An efficient adaptive sequential Monte Carlo method for Bayesian model updating and damage detection

摘要

This paper reports the development of an efficient adaptive sequential Monte Carlo (ASMC) method for Bayesian model updating and damage detection of a structural system using measured vibration data. The proposed method can efficiently tackle two challenging problems commonly encountered in Bayesian inference, namely, identifying the posterior probability density function (PDF) in a complicated parameter space and evaluating the high-dimensional integral. The posterior PDF is identified through sampling from a series of bridge PDFs. A new formulation based on the idea of a backward kernel is proposed. This formulation makes use of the process of sampling at multiple levels and the optimal situation in which the importance density equals the bridge PDF. A new adaptive sampling scheme using importance weights is proposed to generate samples in the important region of the posterior PDF. Rather than directly controlling the uncertainty measure of the bridge PDF in each level, the ASMC method allows the important regions of these PDFs to change adaptively. The model updating methodology was experimentally verified using a four-floor shear-building model. The effects of different amounts of measured information on the uncertainty of the model updating results were studied. The application of the proposed methodology in structural damage detection was experimentally investigated using a scaled transmission tower model. The probability of damage was calculated using the posterior PDF constructed by the ASMC method. The structural damage was clearly identified from the probability of damage in the case studies.