Gaussian Process Strain Pre-extrapolation and Uncertainty Estimation for Inverse Finite Elements

The Inverse Finite Element method (iFEM), employing a network of strain sensors installed on a structure reconstructs the displacement field independently of the structural loading conditions and material properties. However, the solution is compromised when the sensor network, due to logistic or cost constraints, is sparse and measureless finite elements are present. To overcome this issue the iFEM minimizes a weighted functional, assigning smaller weights to the elements missing experimental measures. Strain field pre-extrapolation techniques have been proposed to improve the iFEM performance, although still assigning arbitrarily small weights to the extrapolated strains. The current paper proposes a Gaussian Process as the pre-extrapolation technique for the strain field, which natively incorporates measurement uncertainty, therefore providing a metric to assign the functional weights, as well as confidence intervals for the displacement field computed through the iFEM. The proposed technique is validated with a virtual experiment; advantages and limitations of the proposed approach are also discussed.