Frequency Response Function-based Structural Finite Element Model Updating Utilizing Bayesian Approach:Formulation And Experimental Verification

Over the past years,finite element model updating based on frequency response function(FRF)has been widely studied by a number of researchers.Unfortunately,most of them are restricted to treating the deterministic case,which can not accommodate the influences of the multiple uncertainties.In this regard,this thesis is devoted to studying frequency response function-based model updating accommodating multiple uncertainties under the support of the National Science Foundation of China entitled“Uncertainty Quantification and Propagation Mechanism for Frequency Response Function-based Structural System Identification”.In this thesis,the frequency response function-based structural finite element model updating procedure utilizing Bayesian theory is formulated,and the posterior uncertainty of the updated parameters are solved by transitional Markov chain Monte Carlo(TMCMC)so that both the most probable values and their posterior uncertainties are obtained simultaneously.To address the computational inefficiency of the problem considered,this paper proposes a new fast numerical solution by incorporating the concepts of vectorization and parallel computation.As a result,the efficiency of the model updating procedure is greatly improved.Finally,the efficiency and accuracy of the proposed method are verified by a numerical example and an experimental study.The main contribution and conclusion of this thesis are outlined as follows:1.Based on the probabilistic model of frequency response function,the statistical relationship among the theoretical model containing the parameters to be updated and the measurements are established,then the likelihood function is formulated.Based on the framework of Bayesian system identification,an objective function is formulated by incorporating the prior information of the updated parameters and the likelihood function.The objective function can transfer the problem of model updating into an optimization problem.Then TMCMC algorithm can be used to solve this optimization problem by obtained the most probable values as well as their uncertainties.2.When using TMCMC for optimization,one has to repeatedly resort to calculating the objective function corresponding to different samples.For each time of calculating the objective function,one has to implement a number of loop operations whose number is closely dependent on frequency points andmeasurements.The computational cost will increase significantly with the number of frequency points and the number of measurements.To address the problem of computational inefficiency of the objective function,the concept of vectorization is adopted in this thesis to analytically derive the vectorized objective function so as to avoid calculating the objective function using time-consuming loop operations.3.Another critical issue of solving the Bayesian model updating problem lies in the large number of samples generated in implementing TMCMC.To improve the efficiency of Bayesian updating,parallel TMCMC strategy is proposed.By employing the “divide and conquer” strategy,this study makes full use of the parallel computation capacity of different cores of CPU and the distributed computation capacity of a number of CPUs of different computers,the objective function for different set of samples can be calculated simultaneously without queuing too long for different samples.Therefore,the computational efficiency of the proposed method can be improved greatly by the parallel TMCMC.4.Based on the responses of a numerical example and an experimental study,the accuracy and robustness of the proposed model updating methodology are validated.Results show that,by comparing with the conventional least square method,the method proposed in this study can obtain more satisfactory results.Furthermore,the method proposed in this study can quantify the posteriori uncertainty of updated parameters.Guaranteeing the accuracy of the updated results,the fast numerical solution proposed in this study can greatly improve the computational efficiency by saving the computation cost up to more than 20 times.Through parametric analysis,one can figure out that the uncertainty of stiffness and mass parameters decreases with the increase of the length of sampling time,bandwidth and the number of samples.