A Probability-Based Likelihood Function for Bayesian Updating of a Bridge Condition Deterioration Model

Abstract

To predict the future condition of a bridge, statistical models for the time-in-condition rating (TICR) can estimate the time that a bridge stays in a given condition and then predict the future condition of the bridge. However, existing research typically uses the probability density functions as the likelihood function when the TICR is estimated by Bayesian updating, in which the change in the condition rating (CR) between two consecutive inspections is assumed to occur at the later inspection, which ignores the uncertainty of the time of the condition change. This assumption will introduce an error, which is particularly significant when the two consecutive inspections are separated over a long time. In addition, a large amount of existing bridge inspection data in China has not been fully recorded; for instance, a lot of bridge inspection data only contains the CR of the bridge from the last inspection. Current research that is based on the TICR has difficulty using this incomplete data. To solve these difficulties, this paper proposes a probability-based likelihood function for the Bayesian updating of the TICR models, which could estimate the distribution of the TICR more accurately using fully recorded or single data. The accuracy of the proposed method is verified with numerical examples, and the results from different methods are discussed. Then, the effect of using complete and single data are examined. The proposed method is applied to the CR of the superstructures of reinforced concrete bridges in Beijing that uses the real inspection data, and the future deterioration risk is evaluated using the updated TICR models.