A dual surrogate driven L-moments based robust design with scarce samples in the presence of extremes

Robust Design architectures permit identifying designs in the input space that minimize the mean as well as the spread of the response in the performance space, when the input variables are uncertain. Often, information about uncertainties is not readily available and are usually characterized by scarce samples that might contain extremes. Since extremes are part of the data, they cannot be excluded but including extremes alter the measures of spread such as standard deviation. Hence, it is imperative to develop a robust design architecture where the measure of spread estimations are less sensitive or insensitive to extremes. We propose using L-moments to estimate the measure of spread, the second L-moment (l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_2$$\end{document}) and use it in the robust design formulation. We consider the cases of design variables which can be deterministic or random, and random variables. Hence, we use a dual surrogate framework where a design surrogate is built first. At each point in the DoE, scarce samples that might include extremes of the random variables are propagated through the design surrogate. Mean and measure of spread are computed by the L-moments approach at each point in the DoE, from the responses computed upon propagation, and used to build analysis surrogate which is used for identifying the robust design. The proposed approach is demonstrated on 2D Aspenberg function, 5D truss and 17D rotor disk design examples. The results reveal the superiority of the proposed approach over the conventional formulation.