article, we consider the matching from the point of view of inverse problems. The question addressed here is, how to choose the elastic, electromagnetic, and piezoelectric material parameters so that a target resonance frequency is achieved, and the band-pass impedance response outside the resonance is matched to a target profile. The methodology is based on Bayesian formulation of the problem using a new Sequential Monte Carlo (SMC) sampling technique of the posterior probability density. The algorithm suggested in this work is based on a sequential approximation of the posterior density, combining the method with the auxiliary particle techniques.