Nonlinear identification via connected neural networks for unsteady aerodynamic analysis

In the present work, a nonlinear system identification strategy is proposed which is based on the series connection of a recurrent local linear neuro-fuzzy model (NFM) and a multilayer perceptron (MLP) neural network. The NFM with output feedback is initially used for multi-step ahead predictions, whereas the MLP neural network is a posteriori employed to perform a nonlinear quasi-static correction of the NFM's time-series response. The novel identification approach is utilized exemplarily as a reduced-order modeling (ROM) technique to lower the computational effort of unsteady aerodynamic simulations, although the approach is generally applicable to any nonlinear identification task. In order to demonstrate the method's fidelity for unsteady aerodynamic modeling, the NLR 7301 airfoil is investigated at transonic flow conditions, while the motion-induced aerodynamic forces are considered in particular. Therefore, the pitch and plunge degrees of freedom are simultaneously excited via forced motions to obtain the training data for model calibration, while the respective aerodynamic response is computed using a computational fluid dynamics (CFD) solver. The sequential nonlinear identification process as well as the generalization of the resulting model is presented. Besides, a Monte-Carlo-based training procedure, which is novel in the context of aerodynamic reduced-order modeling, is introduced to estimate statistical errors. It is shown that the essential linear and nonlinear system characteristics are accurately reproduced by the new approach compared to the full-order solution. Moreover, by examining the results in comparison to established ROM methods it is indicated that the connected neural network approach leads to an enhanced simulation and generalization performance.