Research On Finite Element Model Updating Method Based On Kriging Model

One of the main limitations of the model updating in engineering applications is computational efficiency.The surrogate model can accurately describe the complex implicit relationship between structural parameters and response through simple display function,then replace the complex and time-consuming finite element model for numerical analysis,and can be integrated with various optimization algorithms,which reduces the complexity of the problem,and improves the computational efficiency and accuracy.Therefore,the optimization method using the surrogate model has attracted much attention of researchers.Different from other surrogate models,Kriging model can not only give the estimate of unknown function,but also get the error estimate of the estimate.At present,most of the methods use frequency as the response of surrogate model.Compared with frequency,frequency response function(FRF)can provide more structural vibration information,but there are few applications in the surrogate model as response.In addition,the analysis data needed for model updating is mainly provided by the sensors arranged on the structure,and the sensor arrangement directly affects the results of model updating.Based on this,this thesis first studied the optimal sensor placement,and then the method based on Kriging model was used to modify the parameters and identify the damage of the structure.The main contents are as follows:Considering that the drawbacks of distance coefficient weighting correction method for Fisher information matrix in optimal sensor placement,the mode contribution and distance coefficient was used to modify the model error covariance in Fisher information matrix.Firstly,the relationship between Fisher information matrix and information entropy was illustrated;secondly,considering the impacts of model error on Fisher information matrix,Euclidean distance and mode contribution coefficient were used to modify the model error covariance matrix;thirdly,sensor placements were obtained by maximizing the determinant of the modified Fisher information matrix using forward sequential algorithm.According to three evaluation criterions,the efficiency of different modification methods was compared using a truss model.The results show that compared with the traditional Fisher criterion and the directly weighted modified Fisher information matrix,the method can obtain better evaluation values,and effectively avoid the aggregation of the sensor placements at the same time.To improve model updating efficiency,Kriging model was introduced into FRF-based model updating.The optimal excitation point was selected using modal participation criterion.The updating parameters were determined and initial sample points were chosen via design of experiment(DOE),and Kriging model was built using the corresponding acceleration FRFs.Then,Kriging model was improved via new sample points using mean square error(MSE)criterion,and was used to replace the finite element model to participate in optimization.Cuckoo algorithm was used to obtain the updating parameters,where the objective function with the minimum frequency response deviation was constructed.The method was applied to the model updating and damage identification of a plane truss structure,and the results were compared with those by the second-order response surface model(RSM)and the radial basis function model(RBF).The analysis results show that the method can improve the computational efficiency while satisfying the computational accuracy,and has less dependence on the number of sample points,errors of updating parameters are less than 0.2%.After updating,the curves of real and imaginary parts of acceleration FRF are in good agreement with the real ones.It also shows that single damage of location and extent,multiple damages of extent can be both accurately identified by this method;and the noise has a little influence on damage identification results,but the location of measurement points has some influence on it.