Reliability-based design optimization by adaptive-sparse polynomial dimensional decomposition

This paper puts forward two new methods for reliability-based design optimization (RBDO) of complex engineering systems. The methods involve an adaptive-sparse polynomial dimensional decomposition (AS-PDD) of a high-dimensional stochastic response for reliability analysis, a novel integration of AS-PDD and score functions for calculating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, encompassing a multi-point, single-step design process. The two methods, depending on how the failure probability and its design sensitivities are evaluated, exploit two distinct combinations built on AS-PDD: the AS-PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the AS-PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the AS-PDD approximation and score functions. In both methods, the failure probability and its design sensitivities are determined concurrently from a single stochastic simulation or analysis. When applied in collaboration with the multi-point, single-step framework, the proposed methods afford the ability of solving industrial-scale design problems. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new methods provide more computationally efficient design solutions than existing methods. Furthermore, shape design of a 79-dimensional jet engine bracket was performed, demonstrating the power of the AS-PDD-MCS method developed to tackle practical RBDO problems.