A Functional Bayesian Method for the Solution of Inverse Problems with Spatio-temporal Parameters Authors:

A Functional Bayesian (FB) methodology is introduced for the calibration of constitutive parameters spatially distributed within a model. The probabilistic solution to the inverse problem consists of assimilating the uncertainty captured from the actual material responses into the material parameters. A case study is introduced to illustrate the applicability of the method, where a soil model built in LS-DYNA is parameterized using surface displacement fields read from stereo digital images taken during a series of triaxial tests performed under similar conditions. The implementation of the FB method yields probability density functions of the parameters and its corresponding correlation structure. The parameters field is efficiently sampled using the Polynomial Chaos Decomposition method (PC) which allows for spatial non-stationary and nonGaussian material representations. The posterior integration is performed via Markov Chain Monte Carlo techniques. Results show extended inferences about the material behaviour due to probabilistic description of the material variability.