High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

Abstract

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.

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. Pflüger, Springer International Publishing, 2016

Cited by in corpus (9)

• Parallel cross interpolation for high-precision calculation of high-dimensional integrals
• Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
• A Low Rank Tensor Representation of Linear Transport and Nonlinear Vlasov Solutions and Their Associated Flow Maps
• Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities
• Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins
• A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
• IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains
• A mass-conserving sparse grid combination technique with biorthogonal hierarchical basis functions for kinetic simulations
• An efficient stochastic particle method for high-dimensional nonlinear PDEs