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

TL;DR

This paper introduces an adaptive-sparse polynomial dimensional decomposition method for efficient stochastic design optimization, enabling accurate sensitivity analysis and practical application to complex engineering problems.

Contribution

The paper develops a novel adaptive-sparse PDD approach combined with score functions for efficient sensitivity analysis in high-dimensional stochastic optimization.

Findings

More computationally efficient than existing methods

Accurate estimation of moments and failure probabilities

Successful application to a jet engine bracket with 79 variables

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.