A Comparative Study Between the Generalized Polynomial Chaos Expansion- and First-Order Reliability Method-Based Formulations of Simulation-Based Control Co-Design

Abstract

Reliability-based control co-design (RBCCD) formulations have been developed for the design of stochastic dynamic systems. To address the limitations of their current formulations, and to enable higher-fidelity solutions for complex problems, a novel reliability-based multidisciplinary feasible (MDF) formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) and a new reliability analysis method using generalized polynomial chaos (gPC) expansion for RBCCD were developed in previous work. Although the gPC expansion method was initially selected for the reliability analysis of simulation-based RBCCD, its performance against state-of-the-art, the most-probable-point (MPP) method, has not been established yet. Therefore, in this work, the first-ever MPP-based formulations of RB-MDF-MDSDO are developed, and using two engineering test problems, the new formulations' solution efficiency and accuracy are compared to those from the gPC-based formulation. Numerical results reveal that the gPC expansion method is marginally more accurate than the MPP algorithms, and therefore, it is more suitable for accuracy-sensitive applications. Conversely, the MPP algorithms are much more efficient, and thus, are more attractive for problems where solution efficiency is the priority.