Load limits, which appear to be routinely exceeded by trucks, occasionally result in road bridge failures. Therefore, predicting failures is crucial for safeguarding road safety. Past studies have largely focused on forecasting bridge failure event probability using the reliability analysis method, whilst occasionally accounting for vehicular overloading effects. Only recently, a study has investigated design traffic overloading event frequency using generalised linear regression models (GLRMs), including a power component and negative binomial regressions (NBRs). However, as far as the authors know, artificial neural network models (ANNMs) have never been applied to this field. This paper is an attempt to fill in these gaps. First a frequency-based metric of traffic overloading was adopted as a driver of failure probability. Second, two alternative ‘frequency’ models were specified, calibrated, and validated. The former was based on a GLRM, the latter on ANNMs. Then, these models were compared using regression plots (RPs), measures of errors (MoEs) and the ratio between the number of observed vs predicted design load overcoming events to evaluate their performance. The models analysed more than 2 million weigh-in-motion (WIM) data records from a pilot station on a bridge on a heavily used ring road in Brescia (Italy). Results showed that ANNMs outperformed GLRMs. ANNMs have a higher correlation coefficient (between predicted and target frequencies), lower MoEs, and a closer-to-unity ratio (between predicted and target frequencies). These findings may increase prediction accuracy of design traffic overloading events and give road authorities more effective traffic management to protect bridges from load hazards.