Finite Element Model Updating Method Based On Bayesian Theory

With the development of science and technology and the progress of human civilization,various engineering buildings emerge in endlessly.Influenced by natural and human factors,the structural performance will decrease with the passage of time.Therefore,it is necessary to monitor the health of the structure in service.In structural health monitoring,it is necessary to establish an accurate finite element model to reflect the actual characteristics of the structure.Influenced by factors such as meshing,boundary conditions and material physical parameter uncertainty,the finite element model is different from the real structure.The finite element model needs to be modified to make it as close as possible to the actual structure,so as to ensure the practical significance of structural dynamic analysis and monitoring.Due to the wide range of uncertainties in the actual structure,the traditional finite element model has limitations.Model updating and damage identification considering uncertainties have attracted the attention of researchers in recent years.Based on this,this thesis combines theoretical analysis,numerical calculation and experimental analysis to investigate the finite element model updating and model updating based damage identification.The main contents include:This thesis briefly introduces the Bayesian theory,the Metropolis-Hasting(MH)sampling algorithm in the Markov chain Monte Carlo method(MCMC),and the basic theory of finite element model updating based on the support vector machine(SVM)surrogate model.The maximum entropy value is introduced into the Bayesian method to derive the maximum value of the posterior probability density function of the parameter to be updated,which is the basis for the model updating.In view of the fact that the standard MCMC method is not easy to converge,and the rejection rate is high,the new bird nest update idea in the cuckoo algorithm is integrated into the MH sampling algorithm to obtain the improved MH sampling algorithm,so as to obtain the model updating method based on the improved MH sampling algorithm.A linear system with three degrees of freedom(DOFs)and a plane truss model are used to verify the effectiveness of the proposed algorithm.The results show that the Markov chain of the updated sample has better mixing performance,and the probability of stagnation is low,and the relative error of the parameters is less than 2%.The laboratory steel cantilever beam model is used for modal test,and the physical parameters of the cantilever beam are updated based on the improved model updating method of MH sampling algorithm to verify the validity and practicability of the method.Then the damage identification is studied based on the frequency method and the modified finite element model updating method,the single damage of location and extent,multiple damages of extent under different damage states are identified accurately,and the effectiveness and reliability of the method are verified,and the results show that the maximum identification error is less than 2%.