Based On Hilbert-huang Transform And The Local Mean Decomposition Variable Structure Modal Parameter Identification

The study of time-varying structures is a current issue in structural dynamics. Especially the inverse problem about modal parameter identification for time-varying structures is not very perfect at present. However, there are many problems to be urgently solved for time-varying structures in engineering such as a large spacecraft flexible structure, a launching rocket and bridge vibration causing by high-speed train, etc.Therefore, the present situation of research on time-varying structural modal parameter identification is firstly reviewed. Two methods of time-frequency analysis, Hilbert-Huang transform (HHT) and local mean decomposition (LMD), are studied and applied in time-varying structural modal parameter identification in this paper. The main research contents and conclusions are as following:1. Comprehensively review the methods and the research progress of time-varying structural modal parameter identification. Several time-frequency analysis methods and their applications in time-varying structural modal parameter identification are briefly introduced.The development and applications of HHT and the application prospect of LMD are discussed.2. Briefly introduce the fundamental definitions of Hilbert transform and instantaneous frequency. The concepts of intrinsic mode function (IMF), empirical mode decomposition (EMD), Hilbert spectrum and Hilbert marginal spectrum are outlined.The performance of EMD, adaptive time-varying filter decomposition (ATVFD) and extrema mean mode decomposition (EMMD) are compared with each other. The fundamental principle and the method of LMD are introduced. The advantages of LMD are compared with those of EMD. LMD has advantages over HHT in extracting the instantaneous amplitude and instantaneous frequency of the multi-component, amplitude-modulated and frequency-modulated (AM-FM) signals by the analysis of a provided instance.3.Two new methods of time-varying structural modal parameter identification based on HHT and LMD are proposed. According to the good performance of EMD and LMD in extracting structural single order instant response component, this two methods are used to identify the modal parameters of time-varying single degree of freedom (SDOF) structure and multi-degree of freedom (MDOF) structure. Results of numerical simulations show that the proposed methods are simple and have good precisions, and LMD has obvious advantages over HHT in some situations.4. Design an experimental device comprising a cantilever beam and the adjustable additive mass and stiffness. Based on the method above-mentioned, modal parameters of the time-varying structure are identified from the free vibration responses of the beam with continuous mass change, continuous stiffness change and fast stiffness change. The identified results are compared with the modal parameters identified under several specified conditions corresponding to the time-invariant structure and obtained by finite element analysis. The validity and practicability of the methods proposed in this paper and the superiority of LMD are investigated and verified.