Finite Element Model Updating Method Based On Bayesian Theory And Subset Simulation Optimization And Its Applications

Establishment of accurate finite element model is the basis of structural dynamic response prediction,damage identification,health monitoring and performance evaluation.Since the existence of test errors and model errors,it is necessary to modify the finite element model based on the measured data that conforms to the status quo of the structure.Because of the uncertainty of prediction errors,especially the measured data are used by the environmental vibration test of structures,it is particularly important to quantify the uncertainty of model parameters for its lower signal-to-noise ratio than excitation test.Bayesian model updating method not only get the optimal value of model parameters,but also obtain the quantitative uncertainty of model parameters.However,Bayesian model updating method based on numerical optimization is not suitable to solve multi-peak,discontinuous and non-linear problems.The values of updated model parameters are often local optimization solutions.Although bayesian model updating method based on stochastic optimization method has advantages in global optimization,because of the large amount of calculation,and most of the methods can not be effectively used to modify the refined finite element model of the actual structure.Therefore,the finite element model updating method based on environmental vibration testing and Bayesian theory were studied,which proposes an efficient method to obtain the global optimal solution,which is applied to automatically update the refined finite element model of practical engineering.The main contents and the conclusions of this paper are as follows:(1)A finite element model updating method based on Bayesian theory and subset simulation optimization algorithm is proposed.The idea of the method:The most probable values and variation coefficients of structural modal parameters were obtained from environmental vibration test data by the Bayesian modal parameter identification methods.The objective function derived using Bayesian theory by subset simulation optimization algorithm with high efficiency of sampling.The most probable values and coefficients of variation of the updated parameters are obtained.The efficient subset simulation optimization algorithm is extended to the global optimal solution of model parameters.The coefficient of variation is calculated by using the most probable value of the model parameters.The proposed method is applied to the numerical model,and the updated results are in good agreement with the numerical solutions,which verifies the correctness of the proposed method.Compared with the model updating method based on Bayesian theory and MCMC stochastic optimization,the proposed method guarantees global optimization solutions and is more efficient in sampling(2)The two-degree-of-freedom numerical model is used to analyze the influence of the proposed method for the parameters of the algorithm,such as the number of samples on layers,the probability of layers and the termination criterion.The results show that:The number of samples of layers has little effect on the convergence rate,but it affects the coverage of samples in the design space.The smaller the interlayer probability is,the faster the convergence rate is.However,when the amount of calculation is acceptable,the adaptive interlayer probability is suggested to improve the reliability of the optimization results.The statistical characteristics of the modified parameters are very important in model updating.So the standard deviation of the simulation samples of layers should be used as the control condition of the termination criterion under the agreed accuracy.The proposed method is applied to modify the finite element model of a four-story frame structure with known test data of simulated environmental vibration.The relationship between the measured information and the corrected parameters,and the influence of the errors between the measured points and the corrected points for the updated results are analyzed.The results show that:It is impossible to update the model that the measured information is too little or that the measured information and the model updated parameters do not correspond.The accuracy of the updated parameters decreases with the increase of the correction point and the point of testing error.(3)The proposed method is applied to refined finite element model updating of a high-rise masonry structure based on environmental vibration test data.Firstly,the environmental vibration test of the masonry structure is carried out,and the modal parameters of the structure are identified;Secondly,the refined finite element model is established by SAP2000.Finally,the modal information of the structure identified as the basis of the modified value.By using the proposed method and based on the interaction between software,the proposed method automatically update the finite element model of the structure.The uncertainties of the model parameters and their quantifications are obtained,which provide a reference model for the subsequent response prediction and performance evaluation of the masonry structure.