Stochastic parameter identification using an augmented Subset Simulation method

Abstract

In this contribution, a method for parameter estimation based on the idea of Subset Simulation is presented, originally developed for reliability analysis and recently adopted for Bayesian model updating. An analogy between model updating and reliability problems is obtained by formulating the former in such a way that samples of the posterior distribution are interpreted as failure samples of the latter. In the case of high-dimensional problems with multiple uncertain parameters to be estimated, the evaluation of the full posterior distribution may not be feasible due to computational hurdles. In addition, when model updating is performed based on experimental field data (as opposed to virtual experiments), the solution is usually not unique. A novel approach is presented that addresses these challenges in a two-step procedure, where Subset Simulation is employed to identify the most probable point, and additional Markov chains are used to find possible additional solutions in regions not explored by Subset Simulation in the sparsely populated simulation space. It should be emphasized that the current approach does not explore the full posterior probability density function, but focuses on determining the identification of solution points (or solution regions, respectively) that satisfy certain quality criteria, which is typically required in an industrial context. Case studies integrating parallel computing demonstrate the framework’s ability to efficiently determine the unknown parameters based on experimentally obtained frequency response functions.