PSI - Issue 78

Michele Mattiacci et al. / Procedia Structural Integrity 78 (2026) 1159–1166

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5. Comparative Discussion

The two monitoring strategies presented in this study di ff er fundamentally in their conceptual and operational foun dations. The first approach is a fully data-driven methodology that integrates time-dependent MLP regressors within the nonlinear cointegration framework to isolate damage-sensitive residuals from strain measurements. These residu als, inherently robust to environmental and operational variability, enable real-time detection of structural anomalies at both global and local levels. Specifically, they support not only the identification of damage but also the estimation of its severity and the localization of the most a ff ected areas. However, while the method o ff ers valuable insights into the nature of the observed damage, it does not allow for a formal classification of the underlying damage mechanism. Conversely, the second approach is model-based and centers on the development of a high-fidelity FE model of the monitored structure. Distinct damage mechanisms are encoded into a population of Kriging-based surrogate models to allowe ffi cient inverse calibration from measured strain data. By employing the BIC, this method not only detects and localizes damage but also addresses the classification task by identifying the most plausible failure mechanism among those initially hypothesized. Moreover, it enables the quantification of the damage severity by evaluating the sti ff ness multiplier values immediately following the onset of the identified mechanism. Lastly, both methodologies might po tentially be employed across a wide range of masonry building typologies, including towers, cathedrals, palaces, and bridges. Their adaptability to di ff erent structural configurations and damage scenarios makes them promising tools for the static monitoring of complex heritage assets under real-world conditions. When compared across multiple evaluation criteria, these strategies reveal complementary strengths as well as some limitations. In terms of detection accuracy and sensitivity, the data-driven method might be potentially able to capture subtle deviations from baseline behavior through the e ff ective modeling of the EOV influence on each sensor output, while the model-based technique should o ff er precise quantification and localization via direct correlation with structural parameters. Regarding robustness to environmental and operational variability, the nonlinear cointegration approach may exhibit superior inherent filtering capabilities, ensuring reliable damage indicators even under changing ambient conditions, whilst the model-based strategy relies on prior data preprocessing; in fact, it is not inherently immune to EOV without employing other compensation techniques. From the standpoint of interpretability, the model based strategy might hold a significant advantage, as its outcomes are framed in terms of physically meaningful parameters and damage scenarios, thereby providing actionable insights. Conversely, the cointegration-driven method should have a moderate level of interpretability since residuals are statistical features, less directly correlated to the physical phenomenon. Computational e ffi ciency further di ff erentiates the two: the data-driven method, once trained, could support real-time monitoring with minimal computational cost, whereas the model-based approach, although optimized via surrogate models, should remain more resource-intensive due to the underlying inverse calibration process. Concerning implementation requirements, the former necessitates long-term, undamaged monitoring data, making it readily deployable and automatable with reduced or no modeling expertise required. In contrast, the latter relies on a detailed structural model and the definition of plausible damage scenarios, demanding a more significant engineering knowledge / judgement for model development and calibration. Lastly, the generalization potential of the data-driven method should allow for broader applicability across di ff erent structures and monitoring networks, while the model-based strategy remains structure-specific, requiring customized model classes for each application. These considerations, however, remain subject to further validation and should be confirmed through dedicated experimental campaigns and / or extended numerical analyses to comprehensively assess the comparative performance of the two approaches under varied and realistic conditions.

6. Conclusions and Future Perspectives

This study has presented and conceptually compared two complementary strategies for the structural health mon itoring of masonry buildings based on strain measurements. The first approach, rooted in nonlinear cointegration theory and empowered by time-dependent neural networks, o ff ers a robust data-driven framework capable of real time damage detection and localization, with strong resilience to environmental and operational variability, yet unable to properly classify the identified mechanism. The second model-based strategy relies on a population of surrogate models derived from a high-fidelity FE model, enabling not only the detection and localization of damage but also