PSI - Issue 78

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

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Fig. 2: Schematic overview of the proposed model-based methodology, illustrating the main workflow and key components of the framework.

Following the forward simulation phase, each damage scenario is discretized into a set of macro-elements M i , defined by clustering finite elements that exhibit severe damage (typically identified by a damage threshold d t > 0 . 8 ÷ 0 . 9, where d t represents the damage parameter in traction in the CDP model). These macro-elements, which correspond to dominant crack patterns, are parametrized by sti ff ness multipliers k i , where i = 1 , 2 , . . . , p (being p the macro-element number), that scale the elastic modulus of the elements within each macro-element. Given the computational expense of evaluating the FE model response over a range of sti ff ness parameters, sur rogate modeling is introduced. Kriging-based surrogate models are constructed for each model class, mapping the relationship between the sti ff ness multipliers x = [ k 1 , k 2 , . . . , k p ] ⊤ ∈ R p and the strain values at sensor locations. The parameter space is defined over a bounded domain D = { x ∈ R p | a i ≤ k i ≤ b i } , where [ a i , b i ] are physically meaning ful bounds for each multiplier. To populate the starting dataset, a set of samples is generated using Latin Hypercube Sampling (LHS) over D , and FE analyses are performed for each sampled combination to compute the strain response at sensor locations. The resulting dataset is divided into training and testing subsets to construct and validate the Krig ing models. Each surrogate model is specialized to predict the strain response at a specific sensor location under a given model class. Once the surrogate models are validated, damage identification is performed on actual strain time series measured from the monitored structure, after proper preprocessing to mitigate the e ff ects of environmental and operational variability. The inverse calibration problem is then solved by minimizing the cost function, according to Section 2.3, describing the mismatch between the measured strains and the surrogate model predictions. This procedure enables the tracking of the estimated sti ff ness multipliers over time for each model class, thereby providing valuable information on the potential onset and progression of structural response degradation. This happens because once a damage event occurs, correspondent variations of the sti ff ness multipliers are observed for all the defined classes. Nevertheless, this calibration alone is not su ffi cient to unambiguously identify the damage mechanism most consistent with the observed structural behavior. To this end, the BIC is employed as a model selection metric, allowing for the comparison of the competing model classes. By jointly evaluating the goodness of fit between model predictions and experimental data, along with the complexity of the surrogate models, the BIC assigns a quantitative score to each class. The class associated with the lowest BIC value is considered the most probable representation of the structural state. This final step completes the proposed model-based monitoring strategy, enabling not only the damage detection and the estimation of its severity and location, but also the selection of the most plausible damage mechanism among those initially hypothesized from the reference FE model, namely its classification. As such, the methodology provides a valuable tool for supporting post-event diagnostics and informed decision-making.