A Bayesian formulation for the optical monitoring of deformation process by digital image correlation

In this communication reference was made to the inverse problem of detecting displacement fields by optically monitoring through a single camera the in plane deformation process of a flat domain. A Bayesian, stochastic formulation was proposed for such Digital Image Correlation (2D DIC) problem, in the framework of a finite element discretization for the kinematic field. The focus was posed on a suitable observation or measurement equation ensuring identifiability of the state parameters, herein represented by the nodal displacements. The peculiar features of the DIC problem, severely ill posed, have led to adopt a vector measurement equation in implicit form: it was derived by prescribing stationarity of the L2 objective function, which quantifies the mismatch between a pair of digital images acquired at different time instants. Once such equation was specified, the residual vector and the sensitivity matrix, key ingredients of Bayesian approach, turned out to coincide with pseudo load vector and pseudo stiffness matrix governing the linear incremental problem (i.e. the Newton-Raphson iterations) for finite element DIC. Updating Bayesian equations provided current displacement estimates endowed with covariance matrices quantifying their degree of uncertainty, on the basis of previous estimates and of the new experimental information. Preliminary results were discussed, with reference to synthetic data