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Title page for ETD etd-03282008-125137

Type of Document Dissertation
Author McFarland, John Milburn
Author's Email Address john.m.mcfarland@vanderbilt.edu
URN etd-03282008-125137
Title Uncertainty Analysis for Computer Simulations through Validation and Calibration
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Sankaran Mahadevan Committee Chair
Bruce Cooil Committee Member
Gautam Biswas Committee Member
Laura Swiler Committee Member
Prodyot K Basu Committee Member
  • model calibration
  • model validation
  • bayesian statistics
  • surrogate modeling
  • Gaussian processes
  • Uncertainty (Information theory) -- Mathematical models
  • Computer simulation -- Evaluation
  • Computer programs -- Validation
Date of Defense 2008-03-20
Availability unrestricted

Modeling and simulation have played an increasingly important role in the design and analysis of engineering systems. High-consequence decisions are often informed strongly by numerical results obtained through the use of computational simulations, such as finite element models. This work is concerned with the development and improvement of methods that support the quantification of the uncertainty associated with predictions obtained using computer simulations.

One avenue for addressing this uncertainty is the process known as model validation, which is concerned with comparing simulation predictions with experimentally observed outcomes for the purpose of developing confidence in the simulation model. One objective of this dissertation is to develop a better understanding of how quantitative statistical decision making tools can be better used to support the validation process.

The primary focus of this dissertation, however, is to explore how the uncertainty associated with model predictions can be addressed by quantifying uncertainty associated with estimated parameters. Virtually all large-scale computer simulations possess some input parameters that are not directly observable (and may not even represent physical quantities) and must be estimated using experimental data. The process of estimating these inputs is typically referred to as model calibration, because it involves adjusting the unknown inputs in order to improve the agreement between the model output and available data.

This dissertation shows that by quantifying the uncertainty in estimated calibration parameters in a meaningful way, this uncertainty can then be propagated through the computer simulation in order to quantify the resulting uncertainty associated with new predictions made using the computer simulation. Bayesian inference and Gaussian process surrogate modeling techniques are employed to develop comprehensive representations of uncertainty for expensive simulations. Other practical considerations are addressed as well, such as the use of surrogate modeling techniques to develop approximations to simulation models with highly multivariate (e.g., time series) output.

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