Ensuring bridges' structural integrity is crucial for safety and resource optimization. Accelerometers offer a wealth of structural data easily collected to capture the structural dynamic response, essential for tasks like damage detection and life-cycle assessment. However, developing efficient, accurate, and reliable data processing methods remains a challenge.

Over time, a plethora of data-driven and physics-based methods have been devised to improve feature extraction accuracy. Among the hybrid methods, graph neural networks (GNNs) have recently been emerging as a standout choice. Originating from fields like biology and traffic prediction, GNNs show promise by integrating physical information into data-driven approaches, leveraging the strengths of each method. Consequently, GNNs exhibit exceptional performance in predicting critical structural insights.

This research proposes a GNN architecture for converting acceleration signals into strains, overcoming limitations associated with direct strain signal acquisition for life cycle assessment aim. Through a numerical case study, we demonstrate the efficacy of GNNs in Structural Health Monitoring, showcasing their significant potential in improving bridge assessment strategies.

Small changes in an elastic structure, such as additional compliance due to local damage (cracks) or variation of inertial properties, influence the spectrum of natural frequencies. The energy approach allows to estimate the small frequency shifts when the vibration modes of the unperturbed (original) structure are available, which greatly simplifies the solution of problems of structural optimization and damage identification. The asymptotic proof of the relations of the energy approach is easy in case of simple changes in mass distribution or stiffness. The situation becomes more sophisticated when the perturbed structure possesses richer kinematics than the original, i.e. when the perturbed vibration modes become incompatible with the constraints of the original structure. Thus, it is common to model cracks in beams or plates by local hinges with rotational springs, which essentially introduces new degrees of freedom. Another example is the correction of the vibration frequency due to shear flexibility compared to a Bernoulli-Euler beam or Kirchhoff plate model. Elastic supports also fall into this category. The present contribution provides a novel mathematical proof of the energy approach using methods of structural and analytical mechanics. By performing the analysis at the abstract level of a discretized model, we capture the full variety of linearly elastic structures ranging from 3D continua to rods, plates, and shells. Using this technique, we show for the first time that the simple relations of the energy approach lose their validity in the situation of multiple (repeating) natural frequencies and must be replaced by a specially constructed eigenvalue problem of reduced dimensionality. The theoretical analysis is illustrated by simple “toy models”, which demonstrate the asymptotic accuracy of the linearized relations for frequency increments. Furthermore, we investigate the practically relevant problem of the vibrations of a square plate with added line mass or a crack of arbitrary shape, modeled as a rotational spring.

Structural identification and structural health monitoring often require the development of surrogate models. This is mainly for their reduced computation time, but also for other reasons, such as the possibility of offline computation without the need to access the licensed software. The basis for fitting a surrogate model is the evaluation points, which are sampled over the domain of the selected parameters and evaluated by the parametrised finite element model. When the quantities of interest are the modal properties, additional challenges linked to the mode classification arise. These challenges will be presented and discussed using a timber structure example.

There are several possible criteria for classifying the computed modes into fitting groups. One might use the order of the natural frequencies as a criterion, however, that would lead to incorrect classification in the presence of mode crossing. On the other hand, if the mode shape correlation to a reference evaluation point is chosen, the phenomenon of mode veering would lead to discontinuous jumps between the modes. While more advanced mode tracking procedures that follow the evolution of the natural frequencies and mode shapes alongside continuously varying the modelling parameters may appear to offer a superior alternative, they are prone to fail around the coalescing point. Additionally, spatial aliasing that occurs due to improper discretisation may add to the complexity of the problem at hand.

A case study of a timber structure showcases the challenges of mode crossing, mode veering, and spatial aliasing. We present the techniques for improving the success of mode classification and the overall accuracy of the surrogate model. Finally, we update the model using modal data obtained by shaker testing of the structure.

Financial support of EU Horizon Europe for the BUILDCHAIN project (grant agreement 101092052) is gratefully acknowledged.