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Homogeneous chaos basis adaptation for design optimization under uncertainty: Application to the oil well placement problem

Published online by Cambridge University Press:  03 August 2017

Charanraj Thimmisetty ,
Panagiotis Tsilifis  and
Roger Ghanem
Charanraj Thimmisetty
Affiliation:
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, USA
Panagiotis Tsilifis
Affiliation:
Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California, USA
Roger Ghanem*
Affiliation:
Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California, USA
*
Reprint requests to: Roger Ghanem, Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089, USA. E-mail: ghanem@usc.edu
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Abstract

A new method is proposed for efficient optimization under uncertainty that addresses the curse of dimensionality as it pertains to the evaluation of probabilistic objectives and constraints. A basis adaptation strategy previously introduced by the authors is integrated into a design optimization framework that construes the optimization cost function as the quantity of interest and computes stochastic adapted bases as functions of design space parameters. With these adapted bases, the stochastic integrations at each design point are evaluated as low-dimensional integrals (mostly one dimensional). The proposed approach is demonstrated on a well-placement problem where the uncertainty is in the form of a stochastic process describing the permeability of the subsurface. An analysis of the method is carried out to better understand the effect of design parameters on the smoothness of the adaptation isometry.

Keywords

Adapted BasesKarhunen–Loeve ExpansionOptimization Under UncertaintyOptimal Well PlacementPolynomial Chaos Expansions
Type
Special Issue Articles
Information
AI EDAM , Volume 31 , Special Issue 3: Uncertainty Quantification for Engineering Design , August 2017 , pp. 265 - 276
Copyright
Copyright © Cambridge University Press 2017 

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