Uncertainty Analysis Of Aircraft Flight Mechanics Parameters Based On Chaotic Polynomial Expansion

There are complex uncertainties in the motion of aircraft in the atmosphere due to the coupling of atmospheric environment,overall parameters and control deviation,resulting in the uncertainty of flight state parameters.Considering these uncertain factors alone,the impact on the aircraft can be ignored,but when these factors are coupled with each other,the launch of the aircraft may fail or even lead to more serious safety accidents.The classical safety factor method directly uses the mean value of these parameters,but its calculation results do not fully consider the uncertainty factors.In this paper,an efficient and accurate uncertainty propagation process is developed to realize the uncertainty propagation from aircraft design parameters to the state response in motion.(1)Six degree of freedom dynamic model modeling and state response analysis of aircraft.Firstly,the earth model is established for gravity calculation,and various coordinate systems used in the aircraft dynamic model are determined,and the rotation quaternion is used to realize the transformation between coordinate systems.Then,the various parameters involved in the flight process of the aircraft are described,including the attitude angle,attack angle and other important angles of the aircraft,as well as some parameters of the launch point and projection point that change with the flight time.Then the force and moment of the aircraft in flight are analyzed and calculated.Secondly,the control equations of the aircraft are established,and the six degree of freedom flight dynamics model is established by using the numerical integration method according to the translation and rotation equations of the mass center of the aircraft.Finally,based on the six degree of freedom flight dynamics model of the aircraft,the state response analysis of the aircraft is completed under certain wind field conditions.It lays a foundation for the research of the uncertainty problem in the follow-up aircraft flight.(2)Global sensitivity analysis of aircraft state response based on optimal polynomial.Latin hypercube sampling method is used to extract design parameter samples and state response samples to construct polynomial model.Based on a structure selection technique with error reduction ratio as the standard,the optimal polynomial model is obtained by selecting the sub items of the polynomial model.Because of the simple structure and explicit expression of the optimal polynomial model,it is used to replace the original six degree of freedom dynamic model for Sobol direct integration,so as to realize the global sensitivity analysis of aircraft state response efficiently and accurately.(3)Uncertainty propagation analysis of aircraft state response based on Optimal Chaotic polynomial.Based on the results of global sensitivity analysis,the secondorder derivative method is used λ-Pdf is used to fit the original probability distribution of design parameters.Latin hypercube sampling method is used to extract design parameter samples and state response samples.Based on these samples and Gegenbauer orthogonal polynomials,complete chaotic polynomials are constructed.Then the optimal chaotic polynomial model is selected by using structure selection technique.Based on the orthogonal characteristics of orthogonal polynomials,the first four order statistical moment information of each state parameter is quickly calculated by using the coefficients of the optimal chaotic polynomials,so as to realize the uncertainty propagation analysis of aircraft state response.