Theoretical And Experimental Research On Identification Method Of Frequency-varying Nonlinear Dynamical System

Identification of nonlinear dynamical system is to estimate model and parameters that describing dynamic characteristics of system.Generally speaking,conventional identification is that getting the estimated form on the basis of existing datas and prior knowledge,then identifying some or all of coefficients of equation with various motion state by using theory of identifying,determining dynamic model of system accordingly.Dynamic systems almost contain all kinds of nonlinear factors in engineering practice,and nonlinear frequency is one of these factors.The theory study on identification of frequency-varing dynamic system is not yet perfect currently,so accurate estimate of the form which represents control equation of dynamic system and the formation of frequency-varing properties are to be further studied in-depth.This paper takes the simple beam-particle medium system with steady-state excitation and the static bearing system of domestically produced aeroengine as the objects of research,and identifies model and parameters of the two systems with the proposed multidimensional least-square method and frequency-domain analysis based on conventional vibration test technology.The results showed that nonlinearity of the two vibration systems were derived from frequency-varying characteristics of the system parameters.The main works of this paper are:1.Proposed a wavelet denoising method with weighted average threshold based on GA in view of traditional denoising that needed to estimate statistics of noise in advance and the limitation of soft threshold denoising,and verified denoising effect and applicability of the method through two instances-analogy sinusoidal signals with noise and Lorenz chaotic signals with noise respectively.The denoising method is a combination of soft and hard threshold denoising,and estimation of statistics of noise in advance is not needed,it could eliminate noise in the measured signal and improve SNR significantly.Signal preprocessing of the simple beam-particle system with harmonic excitation and the static bearing system of the domestically produced aeroengine could be applied by the denoising method.2.Proposed the multidimensional least-square method based on the theory of least-square to identify model and parameters of the dynamic bifurcation system with simple beam-particle medium when it showed obvious leap.The identification parameters exhibited obvious frequency-varying characteristics in the total frequency domain when experimental amplitude-frequency curve had obvious leap according to results,the frequency varying linear system will mutate into frequency-varying nonlinear system along with frequency increasing,and the nonlinear characteristics mainly come from nonlinear stiffness,it's reason that the amplitude-frequency characteristic of system is similar to Duffing equation.Results also showed that different parameter exhibited different frequency-varying characteristic,linear mass,damping and stiffness under different working condition exhibited a obvious leap along with frequency increasing,and the leap frequency is equal to the frequency when amplitude-frequency curve happened to leaping under the same condition,In addition,different sweep direction and buried depth will have great influence on results of the parameters.At the same time,proposed the degree raising-power descending method to solve the second order differential equation that contains higher order term when verifying accuracy of the identification results that describing the model.3.Proposed indirect loading and a complete set of test method for dynamic flexibility with complex rotary machinery under limited space,and the test method was integrated by technology of acquisition and modification of multipoint symmetric displacement,indirect load under limited space,calibration and effective access of excitation and loading with no bias.Achieved the identification and access of dynamic flexibility under different fulcrum of the domestically produced aeroengine with the proposed denoising method and the frequency-domain analysis method.Identification results showed that flexibility at first and second fulcrum exhibited obvious frequency varying characteritics and influence of different frequency and amplitude on dynamic flexibility was researched,in addition,it got the transfer rule of dynamic flexibility between different sections in the first fulcrum.