Low dimensional model development using double proper orthogonal decomposition and system identification

Siegel S., Cohen K., Seidel J., Aradağ Çelebioğl S., McLaughlin T.

4th AIAA Flow Control Conference, Seattle, WA, United States Of America, 23 - 26 June 2008 identifier

  • Publication Type: Conference Paper / Full Text
  • City: Seattle, WA
  • Country: United States Of America
  • TED University Affiliated: No


For feedback control of complex spatio-temporally evolving flow fields, it is imperative to use a global flow model for both flow state estimation, as well as controller development. It is important that this model correctly presents not just the natural, unforced flow state, but also the interaction of actuators with the flow for both open and closed loop situations. It is difficult and in some cases impossible to develop such a model with the traditional POD-Galerkin approach. This is due to the fact that the truncation of the mode set leads to structural instabilities. Furthermore, boundary conditions for time dependent actuation are often difficult to implement. Lastly, the presence of turbulence in higher Reynolds number flow fields leads to severe problems in the projection. For these reasons, a new approach to low dimensional modeling is introduced in this paper. An extension to POD, the so called Double POD decomposition, is employed to facilitate derivation of POD modes for transient flow fields. These modes can correctly span a large number of flow conditions, caused by changes in actuation, Reynolds number or other parameters of technical interest. Next, the original data is projected onto the truncated DPOD mode set, leading to a set of mode amplitudes. The final step in model development used nonlinear system identification techniques, in particular, the ANN-ARX method (Artificial Neural Network - Auto Regressive eXternal Input) is employed to develop a numerical model of the temporal evolution of the flow. This resulting model can correctly capture open loop transient flow behavior for a parameter space large enough for controller development, and is inherently stable even for hydro dynamically unstable flow fields.