| Author | Kinshuk Panda and Jason E. Hicken |
|---|---|
| Title | Hessian-based Dimension Reduction for Optimization Under Uncertainty |
| Year | 2018 |
| Journal | 2018 Multidisciplinary Analysis and Optimization Conference |
| Pages | 3102 |
| Publisher | American Institute of Aeronautics and Astronautics, Inc., |
| Abstract | We present an uncertainty propagation method for computing the expected value and variance of a quantity of interest (QoI), which can then be used in a robust design optimization. To avoid intractable costs due to high-dimensional integrals, we use the Hessian of the QoI to identify the dominant nonlinear directions. Specifically, the dominant Hessian eigenmodes provide the dimensions along which the QoI is integrated in stochastic space. Explicit computation of the Hessian is avoided by using Arnoldi’s method to estimate the eigenmodes. The method is applied to multi-dimensional quadratic functions and its accuracy is examined for synthetic eigenmodes. |
| PDF File |  Download |
| DOI Link | 10.2514/6.2018-3102 |