Stiffness tensor estimation of anisotropic crystal using point contact method and unscented Kalman filter

The potential application of Lithium Niobate (LiNbO₃) crystal is immense, specifically in the domain of meta-surfaces and nano-resonators. However, the practical application of LiNbO₃ is impeded due to unreliable experimental techniques and inaccurate inversion algorithms for material characterization. In the current research, material characterization of anisotropic crystal is proposed by exploring the wavefield evolution in the spatial and temporal domains. The presented framework has three major components: a physics-based mathematical model (Christoffel equation), a novel experimental technique, and an inversion algorithm based on Bayesian filtering. An experimental technique based on Coulomb coupling is devised to visualize the propagation of ultrasonic waves in an anisotropic crystal. The crystal is characterized by measuring the directional-dependent acoustic wave velocity from the spatial-temporal information of the wave propagation. The anisotropic constitutive properties of the crystal are estimated by exploring the wave velocity in the Bayesian filtering algorithm. The proposed algorithm is based on the probabilistic framework that integrates the experimental measurement in a physics-based mathematical model for optimal state prediction of stiffness tensor through the Bayesian filtering algorithm. In particular, we utilize the unscented Kalman filter (UKF) in conjunction with the plane-wave Eigen solution to estimate the constitutive parameters. In the presence of measurement uncertainties, the performance of the optimal prediction algorithm is illustrated by comparing the estimated parameter with the corresponding theoretical value. The comparison demonstrates that the proposed inversion algorithm is efficient and robust and performs satisfactorily even with significant measurement uncertainties.