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Data-Driven Balanced Truncation for Predictive Model Order Reduction of Aeroacoustic Response

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Rapid prediction of the aeroacoustic response is a key component in the design of aircraft and turbomachinery. In this work, we propose a technique for highly accelerated prediction of aeroacoustic response using a data-driven model reduction approach based on the eigensystem realization algorithm (ERA). Specifically, we create and compare ERA reduced-order models (ROMs) based on the training data generated by solving the linearized and nonlinear Euler equations, and we use them to predict the aeroacoustic response of an airfoil in a purely predictive setting subject to different types of gust loading. Activating each input channel separately in the full-order model (FOM) to generate the Markov sequence for training makes it computationally challenging to use the ERA in aeroacoustics applications. We address this bottleneck by first proposing a multifidelity gappy POD method to reduce the computation cost on the FOM and ROM levels by querying the high-resolution FOM only for the input channels identified by gappy POD. Second, we use tangential interpolation at the ROM level to reduce the size of the Hankel matrix. The proposed methods enable application of the ERA for accurate online acoustic response prediction, and they reduce the offline computation cost of ROMs.