Shape optimization under stochastic conditions by design-space augmented dimensionality reduction

The paper presents a methodology to reduce the design-space dimensionality in reliability-based robust optimization problems for shape design, with the aim of improving the efficiency of the optimization process. The method is based on a generalized Karhunen-Loève expansion (KLE) and the definition of geometric and physics-based variance associated with the design space. The geometric variance originates from the shape modification method, whereas the physics-based variance stems from multidisciplinary multi-physics computations (performed with low-fidelity solvers) at different design conditions. Combining geometric and multidisciplinary multiple-conditions physics-based variability with KLE provides the foundation for a design-space augmented dimensionality reduction (ADR) method, which extends authors' previous work. Herein, the ADR effectiveness and efficiency is demonstrated for the optimization of a destroyer-type vessel to improve calm water and seakeeping performance in a stochastic environment. The method presented goes beyond the current application and is suitable in all areas where shape design is of primary importance (such as fluid dynamics, structural, and heat transfer applications), involving complex and expensive simulations.