Research On Parameterized Finite Element Updating Method Based On Bayesian Evidence Inference

After several decades of development,the finite element method has been widely used in engineering structure.However,due to various theoretical assumptions,boundary condition approximation and geometrical material characteristic parameters and other uncertain factors,the finite element model has been used to calculate the response.There is a certain deviation between the measured responses.The finite element model updating technique based on the experimental modal analysis is an effective means to improve the accuracy of the finite element model.The method uses the measured low-order modal parameters to modify the structural finite element model,and obtains the inverse coincidence of the modified finite element model,and as a basis for structural vibration control and health monitoring and other areas of research.However,in the practical application,the overly complicated finite element model is not conducive to the model revision.Therefore,in order to effectively control the complexity of the finite element model to be modified,this paper,under the support of the National Natural Science Foundation of China(NO:51208390)in the framework of statistical and information theory,a parametric finite element modified model selection method based on Bayesian evidence inference and information gain is developed to solve the problem of parameter selection in the model of finite element model.The main research contents are as follows:(1)A method of selecting the finite element model based on Bayesian theory is proposed.By introducing information divergence index,quantitative information is extracted from the measured data.The finite element model is used to modify the model.The complexity of the parameters to be punished,the complexity of the model parameters and the complexity of its information to get a balance;(2)Based on the Metropolis Hasting sampling algorithm in the Monte Carlo Markov chain numerical simulation method,a high-dimensional multivalued numerical integration method for calculating the posterior distribution of the parameters to be corrected is developed,and the mathematical expectation The model data coincidence degree and the information gain,so as to realize the evidence factor calculation of different class models;(3)Based on the numerical simulation and laboratory model test of the finite element model of the two-layer bolted steel frame with beam-column and column-foundation semi-rigid connection,the corrective model of the modified finite element model proposed in this paper is correct The results show that the proposed method can effectively balance the complexity of the finite element model modeling parameters and its corresponding information theory,so that the obtained finite element model can satisfy the model and the measured data and the degree of parameterization is relative simple.