Identification Of Time-varying And Nonlinear Systems Based On Variational Modal Decomposition And Time-frequency Analysis

In the actual operation process,the change of environment and load will lead to the time-varying and nonlinear characteristics of civil engineering structure,such as the change of cable force of cable-stayed bridge,bridge vibration caused by train crossing the bridge and ambient temperature,which will lead to the change of structural dynamic characteristics with time.Therefore,the research on the identification methods of characteristic parameters such as instantaneous frequency of time-varying and nonlinear structures has important scientific value and engineering practical significance.In this thesis,the identification of characteristic parameters such as instantaneous frequency of time-varying structures and nonlinear systems is studied by using the combination of variational modal decomposition and high-precision time-frequency analysis.The main research contents of this thesis include:(1)The solution method of vibration response of linear time-varying system and the concepts of instantaneous frequency and signal-to-noise ratio are briefly described;Two typical single degrees of freedom nonlinear systems,Duffing and van der Pol nonlinear systems,are introduced.The average method is used to solve the nonlinear system and the least square method is used to fit the parameters of the nonlinear system.(2)The basic principle and algorithm flow of variational mode decomposition(VMD)are briefly described.The ability of VMD and empirical mode decomposition(EMD)to decompose multi-component signals is compared.The results show that VMD has better anti-mode aliasing ability and the decomposition effect is better than EMD.The anti-noise performance and signal reconstruction ability of five time-frequency analysis methods such as short-time Fourier transform(STFT),reassignment method(RM),synchrosqueezing short-time Fourier transform(FSST),synchroextrcting transform(SET)and Local maximum synchrosqueezing transform(LMSST)are compared.The results show that SET and LMSST have stronger energy focusing ability than STFT,RM and FSST,and the signal reconstruction ability of LMSST is better than SET.(3)A method combining VMD and SET is proposed,which solves the problem that SET cannot separate multi-component signals with close frequency component intervals,and has high energy aggregation and strong signal decomposition ability.The numerical examples of multi-component time-varying signals,free vibration response signals of two degrees of freedom time-varying structures and the experimental verification of time-varying cables show that this method is suitable for time-varying system identification and has high accuracy.(4)Combined with VMD and LMSST,a high-precision multi freedom nonlinear system identification method is proposed by using ridge detection algorithm and synchroextrcting operator to identify and extract the trajectory of instantaneous frequency on the spectrum.Numerical examples of two typical nonlinear systems,Duffing and Van der pol nonlinear free vibration system,show that LMSST method can obtain the instantaneous frequency and other characteristic parameters of nonlinear system.A numerical example of a two degrees of freedom shear type building structure with nonlinear stiffness shows that after the vibration response of the two degrees of freedom nonlinear system is predecomposed by VMD,the LMSST method can obtain the instantaneous frequency and other characteristic parameters of the two degrees of freedom nonlinear system.