Bayesian optimization of cooperative components for multi-stage aero-structural compressor blade design

Abstract In turbomachinery axial compressor development, detailed multi-stage 3D blade optimizations enable better designs than their common single-stage counterparts. However, this design problem entails a prohibitive computational effort for industrial application. It is very high-dimensional and highly constrained and involves expensive aerodynamic and structural design evaluations. Bayesian optimization (BO) is well suited for the two latter characteristics but suffers from the curse of dimensionality. In contrast to previous approaches, we exploit the problem’s multi-component structure to overcome this challenge. We propose to decompose the overall optimization task into lower-dimensional component subproblems. Component interactions are fully taken into account by a sequential cooperative procedure, named cooperative components BO (CC-BO). This enormously facilitates the BO without the need to modify the overall system evaluations. Additionally, we propose a variant with random subproblem decomposition. We analyze the working mechanisms of informed and random CC-BO and compare their performance to standard BO and state-of-the-art algorithms on two problems: a 100D multi-component Branin function and a 223D 4-stage aero-structural compressor blade design. Both proposed approaches significantly enhance the originally poorly performing BO and largely outperform the compared algorithms. The informed version shows an additional advantage for the well-known multi-component structure of the analytical problem. The increased flexibility of random CC-BO makes it the best choice for an efficient global optimization of the multi-stage blade design. It can be readily applied to other high-dimensional constrained optimization tasks.