Title: Reduced Order Modeling Techniques for Design Optimization under Uncertainty

Speaker: Kurt Maute and Gary Weickum, University of Colorado

Date/Time: Tuesday, October 9, 2007, 9:00 am – 10:00 am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: The need for accounting for uncertainty in design optimization is widely recognized. However most design optimization methods developed and used in academia and industry are still based on idealized models. While modeling aleatory and epistemic uncertainty alone presents numerous challenges, the computational burden of predicting the effect of uncertainty on the design criteria of interest within the optimization process renders the application of robust and reliability-based design approaches impractical. A variety of model reduction techniques has been presented in the literature to reduce the computational costs, most of which aim at reducing the number of design, uncertainty, and/or state variables.

This talk focuses on algebraic methods for reducing the number of state variables by Galkerin-type projection methods. We will present and discuss different methods for constructing and updating basis functions which capture the response in a subdomain of the design / uncertainty variable space. For the purpose of uncertainty quantification, the performance of the reduced order modeling approaches will be studied using sampling, reliability, stochastic response surface, and spectral stochastic finite element methods. The computational efficiency of reduced order modeling techniques for design optimization uncertainty will be demonstrated using a gradient based design optimization framework evaluating stochastic design criteria via a spectral stochastic finite element method. The numerical examples involve shape optimization problems of linear elastic plate and shell structures with parametric and stochastic field uncertainty.

CSRI POC: Mike Eldred, (505) 844-6479