Optimal sensor placement for learning extreme events from surface pressure on an airfoil

This work addresses the data-driven forecasting of extreme events in airfoil flow. For certain Reynolds numbers and flow configurations, airfoils are subject to sporadic high amplitude fluctuations in the aerodynamic forces. These extreme excursions may be seen as prototypical 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. We build on the work of Rudy & Sapsis (2022) who explored a variety of machine learning models to learn the mapping from pressure measurements along the airfoil surface to the drag coefficient exhibiting the extreme events. In this work we investigate the spatial dependence of the temporal correlation and mutual information between the surface pressure sensors and the aerodynamic forces, with a specific focus on rare, high amplitude excursions of the later. These extreme excursions are found to be associated with the instabilities of certain temporal frequencies. We employ these findings to develop an algorithm to optimally place pressure sensors to efficiently learn the extreme event dynamics from a sparse distribution of sensors. We then further exploit the previously mentioned instability mechanism to define and compute an observable which tracks the growth of locally unstable frequency components. This observable allows us to efficiently and accurately forecast imminent extreme excursions in the drag coefficient from observations of as little as a single pressure sensor.