Development of Bayesian structural damage detection methodologies utilizing advanced Monte Carlo simulation

Abstract

This thesis reports the three stages in developing theoretically rigorous, efficient and reliable structural damage detection methods for civil engineering structures using measured vibration data from field tests. It is clear that excitation forces are extremely difficult to measure in field tests. To overcome this difficulty, natural frequencies and mode shapes are generally adopted for structural model updating and damage detection without the knowledge of excitation forces. In the proposed method, the modal parameters of the target structure are identified through ambient tests following the fast Bayesian fast Fourier transform (FFT) modal identification method in conjunction with the least square method for assembling mode shapes from multiple setups. The development of the proposed structural damage detection method involved three stages. Each stage overcomes some key difficulties of the previous stage. In the first stage, a novel substructure based damage detection method was developed by integrating with Bayesian model updating. The basic idea was to compare the posterior probability density functions (PDFs) of the structure’s stiffness parameters in the undamaged and possibly damaged states. The posterior PDF of the uncertain parameters was approximated by the Gaussian PDF. The method was verified using impact hammer test data from a transmission tower. The method is successful when the uncertainty of the model updating problem is small and there is an unique solution in parameter space of interest. However, estimation of the uncertainties associated with the model updating results was misleading when this problem became unidentifiable. To overcome this difficulty, in the second stage, a new formulation of the posterior PDF of the uncertain parameters was derived and Markov chain Monte Carlo simulation (MCMCS) was performed to sample a set of models in high probability regions for approximating the posterior PDF. The sampling process was divided into multiple levels. At each level, bridge PDFs, which finally converged to the posterior PDF, were constructed. A novel stopping criterion for the MCMCS algorithm was proposed from the insight of the derivation of the posterior PDF. This stopping criterion is crucial for the MCMCS algorithm to calculate the posterior uncertainties and the probability of damage. The probability of damage was calculated based on the posterior PDFs of stiffness parameters for the undamaged and possibly damaged structure. Based on the samples from MCMCS, a new formulation was derived to approximate the probability of a model class for Bayesian model choice. The MCMCS-based model updating was first illustrated using ambient vibration data of a relatively simple shear building. The MCMCS-based Bayesian structural damage detection was then verified by ambient vibration data from a relatively complex steel frame. Finally, the proposed method was used for structural model updating and Bayesian model choice of the coupled slab system of an existing building based on the ambient vibration data measured from the field test. The experimental verification results were very encouraging, demonstrating that the MCMCS-based method could handle uncertainty problems even in unidentifiable cases. One shortcoming of the MCMCS is that the performance and convergence of the sampling process was heavily dependent on an algorithmic parameter (it controls the change in variance of the bridge PDF at each sampling level), the value of which needs to be decided based on experience. The adaptive sequential Monte Carlo simulation (ASMCS) method was developed to resolve this shortcoming. Based on the idea of backward kernel, a new formulation was developed. This formulation makes use of the physical process of the sampling in multiple levels and the optimal situation in which the importance density equals to the bridge PDF. A new adaptive sampling scheme by using the importance weights was proposed to concentrate the samples in the important region of the posterior PDF. The convergence criterion was naturally obtained from ASMCS. The detailed procedures of this method was illustrated experimentally using data from a relatively simple shear building, and the ASMCS-based structural damage detection was then verified using measurements from a scaled transmission tower.

Date of Award	2 Oct 2015
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Heung Fai LAM (Supervisor)