The Model-Assisted Probability of Detection (MAPOD) technique employs extensive simulations to generate statistically independent datasets for assessing the reliability of Structural Health Monitoring (SHM) systems via Probability of Detection (POD) curves. While MAPOD follows the classical POD procedure described in MIL-HDBK-1823A, simulation tools, though effective in representing structural uncertainties, struggle to capture system, operational, and environmental variations—limiting the realism of simulation-based POD analyses. Moreover, the standard POD approach assumes a linear relationship between damage size $a$ and its indicator and cannot be directly applied to monitoring scenarios with statistically dependent measurements.

This paper introduces a novel method that combines simulated damage scenarios with experimental data from Guided Wave Structural Health Monitoring (GWSHM) systems to account for all uncertainties and allow for the integration of the individual fingerprint of an SHM system. The proposed Augmented POD (A-POD) method removes the need for a predefined relationship between damage size $a$ and its indicator, making it applicable to any damage growth trend. The A-POD method is validated using data from a PZT-based GWSHM system exciting the fundamental torsional mode in a steel pipe. Simulated corrosion damage data are merged with experimental baseline data, and artificial defects are introduced for validation. The A-POD and MAPOD results agree well for linear trend growth cases, while the A-POD demonstrates strong reliability and adaptability, when the dataset lacks linearity.

Probability of Detection (POD) curves represent the standard methodology for reliability assessment in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Recent studies have highlighted several challenges in extending POD methodologies from NDE to SHM, including the spatial and temporal correlation of data. Among these challenges, data fusion plays a crucial role. SHM systems often rely on multiple sensors, which may use the same sensing technology or be part of a heterogeneous sensor network composed of complementary technologies, each sensitive to specific damage types.

In this context, POD fusion is of paramount importance, as engineers require decision-making tools capable of assessing the overall detection performance of the SHM system. POD of fused data can be obtained either by aggregating all measured damage indexes into a single one (early fusion), or as the combination of the PODs of the singular measurements (late fusion). These aggregation methods may provide different PODs, and the distinction can be non-trivial.

In this paper, we compare four fusion strategies for a two-sensor system at fixed system-level Probability of False Alarm (PFA): (i) late fusion under the independence approximation (L1) and late fusion without any independence assumption (L2), (iii) early fusion linear combination with equal weights (E1), (iv) and with optimal weights derived from the maximal-ratio-combining (MRC) solution (E2). All four are analysed via Monte Carlo simulation within a normalised parametrisation, isolating and emphasizing the importance of sensor SNR and noise correlation ρ.

Two effects of practical relevance emerge. The independence approximation in late fusion becomes increasingly optimistic as sensor data become more correlated, underestimating a₉₀ by a margin that grows monotonically with ρ. Optimal early fusion systematically outperforms equal weighting, with a gain that also grows with ρ and, at high correlation, reduces to effectively discarding the redundant weaker sensor. These findings show the importance of considering data correlation in POD fusion and provide quantitative guidelines for fusion-strategy selection in NDE/SHM, paving the way for the extension to time-correlated signals typical of continuous SHM applications.

The transition of SHM and NDE from research prototypes to industrial applications remains hindered by the lack of appropriate reliability metrics that account for the spatial nature of damage identification. While the Receiver Operating Characteristic (ROC) has been widely adopted for performance assessment, its application to damage localization poses practical and fundamental challenges that emerge from the underlying binary classification paradigm. This paper introduces the Distance-Weighted ROC (DW-ROC) to address these challenges, while retaining the familiar interpretability as a compromise between sensitivity and specificity, which were crucial to the popularity of the ROC.

Starting from concrete application cases and progressing in increasing levels of abstraction, this paper demonstrates the following limitations of the standard ROC. It is too inflexible in the off-grid case where damage is not located at predefined imaging points. It lacks nuance towards localization error, and is unable to rank methods according to their localization accuracy. Finally, it treats all false positives and negatives as equally problematic regardless of their spatial proximity to actual damage. These limitations lead to inappropriate oversimplifications and produce misleading performance comparisons, thereby hindering development and validation of SHM systems.

The proposed DW-ROC method extends the ROC by introducing fuzzy membership functions that weight the scoring of true and false positives based on spatial proximity to actual damage. The approach smoothly penalizes localization errors while preserving the interpretability and conventions of standard ROC analysis. The DW-ROC requires only a single, physically meaningful parameter that sets the distance at which a predicted positive transitions from mostly true-positive to mostly false-positive, making it adaptable across different use-cases and methods.

Numerical verification demonstrates that the DW-ROC retains the ability to rank damage maps according to background noise, and offers in addition the ability to rank according to localization accuracy. Moreover, it handles the off-grid case without requiring ad-hoc adjustments or arbitrary margins of localization error. Finally, it remains consistent with established conventions by providing an Area Under the Curve (AUC) metric where 0.5 corresponds to random guessing, and 1.0 to perfect performance.

Validation was conducted after inspecting two representative structures with a vibration-based damage imaging technique, using accelerometer measurements in the modal frequency range, and a data-driven model of their baseline dynamics.The DW-ROC produced more representative performance evaluations than the ROC. It successfully distinguished between damage maps that confused the standard ROC, and matched expert assessment. This provided a powerful tool to compare methods and parameters, and enabled automated, synthetic overviews of performance over large datasets.

This paper contributes to industrial acceptance of SHM systems by introducing a strategy for performance assessment that accounts for the peculiarities of the damage localization task. By acknowledging the spatial nature of localization performance while retaining familiar ROC interpretability, the DW-ROC enables more faithful modality comparison studies of damage imaging, across different structures, applications, and SHM methods. The insights and results presented in this paper constitute a practical step toward quality assessment strategies that support the transition of SHM and NDE from research demonstrations to routine industrial applications.

Structural Health Monitoring (SHM) aims to enhance infrastructure reliability by reducing unnecessary inspections, minimizing downtime, and preventing failures. However, noise in sensor data remains a persistent challenge, often arising from sensor degradation, environmental variability, or transmission errors. This noise is typically non-stationary and can follow time-varying patterns that affect the reliability of observations. Partially Observable Markov Decision Processes (POMDPs) provide a framework for optimizing inspection and maintenance policies to achieve cost-effective decision-making without compromising safety. Yet, POMDP formulations often rely on bounding assumptions such as access to high-quality, noise-free observations, and standard models typically do not update this assumption during operation. This simplification overlooks the complex nature of noise in monitoring data, causing belief updates to become overconfident and leading to suboptimal, locally optimal maintenance policies. To address this, the study proposes a Noise-aware Observation-Integrated POMDP (NOI-POMDP) framework that explicitly incorporates the noise-generating process as a dynamic and learnable component of the observation model (Fig. 1). The SHM agent updates beliefs from noisy observations while the underlying NOI-POMDP explicitly represents how time-varying sensor noise affects state information, enabling adaptive belief updates and improving long-run decision quality. The methodology is demonstrated through a beam SHM case study where structural condition is identified using vibration-based features derived from sensor measurements. Across simulated deterioration processes and varying noise patterns, the NOI-POMDP framework demonstrates improved decision quality compared to conventional fixed-noise POMDP formulations. Results show increased policy robustness under severe noise variability and improved state estimation accuracy, leading to balanced inspections and lower long-term lifecycle costs while maintaining safety constraints.