Accurate knowledge of in-service loads is fundamental to damage prognosis for structures. Ideally, such information would be obtained from permanently installed strain sensors distributed throughout the structure; yet in real-world scenarios, this is not feasible. As an alternative, data-driven models can be developed to predict the quantities of interest from routinely recorded operational data (e.g., flight telemetry), which are often informative of the underlying structural response. However, the ability of these models to make reliable predictions is connected to the acquisition and exploitation of labelled data. At the same time, data sparsity remains a common challenge, arising from transmission issues, sensor malfunctions, or other operational constraints.

Along these lines, this work employs Gaussian Process (GP) regression for monitoring an airframe structure under data sparsity. Specifically, a virtual load monitoring framework is developed that reconstructs strain histories at hot spots from standard flight data. To address data sparsity, the study extends conventional GPs into multi-task GPs, enabling information sharing between correlated strain sensors. GPs were chosen because they adopt a flexible, non-parametric approach to modeling the data, avoiding the need to assume a predefined parametric form. Also, they provide probabilistic predictions with credible uncertainty estimates, while sparse variational approximations ensure computational efficiency in large-scale problems. However, in their standard form, they can only handle single outputs. Multi-task extensions reformulate the problem as vector-valued regression, exploiting cross-task covariance to transfer statistical strength from data-rich domains to data-poor ones.

The framework is demonstrated using experimental data obtained from the flight of a UAV structure. To evaluate the robustness of the employed models in imbalanced dataset settings, some parts of the time series were hidden from training. Results show that the multi-task GP yields better predictive accuracy and more consistent uncertainty estimates in the masked (white) areas compared to single-task GPs. This can be seen in Figure 1. The analyzed scenario highlights the value of the multi-task learning approach. This lies in its ability to use data from specific operational states (or missions) to enhance predictive performance in other, unobserved states.

The reliable identification of a structure’s modal properties from in situ vibration data often uses parametric, multi-order methods like time-domain SSI-Cov or frequency-domain p-LSCF (PolyMAX). Traditionally, this process relies on manual interpretation of complex stabilisation diagrams, which is time-consuming and prevents efficient, long-term continuous monitoring. To overcome this, the field has successfully shifted toward Automated Operational Modal Analysis (AOMA), leveraging clustering algorithms to automatically group similar modal estimates obtained across several model orders.

However, in the case of dam monitoring, though successful results have been achieved with hierarchical clustering, a significant challenge persists: harmonic excitation, particularly from nearby power plants, can introduce strong non-structural frequencies that are easily mistaken for true vibration modes, creating a source of bias in the identified modal properties. To improve the robustness of automated systems, it is essential to develop methodologies that reliably distinguish between legitimate structural estimates and these external “intruders”.

This work proposes a post-tracking methodology based on Gaussian Mixture Models applied to tracked modal estimates of a concrete arch dam. By combining features derived from identified poles uncertainties, damping ratios, and frequency stationarity, the method separates structural modal estimates from harmonic contamination without relying on site-specific thresholds, exploiting the statistical contrast between diffuse structural populations and highly concentrated harmonic signatures.

Abstract: The scarcity of long-term vibration data real-world structures remains a significant barrier to the application of machine learning in structural health monitoring (SHM). Available datasets are often short, unlabeled, and affected by operational and environmental variability, limiting the generalization of data-driven models. This paper proposes a framework that combines unsupervised learning and domain adaptation to enhance model transferability under limited data. An autoencoder is trained on commissioning data from a source structure to extract latent features that represent key dynamic characteristics. These embeddings act as unsupervised, damage-sensitive indicators. To adapt across domains, two complementary strategies are introduced: (i) latent-space realignment using the Procrustes method for geometric alignment, and (ii) selective decoder retraining with unlabeled target data. This enables efficient adaptation without full retraining. The framework is validated on the Z24 bridge benchmark, successfully adapting to seasonal and damage variations using only output data, and later transferred to the New Bridge, one of the twin bridges over the Itacaíunas River in Brazil. Results show robust latent-space alignment, accurate reconstruction, and effective generalization under domain shifts. Overall, the method offers a computationally efficient approach for transfer learning in SHM, reducing dependence on labeled datasets while preserving sensitivity to structural and operational changes.

In the structural monitoring of full-scale structures, it is essential to analyse the temporal evolution of specific parameters to accurately evaluate the health condition of the structure. A comprehensive understanding requires a sufficient amount of heterogeneous data capable of describing different aspects of structural behaviour. In this context, the integration of remotely acquired data, such as satellite data, into monitoring protocols could be strategic for filling gaps in in-situ measurements, offering extended and continuous time series.

Considering the structure, the environment, and the soil as an integrated system, this study proposes a method for reconstructing historical time series of soil parameters that could influence structural response. The model used is based on Sparse Bayesian Learning (SBL) and combines remotely sensed data with local measurements, achieving an accurate reconstruction of in-situ parameters.

This approach allows for the simulation of soil and structural behaviour even in the absence of direct data, improving the ability to distinguish between physiological variations and real signs of damage. This is essential to avoid interpretative errors that could compromise the effectiveness of monitoring and the safety of structures.

The health of structures has been increasingly monitored to identify potential loss of integrity throughout their lifetime, a problem intensified by their sustained operation. Although damage-sensitive metrics can be derived from the system's input and output data, this task can become complex if the structure operates in a closed loop with active control to reduce its vibration. In this case, in addition to the disturbance acting on the structure not being measurable, the input signal applied to the system becomes correlated with the disturbance due to feedback. As an alternative, we investigated adding a small known excitation signal to the system during its operation to obtain a data-driven model of its dynamics. Furthermore, we implemented a state observer based on this model to jointly estimate the system states and unmeasured inputs, such as the unwanted disturbance. In this context, closed-loop health monitoring was investigated for a cantilever beam subjected to different disturbance signals and structural integrity conditions. Variations in the modal properties of the models obtained over the system's operation can be used to detect damage to the beam. The health condition of this structure was also quantified by identifying its behavior separately from the estimated effects of the undesired disturbance. As a result, we hope to contribute to the monitoring of structures operating in closed loop with active vibration reduction.

Civil infrastructures form the backbone of modern society, yet their increasing age and progressive deterioration have become a pressing global issue. Structural Health Monitoring (SHM) has emerged as a key tool to assess and manage the condition of such assets in real time. By installing permanent sensors, SHM systems continuously record the structural response under operational and environmental conditions, enabling the detection of potential degradation that could affect safety or serviceability. In most SHM applications, monitoring thresholds are established so that exceeding them triggers an alarm. However, despite their widespread use, there is still no standardized or physically interpretable methodology for defining such thresholds.

Conventional approaches typically rely on data-driven techniques such as statistical process control (SPC), damage indices, or probabilistic criteria based on the probability of detection and false alarm. More recent developments have introduced machine learning and novelty detection algorithms to automatically identify anomalous behaviors. Nevertheless, these methods often lack explicit connection to the underlying structural models and, consequently, to the actual state of structural reliability. As a result, exceeding a threshold does not necessarily correspond to a true damage condition, and the subsequent management actions remain ambiguous.

Over the past decade, a growing consensus has emerged that SHM should not only serve to enhance knowledge of structural conditions but also to support decision-making. Within this paradigm, the definition of monitoring thresholds should be grounded in decision theory. Expected Utility Theory (EUT), originally introduced by von Neumann and Morgenstern and later extended by Raiffa and Schlaifer, provides a formal framework for modeling rational decisions under uncertainty. In the SHM domain, EUT has been used to quantify the value of monitoring information and to guide optimal sensor placement; however, a comprehensive integration of reliability assessment and decision theory for threshold definition is still lacking.

This study introduces a decision-based framework for defining monitoring thresholds derived from decision theory principles—hereafter referred to as decision-based thresholds. Building upon a reliability-based SHM model, the proposed framework maps optimal decisions, as determined by EUT, directly into the monitoring observation space. This allows operators to make informed management decisions directly from sensor data, without the need for abstract probabilistic computations. The formulation clarifies how prior knowledge on the quantities of interest, model uncertainties, and monitoring observations interact within a unified probabilistic–decision framework. Finally, the proposed framework is applied to representative case studies, offering practitioners practical and effective tools to support optimal decision-making in the context of civil infrastructures.