High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition
Contribution to Book
Sparse Grids and Applications - Stuttgart 2014
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.
Rahman, Sharif, Xuchun Ren, Vaibhav Yadav.
"High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition."
Sparse Grids and Applications - Stuttgart 2014, Jochen Garcke and Dirk Pflüger (Ed.), 109: 247-264 Cham, Switzerland: Springer International Publishing.
doi: 10.1007/978-3-319-28262-6_10 source: https://doi.org/10.1007/978-3-319-28262-6_10 isbn: 978-3-319-28262-6