Increasing demand for new infrastructure and ageing of existing infrastructure has made management of infrastructure a key challenge of this century. Replacement of all ageing civil infrastructure is economically and environmentally unsustainable. Civil infrastructure elements possess reserve capacity beyond code requirements due to conservative construction and design practises. Monitoring and interpreting structural responses helps understand real structural behaviour and this leads to accurate quantification of reserve capacity. To assess reserve capacity, predictions of structural behaviour are required under conditions that differ from those present during monitoring. Such predictions are sensitive to the accuracy of data-interpretation. Error-domain model falsification (EDMF) is a probabilistic data-interpretation methodology that provides accurate interpretation of measurement data in the presence of uncertainties from sources such as modelling assumptions, environmental conditions and sensor noise. The major challenge associated with model-based data interpretation is the selection and exploration of multi-dimensional parameter spaces (model classes) for solutions using time-consuming physics-based models. Moreover, no research so far has evaluated compatibility of EDMF with other methods for data-interpretation. Addressing these challenges forms the primary objectives of this thesis. EDMF is analytically and numerically shown to be compatible with Bayesian model updating using a modified likelihood function. Data-interpretation of five full-scale case-studies demonstrates that EDMF has clear advantages over Bayesian model updating for engineering applications. A methodology for selecting appropriate parameters for identification (model-class selection) is presented in this thesis. Using this methodology, the engineer is able to reduce the size of the parameter space that needs to be explored using computationally expensive physics-based models. Surrogate models have often been used to replace physics-based models to explore more efficiently the parameter space. However, using surrogate models increases uncertainty and this leads to loss of precision in interpretation of measurement data. A multi-fidelity approach for EDMF is presented here, which successfully reduces computational cost without precision loss. Practical use of any data-interpretation methodology involves simultaneous requirements of accuracy, flexibility and transparency. Such characteristics favour ease of understanding and amenability to inevitable changes. Accuracy and precision of data interpretation using EDMF are evaluated using leave-one-out cross-validation. Moreover, EDMF, when utilised with grid sampling, has advantages for use in practise due to its ability to iteratively incorporate new information. Amenability for real-world applications is validated using five full-scale case studies. The primary conclusion of this thesis is that new methods for model-class selection and multi-fidelity modelling help improve the quality of data-interpretation. More generally, methodologies developed in this thesis facilitate efficient and accurate interpretation of measurement data to assist asset managers.