AN EFFICIENT COMPUTATIONAL METHOD FOR PARAMETER IDENTIFICATION IN THE CONTEXT OF RANDOM SET THEORY VIA BAYESIAN INVERSION

International Journal for Uncertainty Quantification, vol. 11, pp. 1–18

Abstract

This work deals with parameter identification problems in which uncertainties are modeled using random sets (RS), i.e., set-valued random variables. Dempster's rule of combination is applied for replacing the role of Bayes' rule to infer the posterior, which is also a RS. The considered framework allows accounting for mixed epistemic-aleatory uncertainty descriptions such as probability boxes and intervals. In this paper, we aim at an efficient computational method to sample the posterior RS using stochastic methods developed for Bayesian inverse problems. To this end, by applying the capacity transformation method, the considered problem is translated into a Bayesian inverse problem, and the region at which the posterior RS concentrates is exploited using a Markov Chain Monte Carlo (MCMC) algorithm. To sample the posterior RS, we approximate it as a random finite set whose domain consists of points obtained from the MCMC algorithm. Because the forward model could be computationally expensive and is required to be evaluated at many points, we construct a polynomial chaos expansion-based surrogate model for it. The developed approach is demonstrated with a numerical example in which measurement errors are noisy and also contain unknown but bounded biases.

Authors 2

1. Truong‐Vinh Hoang Aachen Chair of Mathematics for Uncertainty Quantification

   RWTH Aachen University · Technische Universität Braunschweig

   Affiliation as printed

   Chair of Mathematics for Uncertainty Quantification, RWTH-Aachen University, Germany; Institute of Scientific Computing, Technische Universität Braunschweig, Germany

   Chair of Mathematics for Uncertainty Quantification, RWTH-Aachen University, Germany

   Institute of Scientific Computing, Technische Universität Braunschweig, Germany

2. Hermann Georg Matthies

   Technische Universität Braunschweig

   Affiliation as printed

   Institute of Scientific Computing, Technische Universität Braunschweig, Germany