Automatic differentiation using vectorized hyper dual numbers
Abstract
Sensitivity analysis is a method to measure the change in a dependent variable with respect to one or more independent variables with uses including optimization, design analysis and risk modeling. Conventional methods like finite difference suffer from both truncation, subtraction errors and cannot be used to simultaneously calculate derivatives of an output with respect to multiple inputs (commonly seen in optimization problems). Automatic Differentiation tackles all these issues successfully allowing us to calculate derivatives of any variable with respect to the independent variables in a computer program up to machine precision without any significant user input. Vectorized Hyper Dual Numbers, an extension of Hyper Dual Numbers, which allows the user to automatically calculate both the Hessian and derivative along with the function evaluation is developed for this thesis. The method is then used for the sizing and layup of a composite wind turbine blade as a proof of concept.
Degree
M.S.A.A.
Advisors
Yu, Purdue University.
Subject Area
Applied Mathematics|Aerospace engineering
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