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.Comment: 18 pages, 2 figures, to appear in Sparse Grids and
Applications--Stuttgart 2014, Lecture Notes in Computational Science and
Engineering 109, edited by J. Garcke and D. Pfl\"{u}ger, Springer
International Publishing, 201
