Parameter Identification Of Time-varying Structure Research Based On Wavelet Transform

In recent years, more and more structural health monitoring (SHM) systems have been installed in large civil engineering structures. The parameter (modal and physical) identification is one of the key issues in SHM. For time invariant system, there are presently many identification methods available. However, many practical engineering structures are time-varying. It is very important to identify time-varying parameters, including modal parameters and physical parameters, for consistent structural health monitoring and damage detection. Another issue is the structural nonlinearity, which may aise from material, geometry and structural damage. The usual linear theory can't represent the behavior of nonlinear structures. This dissertation presents a wavelet-based parameter (modal and physical) and nonlinearity identification methodology of time-varying structures. The work is focused on theory, simulation and experiment verification. The main research work of the dissertation is as follows:(1) The dissertation starts with the state-of-the-art research of SHM and damage detection and reviews of the recent development of parameter identification for time invariant and time-varying systems as well as nonlinear identification. The research background and importance values of the dissertation are clarified. The main contents and contribution of the dissertation are also summarized.(2) Two methods of extracting wavelet ridges are proposed. The one adopts the iterative algorithm based on phase information of wavelet coefficients. The singular value decomposition (SVD) technique is implemented to decrease the influence of noise. Another method extracts wavelet ridge based on the maximum modulus of wavelet coefficients. It uses a penalty function to smooth the discontinuous of wavelet ridges, so that the problem is transformed to an optimization problem. The wavelet ridges are finally extracted by using dynamic optimization method. Once the wavelet ridges are obatned, the instantaneous frequencies are identified from these wavelet ridges.(3) A method of identifying instantaneous frequencies of time-varying structures is presented based on the continuous wavelet transform. A new time-varying cable experiment is designed and relized. The linear and sinusoidal varying tensions are respectively applied to the cable, which results in the time-varying cable stiffness. The instantaneous frequencies are identified using the presented method and the identified results are compared to the natural frequencies of the same cable bearing different fixed tensions. It is demonstrated that the method is effectively and anti-noise to some extent.(4) A method of identifying physical parameters of time-varying structure based on discrete wavelet transform is presented. The time-varying parameters are expanded into approximate signal and detailed signal at multi-scale by discrete wavelet transformation. The time-varying physical parameters are eatracted only from the approximate signal with detailed signal being ignored. In such a way, the time-varying problem is transformed to the time invariant problem. The scale expand coefficients of low frequencies are identified using a least square method, and then the original time-varying parameters are reconstructed. The Tikhonov regularization is used to regularize the ill-posed problem of identification equation caused by noise. The effectiveness and accuracy of the proposed method are validated via a numerical simulation of a two-story frame structure with time-varying stiffness and damping. The results show that the presented algorithm can be used to identify effectively time-varying stiffness, and the identified damping is very sensitive to noise.(5) A procedure to identify the nonlinear structure system is presented based on wavelet transform. By using a concept of the skeleton curve of nonlinear structure, a nonlinear system is approximately equivalent to a time-varying system. According to the maximum value of modulus of wavelet coefficient, the wavelet ridges and wavelet skeleton are extracted, which is used to identify the instantaneous frequencies and amplitudes. Then the skeleton curve of a nonlinear structure can be obtained. In such a way, the structural nonlinearity can be identified accordingly. The effectiveness and accuracy of the presented method are addressed via a numerical simulation of a structure with a cube-varying nonlinear stiffness.