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Contribution to Book
High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition
Sparse Grids and Applications - Stuttgart 2014
  • Sharif Rahman, University of Iowa
  • Xuchun Ren, Georgia Southern University
  • Vaibhav Yadav, San Diego State University
Document Type
Contribution to Book
Publication Date

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic response for statistical moment and reliability analyses; a novel integration of the adaptive-sparse PDD approximation and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and standard gradient-based optimization algorithms. New analytical formulae are presented for the design sensitivities that are simultaneously determined along with the moments or the failure probability. Numerical results stemming from mathematical functions indicate that the new method provides more computationally efficient design solutions than the existing methods. Finally, stochastic shape optimization of a jet engine bracket with 79 variables was performed, demonstrating the power of the new method to tackle practical engineering problems.

Citation Information
Sharif Rahman, Xuchun Ren and Vaibhav Yadav. "High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition" Cham, SwitzerlandSparse Grids and Applications - Stuttgart 2014 Vol. 109 (2016) p. 247 - 264 ISSN: 2197-7100
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