Journal
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
Volume 22, Issue 4, Pages 602-624Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17415977.2013.823411
Keywords
bayesian framework; generalized polynomial chaos; Karhunen-Loeve expansion; hyper-parameters
Funding
- Basic Science Research Program through the National Research Foundation of Korea (NRF)
- Ministry of Education, Science and Technology [2010-0025484]
- KI Project through KAIST Institute for Design of Complex Systems
- National Research Foundation of Korea [2010-0025484] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent stationary Gaussian processes with uncertain hyper-parameters describe uncertainties of the model structure and parameters, while Karhunen-Loeve expansion is adopted to spectrally represent these Gaussian processes. The Karhunen-Loeve expansion of a prior Gaussian process is projected on a generalized Polynomial Chaos basis, whereas intrusive Galerkin projection is utilized to calculate the associated coefficients of the simulator output. Bayesian inference is used to update the prior probability distribution of the generalized Polynomial Chaos basis, which along with the chaos expansion coefficients represent the posterior probability distribution. The proposed method is demonstrated for calibration of a simulator of quasi-one-dimensional flow through a divergent nozzle with uncertain nozzle area profile. The posterior distribution of the nozzle area profile and the hyper-parameters obtained using the proposed method are found to match closely with the direct Markov Chain Monte Carlo-based implementation of the Bayesian framework. Efficacy of the proposed method is demonstrated for various choices of prior. Posterior hyper-parameters of the model structural uncertainty are shown to quantify acceptability of the simulator model.
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