Research On Robust Flutter Analysis And Model Validation

Actual aeroelastic systems are highly sophisticated systems and have various uncertainties. Robust flutter analysis which was developed to examine the robust stability of uncertain aeroelastic systems currently is one of the aeroelastic research hotspots in international community. Furthermore, this approach has been successfully applied to flight flutter test. Based on the overall review of robust flutter analysis and its application in practical engineering, this dissertation investigated the robust flutter analysis methods for linear and nonlinear aeroelastic systems with uncertainties and model validation approaches. The main research work presented in this dissertation includes:(1) For linear robust flutter analysis, an analysis method using flight altitude as the perturbation variable is proposed. The air density and sound speed of standard atmosphere model are approximated as a polynomial function of altitude, such that the system only depends on a single parameter, i.e. the flight altitude, to describe the stability and flight condition. The predicted robust flutter boundary is independent of the initial values of the flight altitude. This method is suitable for Constant-Mach flight flutter test and provides valuable reference for flight envelope expansion.(2) For nonlinear aeroelastic systems, two types of uncertainty named vanishing and nonvanishing perturbation are investigated respectively byμ-analysis method. For vanishing perturbations, the perturbed system can be linearized at the equilibrium point andμ-method can be used directly to examine the robust stability of the linearized system. For nonvanishing perturbations, the influences of uncertain parameters on the equilibrium point are taken into consideration, and the functional relationships between them are expressed as Taylor series in order to consider the robust stability problems of systems with nonvanishing perturbations inμ-analysis framework.(3) By computing the value sets of the characteristic polynomials of the linearized systems, zero exclusion condition and the motion track of the value sets on complex plane can be applied to check the stability of the entire family of the characteristic polynomials. The flutter speeds of the best-case and worst-case in the family of plants are obtained. On the basis of previous results, the robust stability problem is transformed into constraint satisfaction problem according to the value sets conditions which make the characteristic polynomials stable. The robust stability of the polynomials can be obtained by determining the existence of the solution of the constraint satisfaction problem in the given parameter intervals. This approach is applicable to a very general case where the polynomial coefficients are nonlinear continuous functions of the uncertain parameters.(4) The uncertainty modeling of aeroelastic systems, especially the model validation problems are investigated in this dissertation. The linear fractional transformation model of uncertain aeroelastic system is established. The validity of the model set is tested by model validation method based on matrices interpolation theory and the magnitudes of the uncertainties are estimated successfully.(5) By taking the influences of noise into consideration, the errors between actual system and nominal model are assigned to noise and uncertainties and the effect of reducing the conservatism is verified. Furthermore, the proportion relationship of the magnitudes of each uncertainty is studied in order to investigate the methods which could reduce the conservatism of the predicted results more effectively.At last, the research work of this dissertation is summarized and the prospective of further research is discussed.