| Post-stall maneuverability is one of the important performances of the new generation fighter.When the fighter is maneuvering rapidly,complex flow phenomena such as shock wave,flow separation,vortex formation and rupture may appear in the flow field around the aircraft.At this time,the aerodynamic force and moment acting on the aircraft will show obvious nonlinear and unsteady characteristics.In this case,the traditional aerodynamic derivative model has been difficult to apply,so it is necessary to explore an effective nonlinear unsteady aerodynamic modeling method.Aiming at the problems existing in nonlinear unsteady aerodynamic modeling,three aspects of research are carried out in this paper.The first aspect is to propose the concept of unstable dynamic process.By analyzing the response composition of the system after being excited,it is found that the aerodynamic force will first go through an unstable dynamic process,and then transition to a stable process.The traditional research on the modeling of unsteady aerodynamics has always been aimed at the stable hysteresis of aerodynamic force,ignoring the unsteady dynamic process before the aerodynamic force reaches stability,while the fast maneuvering process of aircraft can hardly be a continuous stable vibration.most of them are in the initial unsteady dynamic process,so it is necessary to introduce the influence of unsteady dynamic process into the modeling of unsteady aerodynamic force.The second aspect is to study unsteady aerodynamic modeling from the perspective of system identification.By designing appropriate nonlinear excitation signals to reflect the nonlinear effects of the system,it is possible to predict aerodynamics of different motions with only one excitation.The third aspect is aimed at specific mathematical models and machine learning methods,using CFD(Computational Fluid Dynamics)as a tool to provide data to solve the model parameter identification and training methods of learning methods.The main contents of this paper are as follows:1.Unstable dynamic process analysis.Based on the analysis of a large number of existing unsteady aerodynamic modeling studies,with the help of vibration theory,it is found that the response of the system after harmonic excitation includes free vibration and forced vibration.Free vibration will decay to zero over time.Finally,forced vibration remains.The overall response of the system will first go through an unstable dynamic process,and then transition to a stable process.The concept of unsteady dynamic process of unsteady aerodynamic force is put forward by analogy.Most of the existing unsteady aerodynamic modeling studies are based on the forced vibration test data,that is,stable hysteresis,ignoring the initial unsteady dynamic process.From the perspective of system identification,the whole response process data after the object is excited is taken as a sample to realize the modeling and prediction of the unstable dynamic process.2.Identification and excitation of Volterra series.The Volterra series is used to model the nonlinear system,and the excitation is designed from the perspective of system identification to identify the Volterra kernel to realize the prediction of the entire dynamic response process of the system including the unstable dynamic process.With the increase of kernel order,the number of parameters to be identified in Volterra kernel increases exponentially.In order to reduce the parameters to be identified,the first-order kernel and second-order kernel of Volterra are expanded based on the piecewise quadratic multiwavelets,and the problem is transformed into the estimation problem of expansion coefficients.Aiming at the nonlinear excitation problem encountered in Volterra second-order kernel identification,an input suitable for second-order kernel identification is designed,which is called two-dimensional frequency sweep.The verification of two typical nonlinear systems shows that this input can excite the nonlinear characteristics of the system better than the ordinary frequency sweep signal.3.Unsteady aerodynamic modeling of Volterra series based on multiwavelet decomposition.Taking the first three-order kernels of the Volterra series as the model,the unsteady aerodynamic force of the unsteady dynamic process is studied by the lift coefficient,drag coefficient and pitching moment coefficient of the NACA-0012 airfoil at 0.8 Mach with heave motion.By taking the data of the whole aerodynamic response process after the object is excited as a sample for parameter identification,it is realized that both stable hysteresis and unstable dynamic processes can be predicted.For the dimensional disaster caused by the third-order kernel of Volterra,the dimension of the equation is reduced by using the decomposition characteristic of wavelet multi-resolution analysis in time and frequency.Finally,the problem of solving high-dimensional ill-conditioned equations is transformed into low-dimensional equations,and the stable solution is obtained.For the nonlinear excitation problem encountered in the third-order kernel identification of Volterra,the two-dimensional frequency sweep design method in the previous chapter is used for reference,an excitation signal suitable for third-order kernel identification is designed.4.Nonlinear unsteady aerodynamic modeling based on least square support vector machine.Using least square support vector machine(LS-SVM)as machine learning method,the unsteady aerodynamic modeling of unstable dynamic process is studied by taking the lift coefficient,drag coefficient and pitching moment coefficient of RAE-2822 airfoil in heave and pitching motion under Mach 0.8 as examples.By collecting the data of the entire response process after the object is excited as a sample for training,it can not only predict the stable hysteresis but also the unstable dynamic process.Based on the research on excitation design in the first two chapters,a general excitation input suitable for nonlinear system identification is designed.In the model training,the input form is selected based on the physical characteristics of the unsteady aerodynamic force,and the reduced frequency is avoided as a parameter.Finally,only one excitation is needed to predict the aerodynamic forces of different simple harmonic motions.It can also predict the aerodynamic forces of other non-harmonic motions.5.Unsteady aerodynamic modeling at high angle of attack based on least square support vector machine.The aerodynamic modeling of unstable dynamic process of the wing maneuvering in the range of high angle of attack is studied.By designing nonlinear excitations and using the entire response process data after the system is excited for training,unified prediction of stable hysteresis and unstable dynamic processes is achieved,and both simple harmonic motion and other motions can be predicted.The effect of the reference state on the unstable dynamic process is verified by the lift,drag and pitch moment coefficient of the wing under different reference states.The results show that in some cases the unstable dynamic process and the stable hysteresis basically coincide,that is,the unstable dynamic process is not obvious.In other cases,there is a clear difference between the unstable dynamic process and the stable hysteresis loop.The aerodynamic force needs to pass through a period of unstable dynamic process before transitioning to the stable stage. |
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