Hilbert-huang Transform And Its Linear Time-varying Applications In The Identification Of Structural Modal Parameters

Vibration modal parameters are the main parameters that determine the dynamic characteristics of structures, which can offer important reference to structure modeling, model updating, sensitivity analysis, vibration control and damage detection. However, so far studies on modal parameter identification have been mainly limited to linear time-invariant structures. Modal parameter identification for a linear time-varying structure is so difficult that many problems to it are not to be solved. This paper applies the Hilbert-Huang transform (HHT) to structural modal parameter identification, and the focus is on the application of HHT to identify the modal parameters of time-varying structures. The main contents are detailed as following:1. Comprehensively review the classical modal parameter identification methods. The research progress on modal parameter identification of time-varying structure is introduced. Several common used time-frequency analysis methods and their applications in modal parameter identification are briefly narrated, in which development and applications of HHT are emphasized.2. Briefly introduce the fundamental definitions of Hilbert transform and instantaneous frequency. Intrinsic mode function (IMF), empirical mode decomposition (EMD), Hilbert spectrum and Hilbert marginal spectrum are also introduced. The comparisons among the results of HHT, wavelet analysis and Fourier spectrum analysis are made, aiming at presenting new idea or method to apply HHT to structural modal parameter identification.3. Propose the HHT-based method to identify the modal parameters of linear time-invariant structures. The modal parameter identification of single degree of freedom (SDOF) structure from its forced dynamic response under harmonic input is formulated. On this basis, the modal parameter identification of multi-degree of freedom (MDOF) structure under different kinds of input is also studied in depth. Results of numerical simulations show the simplicity and accuracy of the method.4. Present the HHT-based method to identify the modal parameters of a linear time-varying structure with SDOF from its free vibration responses. Taking into consideration the outstanding characteristics of EMD in extracting the transient response of each mode, the presented method is extended to identify the modal parameters of linear time-varying structure with SDOF and MDOF from their forced dynamic responses. Compared with the existing methods, the method presented in this paper is simple and easy to understand. Results of numerical simulations of the linear time-varying SDOF structure and 2-DOF structure show the validity and efficiency of the method.5. Design an experimental device comprising a cantilever beam and an adjustable additive mass. Based on the method above-mentioned, modal parameters of the time-varying structure are identified from the free vibration responses of the beam. The identified results are compared with the modal parameters identified under two given conditions and obtained by finite element analysis so as to investigate the validity and practicability of the method proposed in this paper.