Perturbation Analysis And Substructure Technique Based Finite Element Model Updating Method

In the past few years, vibration-based finite element model updating method havebeing rapidly developed and applied to damage detection of structure. Due to thecomplexity and large size of civil structures, the measurement of modal data and finiteenement modeling are inevitably mixed with random errors, thus stochastic method isoften used in model updating process. To improve the efficiency of model updatingprocess, substructure technique is introduced in this thesis. Considering the uncertainty,stochastic finite element model updating approach is applied to estimate the statisticalinformation of elemental stiffness parameter.Firstly, the basic theory of perturbation method and the substructure-based modelupdating is introduced. They are the foundation of the substructure-based stochatisticmodel updating, and will be used in the following derivation.Secondly, the perturbation method considering uncertainty of finite element modeland experimental measurement is derived in the third and the fourth part. The proposedmethod is realized on Matlab platform, and is verified by the numerical analysis of athree-span frame and the Guangzhou television tower. For comparison, the popularlyused Monte Carlo simulation technique and the traditional perturbation method of globalstructure are also employed to verify the reliability and calculation efficiency of theproposed method.Both the two numerical example proves that the substructure-based perturbationmethod can calculate the statistical results of the elemental stiffness parametersaccurately and efficiently. In particular, when the proposed method is applied to theGuangzhou television tower to calculate the statistical results of the elemental stiffnessparameters, the time caused by the proposed method is about one thirds of the traditionalglobal perturbation method. Finally, the proposed method is verified by a laboratory steel frame in this thesis. Acut is introduced to simulate the structural damage. The frame structure is analyzed by theproposed method and global perturbation method, and the results of the three methodsmatch to each other very well. This again proves that the proposed substructure-methodstochastic finite element model updating is effective and efficient to be applied to thecivil structures.