Novel parameter update for a gradient based MCMC method for solid-void interface detection through elastodynamic inversion

Abstract

A method is developed for the explicit identification of solid-void interfaces in a Bayesian framework using a statistically efficient gradient based Markov Chain Monte Carlo (MCMC) algorithm called Hamiltonian Monte Carlo (HMC). The elastodynamic inversion is carried out in a Finite Element discretized domain considering parameterized representations of the actual interface between the elastic solid and void embedded in the solid itself. Using a reference configuration, a parameter update procedure is designed, to ensure reversibility of the HMC algorithm, thereby satisfying the detailed balance condition. The quality of mesh at every parameter update is maintained through a simple mesh moving strategy that introduces volume scaled Elastic modulus in the mesh moving stage. HMC gradient computation procedure is detailed for a general parameterization of the interface. Integration of these techniques with the HMC algorithm enables the continuous variation of parameters and maintains continuity of the Hamiltonian. The performance of the proposed method is investigated with respect to two solid-void interface identification problems, one of well-defined and the other of arbitrary geometry. Results show that the proposed method performs well, maintaining a good mesh quality after each parameter update. The Markov chains converge and statistical descriptions of the inferred parameters are obtained.