Open Access

Digitale Zwillinge bieten wertvolle Einblicke in das Verhalten von Bauwerken und ermöglichen eine fundierte Entscheidungsfindung. Durch den Einsatz von Simulationen, die auf physikalischen Gesetzen beruhen, ist es möglich, Vorhersagen über die Struktur auf der Grundlage zukünftiger oder hypothetischer Situationen zu treffen. Die Verwendung solcher Simulationen impliziert jedoch eine Reihe von Annahmen und Vereinfachungen, die unvermeidbare Fehler in die Vorhersagen einbringen. Die Quantifizierung dieser Unsicherheiten ist der Schlüssel für den Einsatz zuverlässiger digitaler Zwillinge von Brücken.

Simulation-based digital twins must provide accurate, robust, and reliable digital representations of their physical counterparts. Therefore, quantifying the uncertainty in their predictions plays a key role in making better-informed decisions that impact the actual system. The update of the simulation model based on data must then be carefully implemented. When applied to complex structures such as bridges, discrepancies between the computational model and the real system appear as model bias, which hinders the trustworthiness of the digital twin and increases its uncertainty. Classical Bayesian updating approaches aimed at inferring the model parameters often fail to compensate for such model bias, leading to overconfident and unreliable predictions. In this paper, two alternative model bias identification approaches are evaluated in the context of their applicability to digital twins of bridges. A modularized version of Kennedy and O'Hagan's approach and another one based on Orthogonal Gaussian Processes are compared with the classical Bayesian inference framework in a set of representative benchmarks. Additionally, two novel extensions are proposed for these models: the inclusion of noise-aware kernels and the introduction of additional variables not present in the computational model through the bias term. The integration of these approaches into the digital twin corrects the predictions, quantifies their uncertainty, estimates noise from unknown physical sources of error, and provides further insight into the system by including additional pre-existing information without modifying the computational model.

Simulation-based digital twins of bridges have the potential not only to serve as monitoring devices of the current state of the structure but also to generate new knowledge through physical predictions that allow for better-informed decision-making. For an accurate representation of the bridge, the underlying models must be tuned to reproduce the real system. Nevertheless, the necessary assumptions and simplifications in these models irremediably introduce discrepancies between measurements and model response. We will show that quantifying the extent of the uncertainties introduced through the models that lead to such discrepancies provides a better understanding of the real system, enhances the model updating process, and creates more robust and trustworthy digital twins. The inclusion of an explicit bias term will be applied to a representative demonstrator case based on the thermal response of the Nibelungenbrücke of Worms. The findings from this work are englobed in the initiative SPP 100+, whose main aim is the extension of the service life of structures, especially through the implementation of digital twins.

Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management.

Fiber optic sensors (FOS) are increasingly used for structural health monitoring of bridges, providing dense and distributed strain measurements. An especially relevant application is the detection and localization of tendon breaks, where not only the occurrence but also the depth of the damaged tendon must be identified. To explore this possibility, an experimental setup was established to reproduce the boundary and loading conditions of a bridge tendon, and FOS strain observations were collected during controlled failure events. A finite element (FE) model of this experiment was developed and is used here as a gray-box simulator. Its parameters are calibrated against the FOS data, and the resulting probabilistic characterization is transferred to more realistic models in which different tendon depths are simulated and compared to observed deformation fields. Because of the complexity of the tendon break phenomenon, model form uncertainty (MFU) plays a decisive role. Bayesian calibration is performed while explicitly accounting for MFU through an embedded representation in which a prescribed set of parameters captures the model–reality discrepancy. This formulation enables the quantified MFU to be consistently propagated to other models and quantities of interest. Due to the computational cost of FE simulations, Gaussian Process surrogates are employed, and their predictive uncertainty is incorporated into the calibration to ensure coherent uncertainty propagation. The calibration reveals that some observations cannot be represented by any admissible parameter values, indicating structural model inadequacies. To identify and characterize these, an influence analysis of the observations on the posterior distribution is carried out. The φ-divergence between posterior distributions with and without individual observations is evaluated to quantify their impact on the calibrated posterior. Furthermore, by examining the influence on the marginal posterior components within the embedded MFU formulation, it becomes possible to determine which observations drive the parameters associated with model discrepancy and which parameters are most affected, guiding model refinement and experimental design. Finally, when the calibrated parameters are transferred to alternative models, the separability of predictions for different tendon depths is analyzed. The overlap between predictive distributions is quantified to determine the minimum resolvable depth difference and regions of non-separability arising from MFU. This analysis defines the achievable resolution for tendon break localization and informs optimal sensor placement strategies under uncertainty.