Structural Instantaneous Modal Parameter Identification Based On Fractional Fourier Transform

In recent years,the bridges' health monitoring system has been widely used in civil engineering,and modal parameter identification,as one of its core technology and theoretical basis,has gradually become a research hotspot in the field.At present,researchers have proposed a variety of operational modal parameter identification methods,such as frequency domain method and time domain method.However,to some extent,many civil engineering structures show time-varying characteristics,so the longterm health monitoring data of bridges are essentially non-stationary signals.As a generalized form of traditional Fourier transform,fractional Fourier transform(FRFT)has attracted extensive attention in recent years.It can provide both local characteristics of signals in time domain and frequency domain,so it is suitable for processing nonstationary signals.On the basis of referring to a large number of literatures on modal parameter identification,the paper conducts an in-depth study on FRFT in terms of theory,simulation analysis and experiment.The main contents and conclusions of the dissertation are as follows:(1)The development status of health monitoring system are introduced,and the significance of operational modal analysis is pointed out.Some typical operational modal parameter identification methods are summarized and the research background and significance of the dissertation are clarified.(2)The development of FRFT and its application are introduced,and its basic definition and properties are summarized.It is verified that FRFT is the generalized form of traditional Fourier transform through a simulation.With one more free parameter p,it is more flexible and suitable for processing chirp non-stationary signals.(3)The basic principle of chirp signal detection and parameter estimation is introduced.Chirp signal will be expressed as an impulse function in the optimal transform order,so as to realize its detection and parameter estimation.(4)In order to analyze the influence on results under different signal-to-noise ratios,single and multi-component chirp signals are detected with or without noise respectively.The results show that FRFT has certain noise resistance.At the same time,the influence of undersampling and oversampling conditions on the estimation is studied,and the results are verified.(5)The mathematical model and time-frequency characteristics of sinusoidal frequency modulation signal are introduced.Then the basic concept of instantaneous frequency is described.A method is introduced to identify the instantaneous frequency of time-varying structures by combining FRFT and cubic polynomial function.The effectiveness is verified by simulation analysis and experiment.