Robust Identification of Object Elasticity

Abstract

Quantification of object elasticity properties has important technical implications as well as significant practical applications, such as civil structural integrity inspection, machine fatigue assessment, and medical disease diagnosis. In general, given noisy measurements on the kinematic states of the objects from imaging or other data, the aim is to recover the elasticity parameters for assumed material constitutive models of the objects. Various versions of the least-square (LS) methods have been widely used in practice, which, however, do not perform well under reasonably realistic levels of disturbances. Another popular strategy, based on the extended Kalman filter (EKF), is also far from optimal and subject to divergence if either the initializations are poor or the noises are not Gaussian. In this paper, we propose a robust system identification paradigm for the quantitative analysis of object elasticity. It is derived and extended from the $\mathcal{H}_\infty$ filtering principles and is particularly powerful for real-world situations where the types and levels of the disturbances are unknown. Specifically, we show the results of applying this strategy to synthetic data for accuracy assessment and for comparison to LS and EKF results, and using canine magnetic resonance imaging data for the recovery of myocardial material parameters.