Random vibration data-based Structural Health Monitoring (SHM) systems are attractive due to various advantages, including their global capability which implies operation even under a minimal number of sensors, their ability to operate under naturally available excitation, as well as the availability of high precision data acquisition and sensor technology. Yet, their performance may be seriously compromised by the effects of varying Environmental and Operating Conditions (EOCs). For this reason, robust SHM is of critical practical importance and has received significant attention over the past several years.

In this context, the Functional Model (FM) based robust damage detection method, which may be thought of as an important generalization and improvement of regression-type approaches, is particularly attractive and has been shown to achieve high performance even for early-stage damages. Yet, like other such approaches, it requires measurability of the EOCs for its training – a condition that may not be possible to satisfy in some practical applications. To overcome this limitation, a significant modification of the method which is based on a re-parametrized form of the FM, was introduced in one of our recent conference papers.

The goal of the present study is to further explore the FM method in the unmeasurable EOC case by providing insights and generalizations, while also considering a challenging case study in which the EOCs are not only unmeasurable but also spatially dependent. The methodological insights and generalization refer to the properties of the reparametrized FMs and their extension in the case of multiple EOCs. The challenging case study refers to an aluminum truss subject to a thermal field which is gradually expanding over the structural topology.

The structure is modeled via a Finite Element representation in ABAQUS, with a part gradually exposed to the thermal field being pseudo-statically brought to a temperature of 0 °C, while the other part remains at −50 °C. The structure is subject to an unmeasurable random uncorrelated force excitation at its free end, with the resulting vibration response measured using a single sensor. Various damage scenarios are considered, with each one characterized by 10% stiffness reduction for an individual truss member.

The FM based method employs a re-parametrized Functionally Pooled ARMA(12,9) identified from a limited number of vibration response signals corresponding to selected thermal states with the structure in its pristine state. Damage detection performance is assessed through a total of 525 Monte Carlo simulations across a wide range of thermal states – including intermediate ones not used for model training – and under four damage scenarios.

The damage detection performance achieved is presented via Receiver Operating Characteristic (ROC) curves and is characterized by 97% / 93% TPR (true positive rate) at 5% FPR (false positive rate) for three of the damage scenarios and the fourth one, respectively. This performance is considered quite good under the single sensor configuration, with improvements expected with the use of more sensors. Comparisons with other state-of-the-art methods indicate the superior detection performance achieved by the FM based method.

Static monitoring of bridge bearings is a valuable tool for assessing their long-term response to thermal and operational loads. In this study, a grey-box modelling framework is used to describe the relationship between temperature and bearing displacements. The model combines data-driven Gaussian Process regression with simple physical constraints, providing both reliable and interpretable predictions of thermally induced movements. The work focuses on analysing and interpreting the prediction residuals, defined as the differences between the measured responses and those expected from the physical model.

The case study concerns a highway viaduct instrumented with displacement and temperature sensors at the abutment bearings. The grey-box model is trained on long-term monitoring data covering a wide range of environmental conditions. Statistical metrics confirm that the model reproduces the main thermal trend of the bearing response with good accuracy. However, residual analysis reveals systematic deviations from the linear thermo-mechanical behaviour assumed in the physical formulation, suggesting that additional physical processes are at play.

To explore these effects, the residuals are analysed, highlighting time-dependent patterns and correlations with both temperature history and time of day. These patterns are not randomly distributed but show cyclic behaviours consistent with frictional or stick–slip effects at the bearing interfaces. Such mechanisms, often overlooked in purely data-driven or simplified mechanical models, can produce asymmetric or hysteretic displacement–temperature relationships. These effects tend to evolve over time, reflecting the non-linear thermo-mechanical behaviour of the sliding bearings.

By combining physically informed learning with detailed residual analysis, the proposed approach improves predictive accuracy and enhances the interpretability of the underlying structural behaviour. The results show that residuals can provide meaningful physical insights. In particular, the observed time-dependent patterns, likely related to frictional phenomena, suggest that predictive discrepancies themselves can be used as health indicators. This highlights the potential of residual analysis to enhance the interpretability and diagnostic capability of data-driven SHM frameworks for understanding the long-term behaviour and deterioration of bridge bearings.

Climate-induced freezing events can significantly alter the dynamic behaviour of bridge structures, leading to abrupt shifts in modal frequencies that may obscure true structural conditions or mimic damage scenarios. The negative consequence of these shifts is the emergence of false alarms in structural health monitoring (SHM) of these structures, resulting in misinterpretation of healthy states as damage and unnecessary maintenance interventions. To address these challenges, this study presents an unsupervised anomaly detection approach for identifying freezing-induced anomalies in long-term bridge modal frequency data without relying on temperature records. The proposed anomaly detector first learns the normal dynamic behaviour of the monitored bridge under non-freezing conditions. When climate–induced freezing events occur, causing sudden increases in modal frequencies, the trained anomaly detector automatically identifies and flags these events, wherein the freezing-induced anomaly scores exceed a predefined decision threshold. The detected anomalies are subsequently cross-validated against environmental data to confirm their correspondence with actual freezing periods. Modal frequency datasets from two bridge structures subjected to freezing conditions are employed to validate the proposed approach. Results indicate that the unsupervised detection of climate-induced freezing events can effectively reduce false alarms in SHM of bridges without requiring labelled data for decision-making.

Structural health monitoring (SHM) is challenged by environmental and operational variations (EOVs) that mask changes in damage-sensitive features (DSFs). Mitigating these effects, known as data normalisation, remains a central challenge in SHM. Regression-based approaches address it by explicitly modelling EOV-DSF relationships, enabling grey-box formulations that incorporate physical knowledge, such as a temperature-natural frequency dependence. Such relationships, however, often hold only within specific operating regimes: freeze-thaw transitions, for example, can induce abrupt switches in a structure's dynamic properties. This study presents a framework that combines Gaussian processes (GPs) with local modelling to capture such regime switches while allowing the level of physical knowledge to vary across regimes. Two methods are presented: (i) a physically informed change-point kernel for GPs that encodes regime changes within the kernel, and (ii) a Mixture-of-Experts formulation that partitions the data and fits regime-specific GP models. Both are evaluated on the Leibniz University Test Structure for Monitoring (LUMO), a 9~m lattice tower, where natural-frequency switching has been linked to freezing and thawing of the foundation soil. Across the case study, both approaches outperform state-of-the-art regression-based normalisation and substantially reduce the risk that regime-induced variability is misinterpreted as damage. The results indicate that regime-aware, physics-informed GP models offer a more reliable and physically interpretable route to data normalisation in long-term SHM.