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Title: Calibration of expensive computer models using engineering reliability methods
Author: Gong, Zitong
ISNI:       0000 0004 7659 1011
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2018
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The prediction ability of complex computer models (also known as simulators) relies on how well they are calibrated to experimental data. History Matching (HM) is a form of model calibration for computationally expensive models. HM sequentially cuts down the input space to find the fitting input domain that provides a reasonable match between model output and experimental data. A considerable number of simulator runs are required for typical model calibration. Hence, HM involves Bayesian emulation to reduce the cost of running the original model. Despite this, the generation of samples from the reduced domain at every iteration has remained an open and complex problem: current research has shown that the fitting input domain can be disconnected, with nontrivial topology, or be orders of magnitude smaller than the original input space. Analogous to a failure set in the context of engineering reliability analysis, this work proposes to use Subset Simulation - a widely used technique in engineering reliability computations and rare event simulation - to generate samples on the reduced input domain. Unlike Direct Monte Carlo, Subset Simulation progressively decomposes a rare event, which has a very small probability of occurrence, into sequential less rare nested events. The original Subset Simulation uses a Modified Metropolis algorithm to generate the conditional samples that belong to intermediate less rare events. This work also considers different Markov Chain Monte Carlo algorithms and compares their performance in the context of expensive model calibration. Numerical examples are provided to show the potential of the embedded Subset Simulation sampling schemes for HM. The 'climb-cruise engine matching' illustrates that the proposed HM using Subset Simulation can be applied to realistic engineering problems. Considering further improvements of the proposed method, a classification method is used to ensure that the emulation on each disconnected region gets updated. Uncertainty quantification of expert-estimated correlation matrices helps to identify a mathematically valid (positive semi-definite) correlation matrix between resulting inputs and observations. Further research is required to explicitly address the model discrepancy as well as to take the correlation between model outputs into account.
Supervisor: Diaz De La O, Francisco Alejandro ; Beer, Michael Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral