Quasi-linear neural networks: Application to the prediction and control of unsteady aerodynamics

摘要

The present work describes a new technique for the modeling of unsteady aerodynamics using neural networks. Surface pressure readings obtained from an airfoil pitched at constant rate between 0 and 60 degrees were evaluated for 6 different pitch rates and 9 different span locations. Using 5 of the 54 records as a training set both a nonlinear and a linear neural network were trained on the time-varying pressure gradients. Thus, post-training, given the pressure distribution at any time (t) the models should predict the pressure distribution at time (t+△t). In addition, following training a linear equation system was calculated from the weight matrices of the linear neural network. The performance of both the linear equation system and the nonlinear network were evaluated using both sum-squared error and waveform correlations of the predicted and measured data. The results indicated that both models accurately predicted the unsteady flow fields to within 5% of the experimental data. Sum-squared errors were less than 0.01 and correlations were highly significant r > 0.90, (p < 0.01), for all 15 predicted pressure traces in each data set. Further, both models accurately extrapolated to any of the 49 records not used during training. Again, sum-squared errors were less than 0.01 and correlations were highly significant r > 0.90, (p < 0.01), in all cases. Overall, the results clearly indicated that it was possible to predict a wide range of unsteady flow field conditions including novel pitch rates and novel span locations. Further, the results clearly showed that these techniques facilitated the mathematical quantification of these unsteady flow fields. A linear equation system was readily calculated from the linear neural network. The capability to predict this phenomenon across a wide range of flight envelopes in turn provides a critical step towards the development of control systems targeted at exploiting unsteady aerodynamics for aircraft maneuverability enhancement.