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

摘要

Abstract: The present work describes a new technique for themodeling of unsteady aerodynamics using neuralnetworks. Surface pressure readings obtained from anairfoil pitched at constant rate between 0 and 60degrees were evaluated for 6 different pitch rates and9 different span locations. Using 5 of 54 records as atraining set both a nonlinear and a linear neuralnetwork were trained on the time-varying pressuregradients. Thus, post- training, given the pressuredistribution at any time (t) the models should predictthe pressure distribution at time (t$PLU$Delta@t). Inaddition, following training a linear equation systemwas calculated from the weight matrices of the linearneural network. The performance of both the linearequation system and the nonlinear network wereevaluated using both sum-squared error and waveformcorrelations of the predicted and measured data. Theresults indicated that both models accurately predictedthe unsteady flow fields to within 5% of theexperimental data. Sum-squared errors were less than0.01 and correlations were highly significant r $GRT0.09, (p $LS 0.01), for all 15 predicted pressuretraces in each data set. Further, both modelsaccurately extrapolated to any of the 49 records notused during training. Again, sum-squared errors wereless than 0.01 and correlations were highly significantr $GRT 0.90, (p $LS 0.01), in all cases. Overall, theresults clearly indicated that it was possible topredict a wide range of unsteady flow field conditionsincluding novel pitch rates and novel span locations.Further, the results clearly showed that thesetechniques facilitated the mathematical quantificationof these unsteady flow fields. A linear equation systemwas readily calculated from the linear neural network.The capability to predict this phenomenon across a widerange of flight envelopes in turn provides a criticalstep towards the development of control systemstargeted at exploiting unsteady aerodynamics foraircraft maneuverability enhancement.!20