General-Surrogate Adaptive Sampling using Interquartile Range for Design Space Exploration

[+] Author and Article Information
Yiming Zhang

333 MAE-A, Mechanical and Aerospace Engineering Gainesville, FL 32611-6250 yimingzhang521@ufl.edu

Nam H. Kim

Department of Mechanical & Aerospace Engineering Gainesville, FL 32611 nkim@ufl.edu

Raphael T. Haftka

PO Box 116250 1 Gainesville, FL 32611 haftka@ufl.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received January 23, 2019; final manuscript received July 12, 2019; published online xx xx, xxxx. Assoc. Editor: Gary Wang.

ASME doi:10.1115/1.4044432 History: Received January 23, 2019; Accepted July 17, 2019


Surrogate model is a common tool to approximate system response at untested points for design space exploration. Adaptive sampling has been studied for improving the accuracy of surrogates iteratively by introducing additional sample (simulations and experiments). New samples are often selected based on the estimated uncertainty in the design space. While some surrogates such as Kriging have readily available uncertainty models for their predictions, other surrogates do not. Consequently, there have been studies of using cross-validation tools to estimate prediction uncertainty, such as the Universal Prediction Distribution(UPD). In this paper, an adaptive sampling scheme for general surrogates is proposed based on cross-validation and interquartile range (IQR). A population of surrogate models is first developed from cross-validation. The uncertainty is then estimated from the IQR of these surrogates at a given point. New samples are added iteratively at the point with maximum IQR for design space exploration. The proposed scheme is illustrated using Kriging, Radial Basis Function and Neural Network surrogates. The proposed scheme is evaluated using four algebraic test functions. For these functions, it was found to be more accurate and robust than Kriging with its own uncertainty model. The proposed scheme is more accurate than the Universal Prediction Distribution for three out of the four test functions. For a fixed number of samples, the IQR-based adaptive sampling also proved to be more accurate than all-at-once sampling in most cases even when the estimated uncertainty was only mildly correlated with prediction errors.

Copyright © 2019 by ASME
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