Optimal performance of civil infrastructure is an important aspect of liveable cities. A judicious combination of physics-based models with monitoring data in a validated methodology that accounts for uncertainties is explored in this paper. This methodology must support asset managers when they need to extrapolate current performance to meet future needs. Three model-based data-interpretation methodologies, residual minimization, Bayesian model updating and error-domain model falsification (EDMF), are compared according to their ability to provide accurate interpretations of monitoring data. These comparisons are made using a full-scale case study, a steel-concrete composite bridge in USA. Validation of data interpretation is carried out using cross-validation (leave-one-out and hold-out). A joint-entropy metric is used to evaluate the extent to which the data that is used for validation contains information that is independent of data used for interpreting structural behaviour. Once accurately updated and validated knowledge of structural behaviour is available, it is employed to make predictions of remaining fatigue-life of the bridge. Validated identification of structural behaviour helps ensure accurate predictions of capacity of bridges beyond their design lives. EDMF and a modified form of Bayesian model updating are analytically and numerically equivalent, while EDMF has several practical advantages. Both methods provide accurate identification and safe estimations of the remaining fatigue life of the bridge. Such enhanced understanding of structural behaviour leads to appropriate decisions regarding civil infrastructure assets.