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A sequential weighted Laplacian‐regularized optimal design for response surface modeling of expensive functions with outliers: An application in linear elastic fracture mechanics
Author(s) -
Martinez Stanford,
Alaeddini Adel,
Langer Kristina
Publication year - 2019
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2483
Subject(s) - outlier , reproducing kernel hilbert space , leverage (statistics) , computer science , nonlinear system , mathematical optimization , response surface methodology , surface (topology) , kernel (algebra) , algorithm , sensitivity (control systems) , mathematics , hilbert space , machine learning , artificial intelligence , engineering , mathematical analysis , physics , geometry , quantum mechanics , combinatorics , electronic engineering
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.