Research On The Modification Of Finite Element Model Based On Bayesian Improved Markov Chain Algorithm

Finite element has becoming an important technical means for structural design,optimization and damage identification.But because construction errors,physical parameters and boundary conditions in the finite element is difficult to accurately value,the analog value from the finite element model according to the design drawings and the measured value of the structure will be different,and thus it is necessary to converge the analog value with the measured value by modifying the finite element model.Deterministic model correction is difficult to consider the uncertainty factors of model parameters and test data.However Bayesian finite element model correction method not only can overcome this shortcoming,but also can use the probabilistic method to correct,and it has become the frontier research direction of the current finite element model correction.In order to solve the problems of large-scale bridge structure,Bayesian model correction is inefficient and difficult to converge when the dimension of the parameters to be corrected is difficult,the application of Bayesian model correction under high-dimensional correction parameters is needed to meet the practical large-scale engineering structure Model correction needs.In this paper,we introduce the delay-free adaptive variance(DRAM)Bayesian algorithm and the multi-chain difference(DREAM)Bayesian algorithm,and propose the Bayesian model correction method based on DRAM and DREAM by selecting the parameters to be modified and the objective function,and then,the applicability of two kinds of Bayesian finite element model correction methods is verified by numerical examples of simple beam,laboratory frame test and dynamic test of large bridge.The main task and result of the research are concluded as follows:(1)According to the principle of DRAM algorithm,by continuing to reject poor new samples in the new generation of each generationand,and in the iterative process,the variance of the new sample is adjusted adaptively to speed up the convergence rate,a Bayesian finite element model correction method based on DRAM algorithm is proposed.5 parameters simple support beam numerical example of model correction demonstrate that the corrected parameters were reduced from 33.3% of the initial error to the corrected 0.6%.In considering 10% of the test noise,the correction error of the correction parameter can be reduced to 10%.But in the calculation process find that DRAM algorithm to be corrected in the initial value of the parameters to be improper selection.(2)Based on DREAM algorithm: through a number of Markov chain synchronization operations,and use the information difference between each chain to significantly improve sampling efficiency,a multi-chain Bayesian finite element model correction method is proposed.10 parameters simple support beam numerical example show that the error of the parameter to be corrected is reduced from the initial 33.3% to the corrected 0.5%,and corrected frequency error to 0.1%,and Modal assurance criteria MAC is close to 1.The test noise is also a good tolerance.(3)In the laboratory build four-tier two-span steel frame model,and Select 11 parameters to be corrected according to the sensitivity selection method.The results of model correction using DRAM and DREAM algorithm are shown that the maximum error of the modified DRAM algorithm is 2.28% and the DREAM algorithm is 1.91%.The minimum modal guaranteed criterion DRAM algorithm is 0.990 and the DREAM algorithm is 0.998,which shows that the DREAM algorithm has better correction effect under the same conditions.(4)According to the structural modal parameters and the parameters to be corrected for the linear hypothesis,starting from the basic principle of DREAM algorithm,It is deduced that when the amount of modal information is less than the number of modified parameters,the two kinds of Bayesian model correction methods can not converge to the true value accurately.And then from the perspective of the use of information,respectively,to explore the use of frequency or vibration model for the effect of model correction.(5)Using the measured modal information of a large continuous rigid frame Bridge,the 18 parameters in the finite element model of the bridge are chosen as the parameters to be corrected.The finite element model is modified by DREAM-based finite element model correction method.The error between the measured frequency and the finite element calculation frequency is reduced to 2%,and the modal guarantee criterion MAC is increased to 0.998,which provides a reference finite element model for structural optimization and damage identification in the later stage of the bridge.