Structural Finite Element Model Updating Based On Probability Statistics

In order to make the finite element model reflect the actual dynamic characteristics of the structure as much as possible,the influence of uncertain factors should be considered in the process of model updating.The theory of probability and statistics is applied to deal with uncertainty in the the model updating problem,which can improve the reliability and stability of the results of model updating.At the same time,model updating requires a lot of iteratations in solving the inverse problem,so it is necessary to construct a mathematical surrogate model of the finite element model to reduce the computational effort.The main contents are as follows:(1)In order to solve the problems of two-step updating and multi-objective function updating in the process of stochastic model updating,a stochastic finite element model updating method based on Cokriging model and single objective function was studied.Firstly,the updated parameters were used as the input of the Cokriging model,and the frequency and mode shapes calculated by the finite element model were used as the output of the Cokriging model to build the surrogate model.Then,a single objective function is constructed to measure the difference between the probability distributions of the two samples.Finally,Coyote Optimization Algorithm(COA)was used to minimize the objective function and directly solve the mean and standard deviation of the parameters.During each iteration,parameter samples were used to calculate the degree of uncertainty of the finite element model response through the Cokriging model.The effectiveness of the proposed method is verified by using a two-dimensional truss structure and a three-dimensional truss structure,and is compared with the method by the multi-objective function.The results show that the complicated process of two-step solving the uncertain parameters is simplified,and an effective solution to the problem of each sub-objective function constraining each other in the process of multi-objective optimization is provided and the computational efficiency is also improved.(2)Aiming at the problem that the standard Markov Chain Monte Carlo(MCMC)sampling algorithm is not easy to converge and has a high rejection rate when the parameter dimension is high to be updated,a updated method based on the optimized of Kriging model and the improved MCMC sampling algorithm was studied.Firstly,the parameters to be updated were used as the input of the Kriging model.Since the strain mode has the mode shapes that can represent the local part of the structure and the global frequency information of the structure,the strain mode was used as the output to establish the Kriging model,and the correlation coefficient of the Kriging model was determined by the bat algorithm.Then,the maximum entropy Bayesian method is used to estimate the posterior probability density function of the parameters,and the Metropolis-Hasting(MH)sampling algorithm is incorporated into the flower pollination algorithm to improve the local and global optimization capabilities.Finally,numerical examples of two-dimensional truss structure and three-dimensional truss structure as well as cantilever beam structure were used to verify the proposed model updating method,and the results are compared with those by the standard MCMC sampling algorithm.The results show that the updated Markov chains are able to converge quickly and the sample acceptance rate is high,and the proposed method is robust to random noise to some extent.