Hierarchical Bayesian Inversion for Quantification of Mixed Aleatory and Epistemic Uncertainties in Model Parameters

Abstract

Uncertainties in the model parameters need to be properly characterized for the reliable and economic performance assesment of structures using a numerical model. Since not all parameters are trivial to measure directly, inverse uncertainty quantification (UQ) techniques, which infer the non-determinism in the model parameters by the measurments of the structural responses, are often necessary. Among such techniques, the class of Bayesian methods has been widely accepted as a coherent probabilistic approach to handle uncertainties in the inverse UQ. However, the main drawback of the conventional Bayesian methods is that they cannot quantify the inherent variability in the model parameters which causes the random failure of the structure. To fill this gap, the hierarchical Bayesian methods have gained increasing attention, in which a proability distribution is assigned to the model parameters to characterize their variability while its hyperparameters are treated as epistemic uncertainty and updated through Bayesian scheme. The first author and his co-workers have recently developed the hierarchical Bayesian approach using the staircase density function (SDF). This approach can consider the lack-of-knowledge on the distribution formats as epistemic uncertainty and infer the true-but-unknown distribution by updating the hyperparameters of SDF. This paper amis to illustrate its fundamental ideas and demonstrate its applicability to the estimation of a broad range of distributions through simple numerical test examples.