Bayesian Based Probabilistic Sampling And Sensitivity Analysis To Finite Element Model Updating Method

In vibration-based model updating, the finite element model is iteratively modified to ensure its vibration properties reproduce the measured counterparts in an optimal way. Due to the inevitable uncertainties in the modeling and measurements, model updating process is better to be tackled in a stochastic manner.First, this thesis introduces Bayes theory to the FE model updating. The standard MH method is utilized to gain the Markov chain of the parameters to be modified. The posterior probability density function of the parameters is derived based on the frequencies and modal shapes of the structure. Afterwards, the porposed MH-based model updating is applied to a simulated cantilever beam. The results demonstrate that the proposed method can identify the structural physical parameters when the amount of the parameters to be modified is small.Second, to raise the sampling convergence and the sample traversal, this thesis introduces the Delayed Rejection Adaptive Metropolis-Hastings(DRAM) method, in which the delayed order of the sample is set and the covariance of the sample is adjusted adaptively. Then the Bayes DRAM sampling based method is applied to the FE model updating of a practical cantilever beam. The proposed DRAM-based method can improve the convergence when a large number of parameters is modified.Third, to increase the efficiency of the Bayesian-based FE model updating. The thesis derives the sensitivity matrix of the posterior probability density function of the modifying parameters, based on the sensitivity matrix of the frequencies and modal shapes with respect to the modifying parameters. The results of the cantilever beam test verify that the Bayes sensitivity based FE model updating method can efficiently identify the structural physical parameters, i.e this method can significantly improve the efficiency of the FE model updating.Additionally, it's known that the local damage of a structure reduces the stiffness of a structure. According to the change of the stiffness before and after damage, the K1/K2 method, the diagram multiplication method and the matrix displacement method are used to estimate the equivalent stiffness reduction. This investigation provide a useful tool for practical damage identification.