Modelling the spatial distribution of heavy vehicle loads on long-span bridges based on undirected graphical model

Vehicle load modelling is highly important for bridge design and safety evaluation. Conventional modelling approaches for vehicle loads have limitations in characterizing the spatial distribution of vehicles. This article presents a probabilistic method for modelling the spatial distribution of heavy vehicle loads on long-span bridges by using the undirected graphical model (UGM). The bridge deck is divided into grid cells, a UGM with each node corresponding to each cell is employed to model the location distribution of heavy vehicles, by which probabilities of heavy-vehicle distribution patterns can be efficiently calculated through applying the junction tree algorithm. A Bayesian inference method is also developed for updating the location model in consideration of the non-stationarity of traffic process. Gross weights of heavy vehicles are modelled by incorporating additional random variables to the vehicle-location UGM, corresponding probability distributions are constructed conditioned on ignoring correlation and considering correlation, respectively. Case studies using simulated data as well as field monitoring data have been conducted to examine the method. Compared with previous studies involving vehicle load modelling, the presented method can implement probabilistic analysis for all spatial distribution patterns of heavy vehicles on the entire bridge deck.