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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.
Bias Identification Approaches for Model Updating of Simulation-based Digital Twins of Bridges
(2024)
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.
The creation and use of Digital Twins of existing structures, such as bridges, implies precise digital replicas that accurately mirror their physical counterparts. Ensuring the trustworthiness of Digital Twins and facilitating informed decision-making necessitates a robust approach to Uncertainty Quantification (UQ). A suitable model-updating scheme is key in preserving the quality and robustness of simulation-based Digital Twins. Model bias, stemming from discrepancies between computational models and real-world systems, poses a significant challenge in achieving this goal. This study delves into the challenges posed by model bias within Bayesian updating of Digital Twins of bridges. Two alternative model bias identification methods —a modularized version of Kennedy and O’Hagan’s approach and another one based on Orthogonal Gaussian Processes — are evaluated in comparison with the classical Bayesian inference framework. A key innovation lies in the modification of the aforementioned approaches to incorporate additional information into the Digital Twin framework via the bias term. This enables the extension of the model non-intrusively, leveraging large pools of data inherent in Digital Twins. The study showcases the potential of this approach to correct predictions, quantify uncertainties, and enhance the system with previously untapped information. This underscores the importance of everaging available data within Digital Twins to identify deficiencies and guide potential future model improvements.
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 tructural 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.
Die Digitalisierung hat sich in vielen Bereichen des Bauwesens durchgesetzt. So sind Planung und Entwurf selbst kleinerer Bauvorhaben heute vollständig digitalisiert. Auch das Monitoring von Bestandsbauwerken ist ohne digitale Datenerfassung, -verarbeitung und -speicherung nicht denkbar. Trotzdem sind Fragen hinsichtlich der strukturierten Speicherung und künftigen Nutzung von Daten noch offen. Einige Aspekte der Digitalisierung wurden im Rahmen des 63. DAfStb-Forschungskolloquiums (Tagungsband: DOI 10.26272/opus4-61338) in Vorträgen und Veröffentlichungen aufgegriffen und werden im Folgenden zusammengefasst.
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.
In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat- FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed.
With the rapid adoption of Digital Twins in recent years, simulation models designed to replicate real-world physical systems have become increasingly common. To achieve accurate representations, it is typically necessary to update model parameters based on observations collected from sensors or measurements of the physical asset. However, no model can fully capture the infinitely complex nature of reality. As a result, quantifying the uncertainty in model predictions is essential for reliable decision-making. Bayesian updating frameworks provide an appealing approach for parameter calibration, inherently accounting for such uncertainties. One often-overlooked source of error is model form uncertainty. This type of uncertainty arises from the fundamental discrepancies between the model and reality, stemming from the assumptions and simplifications made during model construction. Ignoring model form uncertainty can lead to overly confident predictions that fail to accurately reflect sensor observations. To address this, we propose an embedded model form uncertainty framework that attributes the model variability to a stochastic extension of the model's latent parameters. This approach enables the quantification of uncertainties that can be represented by a variation in the model parameters. Of particular interest are scenarios involving noisy observations or additional discrepancies that cannot be directly integrated into the model. By incorporating uncertainty through the parameters, this method not only quantifies uncertainty in predictions but also propagates model form uncertainty to other Quantities of Interest (QoI) that rely on the same model or its parameters. Consequently, QoI computations yield more reliable values, accounting for the potential uncertainties introduced by imperfect models during parameter updating. Moreover, this approach facilitates a more comprehensive statistical analysis of QoI distributions, offering deeper insights into the model's reliability and highlighting areas for potential improvement. By incorporating model form uncertainty, decision-makers can achieve a more robust and nuanced understanding of system behavior and prediction quality.
Die Brückeninfrastruktur in Deutschland und Europa steht aufgrund steigender Verkehrslasten und alternder Bauwerke vor erheblichen Herausforderungen.
Das DFG-Schwerpunktprogramm 2388 „Hundert plus – Verlängerung der Lebensdauer komplexer Baustrukturen durch intelligente Digitalisierung“ (SPP100+) strebt an, durch digitale Innovationen und prädiktive Instandhaltungsstrategien die Nutzungsdauer bestehender Brückenbauwerke zu verlängern.
Der vorliegende Beitrag fokussiert sich auf das SPP100+ zugehörige Cluster „Monitoring und Simulation“, das sieben Teilprojekte umfasst. Die Projekte entwickeln fortschrittliche Methoden zur Überwachung und Zustandsbewertung von Brücken mittels Digitaler Zwillinge, hochauflösender Sensortechnik und numerischer Simulationen. Innovative Ansätze wie nichtlineare Modellanpassungen, stochastische Methoden und künstliche Intelligenz ermöglichen eine präzise und frühzeitige Identifizierung potenzieller Schäden. Die Kombination aus kontinuierlichem Bauwerksmonitoring und effizienter Datenauswertung ist entscheidend für die langfristige Sicherheit und Langlebigkeit bestehender Brücken und trägt darüber hinaus zur Ressourcenschonung bei.
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.