PSI - Issue 78

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

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Fig. 1: Schematic representation of the proposed cointegration-based methodology. The diagram outlines the main steps of the approach, highlight ing the workflow and key components of the framework.

remains in a reference (undamaged) state. Once the regression models are trained, residual time series are computed to quantify the mismatch between measured and predicted strains r i ( t ) = ϵ ( t ) i , meas − g i ( ϵ − i ( t )) , for i = 1 , 2 , . . . , n , where r i ( t ) denotes the residual associated with the i -th sensor. These residuals serve as damage-sensitive features, designed to be stationary under normal operating conditions. To standardize the evaluation across sensors, residuals are normalized using the mean µ i , train and standard deviation σ i , train computed during the training period r ( t ) i , norm = ( r i ( t ) − µ i , train )(3 σ i , train ) − 1 . This normalization facilitates the use of unified control limits for anomaly detection. A global health index is subsequently derived using the Mahalanobis distance computed over the vector of normal ized residuals, enabling system-level damage detection triggered by the change point detection algorithm. Detailed assessment is conducted by analyzing individual residuals within a Shewhart control chart and testing their stationar ity using the ADF test. Since the residuals are constructed to be independent of environmental e ff ects, any significant loss of stationarity is interpreted as evidence of structural change. Furthermore, this strategy allows for damage lo calization, as sensors exhibiting abnormal behavior can be directly associated with the most a ff ected regions of the structure. Such insight enhances the e ffi ciency of post-event inspection activities by directing attention to specific zones exhibiting deviations from the baseline state. The presented methodology, schematically depicted in Figure 2, is grounded in the development and calibration of numerical models capable of representing a wide range of damage mechanisms potentially a ff ecting masonry struc tures. The process begins with the definition of a reference FE model of the monitored structure. To accurately capture the geometric and mechanical behavior of real masonry buildings, the model is developed in three dimensions and incorporates a simplified yet representative configuration of the boundary conditions, typically modeled using linear elastic springs or similar idealizations. To reduce computational burden while preserving global structural behavior, the masonry is represented as a continuous homogeneous equivalent material. This reference model serves as the foundation for generating a population of damage scenarios used in the subsequent inverse analysis. However, the direct use of high-fidelity FE models in continuous monitoring is generally unfeasible due to their high computational cost. To address this limitation, surrogate models (SMs) are employed to map the input-output response of the full FE model while significantly reducing computational demands. Specifically, the reference FE model is used to generate di ff erent model classes representing distinct damage mechanisms—e.g., earthquake-induced loadings via pushover analysis, various foundation settlement scenarios, and so on. The nonlinear structural response is simulated using the Concrete Damage Plasticity (CDP) model to accurately capture the post-elastic behavior of masonry. 4. Model-Based Monitoring through the Selection of Competing Model Classes