A Fast Bayesian Approach For Modal Parameter Identification And Model Updating Of Bridge Engineering

Modal analysis and model updating are viewed as foundations in structural health monitoring,catastrophic disaster analysis and safety assessment of bridge engineering.Over the past decades,Bayesian analysis has attracted widespread attention in modal analysis and model updating due to its strong capability in uncertainty quantification.The thesis is devoted to applying Bayesian analysis in operational modal analysis and model updating for bridge engineering 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,a two-stage fast Bayesian spectral density approach(BSDA)will be adopted for operational modal analysis of bridge engineering.Then the identified dynamic properties(frequency and mode shape)and the measured static displacements will be utilized for model updating within the framework of Bayesian analysis.The posterior distribution of the updated parameters can be solved by Transitional Markov Chain Monte Carlo(TMCMC).To address the computing inefficiency of Bayesian model updating with stochastic sampling,the Kriging surrogate model is adopted to avoid running finite element analysis software repeatedly.The results corresponding to different measured data and the effects of parameter selection on the model updating are investigated.The main contribution and conclusion of this thesis are outlined as follows:1.The Bayesian operational modal analysis is a promising candidate for ambient modal analysis since it presents a rigorous way for deriving the optimal modal properties and their associated uncertainties.It has been proved that the interaction between spectrum variables(e.g.,frequency,damping ratio as well as the magnitude of modal excitation and prediction error)and spatial variables(e.g.,mode shape components)can be decoupled completely by analyzing the statistics of auto-power spectral density and cross-power spectral density.Based on the variable separation technique,a two-stage fast Bayesian spectral density approach(BSDA)could be adopted for operational modal analysis.2.The feasibility and efficiency of the two-stage fast Bayesian spectral density approach are verified by a simply supported beam and two bridges under ambient vibration.The spectrum variables and their associated uncertainties can be identified in the first stage based on the statistical properties of the trace of the spectral density matrix,while the spatial variables and their uncertainties can be extracted instantaneously in the second stage by using the statistical properties of the power spectral density matrix.Results indicate that the proposed method can achieve satisfactory results and it can resolve the difficulties of computational inefficiency and ill-conditioning of conventional BSDA.3.In the context of Bayesian model updating,the likelihood function is derived analytically based on the statistical relationship among the model response(frequencies,mode shapes,and static displacements)containing the parameters to be updated and the modal parameters identified from a two-stage fast BSDA as well as the measured static displacements.As a result,the posterior distributions of the updated parameters given different kinds of measurements are formulated by incorporating the prior information and the likelihood function.The high dimensional posterior PDF can be effectively sampled by using TMCMC,while the Kriging surrogate model is used as surrogate model to address the time-consuming issue due to posterior sampling.As a result,the most probable model parameters as well as their uncertainties of the updated parameters can be achieved rapidly.4.The accuracy and efficiency are verified by a numerical example,a simply supported beam and a bridge subjected to ambient vibration.The model updating results driven by dynamic properties,static displacements,or the combination of static displacements and dynamic properties are investigated in detail.The variability of updated model parameters corresponding to static and dynamic measurements are discussed,which clearly show that the combination of dynamic and static information can result in smaller coefficients of variances of the updated parameters.In addition,model updating with different parameter clusters is also conducted,which show that parameter selection can exert significant effects on the results and it is still an important problem worth of further study in the future.