Bayesian Identification Of Structural Stiffness Using Modal Data

Numerical simulation is widely used in Mechanical Engineering, for instance evaluation of assembly state of structures, prediction of machine error due to vibration and fatigue damage detection. However, the predicted responses of numerical model can hardly agree with those of actual structure under test, which is due to the unknown model parameters(such as material properties, interfaces stiffness) and the presence of modeling error. Therefore, the model updating is developed, whose aim is to obtain the updated numerical model with high reliability and high precision through the identification of model parameters.In the present work, the stiffness parameter is chosen as identification variable,structural modal data(natural frequencies and mode shapes) are used for parameter identification. A linear regression model of unknown stiffness parameters is established based on the dynamic characteristic equation, further the identification of those stiffness parameters is tackled within the Bayesian framework as the modal data is corrupted by noises and the model used for identification is uncertain. The main work conducted in this thesis consists of three parts explained in what follows.(1) A Bayesian identification framework for structural stiffness parameter is established, Markov Chain Monte Carlo method is employed to sample the posterior probability distribution function of unknown parameters.(2) The Lasso model is utilized for sparse modeling of structural stiffness considering the fact that structural damage usually happens at local points, a Markov Chain Monte Carlo algorithm is developed for the use of Bayesian –Lasso learning.The accuracy of structural damage identification is definitely enhanced in comparison with the case without use of the Lasso model.(3) Full modal shape data are hardly measured. The modal shapes are hence seen as hidden variables, an expectation-maximization(EM) method is proposed for the identification of stiffness parameters using incomplete modal data. Moreover, Gaussrandom field theory is used to model the priori information of stiffness parameters,the characteristic parameters of the random field are determined using multivariate kernel density estimation and maximum likelihood estimation, finally a Bayesian-EM algorithm is deduced by fusing physical information of stiffness parameters.The proposed methods are validated through numerical examples. However, the robustness and accuracy of the developed identification algorithm need to be improved especially when modal data for identification are heavily insufficient.