Moving horizon trend identification based on switching models for data driven decomposition of fluid flows

Modal decomposition is popular in fluid mechanics, especially for data-driven analysis. In particular, dynamic mode decomposition 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 is applied to identify the trend of the norm of the residuals that result from the application of dynamic mode decomposition to automatically classify the time evolution of fluid flows. The trend dynamics is modelled as a switching nonlinear system and hence a problem of moving horizon estimation is solved to monitor the behavior of the fluid and quickly identify changes of regime. The stability of the resulting estimation error given is proved. The combination of dynamic mode decomposition and moving horizon estimation provides successful results as shown by processing experimental datasets of the velocity field of fluid flows obtained by a particle image velocimetry.