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Development of Adaptive RBF-HDMR Model for Approximating High Dimensional Problems

[+] Author Affiliations
Songqing Shan

University of Manitoba, Winnipeg, MB, Canada

G. Gary Wang

Simon Fraser University, Surrey, BC, Canada

Paper No. DETC2009-86531, pp. 727-740; 14 pages
doi:10.1115/DETC2009-86531
From:
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 35th Design Automation Conference, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4902-6 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME

abstract

Modeling or approximating high dimensional, computationally-expensive, black-box problems faces an exponentially increasing difficulty, the “curse-of-dimensionality”. This paper proposes a new form of high-dimensional model representation (HDMR) by integrating the radial basis function (RBF). The developed model, called RBF-HDMR, naturally explores and exploits the linearity/nonlinearity and correlation relationships among variables of the underlying function that is unknown or computationally expensive. This work also derives a lemma that supports the divide-and-conquer and adaptive modeling strategy of RBF-HDMR. RBF-HDMR circumvents or alleviates the “curse-of-dimensionality” by means of its explicit hierarchical structure, adaptive modeling strategy tailored to inherent variable relation, sample reuse, and a divide-and-conquer space-filling sampling algorithm. Multiple mathematical examples of a wide scope of dimensionalities are given to illustrate the modeling principle, procedure, efficiency, and accuracy of RBF-HDMR.

Copyright © 2009 by ASME

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