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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.
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.
Accurate and reliable assessment of transportation infrastructures (e.g. bridges) are crucial for ensuring public safety. Simulation-based engineering analyses can be used to assess and predict the health state of structures. Although some of the structural parameters necessary for such simulations cannot be directly measured, they can be inferred from Non-Destructive Testing data, in a typical inverse problem formulation. However, any prediction based on engineering models will never be an exact representation of reality, since many sources of uncertainties can be present: poor physical representation of the problem (model bias); measurement errors; uncertainty on inferred parameters; etc. Uncertainty quantification is, therefore, of utmost importance to ensure reliability of any decision based on the simulations.
This paper investigates the application of the Modular Bayesian framework to perform structural parameter calibration while estimating a function for the model bias. The data for tests comes from an experimental setup and is represented as a combination of a physics-based model, a model bias term and an additive measurement error (considered to be known). In this approach, the inference problem is divided into 3 modules: the first and the second estimate the optimal hyper-parameters of Gaussian Processes (GP) to replace the physics-based and the model bias term, respectively; the third computes the posterior distribution of the structural parameters of interest, taking into account the GPs from the previous modules. By computing a bias-correction function and calibrating the parameters, the modular framework aims at improving the accuracy of the predictions.