Bayesian Treatment of Spatially-Varying Parameter Estimation Problems via Canonical BUS

Paper in proceedings, 2016

The inverse problem of identifying spatially-varying parameters, based on indirect/incomplete experimental data, is a computationally and conceptually challenging problem. One issue of concern is that the variation of the parameter random field is not known a priori, and therefore, it is typical that inappropriate discretization of the parameter field leads to either poor modelling (due to modelling error) or ill-condition problem (due to the use of over-parameterized models). As a result, classical least square or maximum likelihood estimation typically performs poorly. Even with a proper discretization, these problems are computationally cumbersome since they are usually associated with a large vector of unknown parameters. This paper addresses these issues through Bayesian approach, via a recently developed stochastic simulation algorithm, called Canonical BUS. This algorithm is considered as a revisited formulation of the original BUS (Bayesian Updating using Structural reliability methods), that is, an enhancement of rejection approach that is used in conjunction with Subset Simulation rare-event sampler. Desirable features of the method and its performance to treat real-world applications has been investigated. The studied industrial problem originates from a railway mechanics application, where the spatial variation of ballast bed is of particular interest.