Neural Network Estimator for Low-Dimensional Modeling of a Cylinder Wake

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 simulation. The research program is aimed at suppressing the von Karman vortex street in the wake of a cylinder at a Reynolds number of 100. Two sensor configurations were studied, namely a 12 sensor configuration and a four sensor configuration. A low-dimensional Proper Orthogonal Decomposition (POD) is applied to the vorticity calculated from the flow field 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 steady state 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. Results show that for the estimation of the first four modes, it is seen that for the design condition (no noise) 4 sensors using ANNE provide significantly better results than 4 sensors using LSE. Furthermore, ANNE, based on 4 sensors, provides the same level of performance, based on RMS of the estimation error as that obtained using LSE with a 12 sensor configuration.

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