Large-scale structures such as long-span bridges present significant challenges for sensor deployment, as practical constraints limit the number and distribution of sensing devices. These restrictions reduce the achievable spatial resolution and decrease the ability to capture complex deformation patterns. This work presents a physics-informed framework for sensor placement optimisation that leverages inductive biases in Gaussian process (GP) modelling to improve structural monitoring under sparse sensing conditions. The proposed methodology addresses this constraint by constructing GP covariance kernels directly from structural mode shapes derived through finite element analysis, embedding a priori physical knowledge into the prior distribution without requiring any measurement data. This inductive representation establishes a physically consistent baseline for the structural response, enabling optimal sensor locations to be identified through entropy minimisation on the GP prior.

The formulation exploits the modal decomposition of the structural system, where eigenmodes serve as orthogonal basis functions for constructing a Mercer-compliant covariance matrix. Modal weights are introduced to control the relative contribution of each mode to the uncertainty field, allowing the prior to reflect expected dynamic characteristics such as the dominance of lower modes in large-scale structures. Sensor placement is then performed sequentially by selecting the degree of freedom with maximal marginal entropy at each iteration. This strategy aligns with Fisher Information Matrix principles, as both aim to maximise information gain and reduce redundancy by improving the identifiability of the structural response encoded in the modal basis.

The methodology is first illustrated using the canonical example of a simply supported beam. Two weighting strategies - equal modal contributions and decay-weighted modal amplitudes -demonstrate how inductive biases influence the spatial distribution of uncertainty and, consequently, the optimal placement of sensors. In the equal-weight case, entropy peaks align with regions of strong combined modal amplitude, driving sensor placement towards quarter-span locations. When decay-weighted factors are introduced, the uncertainty landscape becomes dominated by the first mode, leading the optimisation to favour midspan and symmetrically distributed positions. These examples highlight the sensitivity of the placement outcome to the physical assumptions embedded in the GP kernel.

The approach is subsequently applied to the Hardanger Bridge in Norway, using a calibrated finite element model that provides realistic modal properties. The optimisation incorporates practical constraints, such as multi-directional sensor capabilities and symmetric placement along the deck to capture torsional modes. The resulting configurations show strong agreement with the deployed monitoring system while offering targeted improvements for observing bending, torsional and tower-related modes. The analysis demonstrates that embedding modal information through inductive biases yields sensor layouts that concentrate on regions of high modal influence, ensuring coverage of both global and local dynamic behaviours.

Overall, the study shows that physics-informed Gaussian processes with inductive biases offer a principled and computationally efficient framework for sensor placement in large-scale structures. By aligning the optimisation with fundamental dynamic characteristics, the method enhances the interpretability and effectiveness of structural monitoring under sparse sensing.

The performance of strain-based Structural Health Monitoring (SHM) systems is highly dependent on the spatial distribution and quality of the sensing network. Inadequate sensor placement can reduce damage sensitivity, increase prediction uncertainty, and compromise the accurate localization of structural defects. This work presents a sensor positioning optimization framework for crack detection in metallic structures using large-scale virtual strain datasets generated via Extended Finite Element Method (XFEM) simulations. A comprehensive database comprising thousands of crack scenarios—varying in position, length, and orientation—is constructed to capture the structural response under diverse damage conditions. The numerical models are previously validated against experimental strain-gauge measurements obtained from fatigue tests on stiffened panels, ensuring realistic representation of strain fields.
Sensor placement is optimized through a combination of strain-based sensitivity metrics and information-theoretic criteria. Strain Difference Coverage (SDC) and Strain Contribution Coverage (SCC) are employed to quantify, respectively, the variability of strain responses across damage scenarios and the relative contribution of each location to the global structural response. In parallel, the Fisher Information Matrix (FIM) is used to evaluate the parameter observability associated with candidate sensor configurations, enabling the identification of layouts that minimize estimation uncertainty.
The proposed framework integrates these complementary approaches to systematically identify sensor locations that maximize damage detectability while reducing the number of required sensors. Results demonstrate that optimized sensor configurations significantly outperform uniform distributions, particularly when considering full crack characterization (location, length, and orientation). Additionally, consistent patterns observed across different techniques highlight the importance of combining optimization methods with engineering judgment to capture physically meaningful sensing regions. The methodology provides a robust, interpretable, and computationally efficient approach for sensor placement optimization in structural SHM applications.

Optimal Sensor Placement (OSP) is a critical component of vibration-based Structural Health Monitoring (SHM), yet its effectiveness is often compromised by the deterministic nature of standard Finite Element (FE) models. This study evaluates two advanced OSP frameworks that explicitly account for epistemic and aleatory uncertainties: a variance-based method that utilizes hierarchical clustering to manage modal sensitivity variance, and a likelihood-maximization method designed to maximize the probability of achieving specific SHM objectives under measurement noise. Using a laboratory-tested glulam timber beam as a benchmark, the research investigates the impact of uncertain material properties and support stiffness on sensor performance. Experimental results from ambient and impact vibration tests serve as the ground truth for validation. The findings reveal that boundary condition uncertainties can lead to significant modal discrepancies, especially for higher modes. Both probabilistic methods identified robust sensor configurations that significantly outperformed random layouts, with the likelihood-maximization method achieving a 65.9% success rate for high-fidelity mode shape reconstruction (MAC ≥ 0.95). By bridging the gap between theoretical optimization and practical structural variability, these frameworks provide a reliable methodology for designing SHM systems in complex, real-world infrastructure.

In a global context driven by energy transition and the imperative to reduce dependence on fossil resources, the development of safe and high-performance hydrogen economy has emerge as a strategic priority for industry. Hydrogen tanks, critical components in the transport and energy sectors, must ensure high reliability throughout their service life. However, ensuring their structural integrity remains a major challenge both during manufacturing and operation, due to damage mechanisms that may be difficult to detect and potentially detrimental to safety. In this context, identifying and qualifying advanced Structural Health Monitoring (SHM) technologies is a key industrial objective.

This study investigates several innovative SHM solutions applied to materials intended for composite hydrogen storage vessels. Two main families of sensors are evaluated: (i) distributed optical fibers capable of providing continuous strain measurements over the full sensing length or specific regions, and (ii) flexible piezoelectric sensors based on P(VDF-TrFE) copolymers, manufactured by screen printing, enabling easy integration into composite structures. These emerging technologies are compared with more conventional devices such as resistive strain gauges and ceramic acoustic emission sensors, in order to assess their performance and sensitivity to damage phenomena.

The experimental work is conducted on two types of standardized specimens: a classical rectangular geometry and a tubular geometry representative of filament-wound tank structures. Some specimens are intentionally pre-damaged through low-energy impact to generate Barely Visible Impact Damage (BVID), a type of defect frequently encountered in composites. All samples are then subjected to quasi-static mechanical tests: monotonic tensile loading for rectangular specimens and NOL-ring (Naval Ordonance Laboratories) tensile tests for tubular specimens, thus approaching conditions reflecting in-service loads.

The results demonstrate strong consistency among the different measurement techniques, both in detecting critical events and in tracking strain evolution. Distributed optical fibers show high capability in accurately localizing stressed areas, while the printed piezoelectric sensors effectively capture damage-related signals, although with a lower event count compared to ceramic sensors. These findings confirm the relevance of the proposed SHM approaches and highlight their potential for future integration into hydrogen storage vessels to enhance in-service monitoring and structural safety.