Harnessing the instability mechanisms in airfoil flow for the data-driven forecasting of extreme events

Abstract: This work addresses the data-driven forecasting of extreme events in the airfoil flow. These events may be seen as examples of the kind of unsteady and intermittent dynamics relevant to the flow around airfoils and wings in a variety of laboratory and real-world applications. W investigate the instability mechanisms at the heart of these extreme events, and how knowledge thereof may be harnessed for efficient data driven forecasting. Through a wavelet and spectral analysis of the flow we find that the extreme events arise due to the instability of a specific frequency component distinct from the vortex shedding mode. During these events this extreme event manifold draws energy from the energetically dominant vortex shedding flow and undergoes an abrupt energy transfer from small to large scales. We also investigate the spatial dependence of the temporal correlation and mutual information between the surface pressure and the aerodynamic forces, with the aim of identifying regions of the airfoil amenable to sparse sensing and the efficient forecasting of extremes. Building on previous work, we show that relying solely on the mutual information for optimal sensor placement fails to improve model prediction over uniform or random sensor placement. However, we show that by isolating the extreme event frequency component offline through a wavelet transform we are able to circumvent the requirement for a recursive long-short term memory (LSTM) network -- resulting in a significant reduction in computational complexity over the previous state of the art. Using the wavelet pre-processed data in conjunction with an extreme event-tailored loss function we find that our model is capable of forecasting extreme events using only three pressure sensors. Furthermore, we find our model to be robust to sensor location -- showing promise for the use of our model in dynamically varying applications.