Nonlinear estimation of transient flow field low dimensional states using artificial neural nets

Cohen, Kelly; Mclaughlin, Thomas; Seidel, Jurgen; Siegel, Stefan; Aradag, Selin

Feedback flow control of the wake of a circular cylinder at a Reynolds number of 100 is an interesting and challenging benchmark for controlling absolute instabilities associated with bluff body wakes. A two dimensional computational fluid dynamics simulation is used to develop low-dimensional models for estimator design. Actuation is implemented as displacement of the cylinder normal to the flow. The estimation approach uses a low dimensional model based on a truncated 6 mode Double Proper Orthogonal Decomposition (DPOD) applied to the streamwise velocity component of the flow field. Sensor placement is based on the intensity of the resulting spatial modes. A non-linear Artificial Neural Network Estimator (ANNE) was employed to map the velocity data to the mode amplitudes of the DPOD model. For a given four sensor configuration, developed using a previously validated strategy, ANNE performed better than two state-of-the-art approaches, namely, a Quadratic Stochastic Estimator (QSE) and a Linear Stochastic Estimator with time delays (DSE).

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