Structural identification via the inference of the stochastic volatility model conditioned on the time-dependent bridge deflection

Abstract

The time-dependent deflection data collected by a structural health monitoring (SHM) system contains information indicating the damage accumulation of prestressed concrete bridges (PSCBs). However, for this information to be used, the results must be fully translated into reliable metrics. Model-based structural identification (SI) targeting the time-dependent deflection of PSCBs is affected by time-dependent material behavior such as creep and shrinkage as well as the unknown path of structural deterioration, which should be considered in a stochastic volatility model (SVM). This paper presents an inference framework for an SVM conditioned on the time-dependent deflection of PSCBs. In this framework, the augmented state space includes the full ranges of the unobserved state variables affecting the time-dependent deflection of PSCBs, namely, structural rigidity, creep, shrinkage, prestress level and dead load level, along with the volatility parameters associated with the deterioration path of structural rigidity, which is modeled via the Wiener process. Exploiting the latent structure of the SVM, a cyclic Markov chain Monte Carlo (MCMC) sampler is proposed to draw samples from the joint posterior distribution of the unobserved state variables and volatility parameters. In an illustrative example, two-year continuous deflection monitoring data of an existing bridge are utilized as the target information for inference. The updated model can indicate the accumulated damage of the case bridge over the monitoring period. The proposed SI framework is able to support accurate probabilistic analysis of the time-dependent deflection of PSCB.