A low-rank nonlinear ensemble filter for vortex models of aerodynamic flows


Robustly estimating the separated flow about an airfoil is critical in the design of any closed-loop controller. Darakananda et al. (Phys. Rev. Fluids, 2018) successfully used an ensemble Kalman filter (EnKF) to sequentially estimate the flow using an inviscid vortex model and distributed surface pressure readings. To tackle challenging inference problems with limited observations, classical localization schemes suppress correlations at long distances. However, these techniques would be harmful in our case due to the existence of physical long-range interactions between vortices and pressure readings. Instead, these interactions are best described as interactions between clusters of variables. This work proposes a systematic procedure to identify these clusters of variables from a nonlinear observation model. By projecting the states and observations onto these new sets of variables, the inference is performed in a low-dimensional subspace of the state and the observations. To perform consistent inference with the nonlinear model, we use the stochastic map filter (SMF): a natural generalization of the EnKF that relies on interpretable nonlinear prior-to-posterior transformations (Spantini et al., arXiv, 2019). We combine the identification of these clusters of variables with the SMF to derive a low-rank nonlinear ensemble filter. This filter is assessed on the response of a translating plate at 20 degrees that undergoes strong and overlapping pulses applied near the leading-edge. Our framework outperforms the EnKF at estimating the surface pressure distribution along the entire plate, with only two pressure sensors (placed at the edges of the plate) for collecting measurements.

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