Methods for high dimensional uncertainty quantification [electronic resource] : regularization, sensitivity analysis, and derivative enhancement
- Gary Tang.
- Physical description
- 1 online resource.
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|3781 2013 T||In-library use|
- Surrogates are used to mitigate the aggregate cost of simulation needed to perform a comprehensive uncertainty quantification (UQ) analysis. A realistic uncertainty analysis of any engineering system involves a large number of uncertainties, and as a result, the surrogates take inputs in a high dimensional space. We investigate surrogates that take the form of a truncated Legendre polynomial series, from which the coefficients associated to each polynomial basis function must be estimated. High dimensional estimation is a known instance of the curse of dimensionality, and for sufficiently "complex'" functions, an unsolved problem. In order to break the curse, we assume the function to be approximated is sparse in the Legendre polynomials and employ the machinery of l-1-regularized regression. We make three contributions under this theme. Firstly, we present a novel approach to choosing sample (design) points and show that it yields lower estimation error over a broad range of functions compared to existing sampling approaches. Secondly, we give a novel sparse estimator that effectively uses (partial) derivative information for estimation and show empirically that estimation using derivatives can be more efficient than function values if the derivatives are sparser than the function. Thirdly, we show that by exploiting the best k-term approximation} property of l-1-methods, we can quickly identify the most signfiicant uncertainties and reduce the dimensionality of the input space accordingly. We conclude by demonstrating the efficacy of these methods in a UQ analysis of a notional vertical axis wind turbine design.
- Publication date
- Submitted to the Department of Aeronautics and Astronautics.
- Thesis (Ph.D.)--Stanford University, 2013.
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