A sequential weighted Laplacian‐regularized optimal design for response surface modeling of expensive functions with outliers: An application in linear elastic fracture mechanics

• Published in: Quality and reliability engineering international Vol. 35; no. 6; pp. 1911 - 1928
• Main Authors: Martinez, Stanford, Alaeddini, Adel, Langer, Kristina
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01-10-2019
• Subjects: Computer simulation; Design optimization; Fracture mechanics; Hilbert space; informative vector machine (IVM); iteratively reweighted least squares (IRLS); Laplacian‐regularized least squares (LRLS); Linear elastic fracture mechanics; optimal design of experiment; Outliers (statistics); Regression analysis; reproducing kernel Hilbert space (RKHS); Response surface methodology; Robustness (mathematics); Sensitivity analysis
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2483

There are several sequential and adaptive strategies designed to reduce the number of experiments in response surface methodology (RSM). However, most of the existing sequential and adaptive methods are sensitive to the existence of possible outliers. In this paper, we propose an active learning methodology based on the fundamental idea of adding a Laplacian penalty to the D‐optimal design and integrate that with robust regression to look for the most informative settings to be measured, while reducing the influence of possible outliers. To leverage the intrinsic geometry of the factor settings in highly nonlinear spaces, we extend the proposed methodology to reproducing Kernel Hilbert space (RKHS). Through an extensive simulation study accompanied by a thorough sensitivity analysis, we show that the proposed framework outperforms traditional RSM designs in the presence of outliers. We also conduct a study utilizing a hierarchical function used in linear elastic fracture mechanics to illustrate practicality of the proposed methodology.