Locally-Optimized Covariance Kriging for Engineering Design Exploration

To alleviate computational challenges in uncertainty quantification and multidisciplinary design optimization, Kriging has gained its popularity due to its high accuracy and flexibility interpolating non-linear system responses with collected data. One of the benefits of using Kriging is the availability of expected mean square error along with a response prediction at any location of interest. However, a stationary covariance structure, as is the case with the typical Kriging methodology, used with data collected adaptively from an optimal data acquisition strategy will result in lower quality predictions across the entire sample space. In this paper, a Locally Optimized Covariance Kriging (LOC-Kriging) method is proposed to address the difficulties of building a Kriging model with unevenly distributed adaptive samples. In the proposed method, the global non-stationary covariance is approximated by constructing and aggregating multiple local stationary covariance structures. An optimization problem is formulated to find a minimum number of LOC windows and a membership weighting function is used to combine the LOC-Krigings across the entire domain. This paper will demonstrate that LOC-Kriging improves efficiency and provides more reliable predictions and estimated error bounds than a stationary covariance Kriging, especially with adaptively collected data.