A Bayesian Probabilistic Approach To Structural Parameter Identification And Application

Under the influence of uncertain factors, such as nonuniformity in material properties, variability in complex constitutive behavior and randomicity in the excitations, uncertainty becomes the essential characteristic of measurement data and structural analysis model, which makes structural physical parameter identification an indeterminate problem. So a new approach capable of dealing with this problem effectively must be developed in order to identify structural physical parameters in a more appropriate way on the basis of classical and determinate identification of structural physical parameter. This thesis establishes a Bayesian probabilistic framework for physical parameter identification that allows for explicit quantification of the uncertainties associated with modeling a system using the Bayesian statistics theory and the Markov Chain Monte Carlo (MCMC) methods, and involves application of this probabilistic framework for damage detection and assessment of civil structures. The main works of this paper are summarized as below:1. A Bayesian probabilistic approach to structural physical parameter identification using the modal parameters of dominant modesThe linear regression models of the physical parameters of structures whose variables are the modal parameters are inferred from the dynamic characteristic equations of structures. Based on these models, the posterior probability density function (PDF) of these physical parameters can be obtained with the Bayesian statistics theory, from which the marginal PDF and optimal estimate of the physical parameters also can be obtained using the Markov Chain Monte Carlo methods. The theoretical analysis and numerical simulations of 3DOF shear building indicate that the approach presented can not only give the optimal estimate of the physical parameters but also get the associated plausibility of updated parameters.2. A Bayesian probabilistic approach to structural physical parameter identification using the recorded structural responsesThe linear regression models of the physical parameters of structures whose variables are the approximation and details of loads and structural responses obtained from multilevel wavelet decompositions are inferred from the multiscale dynamic equations of linear structural systems which are established from differential equations of motion in terms of wavelet multiresolution analysis. Based on these models, the posterior probability density function (PDF) of these physical parameters can be obtained with the Bayesian statistics theory, from which the marginal PDF and optimal estimate of the physical parameters also can be obtained using the Gibbs sampler (GS), a special case of Markov Chain Monte Carlo methods. The theoretical analysis and numerical simulations of 4DOF shear building under earthquake and ambient vibration excitation indicate that the approach presented can not only give the marginal PDF of the physical parameters but also get accuracy of identification satisfying engineering needs under noise.3. A probabilistic method to structural damage detection and assessmentStiffness parameters are identified using the Bayesian probabilistic structural physical parameter identification approach with measured structural response from the undamaged system and then from the possibly damaged system. And, these data are used to calculate the ratios of the identified stiffness parameters of the damaged system and the corresponding values of the undamaged system and the probability that stiffness parameter in any substructure exceeds any specified threshold expressed by a fraction of stiffness loss, which are used to detect and locate damage in structures and quantitatively assess its severity. This presented method is applied to analyze a 4-DOF linear shear building model and the Phaseâ… benchmark study sponsored by the IASC-ASCE Task Group on Structural Health Monitoring, and the results indicates that it successfully identifies the location and extent of damage in structures.