IMA Postdoc Seminar (February 5, 2008)

Speaker: Laura Lurati (IMA)

Title: Design under uncertainty using stochastic collocation

Abstract: Optimization methods generally treat objectives, constraints and parameters as deterministic "perfectly known" values. However, this is often not the case for real problems. Uncertainty may enter the design process as early as the conceptual design phase, through manufacturing, as well as in the use/operation of the final product. Design optimization under uncertainty seeks to minimize the impact of random parameters on the design. Stochastic collocation methods are proposed as the underlying statistical method for robust/reliability design optimization using direct search methods. Examples demonstrate the ease of use of the method as well as its flexibility. Test problems include the robust design of an airfoil over a range of Mach numbers and robust/reliability design of a cantilever beam under manufacturing uncertainty. Possible modifications to the method for efficient representation of multiple random variables are discussed.