PSI - Issue 62

Valentina Giglioni et al. / Procedia Structural Integrity 62 (2024) 887–894 Giglioni et al. / Structural Integrity Procedia 00 (2019) 000–000

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These damage-sensitive features are highly affected by environmental changes, as inferred from Fig. 5a, showing the tracking of the first frequency F1 during normal (first bell curve) and waterlogged conditions (second bell curve), varying the temperature values.

Fig. 5. (a) tracking of F1 during healthy conditions (including N and W data points in the first and second bell curve, respectively), varying the temperature values; (b) the relationship between F1 and F2 for different health-state classes.

After collecting all the features, the relationship between F1 and F2 depending on the type of health-state class is plotted in Fig. 5b. Note that N and W datapoints are correctly contained in the same healthy cluster. Moreover, while M2 data present a little shift from normal conditions, the stiffness reduction induced in the main span, indicated with M3 and M4, clearly appears more discernible. In particular, the second frequency F2 mostly contributes to identify the stiffness reduction when the mass is placed on one side of the main span (M3). This fact is reasonable if considered that this span is remarkably affected by torsional effects in the second mode shape. 3.2. Transfer Learning results: Span 1 ⟷ Span 2 Prior to TL, the first domain is extracted by considering part of healthy data (randomly) and damage data related to the M1 and M2 scenarios, simulated in Span 2. It follows that the second domain includes the remaining portion of healthy data and those data associated to the M2 and M4 classes, describing the stiffness reduction induced in Span 1. The four reference natural frequencies are tracked over time and fed into the NCA and JDA algorithms, yielding two transformed latent features as output, i.e., 1 and 2 . Fig. 6 shows DA results when the interest is in learning to identify a certain damage class (stiffness reduction on the side or centre line) across Span 1 and Span 2. It should be specified that Span 2-related data are denoted by “○”, while the symbol “ × ” is used to represent data referred to Span 1. As first sight, healthy data belonging to different environmental conditions (including N and W classes) can be well aligned. Focussing on Fig. 6a, DA correctly identifies two clear clusters, one of which contains M2 and M4 labels, ensuring the possibility of sharing damage information between the main and the lateral bridge spans. Starting with this transformed distribution, the K-Nearest Neighbours (KNN) algorithm, based on the concept of similarity between close datapoints, is utilised to classify a certain instance depending on the most frequent label among the K nearest neighbours, with K set to 2. In particular, the ML method is applied to perform damage detection using the knowledge extracted from Span 1 to infer diagnosis on Span 2, and vice versa. Both cases are investigated, and the outcomes are reported in terms of confusion matrices on the right side of Fig. 6, where the number of false detection errors are remarkably minimised. Similar results occur when considering stiffness reduction affecting the right side of the deck, represented by M1 and M3 labels (Fig. 6b). The alignment provided by the two latent features still allows one to discern between undamaged and damaged conditions, even though a little shift is present within the damaged cluster. The first reason lies in the fact that the selected features are not sensitive enough if damage occurs in the lateral span; this is particularly evident by applying the mass on one side (M1), because of the limited torsional component exhibited by the