Bayesian Bridge Weigh-in-Motion and Uncertainty Estimation

Abstract

Many researchers have developed bridge weigh-in-motion (BWIM) technology, mainly focusing on the representative value of the estimated axle weights. However, the estimation of the probabilistic distribution of axle weights is also important for understanding the ill conditioning of BWIM formulations and the uncertainty of estimation. Bayesian updating provides a coherent framework for assimilating data into models. Here, Bayesian bridge weigh-in-motion (BBWIM), which combines Bayesian updating and BWIM, is proposed. BBWIM can estimate not only the representative value of axle weights but also the uncertainty of the estimated value and the correlation among estimates. Uncertainties in estimated axle weight are quantitatively discussed with a simple two-axle problem. It is shown that the estimated weights of closely spaced axles have large uncertainty. BBWIM is applied to the measured data for an actual bridge. It is shown that additional information, in the form of a weak constraint on axle weight, namely, that closely spaced axles have similar weights, can reduce the uncertainty of estimated axle weights.