Inferring displacement fields from sparse measurements using the statistical finite element method

A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using Bayesian update. After calibration, (stochastic) forward simulation conducted with identified parameters resolve physical in regions that were not accessible measurement device. shortcoming calibration deemed best represent reality, which only sometimes case, especially context aging structures materials. While this issue often addressed repeated different followed recently proposed statistical Finite Element Method (statFEM). Instead Bayes' theorem update parameters, chosen as stochastic prior updated fit more closely. For purpose, statFEM framework introduces so-called model-reality mismatch, parametrized by three hyperparameters. This makes inference full-field computationally efficient an online stage: If can be computed offline, solving underlying partial differential equation (PDE) unnecessary. Compared PDE, identifying hyperparameters conditioning state on sensor requires much fewer computational resources. paper presents two contributions existing approach: First, we use non-intrusive polynomial chaos method compute prior, enabling complex mechanical models deterministic formulations. Second, examine influence material (linear elastic St.Venant Kirchhoff uncertain Young's modulus) solution. We present results 1D 2D examples, while extension 3D straightforward.