Towards a stochastic inverse Finite Element Method: A Gaussian Process strain extrapolation

The inverse Finite Element Method (iFEM) employing a network of strain sensors reconstructs the full-field displacement on beam or shell structures, independently of the loading conditions and of the material properties. However, the iFEM in principle requires triaxial strain mea-surements for each inverse element, which is practically hardly possible due to space and cost constraints. To relieve this issue, some strain values fed as input to the iFEM are typically computed using strain pre-extrapolation/interpolation techniques, and the iFEM solution is computed minimizing a weighted functional: elements missing experimental measurements are assigned low weights, which are generally set to arbitrarily low values taken from the literature. This paper proposes the use of a Gaussian Process as a strain pre-extrapolation and interpolation technique, which natively provides the extrapolation uncertainty, which in turn is used as a metric to assign the functional weights, and it enables the computation of the uncertainty on the reconstructed displacement field. The proposed approach is tested on a virtual and an experimental case study; advantages and limitations of the proposed technique are discussed.