Efficient aerostructural optimization of helicopter rotors toward aeroacoustic noise reduction using multilevel hierarchical kriging model

Aerostructural design optimizations of helicopter rotors based-on high-fidelity numerical simulations present a great challenge due to extremely large computational costs. In order to improve optimization efficiency by introducing assistance from cheap low-fidelity simulations, this article proposes to use a multilevel hierarchical kriging (MHK) model, which can incorporate three or more levels of fidelity to accelerate the convergence of a high-fidelity aerostructural optimization of helicopter rotors towards the global optimum. The optimization strategy is implemented by three steps. Firstly, a single-fidelity optimization is conducted based on kriging models and low-fidelity simulations. Secondly, a bi-fidelity optimization is performed based on hierarchical kriging (HK) models with pre-calculated low-fidelity samples and additional medium-fidelity samples. Finally, a multi-fidelity optimization is conducted towards the high-fidelity optimum based on MHK models with pre-generated low- and medium-fidelity samples and additional high-fidelity samples. The high-fidelity analysis is defined as coupled computational structural dynamics (CSD) and computational fluid dynamics (CFD) simulations, and the medium- and low-fidelity analyses are defined as merely CFD simulations on fine and coarse computational grids, respectively. To verify the effectiveness of MHK models in rotor optimizations, a blade shape optimization for aeroacoustic noise reduction is carried out by using the proposed optimization strategy. Results show that the total cost of an MHK-based optimization is around 49% less than that of a kriging-based optimization. Besides, by using kriging- and HK-based optimizations the aeroacoustic noises are reduced by 6.84 dB after 175 evaluations and 102 evaluations, respectively, while an MHK-based optimization could achieve the same noise reduction with only 54 evaluations. This example demonstrates that an MHK-based multi-fidelity optimization method can significantly improve the efficiency of aerostructural optimizations for helicopter rotors.