Structural Damage Identification And Reliability Evaluation Based On Grey Theory And Bayesian Analysis

Damage identification and safety evaluation have been hot research topics in the realm of health monitoring of civil structures.The relevant problems should be solved within a probability statistics framework due to uncertainties such as geometric variability,material discreteness,unclear connection and boundary conditions and measurement noises.This thesis first introduced random interval grey numbers into the Bayesian damage identification procedure.A new method has been developed incorporating approximate Bayesian computation with an improved population Monte Carlo sampling algorithm and stochastic response surfaces.Meanwhile,the wavelet packet transform algorithm was combined with grey relational analysis in order to propose a relative wavelet packet energy curvature assurance coefficient for damage identification.Finally,based on the relationship between wavelet packet energy and structural damage severity,an equivalent model,together with a grey prediction model,was established to evaluate and then predict the system reliability.The safety evaluation was achieved according to the reliability predictions.The main contents and research fruits are described as follows.Firstly,in order to improve the rationality of parameter prior distribution selection in Bayesian inference,random interval grey numbers were used to reflect parameter uncertainties.By this means,the drawback of inadequate statistical information in reality could be overcome.Meanwhile,approximate Bayesian computation was adopted to avoid the solution of likelihood functions.The classic population Monte Carlo sampling algorithm was then improved to prevent the phenomenon of unsatisfactory sampling ergodicity of Markov chain Monte Carlo sampling algorithms.Stochastic response surfaces were used to replace finite element models for the purpose of fast computing random responses corresponding to parameter samples.The feasibility of the proposed method has been verified against both numerical and experimental concrete beams.It was found that the combination of the three different algorithms greatly improved the computational efficiency of a Bayesian updating process.Moreover,the proposed method effectively enhanced the practicability of Bayesian inference in damage identification.Secondly,a damage identification method has been investigated based on changes in the wavelet packet energy of a structure.The acceleration time-history data at each measurement point of the structure before and after damage were collected and then decomposed using wavelet packet decomposition.The relative wavelet packet energy vector with respect to each vibrational mode were obtained and then processed by grey relational analysis in order to establish a new index called as a relative wavelet packet energy curvature assurance coefficient.The feasibility of the proposed index has been verified against both numerical and experimental I-beams.The damage identification results were compared with those predicted by the relative wavelet packet energy difference.Lastly,an invariant-dimension-updating grey prediction model,IDUGM(1,1),has been established to simulate and predict the time-variant reliability of an experimental concrete beam.Based on the relationship between total wavelet packet energy and damage severity,an equivalent model was employed to replace the complex reliability model.After that,the equivalent model was incorporated with IDUGM(1,1)and approximate Bayesian computation to propose a time-variant reliability prediction method.The method worked under the specific failure mode of a structure system.Its feasibility has been validated using a numerical seven-bar truss structure.