Neural Network Estimator for Closed-Loop Control of a Cylinder Wake

Abstract

The effectiveness of a non-linear Artificial Neural Network Estimator (ANNE) for feedback flow control on the wake of a circular cylinder is investigated in direct numerical simulations. The research program is aimed at suppressing the von Karman vortex street in the wake of a cylinder at a Reynolds number of 100. Various configurations of sensors, varying both number and location, were studied from just one sensor through 4 sensors. A low-dimensional Proper Orthogonal Decomposition (POD) is applied to the flow field velocity and sensor placement is based on the intensity of the resulting spatial Eigenfunctions. The numerically generated data was comprised of 138 snapshots taken over 11 cycles from the periodic regime. A Linear Stochastic Estimator (LSE) was employed to map the velocity data to the temporal coefficients of the reduced order model and results are compared with those obtained using ANNE. All sensor configurations were studied for four different cases, namely, noiseless data and three levels of increasingly degraded data by injection of random noise. For a given four sensor configuration, ANNE was compared to LSE, Quadratic Stochastic Estimation (QSE) and LSE with time delays (DSE). We show ANNE to be far more robust and accurate in comparison to all of these procedures. Nomenclature