Limit Cycle Oscillation Prediction of Asymmetric External Store Configurations Using Neural Networks

Abstract

*A static artificial neural network is developed to predict limit cycle oscillation (LCO) amplitude levels and frequency of external store configurations on a fighter aircraft. This work is similar to previous networks generated by the authors with the inclusion of continuous analytic descriptors of the aeroelastic modes and the flutter eigenvectors. The current work however uses the analytic descriptors of three normal modes, and allows the neural network to determine the effect of the coupling modes. In addition, asymmetric external store configurations are examined in this neural network, similar only by the missile configurations on the wingtips. A neural network with two layers, one with 37 nodes and the second with 11 nodes, is used for the prediction of the two outputs, LCO amplitude and LCO frequency. The methodology for the analytic descriptors is presented, as well as sample network input training data. The results of the neural network using the analytic descriptors show a capability to predict trends for both the LCO onset speeds and the overall amplitude levels. This neural network was also capable of predicting an observed trend of LCO amplitude levels decreasing partially or completely after a certain airspeed. I. Introduction Non-linear aeroelastic response in the form of Limit Cycle Oscillations (LCO) is a common occurrence on certain fighter aircraft, primarily when carrying external stores. Although moderate LCO amplitudes are not structurally critical to the aircraft, it can interfere with the operational suitability of the aircraft’s mission due in part to the transferred oscillation to the pilot. Limit cycle oscillations are often present for external store configurations that are predicted to be aeroelastically unstable using linear flutter analyses. The linear flutter solution is useful in identifying the LCO sensitive external store configurations, and can accurately predict the frequency of the instability. In addition, previous studies 1,2 have shown that the classical flutter analyses are adequate to identify the modal composition of the LCO instability. However, linear flutter analyses are not capable of predicting the onset speeds and amplitude levels of LCO. A description of LCO, the relationship to classic flutter analysis, and some background are provided in Reference [3]. In this article, LCO is described as sustained periodic oscillations that stabilize in amplitude for a given flight condition. As flight conditions change with increasing Mach or dynamic pressure, especially in the transonic region, the sustained oscillations continue to grow in amplitude, sometimes to unacceptably high levels. In addition, once past the transonic region, generally around 0.95 Mach, the LCO can also diminish in amplitude, which has been deemed “nontypical LCO.” Several analytic methods 4, , , , 5 6 7 8 have been investigated to predict the amplitude levels of LCO on the F-16. These methods include semi-empirical methods based on shock induced trailing edge separation, timedomain computational fluid dynamics, and a transonic small-disturbance approach. Although these methods have shown success in predicting LCO, they have not been practical to run on the large number of external store configurations that must be analyzed. Typical flutter and LCO analyses for the F-16 give an indication of potentially critical configurations. Flight testing is accomplished for some of these configurations to determine in-flight response. The flight test results have shown several consistent trends of LCO, and correlation to the linear flutter analyses. However, as flight testing is becoming more difficult to achieve due to availability of assets and costs, new methods are being examined to reduce the amount of testing while still being able to accurately determine the flutter and LCO characteristics for the increasing number of new external store configurations.