Automated optimal experimental design strategy for reduced order modeling of aerodynamic flow fields

Abstract

Aerodynamic flow fields reveal essential physical insights (such as shocks) that substantially affect aerodynamic performance. However, conventional flow field computations require time-consuming simulations. Alternatively, reduced-order models (ROMs) allow fast flow field predictions, enabling real-time decision-making. Efficient sampling is required to train ROMs without incuring prohibitive costs. In this paper, we propose a fully automated optimal experimental design (Auto-OED) strategy on proper orthogonal decomposition (POD) for ROM-based rapid flow field predictions. Auto-OED uses two individual optimal experimental design (OED) strategies, automatically selects the number of POD bases for the first sampling strategy, and intelligently switches to the second strategy on the fly. We showcased the Auto-OED strategy on airfoil flow field predictions in the transonic regime. OED-based ROMs were constructed over 20 trials for robustness tests with a total of 40 training samples in each trial, including 16 random initial samples by Latin hypercube sampling (LHS) and 24 OED samples. The results demonstrated that the ROM predictions completely based on LHS had an error of 1.6×10−3 while the existing OED strategies-based ROMs over 20 trials achieved a mean error (μerr) of 7.5×10−4 with a standard deviation (σerr) of 9.0×10−5. In contrast, the best Auto-OED ROM achieved the lowest μerr of 7.5×10−4 and lowest σerr of 6.2×10−5. These error reductions confirm the viability of the proposed Auto-OED-based ROM in fluid field predictions and potentially other engineering applications of a similar type.