Moving Horizon Trend Identification Based on Switching Models for Data Driven Decomposition of Fluid Flows

Modal decomposition is pretty popular in fluid mechanics, especially for data-driven analysis. Dynamic mode decomposition (DMD) allows to identify the modes that describe complex phenomenona such as those physically modelled by the Navier-Stokes equation. The identified modes are associated with residuals, which can be used to detect a meaningful change of regime, e.g., the formation of a vortex. Toward this end, moving horizon estimation (MHE) is applied to identify the trend of the norm of the residuals that result from the application of DMD for the purpose to automatically classify the time evolution of fluid flows. The trend dynamics is modelled as a switching nonlinear system and hence an MHE problem is solved in such a way to monitor the time behavior of the fluid and quickly identify changes of regime. The stability of the estimation error given by MHE is proved. The combination of DMD and MHE provide successful results as shown by processing experimental datasets of the velocity field of fluid flows obtained by a particle image velocimetry.